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Towards a global classification of volcanic tremor Unglert, Katharina Claudia 2016

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Towards a Global Classification ofVolcanic TremorbyKatharina Claudia UnglertB.Sc., Technical University/Ludwig-Maximilians-Univ., Munich, Germany, 2008M.Sc., Victoria University of Wellington, New Zealand, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Geophysics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2016c© Katharina Claudia Unglert 2016AbstractVolcanic tremor, a seismic signal with longer durations and lower frequency content compared tolocal earthquakes, is often observed before or during eruptions and may consequently be useful foreruption forecasting. However, the processes generating volcanic tremor are still poorly understood.The main goal of this thesis is to assess systematic similarities and differences among tremor from aglobal sample of volcanoes, which is crucial to successfully constrain plausible source mechanisms.Using time series analysis of seismic signals accompanying three eruptive episodes at Kı¯lauea Vol-cano, Hawai‘i, I show that two characteristic phases of seismicity accompany dike intrusions, andthat a different type of tremor occurs during a period of explosive activity. The signals differ intheir spatial, temporal, and most strongly in their spectral properties. I thus construct a syntheticdataset of spectra that mimic the different spectral shapes observed in Hawai‘i. I use this datasetto evaluate the performance of two pattern recognition algorithms that may facilitate a global com-parison of volcanic tremor spectra. A variety of tests with the synthetic spectra including differentnumbers and character of spectral patterns, as well as increasing levels of noise reveal that PrincipalComponent Analysis and hierarchical clustering, in combination with a newly developed criterionto determine the ideal number of groupings in the data, can successfully identify the correct numberand character of the known spectra. I thus develop a detection algorithm for volcanic tremor andapply the pattern recognition approach to detect patterns in tremor spectra from Kı¯lauea, Okmok,Pavlof, and Redoubt volcanoes. By analyzing the station network for each volcano individually, Ishow that tremor has distinct spatial and temporal characteristics for each of the volcanic settings.A subsequent comparative analysis suggests that several volcanic settings share common spectraltremor characteristics. I identify at least four types of volcanic tremor with systematic variationsamong the four settings, which indicates relationships to volcanic controls such as magma stor-age depth and viscosity. Further analysis of tremor from a larger sample of volcanoes will help toconstrain plausible source processes and ultimately improve eruption forecasting.iiPrefaceThis thesis is based on three papers: One has been published, one has been accepted, and one is inpreparation for publication. Consequently, there is some cross-over among the different papers, inparticular in the introductory sections. Furthermore, some information from Chapter 1 is repeatedin the papers.The idea to investigate volcanic tremor on a global scale wasMark Jellinek’s. I did the necessarybackground research, developed the approach to undertake the multi-volcano comparison, obtainedthe data, and performed all analyses unless indicated otherwise below.A version of Chapter 2 has been published in Journal of Geophysical Research: Solid Earth.The co-authors are Katharina Unglert (first author) and Mark Jellinek. The data analyzed in thischapter were kindly provided by the Hawaiian Volcano Observatory (HVO). I discovered the twocharacteristic phases of seismicity and associated frequency gliding, performed all the calculationsand analyses up to (and including) Section 2.3, made the figures, and wrote the manuscript exceptfor Section 2.4.3. The scalings in Section 2.4.3 were derived by Mark Jellinek on the basis of dis-cussions between him and me about the results. The writing of Section 2.4.3 was a combined effort.Mark Jellinek also provided scientific guidance throughout and commented on the manuscript.A version of Chapter 3 has been published in Journal of Volcanology and Geothermal Research.The co-authors are Katharina Unglert (first author), Valentina Radic´, and Mark Jellinek. The datafrom the three volcanoes shown in this chapter were kindly provided by HVO and the AlaskaVolcano Observatory (AVO). I developed the idea to use spectral shapes for pattern recognitionand to apply automated algorithms to identify the characteristic spectral shapes. Furthermore, Idecided to evaluate the performance of pattern recognition algorithms in a comparative study withsynthetic data before conducting the global comparison on real data. I generated the syntheticdataset, performed all the calculations and analyses, made the figures, and wrote the manuscript.The only exception are the additional tests on non-traditional clustering approaches in Section 5.2,that were suggested and run by Valentina Radic´ in preparation of a follow-up publication separatefrom my PhD. Mark Jellinek and Valentina Radic´ provided scientific guidance throughout the datadevelopment and analysis stage, and commented on the manuscript.A version of Chapter 4 has been submitted for publication. The co-authors are Katharina Un-glert (first author) and Mark Jellinek. The data from the four volcanoes shown in this chapter werekindly provided by HVO and AVO. I developed the idea to perform the analysis separately on theindividual station networks before conducting the multi-volcano comparison. I prepared all datasetsfor processing, performed all calculations and analyses, made the figures and wrote the manuscript.Mark Jellinek provided scientific and editorial guidance throughout.iiiPrefaceJournal PapersChapter 2Unglert, K., and A.M. Jellinek (2015), Volcanic Tremor and Frequency Gliding during DikeIntrusions at Kilauea – A Tale of Three Eruptions, Journal of Geophysical Research: Solid Earth,120(2), 1142–1158, doi: 10.1002/2014JB011596.Chapter 3Unglert, K., V. Radic´, and A.M. Jellinek (2016), Principal Component Analysis vs. Self-Organizing Maps Combined with Hierarchical Clustering for Pattern Recognition in Volcano Seis-mic Spectra, Journal of Volcanology and Geothermal Research, 320, 58–74,doi: 10.1016/j.jvolgeores.2016.04.014.Chapter 4Unglert, K., and A.M. Jellinek (in review), Spectral Pattern Recognition Reveals Distinct Classesof Volcanic Tremor.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Introduction & Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Tremor Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 Time Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Tremor Locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.3 Frequency Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.4 Association with Other Observables . . . . . . . . . . . . . . . . . . . . . 71.2.5 Tremor Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3 The Need for a Global Classification . . . . . . . . . . . . . . . . . . . . . . . . . 121.3.1 Guiding Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.3.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 Volcanic Tremor & Frequency Gliding at Kı¯lauea . . . . . . . . . . . . . . . . . . . 192.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2 Three Eruptions at Kı¯lauea, Hawai‘i . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.1 The 2007 Father’s Day Eruption . . . . . . . . . . . . . . . . . . . . . . . 212.2.2 The 2008 Halema‘uma‘u Explosions . . . . . . . . . . . . . . . . . . . . 222.2.3 The 2011 Kamoamoa Eruption . . . . . . . . . . . . . . . . . . . . . . . 222.3 Data & Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.1 Network & Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.2 Overview of Seismic Signals . . . . . . . . . . . . . . . . . . . . . . . . 232.3.3 Phases of Seismicity During Intrusions . . . . . . . . . . . . . . . . . . . 26vTable of Contents2.3.4 Frequency Gliding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.3.5 Summary of Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . 292.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.4.1 Tremor & Eruptive Styles . . . . . . . . . . . . . . . . . . . . . . . . . . 302.4.2 Phase I: The Early Stages of Intrusion . . . . . . . . . . . . . . . . . . . . 312.4.3 Temporal & Spatial Constraints on Tremor . . . . . . . . . . . . . . . . . 312.4.4 Remaining Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 Principal Component Analysis vs. Self-Organizing Maps . . . . . . . . . . . . . . . 413.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.2 Data and Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.2.1 Synthetic Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.2.2 Preprocessing Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.3 Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.3.1 PCA and Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.3.2 Performance of PCA and Clustering at Higher Noise Levels . . . . . . . . 533.4 Self-Organizing Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.4.1 SOM Topology Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.4.2 Results and Clustering of SOM Patterns . . . . . . . . . . . . . . . . . . 583.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.5.1 Summary of Steps Taken for Each Method: Parameter Choices . . . . . . 603.5.2 Limitations of Typical Volcano Seismic SOM Approach . . . . . . . . . . 613.5.3 Limitations of our Synthetic Data and the PCA Approach . . . . . . . . . 633.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694 Spectral Pattern Recognition Reveals Distinct Classes of Volcanic Tremor . . . . . 714.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.2 Volcanic Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.3 Data and Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.3.1 Distinguishing Tremor from the Background . . . . . . . . . . . . . . . . 744.3.2 Removing Earthquake Signals . . . . . . . . . . . . . . . . . . . . . . . . 744.3.3 Obtaining Tremor Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 774.4 Spectral Pattern Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.4.2 PCA for Multiple Stations at Individual Settings . . . . . . . . . . . . . . 814.4.3 PCA for Comparison Between Volcanic Settings . . . . . . . . . . . . . . 914.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974.5.1 Kı¯lauea: 2007, 2008, 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . 974.5.2 Okmok: 2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99viTable of Contents4.5.3 Pavlof: 2007, 2013 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.5.4 Redoubt: 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.5.5 Implications for Tremor Detection Algorithm . . . . . . . . . . . . . . . . 1024.5.6 Joint Analysis: Lessons Learned . . . . . . . . . . . . . . . . . . . . . . 1034.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.1 Summary of Work and Context for Each Publication . . . . . . . . . . . . . . . . 1105.2 Revisiting the Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116AppendixA Use of Color Maps and Human Perception . . . . . . . . . . . . . . . . . . . . . . . 137A.1 Challenges with Color Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137A.2 Some Ideas for Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139A.2.1 Using Line Graphs Instead of Images . . . . . . . . . . . . . . . . . . . . 139A.2.2 Greyscale Color Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139A.2.3 Perceptually Uniform Color Maps . . . . . . . . . . . . . . . . . . . . . . 141viiList of Tables3.1 Quality measurements and clustering results for different noise levels, PCA vs. SOM 503.2 Quality measurements and clustering results for different SOM sizes at noise level 0.1 563.3 Quality measurements and clustering results for different noise levels based on dif-ference criterion, PCA vs. SOM . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.4 Clustering results for different frequency bands, PCA vs. SOM . . . . . . . . . . . 684.1 Summary of volcanoes, stations, data time period, and number of tremor windows . 76viiiList of Figures1.1 Example seismograms for volcanic tremor. . . . . . . . . . . . . . . . . . . . . . . 31.2 Example spectrograms for harmonic tremor and frequency gliding. . . . . . . . . . 61.3 Schematic for selected tremor mechanisms . . . . . . . . . . . . . . . . . . . . . . 101.4 Schematic for Principal Component Analysis . . . . . . . . . . . . . . . . . . . . 141.5 Schematic for Self-Organizing Maps algorithm . . . . . . . . . . . . . . . . . . . 141.6 Schematic for hierarchical clustering algorithm . . . . . . . . . . . . . . . . . . . 162.1 Map of Kı¯lauea and timeline of important events. . . . . . . . . . . . . . . . . . . 212.2 Spectrograms for 2007, 2008, and 2011. . . . . . . . . . . . . . . . . . . . . . . . 242.3 Spectrograms during intrusions in 2007 and 2011. . . . . . . . . . . . . . . . . . . 252.4 Spectra and RMS velocity in 2007, 2008, and 2011 at AHU. . . . . . . . . . . . . 272.5 Spectrograms showing gliding during 2007 and 2011. . . . . . . . . . . . . . . . . 282.6 Simplified cartoon of Kı¯lauea plumbing system. . . . . . . . . . . . . . . . . . . . 343.1 Examples of different spectral shapes and transitions between them from Kı¯lauea,Redoubt, and Okmok. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.2 Synthetic data setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.3 Normalized synthetic data used as input for pattern recognition algorithms . . . . . 483.4 PCA results for noise level 0.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.5 Cluster evaluation diagnostics, noise level 0.1 . . . . . . . . . . . . . . . . . . . . 523.6 PCA results for noise level 1.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.7 Output from SOM algorithm, noise level 0.1 . . . . . . . . . . . . . . . . . . . . . 553.8 Examples of feature spectra from SOM . . . . . . . . . . . . . . . . . . . . . . . 573.9 Clustering of SOM topology, noise level 0.1 . . . . . . . . . . . . . . . . . . . . . 593.10 Clustering of SOM topology, noise level 0.1, manual selection of k = 3 . . . . . . 603.11 PCA plus clustering method applied to synthetic dataset with flipped Phase II pattern 643.12 PCA plus clustering method applied to synthetic dataset with modified Phase IIpattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.1 Examples for background signal estimation . . . . . . . . . . . . . . . . . . . . . 754.2 Example seismogram showing different cases of our tremor detection . . . . . . . 754.3 PCA and clustering results for network analysis at Kı¯lauea, 2007, 2008, and 2011 . 794.4 Clustering time series for network analysis at Kı¯lauea, 2007 . . . . . . . . . . . . 80ixList of Figures4.5 Clustering time series for network analysis at Kı¯lauea, 2008 . . . . . . . . . . . . 824.6 Clustering time series for network analysis at Kı¯lauea, 2011 . . . . . . . . . . . . 834.7 PCA and clustering results for multistation analysis at Okmok, 2008 . . . . . . . . 854.8 Clustering time series for network analysis at Okmok, 2008 . . . . . . . . . . . . . 864.9 PCA and clustering results for network analysis at Pavlof, 2007 and 2013 . . . . . 874.10 Clustering time series for network analysis at Pavlof, 2007 . . . . . . . . . . . . . 884.11 Clustering time series for network analysis at Pavlof, 2013 . . . . . . . . . . . . . 884.12 PCA and clustering results for network analysis at Redoubt, 2009 . . . . . . . . . 904.13 Clustering time series for network analysis at Redoubt, 2009 . . . . . . . . . . . . 914.14 PCA and clustering results for combined analysis, for proximal stations . . . . . . 934.15 Clustering results for combined analysis, for proximal stations . . . . . . . . . . . 944.16 Clustering time series for combined analysis, proximal stations . . . . . . . . . . . 954.17 PCA and clustering results for combined analysis, for distal stations . . . . . . . . 964.18 Clustering time series for combined analysis, distal stations . . . . . . . . . . . . . 974.19 Zoom into temporal evolution of main clusters during intrusions at Kı¯lauea . . . . 994.20 Detection rates at station RSO during several days in May 2009 . . . . . . . . . . 1024.21 Summary of tremor types in relation to volcano and eruption characteristics . . . . 105A.1 Color use in geoscience publications. . . . . . . . . . . . . . . . . . . . . . . . . . 138A.2 Ordering issues for rainbow color maps. . . . . . . . . . . . . . . . . . . . . . . . 139A.3 Line graph spectrograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140A.4 Greyscale spectrogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140A.5 Spectrogram from Hawai‘i with different color maps. . . . . . . . . . . . . . . . . 142xAcknowledgementsSeveral people have helped me in one way or another during the course of my PhD, and deservemy gratitude. I would like to thank my supervisor, Mark Jellinek, whose continuous enthusiasmabout our work was extremely inspiring, and whose support extended far beyond simple academicquestions. Thanks also to my committee, Catherine Johnson, Valentina Radic´, Diana Roman, andMichael Bostock, for their guidance and encouragement throughout.This work would not have been possible without the data so generously shared by the USGSvolcano observatories, and the countless fruitful discussions with Milton Garces, Jess Johnson,Kostas Konstantinou, Jonathan Lees, Steve McNutt, Mike Poland, John Power, Glenn Thompson,Wes Thelen, Aaron Wech, and many more. Funding through a UBC 4-Year-Fellowship and aVanier Scholarship were a tremendous help. Thanks also to Keegan Lensink, whose work duringhis summer internship was a great help for my data processing.Over the years, my office was always filled with amazing colleagues and friends who neverhesitated to offer a word of advice or a listening ear. My thanks goes to Thomas Aubry, Eric Deal,Kirsten Hodge, Yoshi Gilchrist, Anna Grau, Anna Mittelholz, Genevie`ve Savard, Reka Winslow,and everyone else.Furthermore, I would like to thank the Graduate Student Council and of course all the awesomevolunteers in the Pacific Museum of Earth and with Let’s Talk Science for giving me the chance toexplore some non-academic ways of involvement.I am grateful to the Crichtons, who gave me a home and took me into their family as if I hadalways been there. Thanks also to Susi Iberle, the best friend anyone could wish for, and to all myother friends and family, near and far, who are always there for me. Last but not least, thanks toJames Hickey, for everything.xiChapter 1Introduction & Motivation1.1 OverviewVolcanic eruptions are often preceded and accompanied by a low-frequency (approximately 0.5–10 Hz) seismic signal called “volcanic tremor” (Aki and Koyanagi, 1981; Neuberg, 2000; Kon-stantinou and Schlindwein, 2002; McNutt and Nishimura, 2008), hereafter referred to as “tremor”.Tremor persists for minutes to weeks. Its occurrence is often interpreted as a sign of an impendingeruption (e.g., D’Agostino et al., 2013; Chardot et al., 2015). The reliability of tremor as a fore-casting tool is, however, uncertain, because the underlying physical processes remain unclear (e.g.,Chouet, 1986; Julian, 1994; Benoit and McNutt, 1997; Ripepe and Gordeev, 1999; Neuberg et al.,2000; Lesage et al., 2006; Jellinek and Bercovici, 2011; Dmitrieva et al., 2013; Bean et al., 2014).Tremor is ubiquitous in all tectonic settings, despite the fact that these settings can be fundamen-tally different e.g. in terms of magma composition. Tremor can be described by properties suchas frequency content, amplitudes, or source depth. The spatial and temporal relationships betweentremor properties and other observables1 are often unknown and potentially complicated. A rangeof tremor observations in different locations (Konstantinou and Schlindwein, 2002; McNutt andNishimura, 2008) suggests that tremor may be the expression of a variety of underlying mechanicalprocesses depending on volcanic and tectonic controls (e.g. volcano type, magma composition,tectonic setting, etc.). A systematic classification of tremor from a variety of volcanoes is thus nec-essary to improve understanding of the source processes of volcanic tremor. This is the goal of myPhD.This section provides the necessary background for the following chapters. I give an overviewof tremor observations at many different volcanoes in Section 1.2, and discuss the need for a globalclassification of tremor and outline the most important methods in Section 1.3.1“Other observables” here and in the following sections refers to monitoring parameters such as visual observationsof eruptive activity, ground deformation, infrasound, gas emissions, or composition of erupted products.11.2. Tremor Observations1.2 A Global Survey of Tremor ObservationsThe term “tremor” has been used to describe various seismic signals since the early 20th century(e.g., on Kı¯lauea, Jaggar, 1920). More recently, tremor has been defined as a low-frequency2 , long-lasting3 seismic signal associated with active volcanism (McNutt, 1992; Chouet and Matoza, 2013).Volcanic tremor has been observed in many tectonic and volcanic settings from basaltic oceanislands (e.g. Kı¯lauea, Omer, 1950; Ferrazzini et al., 1991; Patrick et al., 2011a) to more silicic arcvolcanoes (e.g., Mount St. Helens, USA Fehler, 1983; Augustine, USA Reeder and Lahr, 1987; orCordo´n Caulle, Chile Bertin et al., 2015). In the following sections, I give an overview of tremorin terms of its temporal, spatial, and spectral characteristics, discuss their relation to other types ofobservations, and review constraints on source mechanisms. The range of observations summarizedin the following sections motivate a systematic global classification of volcanic tremor.1.2.1 Time DomainMost volcanic tremor episodes have an emergent onset (e.g. Pavlof, USAMcNutt, 1987a, Fig. 1.1(a),or Soufrie`re Hills Volcano, Montserrat Neuberg et al., 1998). However, tremor events with impul-sive onsets have also been observed (e.g. Karymsky, Russia, Johnson and Lees, 2000, or Kı¯lauea,USA, Aki and Koyanagi, 1981). Individual episodes can persist for minutes to hundreds of hours(e.g. Brandsdo´ttir and Einarsson, 1992; Lesage et al., 2006;McNutt and Nishimura, 2008). Tremoramplitudes sometimes vary on timescales of seconds to minutes (e.g. Arenal, Costa Rica Lesageet al., 2006, Kı¯lauea, Patrick et al., 2011a, or Redoubt, USA, Fig. 1.1(c)). The temporal evolutionof these amplitude variations can be systematic such as on Grı´msvo¨tn, Iceland, (“tremor bursts”,Brandsdo´ttir and Einarsson, 1992) or on Nevado del Ruiz, Colombia, (“cyclic tremor”, Chouet,1992), or irregular such as on Arenal, or Redoubt, (“spasmodic” Lesage et al., 2006, , Fig. 1.1(c)).Furthermore, such amplitude variations can transition from one into the other (Brandsdo´ttir andEinarsson, 1992). Long-period earthquakes (LPs) have sometimes been observed to become moreclosely spaced in time and merge into continuous tremor (e.g., at Soufrie`re Hills Volcano, Neuberget al., 1998, Fig. 1.1(b), Kı¯lauea, Koyanagi et al., 1987, and Redoubt, Hotovec et al., 2013).1.2.2 Tremor LocationsLP LocationsAn inability to identify clear phase arrivals within tremor episodes as well as their emergent onsetprevent the use of traditional earthquake location methods (e.g. Konstantinou and Schlindwein,2Tremor is often combined into one category with long-period earthquakes (LPs) or very long period earthquakes(VLPs) based on the hypothesis that tremor is a series of closely spaced LPs (Powell and Neuberg, 2003). For this thesis,LPs are defined as earthquakes with longer periods/lower frequencies than tectonic or volcano-tectonic earthquakes,loosely based on the definitions of Minakami (1960) and Latter (1981). My definition of LPs also includes “hybrid”events from Neuberg et al. (1998). The terms “tremor” and “LPs” here stand for distinct seismic signals that are ingeneral not assumed to be directly related. Potential links between them will be discussed specifically, e.g. if it is anecessary part of a model or observation.3The long duration is in comparison to local earthquakes.21.2. Tremor Observationsvertical component, helicorder plot30 minutes27 March 2016, 23:30 UTC11 hours0 50 100 150 200 250 300time (s)vertical velocity (arbitrary units)300 600 900 12000vertical velocity (arbitrary units)time (s)(a) (b)(c)Figure 1.1: Example seismograms for volcanic tremor. (a) Tremor shows emergent onset at PavlofVolcano, USA, station PVV during an eruptive period in March 2016. (b) Three consecutive 20-minute seismograms on vertical component of broadband station MBGA at Soufrie`re Hills Volcano,Montserrat, time of recording unknown. LPs become more closely spaced in time and eventuallymerge into tremor (Neuberg et al., 1998). Reproduced with permission from Wiley. (c) Tremoramplitude varies over timescales of tens of seconds at Redoubt Volcano, USA, station RSO inJanuary 2009.2002). However, there are other approaches to locating volcanic tremor. Tremor and LPs sometimesoccur during the same period, show similar attenuation of amplitudes with distance, and/or havesimilar spectral characteristics (e.g. Soufrie`re Hills Volcano, Neuberg et al., 1998, or Kı¯lauea,Koyanagi et al., 1987). These similarities could indicate a common source mechanism for tremorand LPs (e.g. Koyanagi et al., 1987; Neuberg et al., 1998). Consequently, the first approach tolocating tremor is to identify LP locations, for example on the basis of differential arrival times(Neuberg et al., 1998). Koyanagi et al. (1987) identify three tremor source depth intervals onKı¯lauea. The shallow (<5 km) and intermediate (5–15 km) intervals show tremor confined to thesummit and the East Rift Zone (ERZ), whereas the deep (30–60 km) tremor source region appearsto be further south and not associated with active vents. Similar to shallow tremor at Kı¯lauea,Neuberg et al. (1998) identify a region approximately 2–3 km beneath the active lava dome as thesource for tremor at Soufrie`re Hills Volcano. Hotovec et al. (2013) find repeating earthquakes thatare assumed to merge into tremor at a depth of approximately 2 km beneath the vent at Redoubt.Tremor Amplitude Decay with DistanceThe amplitude of tremor and its spatial distribution has been used to pinpoint tremor to the summitregion with the central craters at Etna, Italy (Riuscetti et al., 1977; Patane` et al., 2013). Furthermore,on the basis of frequency dependent decay of amplitudes with distance, Riuscetti et al. (1977) are31.2. Tremor Observationsable to distinguish between different source depths for two spectral peaks of the tremor spectrum,one directly beneath the crater floor, and the other approximately 0.5–1 km beneath that surface.Patane` et al. (2013) find tremor sources up to 3 km below the active craters. Aki and Koyanagi(1981) use the spatial distribution of tremor amplitudes to identify deep tremor at Kı¯lauea (∼40 km,Aki and Koyanagi, 1981). At Piton de la Fournaise, Re´union, Battaglia and Aki (2003) use the sitecorrected amplitude distribution in different frequency bands to identify tremor sources at shallowdepths of a few kilometers in close proximity to active vents. Kumagai et al. (2010) develop a moregeneral version of this method, which accounts for anisotropic wave radiation. Ogiso and Yomogida(2012) apply this method to identify a migrating tremor source at 1–2 km within a few kilometers ofthe active crater at Meakandake Volcano. Similarly, tremor locations at Ontake Volcano, Japan, arefound to originate from an increasingly deeper source beneath the active craters before the onset ofthe 2014 eruption (Ogiso et al., 2015). Jones et al. (2012) detect the source of isotropically radiatedP-waves based on seismic amplitudes in different frequency bands at Erta ’Ale. They find tremorsources below the previously active northern crater, the currently active lava lake and in between,at depths of a few hundred meters below the surface and shallower (Jones et al., 2012).Array AnalysisIf a seismic array4 is used, wavefield properties such as time delays of wave arrivals between dif-ferent stations or wave azimuth can be used to make inferences about tremor source locations.Chouet et al. (1997) find tremor to be located generally less than 200 m below the summit crater atStromboli. Array analysis at Etna is used to identify a tremor source below the central crater duringnon-eruptive periods (Del Pezzo et al., 1993), in agreement with the results by Riuscetti et al. (1977)mentioned above. Similarly,Me´taxian et al. (1997) determine the tremor source location at MasayaVolcano a few hundred meters below the volcanic surface in the lava lake in Santiago crater. Byshowing that array analysis techniques can be extended to larger seismic station networks for verylong period (<0.5 Hz) signals, Haney (2010) identify a tremor source location at 2.4 km below thesurface at Okmok Volcano, close to the site of a new cone built during the 2008 eruption.In summary, tremor source locations appear to be restricted to two depth intervals: Deep tremorat a depth of a few tens of kilometers has only been found at Kı¯lauea. Shallow tremor is commonlyfound between the surface and up to a few kilometers depth. It is often located close to current andformer eruptive vents.1.2.3 Frequency DomainSnapshots of Frequency ContentThe most diagnostic tremor properties are often apparent in the frequency domain. I first discusssnapshots of frequency content at isolated moments in time or averaged over a time window, without4i.e. several seismometers with narrow interstation spacing and an overall array size on the order of hundreds ofmeters to a few kilometers (e.g., Gordeev et al., 1990; Chouet et al., 1997)41.2. Tremor Observationstaking into account the temporal evolution. I consider the temporal evolution of tremor frequencycontent in the next section.Typically, the “low” frequency content observed in tremor signals in comparison to local earth-quakes quantitatively ranges between 0.5–10 Hz with most of the energy concentrated between1–3 Hz (Konstantinou and Schlindwein, 2002; McNutt and Nishimura, 2008). Notable exceptionsto both the upper and the lower limit include tremor at Redoubt (up to ∼30 Hz, Hotovec et al.,2013), the Volcano Island Arc (up to 40 Hz on submarine records, Dziak and Fox, 2002), Okmokand Stromboli (very long period tremor, 0.02–0.5 Hz, De Lauro et al., 2005; De Martino et al.,2005; Haney, 2010) and Usu (≤0.1 Hz, Yamamoto et al., 2002).A distinction between narrowband (e.g. Hekla, 1.5–3 Hz, Brandsdo´ttir and Einarsson, 1992,or Ruapehu, 1.8–2.3 Hz, Hurst and Sherburn, 1993) and broadband (e.g. Deception Island, 1–10 Hz, Vila et al., 1992; or Piton de la Fournaise, 1–5 Hz, Battaglia et al., 2005) tremor exists5.Furthermore, tremor is sometimes harmonic with a fundamental mode (typically between 0–2 Hz)and one or more harmonics (Fig. 1.2) such as on Semeru (Schlindwein et al., 1995), Arenal (Lesageet al., 2006), Karymsky (Lees et al., 2004), Redoubt (Hotovec et al., 2013), and Kı¯lauea (Koyanagiet al., 1987).Temporal Evolution of Frequency ContentMany cases of harmonic tremor show a phenomenon called “frequency gliding”. Gliding refersto the gradual shift in frequency of a spectral peak in time. This behaviour has been observed atKı¯lauea for several decades (e.g. Finch, 1949; Aki and Koyanagi, 1981). To my knowledge the term“gliding” was first introduced by Dibble (1972) for a gradually shifting spectral peak in the tremorspectrum at Pu‘u Huluhulu (Kı¯lauea) during the Mauna Ulu eruption in February 1971. The termthen became more common in the 1990s (e.g. Hurst and Sherburn, 1993). Gliding can be dividedinto groups according to three distinct behaviours (Fig. 1.2):1. Sinusoidal, where the location of peaks in spectral space changes approximately periodicallyover time (Semeru, Schlindwein et al., 1995).2. Exponential, where frequency increases or decreases exponentially with time (e.g. Soufrie`reHills Volcano, Neuberg et al., 1998, or Redoubt, Hotovec et al., 2013).3. Irregular, where frequency peaks shift up and down in a seemingly random way (e.g. Arenal,Benoit and McNutt, 1997; Lesage et al., 2006, or Langila, Mori et al., 1989).Gliding episodes typically last from a few minutes (e.g. Redoubt, Hotovec et al., 2013) toapproximately half an hour (e.g. Soufrie`re Hills Volcano, Powell and Neuberg, 2003). However,5Note that the observation of frequency ranges discussed in this section is often based on visual assessment of coloredspectrograms, such as the ones presented in Figure 1.2. Typically, the color maps used for these displays are generic andnot specifically suited for the purpose. Appendix A summarizes some of the challenges related to the use of colormaps,and discusses some possible improvements to the status quo. Whereas such improvements have not been applied inChapter 2, the subsequent chapters include only color maps that are perceptually uniform to avoid bias.51.2. Tremor Observations0123452010006284500 1000 1500 2000 2500 300000 60 120 180 240 300 360 420 480 540 6000 60 120 180 240time (arbitrary) in secondsfrequency (Hz)frequency (Hz)frequency (Hz)Semerutype 1: sinusoidalRedoubttype 2: exponentialArenaltype 3: irregulartiming of explosionFigure 1.2: Example spectrograms for harmonic tremor and each type of frequency gliding. (1)Sinusoidal gliding at Semeru, timing relative to explosion unknown (Schlindwein et al., 1995).Reproduced with permission from Wiley. (2) Exponential upglide at Redoubt prior to an explosion(red star, Hotovec et al., 2013). Reproduced with permission from Elsevier. (3) Irregular up- anddownglides at Arenal before and after 3 explosions (Benoit and McNutt, 1997). Reproduced withpermission from Wiley.61.2. Tremor ObservationsI revisit gliding and introduce a newly discovered, long duration gliding signal (compared to theepisode lengths mentioned above) at Kı¯lauea in Chapter 2. Often, all harmonics in the spectrumglide together, with the lowest harmonic increasing or decreasing in frequency between 0.5–6 Hz(e.g.Mori et al., 1989; Schlindwein et al., 1995; Powell and Neuberg, 2003). A notable exception isRedoubt, where spectral peaks glide up to 30 Hz. The occurrence and character of gliding is oftenused to identify a source mechanism for volcanic tremor. I discuss temporal coincidence of tremorwith variations of other observables and briefly give an overview of potential source mechanismsbelow.1.2.4 Association with Other ObservablesCharacter and Timing Relative to EruptionsMany studies have shown a qualitative temporal correlation of tremor with other observations, suchas eruptive activity and its temporal evolution. McNutt (1992) suggested that 30-60% of tremorepisodes6 accompany volcanic eruptions. If tremor always occurs before the start of an eruptionit could be used for eruption forecasting. However, only approximately 20% of tremor episodesprecede eruptions by 10 days or less (McNutt, 1992). Frequency gliding sometimes precedes ex-plosions (e.g. Powell and Neuberg, 2003; Hotovec et al., 2013). In other cases, however, glid-ing follows explosions (Benoit and McNutt, 1997), or the timing relative to eruptions is unknown(Schlindwein et al., 1995; Neuberg et al., 1998). Some volcanoes show different tremor charac-teristics during eruptive vs. non-eruptive periods: At Shishaldin, USA, tremor shows higher fre-quencies during a sub-plinian eruption in 1999 in comparison to tremor during non-eruptive periodsand Strombolian eruptions (Thompson et al., 2002). Tremor during intrusions at Krafla typicallyhas frequencies above 3 Hz, whereas tremor during eruptions is dominated by energy below 3 Hz(Brandsdo´ttir and Einarsson, 1992). At Piton de la Fournaise, background tremor appears to have anarrow peak at 1 Hz (Battaglia and Aki, 2003), whereas eruption tremor is more broadband between1–5 Hz (Battaglia et al., 2005). In contrast, tremor at Hekla, Iceland, before and during eruptivephases looks similar (Brandsdo´ttir and Einarsson, 1992). During eruptive episodes, tremor ampli-tude appears to be correlated with eruption intensity in terms of erupted products in some cases(e.g. lava fountaining and spattering on Kı¯lauea in the East Rift Zone, at Pu’u O¯’o¯, and at MaunaUlu, Koyanagi et al., 1987; “vigor” of eruptive activity at Krafla, Iceland, and tephra productionrate at Hekla, Brandsdo´ttir and Einarsson, 1992; ash venting at Soufrie`re Hills Volcano, Neuberget al., 2000).Relation to Monitoring ParametersTremor is often accompanied by surface deformation. LPs merging into tremor occurs, for example,during inflationary tilt of the active lava dome at Soufrie`re Hills Volcano (Miller et al., 1998). Voightet al. (1998) observe that maximum seismic amplitude at Soufrie`re Hills Volcano coincided with6An episode is defined by tremor amplitude exceeding the local background amplitude for at least 2 minutes (McNutt,1987b).71.2. Tremor Observationsthe change from inflationary to deflationary tilt. At Kı¯lauea, tremor amplitudes at the summit areelevated after periods of high tilt rates, sometimes with a time lag of a few hours (Koyanagi et al.,1987). In other cases, shallow and intermediate summit tremor at Kı¯lauea occurs during timesof inflation/deflation (Jaggar, 1920; Koyanagi et al., 1987). Similarly, tremor amplitudes duringintrusions at Krafla are high during deflation (Brandsdo´ttir and Einarsson, 1992).Tremor is also observed on infrasonic records (i.e., acoustic tremor). At Fuego, Guatemala, bothseismic and acoustic harmonic tremor is present during a phase of mostly Vulcanian explosions in2009, whereas Strombolian activity in 2008 only produced harmonic tremor on seismograms (Lyonset al., 2013). Similarly, lava effusion at Shinmoedake, Japan, in January 2011 produced harmonictremor visible on seismograms, whereas Vulcanian activity in February 2011 produced seismo-acoustic harmonic tremor (Ichihara et al., 2013). Acoustic emissions are observed together withvolcanic tremor at Arenal (Benoit and McNutt, 1997): Broadband tremor (0.5–7 Hz) accompaniessmall eruptions, usually followed by harmonic tremor and audible gas “chugging”. Similarly, atKarymsky, 10–20% of explosions are followed by seismic and infrasonic harmonic tremor and au-dible chugging (Johnson et al., 1998). Chugging and the corresponding seismic and acoustic tremorare also observed at Sangay, Ecuador (Lees and Ruiz, 2008). The infrasonic signal at Karymsky andSangay usually lags approximately 4 s behind the onset of seismic tremor at comparable distancesfrom the vent. For long lasting tremor episodes at Kı¯lauea, seismic tremor has been observed incombination with infrasonic tremor (Matoza et al., 2010).A relation between tremor and infrasound suggests coupling of some part of the tremor mech-anism with the atmosphere. For example, gas escape may cause a momentum exchange of thevolcanic system with the atmosphere as well as the ground. Indeed, at Fuego, SO2 emissions coin-cide with high tremor amplitudes, typically with time lags between a few and 60 s (Nadeau et al.,2011). High tremor amplitudes also correspond to high SO2 emissions at other volcanoes such asVillarrica, Chile (Palma et al., 2008) or Etna (Leonardi et al., 2000).To summarize, several different volcano monitoring parameters have been associated with vol-canic tremor in space or time in different settings. Many studies utilize the temporal coincidence oftremor and another observable to constrain potential source mechanisms.1.2.5 Tremor MechanismsSimilar to the diversity of observed tremor behaviours, an equally large variety of tremor mecha-nisms has been explored. Several models can be classified in terms of the effective viscosity of themagma (Fig. 1.3).Moving BubblesAt low and intermediate magma viscosities (basalts), excitations related to bubbles in magma areoften used to explain volcanic tremor signals (Fig. 1.3a). Jones et al. (2012) speculate about therole of bubbles in the lava lake at Erta ’Ale, Ethiopia, as source of tremor between approximately81.2. Tremor Observations2–10 Hz. The signal is thought to be related to the detachment of a larger slug from its bubblywake, on the basis of the interpretation of acoustic signals in the same setting (Bouche et al., 2010).Alternatively, they suggest tremor caused by the interaction of bubbles with the lava lake surface(Jones et al., 2012), similar to bubble coalescence at Stromboli, (Ripepe and Gordeev, 1999). Inthe case of Stromboli, Italy, Ripepe and Gordeev (1999) propose a cycle of bubble coalescence andsubsequent bursting to explain seismic and acoustic signals, respectively. They predict an inverserelation between tremor frequency and magma viscosity (Ripepe and Gordeev, 1999). Similarly,Matoza et al. (2010) interpret tremor at Kı¯lauea to be related to the coupled dynamics of magmaand bubbles: According to their model, the broadband component of acoustic tremor is caused byoscillation of a bubble cloud in the conduit system at Pu’u O¯’o¯ crater. Acoustic spectral peaks arerelated to resonance of this oscillation signal in cavities at the vent, and the seismic signal is causedby coupling of this resonance with the solid parts of the system (Matoza et al., 2010). All of themechanisms described above apply to lava lakes and the uppermost part of the plumbing system(i.e., they are limited by bubble nucleation starting at a few kilometres depth for basaltic magmas;Toramaru, 1989). I am unaware of detailed studies of the effect of CO2 exsolution on tremor atdeeper levels, and address this issue, in part, in Chapter 2.Overpressure Driven by Gas AccumulationStudies have suggested that gas exsolution and accumulation can also play a role in tremor gen-eration for slightly higher viscosity magmas (andesites or basaltic andesites, Fig. 1.3(b)). In thesemodels, oscillations are not due to freely moving bubbles as in the low viscosity open vents, but dueto accumulation and periodic release of larger volumes of gas in a closed vent system. A “pressurecooker” analogue is invoked to explain cyclic “chugging” at Karymsky: Gas accumulates beneath aplug of explosion rubble in the vent, until the overpressure leads to an explosive eruption accompa-nied by harmonic tremor on seismic and acoustic records (Johnson et al., 1998; Johnson and Lees,2000). The “clarinet model” at Arenal includes a similar gas overpressure mechanism which causesgases to escape periodically through fractures in the plug, but adds a contribution from resonance offluid in the conduit excited by a pressure wave due to the sudden release of gases at the top (Lesageet al., 2006).Resonating Fluid Filled Magma PathwaysA fluid filled resonator has been previously suggested for Arenal by Benoit and McNutt (1997)and Garce´s et al. (1998). Other examples of resonating fluid filled conduits (Fig. 1.3(c)) as thesource for long period seismicity (LPs and tremor) include Soufrie`re Hills Volcano (Neuberg et al.,2000). Chouet and Julian (1985), Chouet (1986) and Ferrazzini and Aki (1987) theoretically predictharmonic long period seismicity related to crack waves excited by a fluid flow induced pressuretransient. Whereas these models focus on the resulting oscillations of cracks or conduits, Julian(1994) emphasize the importance of the excitation mechanism. His model suggests excitation ofelastic channel walls caused by pressure changes related to nonlinear instabilities in fluid flow,91.2. Tremor Observations1)2)3)4)5)6)shear strainlocalization bubblyannulusopen/closeddegassingpathways(a) (b)(c) (d) (e) (f)7)8)9), 10)11) 12)depth: few 100 m - few km depth: few 100 m - few kmdepth: up to 10s of kms depth:unspecified depth: unspecified depth: >10s of metresacoustic waveselastic wavesconduit resonancegas emissionbubbly magmamonitoring (e.g. seismic, acoustic)fractured plug/lava domeFigure 1.3: Schematic for selected tremor mechanisms including approximate depth constraints.(a)–(d) summarize a variety of mechanisms conceptually, (e)–(f) specifically depict two modelsthat integrate a variety of observations (such as acoustic and seismic data, as well as including ob-servations from more than just one volcanic setting). In (a) and (b), degassing plays a major role forgenerating tremor. The individual models are: 1) resonance of acoustic waves in vent/cavity (Ma-toza et al., 2010), 2) bubble bursting (Ripepe and Gordeev, 1999), 3) bubble coalescence, ascent,and detachment of wake (Ripepe and Gordeev, 1999; Jones et al., 2012), 4) bubble cloud oscilla-tion (Matoza et al., 2010), 5) gas escape through fractures and/or explosion caused by overpressure(Johnson et al., 1998; Johnson and Lees, 2000), 6) conduit resonance due to pressure wave (Lesageet al., 2006), 7) fluid filled resonator (Neuberg et al., 2000), 8) crack waves/nonlinear excitationof conduit walls (note that crack/conduit can also be horizontal, e.g. dike, Chouet, 1986; Julian,1994), 9) stick slip movement of magma column (Denlinger and Hoblitt, 1999), 10) frictional fault-ing due to high strain rates (Thomas and Neuberg, 2012), or due to high stressing rates (Dmitrievaet al., 2013), 11) degassing induced oscillations of valve (analogue to crack waves) and atmosphere(Lyons et al., 2013), 12) oscillation of magma column in bubbly annulus (Jellinek and Bercovici,2011). Note that the mechanisms depicted here are highly schematic. In particular, more compli-cated plumbing and/or hydrothermal systems allow for similar mechanisms to act in parts of theplumbing other than straight conduits, and may cause interactions between different mechanismsand a variety of observations such as frequency gliding.101.2. Tremor Observationsenhanced by the Bernoulli effect (Julian, 1994, 2000). This type of model is not necessarily limitedto the uppermost parts of the volcanic system, and has thus been invoked to explain deep tremor inHawai‘i (Julian, 1994).Earthquake-like MechanismsModels for volcanic tremor for high viscosity magmas can be similar to earthquake generationalong fault planes (Fig. 1.3(d)). Frictional faulting, magma rupture near the conduit walls at highshear strain rates, or stick slip movement of magma along the conduit walls are thought to causeindividual LPs, which can become more closely spaced in time and eventually merge into tremor(at sufficiently high strain or stressing rates, e.g. Soufrie`re Hills Volcano, Denlinger and Hoblitt,1999; Thomas and Neuberg, 2012; Redoubt, Dmitrieva et al., 2013). In particular, these modelsare well suited to explain cyclic behaviour of eruptive activity, seismicity and tilt (e.g., Thomas andNeuberg, 2012). Denlinger and Moran (2014) suggest that a combination of shear failure in highviscosity magma combined with conduit resonance as discussed above causes non-eruptive tremorat Mount St. Helens.Integrative ModelsOften, models have been restricted to explaining one or multiple features of the expression of tremoron seismograms. Recently, attention was turned to incorporate other observables such as infrasoundor tilt (e.g., Thomas and Neuberg, 2012). Lyons et al. (2013) investigate the switch from seismiconly to seismo-acoustic tremor through laboratory experiments (schematically applied to a volcanoin Fig. 1.3(e)): They find that valve oscillation (similar to crack waves,, e.g., Chouet, 1986) relatedto bubble flow can produce seismic harmonic tremor, whereas acoustic tremor is restricted to highstiffness fluids and attributed to the existence of open degassing pathways (Lyons et al., 2013).Geared towards higher magma viscosities, Jellinek and Bercovici (2011) and Bercovici et al. (2013)suggest an oscillation of the magma column within a springy bubble foam or annulus that forms dueto plug flow and shearing of bubbles at high strain rates near the conduit walls (Fig. 1.3(f)). Theyexplain not only the observed content and evolution of frequency and amplitude for some cases oftremor, but also observations such as time-dependent gas flux.No Direct Relation to MagmaA further class of models requires the flow of gas or hydrothermal fluids. These models are linkedthrough the assumption that the source mechanism underlying volcanic tremor may be unrelatedto magma flow. Hellweg (2000), for example, suggests vortex shedding, slug flow, or the periodicrelease of gas through a small outlet as tremor source mechanisms, where each of the three repre-sents a part of a continuous range of flow regimes of hydrothermal fluids or gas. Similarly, Joneset al. (2012) find tremor between 0.4-1.4 Hz located near an area of active fumaroles, and attributetremor to gas flow through cracks. Balmforth et al. (2005) conclude that only fluids at higher flow111.3. The Need for a Global Classificationvelocities than magma can cause volcanic tremor as postulated by the fluid flow model by Julian(1994).Additionally, recent studies have shown that the characteristic low-frequency content and longdurations observed in discrete LPs can be attributed to slow, brittle failure of faults and wavepropagation in poorly consolidated volcanic materials (Bean et al., 2008, 2014; Eyre et al., 2015).Whereas a direct relationship to continuous tremor has not (yet) been shown, the effects may haveimplications for tremor that future work will have to assess.1.3 The Need for a Global ClassificationTremor is ubiquitous at volcanoes in virtually all tectonic settings (see Section 1.2; e.g. Aki and Koy-anagi, 1981; Neuberg, 2000; Konstantinou and Schlindwein, 2002; McNutt and Nishimura, 2008).Most groups of tremor mechanisms outlined in Section 1.2.5 depend on the regime of magma/fluidflow, and are linked to magma/fluid viscosity. Magma composition influences viscosity, and maythus be an important factor contributing to tremor properties. However, despite decades of observa-tional and modelling studies, there are significant challenges to understanding the variety of tremorproperties in relation to their underlying mechanics:• The term “tremor” is an umbrella for a large variety of observations. It is unclear how thecharacteristics of these observations can be separated into groups that relate to the underlyingphysics.• The terminology for tremor is confusing and lacks consistency. For tremor frequency con-tent, for example, the reported values can be the frequency of the highest spectral peak, meanfrequency (Thompson et al., 2002), first spectral peak (e.g. Benoit and McNutt, 1997), fre-quency range (Neuberg et al., 2000; Powell and Neuberg, 2003), or frequency bands (Chouetet al., 1997).• Few studies systematically examine links between the temporal evolution of tremor properties(e.g., frequency gliding) and volcanic processes (e.g., Benoit and McNutt, 1997; Jellinek andBercovici, 2011; Hotovec et al., 2013; Bercovici et al., 2013).• No systematic comparisons of tremor properties as a function of tectonic setting exist.1.3.1 Guiding HypothesesA thorough classification of the complexity of tremor observations in their volcanic and tectoniccontext for a range of settings is crucial to address these challenges. This classification is the maingoal of this thesis. My work is based on the following four hypotheses:(i) Tremor is an expression of volcanic processes, which are also expressed in other monitoringparameters.121.3. The Need for a Global Classification(ii) Volcanic tremor expresses itself in a variety of temporal, spatial, and spectral properties. Theseproperties are distinct for different types of tremor.(iii) The complexity of tremor properties, in combination with other monitoring parameters, canbe mapped into a parameter space based on the volcanic and tectonic context to identify char-acteristic “fingerprints”.(iv) If plausible source mechanisms are identified for different tremor fingerprints, volcanic tremormay be reliably used for eruption forecasting.1.3.2 MethodsTraditional Ways of Analyzing Volcanic TremorTraditionally, two types of analysis have been applied to volcanic tremor: (i) classical time seriesanalysis including assessment of temporal and spatial variations of tremor amplitudes and spectralcharacter (e.g., Riuscetti et al., 1977; Benoit and McNutt, 1997; Johnson et al., 1998; Hotovecet al., 2013; Patane` et al., 2013), and (ii) studies incorporating non-linear dynamics (e.g., Julian,1994, 2000; Konstantinou and Lin, 2004; Konstantinou et al., 2013). For both types, the analysis iscommonly confined to one volcanic setting, sometimes limited to only a few tremor episodes froman individual eruption or eruptive cycle, and patterns are typically identified manually. However,compared to studies at just one volcanic setting, the larger amounts of data inherent to a globalclassification of volcanic tremor require tools for automated pattern recognition. I describe threesuch tools that are relevant to this thesis in the following sections, where I emphasize the basicmethodology and introduce important terminology. Context, details, and reasoning for using eachmethod will be given in Chapter 3.Automated Pattern RecognitionIn Chapter 3, I evaluate two combinations of three methods that can be used for pattern recog-nition. Principal Component Analysis mainly aims at dimensionality reduction, whereas clusteranalysis combines observations into groups based on similarity of observations. Self-OrganizingMaps (SOM) can be thought of as both dimensionality reduction and grouping of observations, asI discuss below.Principal Component Analysis Principal Component Analysis aims to reduce the dimensional-ity of a dataset by aligning the original coordinate system of N dimensions with mutually orthogo-nal directions of maximum variance in the data (e.g., Hotelling, 1933; Bishop, 2006). These direc-tions are called eigenvectors (or modes), following terminology of Hsieh (2009). If the data showpreferential alignment along one or more directions in the original coordinate system (Fig. 1.4),then this alignment is captured by the eigenvectors, and a lower number of dimensions can be usedto describe the most important variations in the dataset.131.3. The Need for a Global Classification(a) (b) (c)original coordinate systemrotated coordinate systemreduced number of dimensionsFigure 1.4: Schematic for Principal Component Analysis. (a) Observations (triangles) in originalcoordinate system (black, number of dimensions N = 2) show strong alignment. (b) Rotatedcoordinate system (red), aligned with directions of maximum variance. (c) Rotated coordinatesystem with reduced number of dimensions (N = 1), capturing most of the variance in the data.Self-Organizing Maps The Self-Organizing Map was introduced by Kohonen (1982, 1990). Thegoal of the SOM approach is to identify patterns in a multidimensional input data space by “map-ping” the original data onto a 2D map of nodes that represents a feature space (Fig. 1.5).(a) (b)original coordinate system sheet of nodes with grouped observationsFigure 1.5: Schematic for Self-Organizing Maps algorithm. (a) Observations in original coordinatesystem, colored according to “similarity” (arbitrary in this case). (b) Two-by-two feature space ofhexagonal nodes onto which observations are mapped (and thus grouped) according to similarity inthe original coordinate system.Each node ri is associated with a model vector mi with N coordinates according to an N -dimensional input data space. The initial model vectors m(0)i are assigned based on the inputdata space. Each data vector Xn (where n is the number of observations) is then assigned toa model vector by finding the minimum Euclidean distance d(0)ni = ||Xn − m(0)i ||. When adata vector Xn is assigned to a model vector, the corresponding node rb (“best-matching unit”)and the ones surrounding it are updated towards the mean of the input data vectors according to141.3. The Need for a Global Classificationm(1)i = m(0)i + h(0)ni [Xn −m(0)i ], where the neighborhood is determined by, for example, a Gaus-sian kernelh(0)ni = α(0)exp(−||rb − ri||22(σ(0))2). (1.1)Here, α is the learning rate factor and σ dictates the width of the Gaussian kernel, i.e. the radius ofsamples that belong to a “neighborhood”. Both α and σ decrease with increasing processing timestep. This process is called the “learning process” and is repeated for a fixed number of processingsteps. Ideally, after a sufficiently large number of iterations the feature vectors and their locationson the 2D map no longer change, and observations are thus assigned to nodes representing a finalfeature space and grouped according to similarity (on the basis of Euclidean distances).The algorithm is available as aMATLAB R© toolbox Vesanto et al. (1999, 2000) (freely availableon http://www.cis.hut.fi/projects/somtoolbox/). Many parameters in the toolbox can be adjusted, outof which the most important ones include:• node lattice size (either as guideline for total number of nodes, or specific x- and y-dimensions),where larger maps can generally capture finer details and variations among observations;• node shape (hexagonal or rectangular) and consequently number of neighbors for each node;• lattice shape (sheet, cylindrical, or toroidal), where cylindrical and toroidal maps imply con-nections of nodes across the ”edges” of the sheet;• shape (e.g., Gaussian or bubble) and radii of neighborhood relationships;• random or linear initialization of model vectors.The number of possible configurations of parameters is large, and the ideal choice depends on thedataset and the questions driving the analysis. My data as shown in Chapter 3 did not show a strongsensitivity to these parameters in several possible configurations. I discuss more details on some ofthe parameters and my final configuration in Chapter 3.Cluster Analysis Agglomerative hierarchical clustering is one of many methods to group obser-vations. Observations are grouped into pairs on the basis of their Euclidean distances and two pairseach are then merged into subclusters to minimizedij =√2ninjni + nj||X¯i − X¯j || (1.2)where ni is the number of observations in cluster i, and X¯i is the corresponding centroid location(Ward’s method, Ward Jr, 1963). Two subclusters each are subsequently combined into largersubclusters, and so forth, until the limit of one large cluster including all observations is reached(Fig. 1.6).The best clustering can be obtained by examining the cluster hierarchy (“dendrogram”, similarto an inverted tree, Fig. 1.6), where a cut-off can be introduced at any given number of clusters.151.3. The Need for a Global ClassificationdendrogramFigure 1.6: Schematic for hierarchical clustering algorithm. Observations are grouped iterativelyuntil the limit of one large cluster is reached. Inset shows dendrogram depiction of cluster structure,indicated by corresponding colors and dashed lined around observations.One of the biggest challenges in cluster analysis is that it requires identification of this cut-off, orequivalently an a priori number of clusters k (e.g. Jain, 2010). The “ideal” k depends on the datasetand the main goal is to find a k that represents the number of clusters that are naturally present in thedata. A variety of criteria exist in the pattern recognition community to determine an optimal choicefor k (e.g. Davies and Bouldin, 1979; Tibshirani et al., 2001; Pakhira et al., 2004; Kuncheva andVetrov, 2006). Many of these criteria are applied in the same space where clustering is performed,and assess clustering based on a measure of variability of observations within individual clusters incomparison to a measure of variability among different clusters. For example, a common choice isthe Davies-Bouldin index (Davies and Bouldin, 1979), which seeks the number of clusters k whichmaximizesDB =1kk∑i=1maxi 6=j{s(i) + s(j)Sij}(1.3)with Sij = ||X¯i − X¯j||, i.e. the Euclidian centroid-centroid distance of each cluster pair, and thesummed within-cluster distance s(j) =∑nki=1 dij , where nk is the number of samples within thek-th cluster. I discuss an alternative choice of criterion in Chapter 3.1.3.3 Thesis OutlineI use the hypotheses and methods to analyze tremor from four different volcanoes in Alaska andHawai‘i to address the aforementioned challenges in the following way.In Chapter 2, I analyze seismicity during a series of eruptive episodes at Kı¯lauea Volcano,Hawai‘i, to determine the best metric to characterize different types of volcanic tremor. I use clas-161.3. The Need for a Global Classificationsical time series analysis to identify two phases of seismicity characteristic for dike intrusions, thatdiffer in terms of the location of their strongest expression, their temporal appearance and evo-lution, as well as their overall spectral shapes. Only the second of the two phases is consideredtremor according to our definition. I explore oscillations of bubble clouds in a geometrically com-plex plumbing system as a possible tremor mechanism by taking into account constraints from (i)the (dis)similarities of tremor properties during two similar dike intrusions, and (ii) the differencesto the other seismic signals. In contrast to the varying properties between the two phases, the dif-ferences between the tremor signal and the seismicity during more explosive eruptions at Kı¯lauealie dominantly in their respective spectra. Because of their similarities in the time domain and thelack of systematic and comparable placement of seismometers at different volcanoes, spectral in-formation thus appears a useful criterion for classification to distinguish between different types oftremor.The manual analysis of the data from Kı¯lauea proved to be too cumbersome to examine timeperiods on the order of several weeks or months for several volcanoes. However, to achieve a globalcomparison, time series of volcanic tremor should be as long as possible. To be able to analyzesuch long time series efficiently, in Chapter 3 I rigorously test two automated pattern recognitionapproaches with a newly constructed and purposely designed synthetic dataset of volcano seismicspectra. The original goal was to assess the performance of an algorithm formed by a combinationof Self-Organizing Maps (SOM) and hierarchical clustering. However, my work reveals that anapproach that combines Principal Component Analysis (PCA) and hierarchical clustering is moreeffective at recovering the major elements of the synthetic data.Following Chapter 3, I apply the newly developed and thoroughly tested combination of PCAand clustering to classify volcanic tremor from four different volcanic settings (Kı¯lauea, Okmok,Pavlof, and Redoubt volcanoes) in Chapter 4. I design an algorithm to detect tremor in continu-ous seismic data by measuring absolute amplitude compared to a specifically defined backgroundsignal. For each tremor window I then obtain the corresponding spectrum, and analyze the tremorspectra (i) from a given station network to assess spatio-temporal and spectral properties of tremorat each volcano individually, and (ii) from one station from each of the volcanoes to characterizesimilarities and differences among tremor signals from a range of settings, which may relate to at-tributes such as edifice type (e.g., stratovolcano vs. shield volcano). The network analysis (i) showsthat several spectral signatures of volcanic tremor occur within a given setting. Their variations intime and space sometimes relate to different processes of volcanic activity, and path effects do notappear to strongly affect spectral shapes at the distances of the stations analyzed here. The multi-setting analysis (ii) reveals that at least four types of tremor are observed across the four settings,and that systematics relationships to volcano characteristics such as open vent volcanism may exist.In summary, my work highlights the importance of analyzing tremor in the light of multipleeruptive cycles through the Kı¯lauea case study. Furthermore, I provide the necessary pattern recog-nition tools to undertake such analysis in an efficient and objective way. The promising resultsfrom the comparison of tremor from four volcanoes show that a global comparison is achievable171.3. The Need for a Global Classificationand may hold the key for a more complete understanding of the processes driving volcanic tremor,which ultimately may improve eruption forecasting.18Chapter 2Volcanic Tremor and Frequency Glidingduring Dike Intrusions at Kı¯lauea – ATale of Three Eruptions7SummaryTo characterize syneruptive/intrusive deviations from background volcanic tremor at Kı¯lauea, Ha-wai‘i, we analyze the spatial and temporal properties of broadband tremor during dike intrusionsinto the East Rift Zone (ERZ) in 2007 and 2011, as well as during explosive eruptive activity atKı¯lauea’s summit in 2008. Background tremor was similar for each event, and the 2008 explo-sions did not affect its properties. In contrast, the intrusions were accompanied by departures fromthis background in the form of two phases of seismicity that were separated in space and time. Inboth 2007 and 2011, Phase I was characterized by a quick succession of discrete events, whichwere most intense at the onset of intrusion near the presumed locations of the dikes intruding intothe ERZ. Phase II, marked by continuous broadband tremor around the summit, followed 10–14 hlater. In 2007, Phase II tremor was accompanied by a monotonic downward shift (glide) of spectralpeaks between ∼0.6 and 1.5 Hz over at least 15 h. During Phase II in 2011, a gradual upward andsubsequent symmetric downward glide between ∼0.6 and 6.6 Hz occurred over 5–10 h, respec-tively. The spectra during both phases differed from the background and 2008, as well as from eachother, indicating different physical mechanisms. Phase I in 2007 and 2011 is probably related tothe mechanics of dike intrusion. Phase II tremor may be characteristic for evolving magma-bubbledynamics related to the geometry of the plumbing system and the style of magma flow.7Reprinted from Journal of Geophysical Research: Solid Earth, with permission from Wiley.192.1. Introduction2.1 IntroductionVolcanic eruptions are often preceded and accompanied by low-frequency (approximately 0.5–10 Hz) volcanic tremor (McNutt and Nishimura, 2008), that persists for minutes to many months(Konstantinou and Schlindwein, 2002). The appearance of this seismic signal is often interpretedas a sign of an impending eruption (McNutt, 1996, 2005; Sparks et al., 2012). The reliability oftremor as a forecasting tool is, however, uncertain. A central challenge is that existing constraintson the characteristic spatial and temporal properties of tremor can be interpreted in terms of manyphysical processes that can act to drive ground oscillations on the order of 1 Hz in volcanic sys-tems (see reviews such as Chouet, 1996b; Konstantinou and Schlindwein, 2002; McNutt, 2005, andreferences therein).A problem common to many studies is that there is insufficient information to recognize whetherthe emergence of tremor or, say, the rate of change in its frequency or amplitude is critically indica-tive of an impending eruption. Such a characterization of baseline tremor and deviations from thebaseline requires observations over multiple eruptive cycles, which is impractical at many volca-noes because eruptions occur infrequently. Three eruptions at Kı¯lauea, Hawai‘i, over the last decadeprovide a novel opportunity to explore deviations from baseline tremor during eruptions with vary-ing styles in one volcanic setting: In 2007 and 2011, intrusions and fissure eruptions in the EastRift Zone (ERZ) involved redistribution of magma in the plumbing system (Poland et al., 2008;Montgomery-Brown et al., 2011; Lundgren et al., 2013). In contrast, more explosive eruptions in2008 were probably related to rockfalls and degassing at the summit (Wilson et al., 2008; Chouetet al., 2010; Orr et al., 2013). Few studies have systematically examined tremor during differentstyles of eruptions (e.g., fissure versus cylindrical vent, Strombolian versus lava fountaining versussub-Plinian activity) (McNutt, 1992; Thompson et al., 2002; Alparone et al., 2003). To providereliable constraints on the extent to which the temporal and spatial properties of tremor are reli-able indicators of characteristic physical mechanisms driving volcanic unrest, we present the firstsystematic analysis of broadband tremor at Kı¯lauea over multiple eruptive cycles. We characterizestatistically stationary as well as time- and space-dependent tremor properties within the contextsof these three eruptions, which are described in Section 2.2. We then use constraints from our dataanalysis (Section 2.3) to investigate temporal and spatial relationships between two observed phasesof seismicity and to discuss how these relationships restrict plausible models for the excitation andfrequency modulation of intrusion tremor signals at Kı¯lauea (Section 2.4).2.2 Three Eruptions at Kı¯lauea, Hawai‘iKı¯lauea Volcano on the Island of Hawai‘i has been erupting almost continuously since 1983 (Garciaet al., 1992; Heliker and Mattox, 2003; Poland et al., 2012). Beneath this basaltic shield, magmamoves up from mantle depths and is stored in a reservoir a few kilometers below the summit caldera(Tilling and Dvorak, 1993; Dawson et al., 1999). At the surface, the caldera with Halema‘uma‘uCrater in the west is separated from Pu‘u ‘O¯‘o¯ Crater in the east by a linear system of faults and202.2. Three Eruptions at Kı¯lauea, Hawai‘icraters defining the East Rift Zone (ERZ) (Fig. 2.1). Magma entering the ERZ from the summit istransported downrift through a horizontal conduit at 2–3 km depth, from where it feeds the ongoingPu‘u ‘O¯‘o¯-Ku¯pa‘ianaha¯ eruption (Tilling and Dvorak, 1993; Johnson, 1995; Okubo et al., 1997;Dawson et al., 1999).AHUKNHOTLPAU STC−155˚15' −155˚10' −155˚05' −155˚00'19˚20'19˚25'0 5km−155˚15' −155˚10' −155˚05' −155˚00'0510depth (km)20072011Halema`uma`u (summit)Pu`u Ō`ōPhase IPhase II05/03 07/0306/03 08/03 09/03 10/03in#ation de#ation in#ationgliding: up downeruptiondrainagesummit lava lakesummit deformationseismic signal$ssures2011ERZ intrusion16/06 18/0617/06 19/06 20/06 21/06in#ation de#ation in#ationsummit deformationPhase IIseaward displacementseismic signal2007ERZ intrusionPhase Igliding: down$ssures eruptionSouth Flank(a) (b)(c)East Rift ZoneMakaopuhiMauna UluFigure 2.1: (a) Map and cross section show located earthquakes over 7 days from ANSS catalogstarting on 16 June 2007 and earthquakes from the HVO catalog starting 5March 2011, respectively.Inset in cross section shows location of map area on the Island of Hawai‘i. Seismic stations areshown as orange triangles. East Rift Zone and other major features mentioned in the text are labeled.(b and c) Timeline of important events over seven days before, during, and after 2007 Father’s Dayand 2011 Kamoamoa eruption. Phase I, Phase II, and gliding will be discussed in detail in thefollowing section. Only events analyzed in 2008 were two out of multiple explosions (19 Marchand 3 September) and the subsequent first sighting of the lava lake, so no timelines are shown.We analyze seismic data from three eruptive episodes since 2007: The 2007 Father’s Day in-trusion and eruption, a period of explosive eruptions related to the formation of the lava lake atthe summit in 2008, and the 2011 Kamoamoa eruption. Whereas the 2007 and 2011 events in-volved magma transport from the summit into the ERZ (Poland et al., 2008; Lundgren et al., 2013),the 2008 episode was characterized by discrete explosions involving magma only at the summit(Chouet et al., 2010; Orr et al., 2013). Similarly, the excitation time scales varied from secondsduring explosions to days during magma flow related to intrusions. The three eruptions thus in-volved excitation over disparate time scales within distinct parts of the magmatic plumbing system.A careful comparison of the tremor signals provides a unique opportunity to identify reliable spa-tial, temporal, and spectral fingerprints for distinct types of volcanic unrest. To provide context forour analysis, we describe the main features of each of these events, respectively.2.2.1 The 2007 Father’s Day EruptionAt 1216 UTC on 17 June 2007, tilt at the summit indicated a change from inflation to rapid deflation(Fig. 2.1; all times here and in the following sections are UTC). A fewminutes later, tilt at Pu‘u ‘O¯‘o¯also changed to deflation and the crater floor began to collapse (Poland et al., 2008). A simultaneous212.3. Data & Resultsincrease in seismicity and inflationary tilt in the ERZ close to Mauna Ulu suggested dike intrusion(Poland et al., 2008). This intrusion lasted until 2030 UTC, 19 June, and was accompanied by asmall eruption from 1015 to 1045 UTC, 19 June (Poland et al., 2008; Fee et al., 2011a). Note thathereafter, “time periods of eruption” refers to the emission of lava and/or ash at the surface, whereas“intrusion” refers to the period of subsurface dike intrusion inferred from deformation.2.2.2 The 2008 Halema‘uma‘u ExplosionsAfter a vigorously degassing fumarole appeared in Halema‘uma‘u crater on 12 March 2008, thefirst explosive eruption on 19 March at 1258 UTC created a vent with a ∼ 35 m diameter (Wilsonet al., 2008). Over 5 months, this vent widened to > 150 m through > 20 intermittent bursts ofdegassing and explosions (Chouet et al., 2010; Fee et al., 2010; Orr et al., 2013). In addition tothe first explosion in March, we chose the largest of these explosions (in terms of mass) for furtheranalysis. This second event occurred on 3 September at 0613 UTC. It was followed by the firstappearance of a lava lake on 5 September (Orr et al., 2008). Lava flows continued to be activebetween Pu‘u ‘O¯‘o¯ and the ocean to the south (Smithsonian Institution, 2010).2.2.3 The 2011 Kamoamoa EruptionEruptive activity from the end of 2010 to early 2011 was dominated by spatter and lava flows fromPu‘u ‘O¯‘o¯, and lava lake convection and inflation at Halema‘uma‘u (Lundgren et al., 2013; Orret al., 2015). Seismicity close to the summit and in the Upper ERZ increased in November 2010.Furthermore, seismicity increased close to Makaopuhi (Orr et al., 2015). At 2342 UTC on 5 March2011, seismicity increased further and tilt at Pu‘u ‘O¯‘o¯ rapidly changed from inflation to deflation at2345 UTC (Fig. 2.1). At approximately 0010 UTC the summit also showed signs of rapid deflation(Lundgren et al., 2013). The crater floor at Pu‘u ‘O¯‘o¯ started to collapse. The lava lake at the summitstarted to drain, and magma withdrawing from the summit and Pu‘u ‘O¯‘o¯ fed a dike intrusion closeto Makaopuhi uprift from Pu‘u ‘O¯‘o¯ (Lundgren et al., 2013; Carbone et al., 2013). This intrusionculminated with a fissure eruption from 0309 UTC, 6 March to 0830 UTC, 10 March, just east ofMakaopuhi (Orr et al., 2015).2.3 Data & Results2.3.1 Network & Data ProcessingContinuous, vertical component seismic velocity data were sampled at 100 Hz. For a good spatialcoverage of seismic signals on Kı¯lauea from the summit to Pu‘u ‘O¯‘o¯, we chose five short-periodsensors (Mark Product L-4 seismometers with a natural frequency of 1 Hz) for further analysis(Fig. 2.1). Prior to analysis, we correct for the effect of the instrument to ensure a flat responsebetween 0.5 and 15 Hz, subsample the time series at 50 Hz, and demean and detrend the data.Unless indicated otherwise, we compute power spectra over 30 min windows with 50% overlap.222.3. Data & ResultsWe use this approach to optimize a practical tradeoff between temporal resolution and processingspeed and chose values similar to other studies (e.g. Power et al., 2013; Richardson and Waite,2013). Our results are, however, independent of the specific choices of window length and overlap.To capture the background state as well as the eruptive/intrusive processes, we included 1 weekof data for each event. Because of our interest in deviations from the steady state of the system, anddue to the relative lack of constraints on processes in the plumbing system during quieter periodsin comparison to the events in 2007, 2008, and 2011, this only includes approximately 1 day ofbackground tremor before each of the intrusion events.2.3.2 Overview of Seismic SignalsThe emergence and the evolution of the seismic signals accompanying the intrusions in 2007 and2011 were distinct from those in 2008. Accordingly, we first describe key features of these signalsin space and time during the two intrusion and ERZ eruption periods in 2007 and 2011 in chrono-logical order. Second, we summarize seismicity during two explosions at the summit in 2008 whenthere were no dike intrusions in the ERZ. Figure 2.2 shows spectrograms over 7 days for the fiveseismic stations between the summit and Pu‘u ‘O¯‘o¯ for the four time periods. During all time pe-riods, the seismic signals close to the summit (west) were distinct from the ERZ/Pu‘u ‘O¯‘o¯ area(east), with the biggest differences in 2007 and 2011.In 2007, continuous tremor with power concentrated below 5 Hz preceded the intrusion closeto Pu‘u ‘O¯‘o¯ (Fig. 2.2(a)). During the intrusion and eruption, there were two phases of seismicity.We define “Phase I” as a strong broadband signal covering our entire frequency range (0.5–15 Hz,Fig. 2.2(a)), which was strongest in the ERZ (in this case at station PAU). It started with the onsetof intrusion and gradually disappeared over the following 1–3 days (Figs. 2.1 and 2.2(a)). The endof Phase I overlapped in time on 17 June with the emergent onset of a comparatively continuous“Phase II.” Its broadband character is similar to Phase I, and it was strongest at station OTL closeto the summit. Phase II decayed to a background level over the following 3–4 days (Figs. 2.1 and2.2(a)).Before the 2011 Kamoamoa eruption, there was no preintrusion tremor phase such as in 2007.The onset of intrusion just before midnight on 5 March was, however, accompanied by a similarPhase I signal (Figs. 2.1 and 2.2(a)). A Phase II signal emerged after approximately 0.5 days. Thissignal was concentrated near the summit and persisted for more than 5 days. A strong broadbandsignal at station STC (closest to the eruption site) was not visible on any of the other stations.It faded out earlier than Phase II. The notable short period of high spectral power on 11 Marchcoincides approximately with the expected arrival of surface waves related to the 2011 To¯hokuearthquake.In terms of the location of the highest intensity and their timing relative to each other, Phases Iand II were remarkably similar in 2007 and 2011 (Fig. 2.3). Furthermore, both Phase II signalsin 2007 and 2011 were accompanied by frequency gliding (i.e., the gradual shift in frequency of aspectral peak over time, on 18–19 June 2007, and on 6–8 March 2011, respectively; Figs. 2.1 and232.3. Data & Results9/1 9/2 9/3 9/4 9/5 9/66/16 6/17 6/18 6/19 6/20 6/21 6/223/16 3/17 3/18 3/19 3/20 3/21 3/223/ 5 3/ 6 3/ 7 3/ 8 3/ 9 3/10 3/11(b) SUMMMIT EXPLOSIONS(a) EAST RIFT ZONE INTRUSIONS400-40dBintrusion flank slip intrusionexplosion explosion lava lake first sightingOTLSTCKNHPAUAHU9/7200820072008OTLSTCKNHPAUAHUfrequency (Hz)frequency (Hz)5105105105102011Phase IPhase IIPhase IPhase IIcontinuous weak tremor, less variation continuous weak tremor, less variationFigure 2.2: (a) Spectrograms over 7 days for the 2007 Father’s Day, and the 2011 Kamoamoaintrusions/eruptions, and (b) for two explosions at the summit in 2008. Each panel shows fivestations ordered from west to east. White areas are periods with data gaps.242.3. Data & Results2.2(a)). To assess the similarity of each phase during the two intrusions in greater detail, we describethe statistically stationary properties of the two phases and the gliding episodes in Sections 2.3.3and 2.3.4.PHASE I PHASE II20072011−202x 10   nm/s4timefrequency (Hz) 13:10 13:20 13:30 13:40 13:502468101214dB20 30 40 50 60 70−202x 10   nm/s4timefrequency (Hz) 6:10 6:20 6:30 6:40 6:502468101214dB20 30 40 50 60 70−202x 10   nm/s4timefrequency (Hz)  1:10 1:20 1:30 1:40 1:502468101214dB20 30 40 50 60 70−202x 10   nm/s4timefrequency (Hz) 12:10 12:20 12:30 12:40 12:502468101214dB20 30 40 50 60 70KNH, 2011/3/6KNH, 2007/6/17 OTL, 2007/6/19OTL, 2011/3/8Figure 2.3: Spectrograms over 1 h (with 4.5 s windows) during intrusions in (top) 2007 and (bottom)2011. One station in the east (KNH) and one in the west (OTL) were chosen for Phase I andPhase II, respectively. Vertical purple lines in seismograms indicate located earthquakes (locationsin Fig. 2.1). During both intrusions, (left) Phase I is dominated by individual events, whereas (right)Phase II shows continuous, nonharmonic tremor.During the weeks that included the explosions on 19 March and on 3 September 2008, there wascontinuous tremor with a lower intensity than tremor during the intrusions (peak RMS amplitudesnot exceeding ∼1.6× 103 nm/s, versus peak RMS up to ∼6.6× 103 nm/s, Fig. 2.4). This weaker,continuous signal in 2008 was strongest at station AHU close to the summit, weaker in the ERZ,and slightly stronger again at station STC close to Pu‘u ‘O¯‘o¯ (Figs. 2.2(b) and 2.4). Both explosionsare visible as short increases in spectral power. The first explosion was accompanied by a slightincrease in tremor frequency bandwidth. A similar change in tremor frequency bandwidth followed252.3. Data & Resultsthe second explosion, but more than half a day later (Fig. 2.2(b)). The spectra before and after theexplosions were very similar for both March and September 2008, and resembled the backgroundspectra in 2007 and 2011 with a power-law decay of spectral power from low to high frequencies(Fig. 2.4).2.3.3 Phases of Seismicity During IntrusionsFigure 2.3 shows 1 h velocity seismograms and spectrograms for typical Phase I and II signalsin 2007 and 2011 from one station in the east (KNH) and one in the west (OTL), respectively.Figure 2.4 shows 1 h spectra from preintrusion/explosion, synintrusion and postexplosion timeperiods from station AHU. We chose this station because signals from the 2008 explosions as wellas from Phase I and Phase II in 2007 and 2011 were each expressed.The Phase I signals shown are approximately 1 h after onset of intrusion and are dominated byindividual events (Fig. 2.3). Larger spikes in the traces correspond to located earthquakes (Fig. 2.1)that show up as vertical stripes, i.e., short-duration broadband signals in the spectrograms. The slopeof a power spectrum is of particular interest because it indicates the similarities and differences inthe energetics of the tremor oscillations: Both the power delivered to the motions and the natureof the dissipation influence the spectral slope. The spectra for Phase I were relatively flat between1 and 10 Hz for both years. In contrast, the preintrusion background in 2007 and 2011, and thespectra from preexplosion and postexplosion periods in 2008 were similar with an approximatelypower law decay from low to high frequencies. The 2007 Phase I signal was strongest at stationPAU with an RMS amplitude of ∼ 3.3 × 103 nm/s. The 2011 Phase I was shorter in duration andfarther east compared to 2007 (strongest RMS amplitude∼3.1×103 nm/s at station KNH; Fig. 2.4).Locations based on envelope cross correlation confirm that Phase I occurred closest to the locationof intrusion in both years (A. Wech, personal communication, 2014) as indicated by the amplitudeand power distribution (Figs. 2.2–2.4).Very few individual earthquakes occurred during Phase II in both 2007 and 2011. The signalsshowed continuous oscillations with spectral power concentrated generally at frequencies below3 Hz. The two highest spectral peaks at station AHU were at ∼0.9 and 1.7 Hz in 2007, and at∼1.1 and 1.4 Hz in 2011 (Fig. 2.4). There were several other peaks at irregular intervals, i.e., notharmonic overtones, and spectral power decayed in a way similar to the background tremor spectra(Fig. 2.4). The amplitudes during Phase II were strongest near the summit (∼ 3.9 × 103 nm/s and∼ 2.8 × 103 nm/s for 2007 and 2011, respectively; Fig. 2.4), confirmed by envelope cross corre-lations of shorter tremor bursts during this period (A. Wech, personal communication, 2014). Thehigh amplitudes toward station STC during Phase II in 2011 (Fig. 2.4) were related to a different,strong broadband signal that rapidly decayed with distance and that appears to be independent fromPhase II (Fig. 2.2). Because of its absence in 2007, we do not treat this signal as part of the Phase IIsignature and only briefly discuss it again in Section 2.4.1.Overall, the similarities in the succession of the two phases, their approximate durations, andtheir spectral features in 2007 and 2011 suggest that they may be characteristic signatures of intru-262.3. Data & Results1 1010−2100102104  2 3 4 5frequency (Hz)spectral powerfrequency (Hz)spectral powerfrequency (Hz)spectral power200720112008pre-intrusionPhase IPhase II10−2100102104  1 102 3 4 510−2100102104  1 102 3 4 5pre-intrusionPhase IPhase IIOTL AHU PAU KNH STCRMS amplitude (nm/s)102103104OTL AHU PAU KNH STCRMS amplitude (nm/s)102103104OTL AHU PAU KNH STC2 km 4.1 km 7.7 km 12.1 km 16.5 kmRMS amplitude (nm/s)102103104AHUAHUAHUpre-explosion< 1 day after explosion> 1 day after explosionMar SepFigure 2.4: Spectra over 1 h during intrusions in (top) 2007 and (middle) 2011, and during explo-sions in (bottom) 2008 for different phases at station AHU (left column) smoothed with a 100 pointmoving average (= 0.056 Hz), and RMS velocity amplitudes at all stations from west to east dur-ing the same time periods. During both intrusions, Phase I has a relatively flat spectrum, whereasPhase II shows continuous, nonharmonic tremor with peaks below 3 Hz. Phase I has the highestamplitudes in the ERZ (stations are ordered from west to east, with distance from the summit inkilometers given below the station name), whereas Phase II is strongest close to the summit (forhigh Phase II amplitudes toward STC in 2011, see text). Spectra in 2008 show no strong differ-ences at different points in time, and amplitudes are strongest at station AHU, generally higher thanthe background for 2007 and 2011 but lower than during the intrusions. Note that amplitudes arenot corrected for site effects and thus do not provide accurate locations.272.3. Data & Resultssion seismicity.2.3.4 Frequency GlidingFigure 2.5 shows frequency gliding at station OTL during the intrusions in 2007 and 2011. Wechose station OTL because gliding is strongest close to the summit (Fig. 2.1). In both years, glidingoccurred during Phase II over a time scale of several hours to days. The gliding peaks are diffuseand buried in other signals, so there is considerable uncertainty in onset times (≥ 30 mins) andfrequency range (≥ 0.1 Hz). There was no gliding in 2008.2007 2011−202 x 10   nm/s4 OTLfrequency (Hz)1234567−202x 10   nm/s4 OTLdatefrequency (Hz)6/18 6/1912dB10 15 20 25 30 35 40 45 50date3/7 3/8dB0 5 10 15 20 25 30 35 403/63/6 3/7 3/82468frequency (Hz)  6/18 6/1912frequency (Hz)  OTLAHUPAUKNHSTC12:00 12:0012:00 12:0012:00 12:0012:00 12:00Figure 2.5: Spectrograms over 60 h (with 360 s windows) during intrusions in (left) 2007 and (right)2011. Panels show (from top to bottom) seismogram, spectrogram below 8 Hz for 2007/below 2 Hzfor 2011 at station OTL and gliding traced at all stations for comparison. Time starts approximately1 h before the onset of intrusion in each case. Vertical purple lines in seismograms indicate locatedearthquakes (locations in Fig. 2.1). Phase I, Phase II, and gliding are visible in both years. In2007, gliding is directed downward between 0.6 and 1.5 Hz. In 2011, both upward and downwardgliding range between 0.6 and 6.6 Hz. All stations show the same gliding frequencies and temporalevolution during 2007 and 2011, respectively, but the signal is strongest close to the summit.In 2007, multiple frequency peaks between 0.6 and 1.5 Hz started gliding downward approxi-mately 14 h after onset of intrusion on 18 June. The gliding event lasted for 15 h, with some furtherslight shifts occurring for another 16 h. During the time of gliding of some peaks, several otherfrequency peaks with similar spectral power remained at constant frequencies. We discuss this si-multaneous occurrence of gliding and stable peaks (i.e., frequency peaks that do not show gliding)in Section 2.4.3.282.4. DiscussionIn 2011, gliding started approximately 10 h after onset of intrusion, on 6 March. The temporalevolution differed from 2007: One frequency peak climbed upward from≤ 1.2Hz to at least 5.6 Hzover 5 h. The upglide was accompanied by increasingly stronger tremor between ∼ 1 and 6 Hz witha sharp (compared to the duration of Fig. 2.5) amplitude decrease around 0000 UTC on 7 Marchand a similarly sharp amplitude increase around 1200 UTC. Approximately 28 h after the end ofthe upglide, there was a symmetric downglide from at least 6.6 Hz to 0.6 Hz over 10 h (and longerfor the weaker, nonharmonic overtones).Despite the differences in gliding frequency range and the direction in time (i.e., upglide versusdownglide), the character and remarkable longevity of gliding episodes in 2007 and 2011 are similarand each episode occurs concurrently with the onset of Phase II.2.3.5 Summary of Main ResultsThe main results of our systematic analysis are:1. Seismic signals (above 0.5 Hz) during eruption periods in the ERZ associated with dike in-trusion are stronger than during explosions at the summit.2. The frequency content and the slopes of 1 h time-averaged spectra before and after the ex-plosions in 2008 are similar to the background preintrusion signal recorded in both 2007 and2011.3. Intrusions and eruptions in the ERZ are marked by two phases of seismicity that overlap intime but are separate in space and distinct in character:a. Phase I is characterized by discrete events, coincides in space and time with the onsetof the intrusions, and lasts for several hours. Its spectral slope is relatively flat over a1–10 Hz frequency band.b. Phase II has an emergent onset 10–14 h after the start of the intrusion, is continuous,is strongest close to the summit, and persists after the end of the eruptions. It is notharmonic and has peak frequencies mainly between 0.7 and 3 Hz, where its spectralslope is approximately flat. Above 3 Hz Phase II shows decaying spectral power similarin character to the preintrusion background in 2007 and 2011 and to the signals beforeand after the explosions in 2008.c. Monotonic frequency gliding over several hours is associated with Phase II. Whereasthe 2011 eruption is characterized by symmetric upglides and downglides, the 2007event is marked by downgliding alone.2.4 DiscussionWe discuss how our observations and their temporal and spatial relationships indicate a dependenceof tremor properties on eruptive style and location (i.e., tremor in 2008 versus 2007/2011 and tremor292.4. Discussionduring 2011 at the summit versus in the ERZ; Section 2.4.1). Furthermore, we discuss why Phase Iis likely related to dike intrusion (Section 2.4.2). In Section 2.4.3 we show how our observationsrestrict plausible Phase II tremor mechanisms using the example of two models for coupled bubble-magma interactions that can account for many of the key features in our data. Lastly, we summarizethe remaining limitations of our analysis and highlight the steps necessary to better understandPhase II tremor (Section 2.4.4).2.4.1 Tremor & Eruptive Styles: Summit Explosions Versus ERZ Intrusions andFissure EruptionsAdditional observations are necessary to interpret key differences between the 2008 and 2007/2011episodes, as well as between the tremor signals at the summit and in the ERZ in 2011. Broadbandtremor accompanying the intrusions is stronger than tremor accompanying explosive activity at thesummit (Fig. 2.4), suggesting that either a different process was causing the signal in 2008, or thatthe same process was weaker in 2008 than in 2007 and 2011. Long-period (LP) and very longperiod (VLP) seismicity (f < 0.5 Hz) was present during the 2008 summit eruptions (Dawsonet al., 2010; Ballmer et al., 2013; Dawson and Chouet, 2014) and is interpreted in terms of fluidprocesses related to degassing, resonance of a fluid-filled crack, and/or rockfall events at the top ofthe magma column that couple into the wall rock at a geometric constriction at approximately 1 kmdepth (Chouet et al., 2010; Dawson et al., 2010; Patrick et al., 2011b; Dawson and Chouet, 2014).Because the weak 2008 broadband tremor coincides with the observation of the LP and VLP sig-nals, it is possible that the observations in these two frequency bands are related. In contrast, therewere no VLP signals during our observed Phase II in 2007 and 2011, which then suggests a differ-ent underlying physical mechanism for our observations. The background spectra for 2007/2011and 2008 have similar shapes, and none of the spectra during 2008 deviate strongly from this back-ground (Fig. 2.4). Phases I and II during the intrusions, however, have distinctly shaped spectrawith energy delivered to the oscillation at 1–10 Hz for Phase I and 0.7–3 Hz for Phase II (Fig. 2.4).This observation indicates that the underlying physical processes governing the signals during the2007 and 2011 intrusions were distinct from those at work prior to the intrusions and during the2008 explosions.In 2011, there is a strong seismic signal at STC that appears to be independent from Phases I andII (Figs. 2.2 and 2.4). Station STC is closest to the erupting fissures, and the amplitude of the signalcorrelates with activity at the fissures (Orr et al., 2015) and decays quickly with distance. Becauseof the localized nature and easily distinguished spectral character compared to the other Phase Iand II signals, as well as its absence in 2007, we do not treat this signal as part of the characteristicintrusion seismicity. A shallow source mechanism related to spattering at the lava surface (Patricket al., 2011a) or to magma flow through a dike intruding toward the fissure (e.g. Chouet, 1988) areplausible. We focus the remainder of our discussion on the Phase I and Phase II signals in 2007 and2011.302.4. Discussion2.4.2 Phase I: The Early Stages of IntrusionDuring other volcanic eruptions discrete events such as those that constitute Phase I merge intoa continuous signal like Phase II (e.g. Neuberg et al., 1998; Hotovec et al., 2013). Furthermore,Richardson and Waite (2013) point out that waveforms from individual LPs show extended signalcodas at distances of a few kilometers away from the source. This suggests that Phase II could bedue to Phase I events becoming more closely spaced in time. However, at Kı¯lauea Phases I and II aredistinct in space, time, and character (Figs. 2.1, 2.2, and 2.4), which suggests distinct mechanismsfor each phase. In both 2007 and 2011, the onset of Phase I temporally coincides with the onsetof deflation at the summit, lava lake drainage (2011), intrusion in the ERZ, and crater collapse atPu‘u ‘O¯‘o¯ (see Fig. 2.1). Generally, magma moves through the previously existing ERZ conduit atKı¯lauea, often without deformation or seismicity (Johnson, 1995; Montgomery-Brown et al., 2011;Bell and Kilburn, 2012). However, Bell and Kilburn (2012) show that shallow dike intrusions areoften preceded or accompanied by sequences of volcano-tectonic earthquakes related to magmaoverpressure. Phase I appeared to be dominated by discrete events and was strongest closest tothe respective onset area of dike intrusion in 2007 and 2011 (Poland et al., 2008; Lundgren et al.,2013). Located earthquakes during this period were confined to the ERZ at shallow depths of 0–4 km (Fig. 2.1). It is thus likely that Phase I is related to the mechanics of dike intrusion in the ERZ,which is consistent with a fading of Phase I as the rate of intrusion declines.2.4.3 Temporal & Spatial Constraints on Potential Phase II Tremor MechanismsIn contrast to Phase I, Phase II is strongest close to the summit and shows long-duration continuoustremor. Many mechanisms can act in a shallow low-viscosity magma-filled plumbing system todrive a persistent order 1 Hz ground oscillation. In this section we briefly summarize which mecha-nisms have been suggested previously and show how our observations over multiple eruptive cyclescan be used to test whether a mechanism (in this case oscillating bubble clouds (e.g., Matoza et al.,2010)) is a plausible source for the signal.Within the elastic walls of the plumbing system the periodic deformation of fluid-filled fracturescan drive oscillations and resonance (Aki and Koyanagi, 1981; Chouet, 1996a; Rust et al., 2008) ortime-dependent fracture propagation (Aki et al., 1977). Within the magma itself, flow through con-duit constrictions and/or vigorous or turbulent overturning motions can impart pressure variationsat the walls that are ultimately transmitted to seismometers (Julian, 1994; Chouet, 1996a; Garce´set al., 1998; Hellweg, 2000) with a period that depends on the geometry of the conduit and magmaflow regime. Depending on the level of volatile oversaturation and configuration of the plumbingsystem, such flow conditions can also give rise to the nucleation and convection of bubbles leadingto bubble gradients (Cardoso and Woods, 1999), foams (Jaupart and Vergniolle, 1988), and to theformation of “bubble clouds,” which can act as driven oscillators (see below) (Matoza et al., 2010).Interactions of bubbles with the top of the magma column in lava lakes and open vents can alsointroduce oscillations with similar amplitude and frequency properties (Fee et al., 2010; Matozaet al., 2010; Jones et al., 2012; Richardson and Waite, 2013).312.4. DiscussionIn our case, mechanisms that require an open vent cannot explain the observed Phase II signalbecause the lava lake, i.e., the free surface of the magma column required, e.g., for bubble burstingmechanisms (Chouet et al., 2010; Richardson and Waite, 2013) did not exist in 2007. Furthermore,neither Phase II nor gliding were observed in infrasound data in 2011 (M.Garces, personal com-munication, 2013). Similarly, based on the continuous character of Phase II from start to end atall stations and its distinct temporal, spatial, and spectral properties compared to Phase I, we favora mechanism that is not based on individual events such as bursting gas slugs (e.g. Chouet et al.,2010; Richardson and Waite, 2013). The lack of harmonic overtones indicates that mechanisms asdiscussed in, e.g., Chouet (1988) or Hellweg (2000) are unlikely here.Frequency gliding accompanying tremor is comparatively less well-studied. It is commonlyassociated with low intensity eruptions and small explosions at basaltic-andesitic arc volcanoessuch as Arenal (Costa Rica (Benoit and McNutt, 1997)), Langila (Papua New Guinea (Mori et al.,1989)), Redoubt (USA (Hotovec et al., 2013)), Sakurajima (Japan (Maryanto et al., 2008)), Sangay(Ecuador (Johnson and Lees, 2000)), Soufrie`re Hills (Montserrat (Neuberg et al., 1998)), and Ve-niaminof (USA (De Angelis and McNutt, 2007)). We are aware of only one other basaltic systemwhere approximately syneruptive gliding has been observed, although it is not well-characterized:submarine NW Rota-1 (Mariana Arc (Caplan-Auerbach et al., 2013)).In general, frequency gliding can be related to time-dependent changes in either the continuoustremor source (e.g. Aki and Koyanagi, 1981; Powell and Neuberg, 2003; Jellinek and Bercovici,2011; Hotovec et al., 2013) or in the elastic properties of the medium through which pressurewaves are transmitted. Gliding has, for example, been analyzed in terms of time-dependent patheffects such as vertical and lateral variations in the gas content, bubble size distribution or bubblenucleation rate (Chouet et al., 1997; Neuberg et al., 2000; Garce´s et al., 1998).The time scales over which such path effects act and evolve are probably determined by motionsin rising magma, which advect existing bubbles and stir dissolved volatiles to form gradients andcause bubble nucleation. For erupting Hawaiian magmas ascending at Vm ∼ 1 m/s (“∼” means“scales as” or “is of the same order of magnitude as”), the time scale to produce path effects relatedto bubble size gradients depends on the ascent distance, in this case the vertical distance from thevolatile exsolution depth toward the surface he. For CO2, SO2, and H2O this time scaleτg ∼ he/Vm ≈ 1− 20 min (2.1)with he ∼ 100–1000 m (Gerlach, 1986; Dixon et al., 1995; Newman and Lowenstern, 2002). Bub-ble concentration and size gradients can also be modified as a result of cross-conduit stirring drivenin response to constrictions, changes in geometry, or inertial effects. An advective “cross-flow”time scale for this stirring across an average dike or conduit width D ≈ 2 m (Parfitt and Wilson,1994; Edmonds et al., 2013) isτf ∼ D/Vm ≈ 2 s. (2.2)On the basis of these time scales, it is not straightforward to understand gliding over hours todays. Additional clues lie in the similarities and differences between the eruptions in 2007, 2008,322.4. Discussionand 2011. In contrast to 2008, the 2007 dike intrusion involved gradual deflation and ∼1 MPadecompression of the summit, paced by slow slip of the south flank of the volcano (Poland et al.,2009; Montgomery-Brown et al., 2011). In 2011, similar summit deflation associated with dikeintrusion in the ERZ suggest a comparable ∼1 MPa decompression, which was accompanied bygradual draining of the Halema‘uma‘u lava lake (Lundgren et al., 2013; Carbone et al., 2013).However, our observations require a mechanism for Phase II that does not rely on a connection tothe atmosphere (see above). Taken together with the spatial and temporal correlations of glidingwith summit deflation and ERZ intrusions/eruptions (Figs. 2.1 and 2.5), the observations thus pointtoward a mechanism that is related to the movement of magma in the summit area. In the follow-ing sections we illustrate how our observations over two similar intrusion/eruption periods restrictplausible length scales and time scales with the example of a tremor mechanism based on bubblecloud oscillations.Magma stirring and bubble cloud oscillationsQualitative similarities among the spatial, temporal, and spectral properties of Phase II tremor in2007 and 2011 suggest a common underlying process. That these episodes emerged and evolvedwith the time-varying magma overpressure regimes inferred to drive violent unrest suggests thatPhase II may be a characteristic response of the present-day Kilauean magmatic system to chang-ing magma flow conditions. The systematic shift in 1-h time-averaged spectral slopes from anapproximately power law decline during preintrusion phases to relatively flattened spectra, charac-terized by power delivered to the oscillations over 0.7–3 Hz frequency band, reinforces this picture(Fig. 2.4). In particular, these results suggest that intrusions involve periodic motions in the magmaacting on time scales of 0.3–1.4 s. Magma stirring and overturning over these time scales, forced byflow through the geometrically complex volcanic plumbing system (Fig. 2.6), is one way to producethis steady forcing.One class of physical model that enables us to explore temporal connections to changing magmadynamical regimes and exploit additional constraints on the structure of the present-day volcanicplumbing system (Fig. 2.6) (Ryan et al., 1981; Johnson, 1995; Lundgren et al., 2013; Edmondset al., 2013) is a modified form of the “oscillating bubble cloud” model, which has been appliedto understand infrasonic tremor observed at Pu‘u ‘O¯‘o¯ in 2007 (Matoza et al., 2010). Oscillat-ing bubble clouds with distinct spectral properties are well-known sources of acoustic noise in thenear-surface ocean and are commonly produced and maintained by breaking waves and turbulentmixing (Leighton, 1994). Similarly, Matoza et al. (2010) argue that turbulent accelerations in ris-ing magma, acting potentially in concert with inertial effects related to flow interactions with solidboundaries, can drive oscillations in compressible “springy clouds” of exsolved gas bubbles with acharacteristic frequencyfc =12pi√3Peφ¯ρmL2c, (2.3)332.4. DiscussionHalema`uma`u Makaopuhi Pu`u Ō`ō~ 1 km~ 100 mdi!use CO2 degassingincreased "owdike intrusionEAST RIFT ZONESUMMITsummit conduitPAUKNHAHUOTLSTC1)Lc ≈ 30 mDmean ≈ 2 mH2O+SO21)2)1 kmCO2H2O+SO2vertical exaggeration ≈ 3xCO2Lc ≈ 90 mcorner "ow2)bubble cloud~ 3 kmcorner "owshallower reservoirERZ conduitdeeper reservoirFigure 2.6: Simplified cartoon of Kı¯lauea plumbing system. Bubble accumulation occurs at twodepths in the summit region, depending on volatile species (insets 1 and 2). Resulting bubbleclouds can drive oscillations that are modulated by magma flow into the ERZ due to dike intrusionssuch as Phase II tremor. See text for more details.which reflects a balance between inertial forces in the magma and a restoring spring forces governedby the gas pressure. Here, Pe = ρmghe is the hydrostatic pressure in the magma at the volatileexsolution depth he, φ¯ is the average porosity of the cloud, ρm is the magma density, and Lc is thecharacteristic scale length for the cloud.Guided by Matoza et al. (2010), for H2O in the conduit we use ρm = 2700kg/m3 andhe = 100 m. We take φ¯ = 0.1 as a lower bound required to define continuous cloud mixturephysical properties such as density, viscosity, and compressibility (Crowe et al., 2011), noting thatmagma viscosities become very large for φ¯ ≥ 0.4 (Gonnermann and Manga, 2007; Moitra andGonnermann, submitted). We thus require Lc ≈ 30–10 m to give fc ∼ 1–3 Hz. In more detail, thegas phase or phases contributing to the cloud gas spring force depend on the depth at which theseoscillations are driven (Gerlach, 1986; Gerlach et al., 2002). Because SO2 exsolution occurs atdepths comparable to H2O we assume that both volatile phases contribute to the gas spring forceat shallow depths (Gerlach, 1986; Gerlach et al., 2002) . Whereas in 2011 the presence of thelava lake confirms magma at these shallow depths at the summit and thus makes this mechanismplausible, the lack of a vent in 2007 raises the question whether magma was comparably shallow(i.e., ∼100 m) and thus whether this mechanism can account for the similarities between 2007 and2011. In contrast, in the summit reservoir at depths below ∼1 km a cloud in the form of a confinedCO2 bubble-rich layer will plausibly form in contact with the roof of a reservoir undergoing eithernatural convection (Woods and Cardoso, 1997) or forced overturning driven by flow into the ERZconduit (Fig. 2.6), which we discuss below. In this case equation (2.3) implies Lc ≈ 90–30 m342.4. Discussionhorizontally for fc ∼ 1–3 Hz.One interpretation for similarities between Phase II in 2007 and 2011 is that Lc was similar. Ingeneral, the concentration of a given dissolved volatile is approximately ∝ √Pg and the exsolvedgas volume ∝ 1/Pg , where Pg is the pressure in the exsolved gas phase at depths less than he. Con-sequently, the mass and volume fractions of an exsolved volatile will increase continuously fromhe to the surface, suggesting that cloud length scales are either on the order of he or proportionalto the interval from he to the depth at which the volatile phase is exhausted (whichever distance issmaller). However, for H2O in the shallow conduit, φ¯ = 0.1 with Lc ∼ he = 100 m gives frequen-cies below what we observe (and resolve). If φ¯ is also increased to better capture the large verticalvariations in porosity that will occur from he to the surface (Gonnermann and Manga, 2007), fcwill decline significantly further below our observations.Alternatively, cloud scales are set by the dynamics of magma flow and their relationship to thegeometric structure of the Kilauean plumbing system. In the shallow reservoir (Fig. 2.6), priorto eruption bubble gradients will grow at the roof in response to natural convection (Woods andCardoso, 1997), and Lc is probably governed by the horizontal length of roof to which the bubblecloud layer is coupled mechanically. Magma draining into the ERZ during eruption will induce acorner flow that may cause bubbles to collect in a triangular region (Fig. 2.6) where Lc is reducedand plausibly proportional to the square root of the area of this confined region.By contrast, the complex geometry of the summit conduit including irregular bends and con-strictions can give rise to three-dimensional “boundary-driven” flows including lateral motions thatstir magma across the conduit (Julian, 1994; Hellweg, 2000), disrupting otherwise vertically con-tinuous bubble clouds, in turn. Such a mechanical control on Lc is not unexpected. Lc and φ¯ in theocean can, for example, be related quantitatively to the character and turbulent mixing properties ofbreaking waves that act to both form and disaggregate bubble clouds (Leighton, 1994). However,for such inertial effects to occur in the summit magma system at Kı¯lauea, the Reynolds number Reof the flow must be much larger than around 103. In the summit conduit Re = ρ¯mVmD/µ ≈ 10–20with magma viscosity µ = 250–400 Pa s (Shaw, 1969) and ρ¯m = 2340kg/m3, where ρ¯m is theaverage density of the magma assuming φ¯ = 0.1, and Vm and D are as above. Under these mod-erate Re conditions lateral turbulent accelerations will be very small compared to the momentumflux carried by the mean flow, unless they are enhanced as a result of geometric effects that driveand guide cross-conduit flows. Assuming the speed of this boundary-driven stirring is comparableto Vm and taking D for a characteristic dike width, the dynamic pressure force corresponding tothe momentum flux carried by these cross-conduit flows ∼ ρ¯mV 2mLcD. The resistance of a bubblecloud to disruption is challenging to characterize. We assume that bubble cloud break up is akin tothe disruption of solid particle-fluid mixtures (Hodge et al., 2012;Moitra and Gonnermann, submit-ted) where the resistance can be described by a mixture “yield force” ∼ σyD2, where the effectiveyield stress for disaggregation of the mixture σy depends on the cloud microstructure (Wildemuthand Williams, 1984; Hoover et al., 2001; Moitra and Gonnermann, submitted), and the effectivestiffness of the cloud depends on the cloud cross-sectional area D2. Balancing this yield force withthe pressure force gives a condition for disrupting vertically extensive bubble clouds to produce352.4. Discussionsmaller clouds with a characteristic length:Lc ∼ σyDρV 2m∝ 1V 2m. (2.4)To sustain long-lived Phase II tremor signals probably requires continuous excitation. Oscilla-tions with a frequency fc ∼ 1/τf = 0.5 Hz can be driven by the same steady cross-conduit stirringthat gives rise to the clouds, provided that oscillations are damped over a time scale that is long incomparison to the time scale of mechanical forcing τf . Driving magma motions will be retardedby viscous stresses proportional to the larger of the strain rates (Vm/D, Vm/Lc). In the summitconduit, where Lc >> D, viscous communication across the conduit width will damp oscillationsover a time scaleτv ∼ ρ¯mD2/µ ≈ 20–40 s. (2.5)For CO2 in the reservoir, assuming that magma stirring with speed Vm during intrusions is overreservoir length scales D ∼ 100 m (Fig. 2.6), τf ≈ 100 s, whereas τv ≈ 104–105 s. An importantdifference to flow in the conduit is that overturning motions in the reservoir are at Re ∼ 1000 andin a comparatively unbounded geometry. Strong vertical and lateral turbulent accelerations in thecorner flow are expected can contribute to driving oscillations in the bubble cloud layer, potentiallyover a range of frequencies.A question remains whether fresh magma is supplied (input) at a rate faster than the loss ofCO2through the summit vent and/or the diffuse degassing region (output), i.e., whether CO2 can remainin the plumbing system long enough to form bubble clouds. Output ofCO2 is mostly confined to thediffuse degassing region (Fig. 2.6) (Poland et al., 2009; Edmonds et al., 2013). Typically, magmasupply, i.e., input, is estimated based on gas emission, it is thus difficult to obtain independentestimates. However, the accumulation of CO2 bubbles close to the top of the summit reservoirhas been suggested previously in relation to deformation around the summit and cyclic activityduring some eruptions (Vergniolle and Jaupart, 1990; Johnson, 1992; Woods and Cardoso, 1997).Furthermore, Poland et al. (2009) suggest that CO2 bubbles may segregate from their parental meltand ascend at higher velocities. Accumulation of CO2 bubbles thus does not necessarily implyaccompanying input of fresh magma. It is possible that this accumulation of bubbles happens at ageometric constriction around 1 km depth below Halema‘uma‘u, as discussed in Section 2.4.1, atthe roof of a large magma reservoir or at the top of dikes and sills.A plausible source mechanism for Phase II in 2007 and 2011 must account for the lack of a sim-ilarly strong, long-lasting Phase II oscillation in 2008. It must also account for essential differencesbetween the time-averaged Phase II and postexplosion spectral slopes in Figure 2.4. The explo-sions in 2008 have been attributed to rockfalls from the crater wall (Patrick et al., 2011b; Orr et al.,2013) or ascent of large gas slugs (Chouet et al., 2010; Chouet and Dawson, 2011). The longevityof signals driven by impulsive magma displacements is governed in form by equation (2.5). Thecharacteristic length scale D ≈ 10 m for either mode of excitation (Chouet et al., 2010; Orr et al.,2013) in the uppermost parts of the conduit gives τv ≈ 600–1000 s, which implies that oscillations362.4. Discussiondriven this way will decay within ∼10–20 min (or less). Alternatively, bubble cloud oscillationscan occur and persist at shallow levels if they are driven by, e.g., convection at modest Re in thelava lake in the top few 100 m (Carey et al., 2013). However, convection velocities Vm ∼ 0.1 m/s(Carey et al., 2013) imply driven oscillations will have a frequency fc ∼ 0.001 Hz (equation (2.2),with D ≈ 100 m), which is below the frequencies we resolve. Finally, whether bubble clouds cancoexist with (or quickly reestablish after) disturbances due to rockfalls or ascending gas slugs is un-clear. Taken together, these predictions suggest that conduit H2O bubble cloud oscillation cannotreadily explain weak tremor in 2008. In contrast, slightly deeper oscillations of CO2 clouds due toreservoir convection may not be strongly affected by the events at the summit vent. The relativelyconstant weak tremor without gliding in 2008 may thus be due to bubble cloud oscillations in theshallow reservoir (Fig. 2.6). The differences in the shapes of the spectra, however, still point towarda different underlying physical mechanism for 2008 compared to 2007/2011.How might changes in magma flow cause gliding?Assuming that bubble cloud oscillations can be excited as we describe, the magnitude of frequencygliding in 2007 and 2011 (Fig. 2.5) can be understood through gradual changes in Lc (equa-tion (2.4)), Pe and φ¯ (equation (2.3)) related to evolving flow and overpressure conditions in themagmatic system. Through equations (2.3) and (2.4), the change in frequency ∆fc ∝ ∆V 2m/√∆φ.The switch from inflation to deflation at the summit in both 2007 and 2011 and the onset of dikeintrusion implies a rapid increase in the speed Vm of magma flowing from the summit conduit andreservoir into the ERZ, that is followed, in turn, by a slow decrease in Vm related to a relatively slowrelief of magmatic overpressure. This speed is reduced further because an increase in φ¯ from 0.1to 0.2, say, will cause magma viscosity to rise by a factor of ∼ 2 (Gonnermann and Manga, 2007;Moitra and Gonnermann, submitted). Consequently, we expect the downglide of fc in 2007 to beby a factor of > 4 or more through effects on Vm, assuming a factor of 2 decrease in flow speed.The frequency will, however, decrease by an additional factor 1/(√2) for a factor ∼ 2 increase inφ¯. Qualitatively, this trend is similar to our observations (Fig. 2.5). We note that the magnitude ofthe inferred change in φ¯ is constrained by its effect on magma rheology: As φ¯→ 0.4, µm becomesvery large and τv → 0, making our observed oscillations impossible (i.e., Re→ 0).ForCO2 in the summit reservoir, the change in Vm is arguably less important than the geometriceffect on the structure of the motions in the reservoir related to its draining into the ERZ. Assumingthat preeruption CO2 bubble cloud oscillations involve a layer of bubble magma extending acrossthe ∼ 100 m or longer roof, the corresponding fc ≈ 0.02 Hz is below our detection limit. Atthe onset of intrusion, gradually increasing flow into the ERZ will introduce a corner flow into thereservoir that will decrease Lc (Fig. 2.6) depending on the geometry of this flow and increase fc,in turn. A slow deflation of the summit will cause a concomitant decrease of Pe, a correspondingincrease in φ¯ and a corresponding downglide (equation (2.3)). A further increase in φ¯ through adecrease in the magma overpressure related to a seaward displacement of Kı¯lauea’s south flank in2007 (Montgomery-Brown et al., 2011) may enhance this effect and explain why the downglide in372.4. Discussion2007 reaches lower frequencies than in 2011.Apart from the lack of flank displacement, tilt data suggest that the temporal evolution of magmatransport from the summit into the ERZ in 2011 was similar to 2007 (Poland et al., 2008; Lundgrenet al., 2013). The observed upglide in 2011 is, thus, initially puzzling. Yet the drop in lava lakelevel (Carbone et al., 2013) implies that magma that has lost most of its CO2 (Edmonds et al.,2013) reenters the summit reservoir. On the basis of the occurrence of the upglide at the end ofthe lava lake drainage we suggest that mixing this CO2-poor magma with magma at the top ofthe shallow reservoir (Fig. 2.6) reduces φ¯ and Lc, causing the observed upglide (assuming that thiseffect is stronger than the simultaneous and opposing effects of deflation). When lake draining stopsthe upglide disappears as a corner flow is reestablished. Assuming Vm ≤ 1 m/s and overturninglength scales ∼ 2 km (Fig. 2.6), if steady state is recovered over, say, ∼ 5–10 overturns (Jellineket al., 1999) this implies mixing time scales ≥ 104 s, the same order of magnitude as the 28 hbreak between the upglide and the downglide in 2011. Subsequently, the effects of deflation, i.e.,decreasing pressure and correspondingly increasing φ¯ and Lc, can drive the observed downglide.A key feature of the data in Figure 2.5 is that the gliding frequencies in 2007 and 2011 are notinteger multiples of the lowest frequency (fundamental) modes. Through equation (2.3) the appear-ance of distinct gliding frequencies suggests vertical variations in φ¯ or Lc related to either spatiallycomplicated changes in the geometry of the summit reservoir or to differing pressure-dependentcontributions of exsolved H2O, SO2, and CO2 to the composition of the bubble clouds. Variationsin geometry that lead to isolated bubble clouds with varying properties are likely particularly in thedeeper (∼1 km) parts of the plumbing system, e.g., if the summit is underlain by a region of inter-connected cracks and reservoirs (Chouet et al., 2010; Baker and Amelung, 2012). Furthermore, wespeculate that oscillations of isolated bubble clouds in a potentially complicated shallow plumbingsystem may not strongly be affected by, e.g., changing flow conditions, which could explain thesimultaneous presence of stable spectral peaks during gliding episodes.The ratios of the gliding frequencies to the fundamental are approximately preserved as theintensity of the tremor decays with distance from the summit. Thus, the source for the majorityof the signal is reliably in the summit region. If the cloud model holds, the fact that Phase IItremor is strongest around the summit and is not observed in the ERZ implies that the majorityof magma degassing is concentrated at the summit. Degassing measurements indicate that this istrue for CO2 which leaves the plumbing system mainly through an area of diffuse degassing eastof Halema‘uma‘u, but not for H2O or SO2, which are found in plumes along the ERZ (Gerlachand Graeber, 1985; Gerlach, 1986; Greenland, 1987) (Fig. 2.6). This suggests that the CO2 cloudmodel is a more likely scenario for the source of summit tremor.2.4.4 Remaining ChallengesWe have illustrated how key temporal and spatial aspects of Phase II tremor in 2007 and 2011might be explained by magma flow-driven bubble cloud oscillations in the conduit or the shallowreservoir beneath the summit. This mechanism is also consistent with an absence of Phase II in382.5. Conclusions2008. Distinguishing between the two scenarios (i.e., conduit H2O/SO2 versus reservoir CO2bubble cloud oscillations) is not straightforward. A remaining question is the exact location(s) of thetremor source(s). Phase II and gliding are expressed most strongly close to the summit. However,whether the exact location corresponds to the shallow lava lake and the underlying conduit, ordeeper parts of the plumbing system related to a bigger reservoir is unknown. Accurately locatingtremor could help to identify the exact location of Phase II tremor within the summit region.Further limitations remain with both bubble cloud models. It is unclear, for example, why theonset of Phase II is delayed by ∼10 h compared to the onset of deflation. The bubble cloud oscil-lation model would predict the motions driving the oscillations to start with the onset of intrusion,and similarly, the onset of gliding to coincide with the onset of pressure changes and/or changesin magma flow velocity. In addition, whereas bubble cloud oscillations may be the driving forcebehind the similar peaks at low frequencies in the Phase II spectra during 2007 and 2011, theseoscillations cannot explain the differences in spectral slope above 10 Hz between 2007 and 2011,which indicates that energy is dissipated in potentially different ways during the two intrusion peri-ods.We explore a magma-driven bubble cloud oscillation model because of the demanding spatialand temporal characters and similarity of Phase II tremor properties in 2007 and 2011. This is onephysical picture and others are certainly possible, if they are permitted by the full set of observa-tions over three eruptive cycles. To make progress, a further study could, for example, focus oncomparing tremor during quieter periods such as inMatoza et al. (2010) to the intrusion tremor an-alyzed here. Systematic differences or similarities in terms of its location, intensity, and appearancein infrasound data can help to confirm or reject the presence of the common underlying physicswe propose. As monitoring data sets become longer, future studies over similarly long time scalesmight hold the key to improving our understanding of processes accompanying volcanic eruptions.2.5 ConclusionsWe systematically analyzed broadband volcanic tremor (peaks below 3 Hz) during three eruptionson Kı¯lauea, Hawai‘i, from 2007 to 2011. Our results show that whereas explosive activity at thesummit in 2008 was marked by continuous weak tremor very similar to the preintrusion backgroundin 2007 and 2011, intrusions and eruptions in the ERZ in 2007 and 2011 were accompanied by twophases of seismicity that were separate in space and time. Phase I is characterized by discrete eventsin ERZ that may be related to dike intrusion, Phase II is a continuous broadband tremor signal closeto the summit. Phase II is accompanied by long-duration frequency gliding (hours to days) withdifferent temporal evolutions and frequency content during two different intrusions. We suggestthat the weak tremor during explosive activity may have a different mechanism than tremor duringthe episodes of intrusion and eruption. Tremor and gliding properties during the intrusions in 2007and 2011 cannot be linked to mechanisms related to an open vent, but, among others, permit anexplanation in terms of driven oscillations of H2O bubble clouds in the shallow parts (∼100 m) ofthe summit conduit system or of CO2 bubble clouds near the top of the shallow summit reservoir392.5. Conclusions(∼1 km).These observations over three eruptions provide critical restrictions in space and time on plau-sibility of models for the underlying mechanics. On the basis of qualitative similarities in 2007 and2011, we argue that Phase II is a characteristic response of Kı¯lauea to intrusions: It is a consequenceof how magma moves through the present-day geometrically complex plumbing system. Our dis-cussion highlights two key knowledge gaps that are useful for future work. Better constraints onthe source location including depth of volcanic tremor in the summit region at Kı¯lauea, and detailedimaging of the summit plumbing system are necessary to determine which of the two bubble cloudscenarios is more likely as the source for summit tremor during intrusions in the ERZ, or whethercontributions from both the conduit and the shallow reservoir are required.40Chapter 3Principal Component Analysis vs.Self-Organizing Maps Combined withHierarchical Clustering for PatternRecognition in Volcano Seismic Spectra8SummaryVariations in the spectral content of volcano seismicity related to changes in volcanic activity arecommonly identified manually in spectrograms. However, long time series of monitoring data atvolcano observatories require tools to facilitate automated and rapid processing. Techniques suchas Self-Organizing Maps (SOM) and Principal Component Analysis (PCA) can help to quickly andautomatically identify important patterns related to impending eruptions. For the first time, weevaluate the performance of SOM and PCA on synthetic volcano seismic spectra constructed fromobservations during two well-studied eruptions at Kı¯lauea Volcano, Hawai‘i, that include featuresobserved in many volcanic settings. In particular, our objective is to test which of the techniques canbest retrieve a set of three spectral patterns that we used to compose a synthetic spectrogram. Wefind that, without a priori knowledge of the given set of patterns, neither SOM nor PCA can directlyrecover the spectra. We thus test hierarchical clustering, a commonly-used method, to investigatewhether clustering in the space of the principal components and on the SOM, respectively, canretrieve the known patterns. Our clustering method applied to the SOM fails to detect the correctnumber and shape of the known input spectra. In contrast, clustering of the data reconstructed bythe first three PCA modes reproduces these patterns and their occurrence in time more consistently.This result suggests that PCA in combination with hierarchical clustering is a powerful practicaltool for automated identification of characteristic patterns in volcano seismic spectra. Our resultsindicate that, in contrast to PCA, common clustering algorithms may not be ideal to group patternson the SOM and that it is crucial to evaluate the performance of these tools on a control datasetprior to their application to real data.8Reprinted from Journal of Volcanology and Geothermal Research, with permission from Elsevier.413.1. Introduction3.1 IntroductionIn volcano monitoring, scientists are faced with the task of correctly identifying patterns of unrestcritically indicative of impending of eruptions (e.g. Sparks et al., 2012; Carniel, 2014). A key com-ponent of volcano monitoring is seismic activity (Sparks et al., 2012). Seismic signals on volcanoescan be classified in terms of their frequency content: Whereas volcano tectonic earthquakes oftenhave a broadband spectrum, low frequency seismicity including long-period events, very long pe-riod events, and volcanic tremor predominantly cover lower frequency ranges of 0.01–5 Hz (Fehler,1983; Neuberg, 2000; McNutt and Nishimura, 2008; Chouet and Matoza, 2013). Based on its dis-tinct spectral properties, this low frequency seismicity is commonly explained by processes involv-ing fluid movement: Examples include moving bubbles (Ripepe and Gordeev, 1999; Matoza et al.,2010; Jones et al., 2012), gas accumulation (e.g. Johnson et al., 1998; Lesage et al., 2006), resonat-ing fluid pathways (Chouet, 1986; Leet, 1988; Julian, 1994; Benoit and McNutt, 1997; Neuberget al., 2000; Hellweg, 2000; Balmforth et al., 2005), or bubble/magma flow (Denlinger and Hoblitt,1999; Jellinek and Bercovici, 2011; Thomas and Neuberg, 2012; Dmitrieva et al., 2013; Lyonset al., 2013). Each of these mechanisms imply a relationship between properties of low frequencyseismicity and volcanic activity. Indeed, approximately 80% of a global sample of volcanic tremorepisodes have been shown to precede or accompany volcanic eruptions (McNutt, 1992). For a givenvolcanic setting, knowledge of typical seismicity and the corresponding spectral patterns before,during, and after eruptions (e.g Carniel et al., 1996; Unglert and Jellinek, 2015) is thus crucial foreruption forecasting.A common approach to analyzing the temporal evolution of volcano seismicity is the visualinspection of spectrograms. For example, Unglert and Jellinek (2015) identify two characteristicphases of seismicity that accompanied two intrusions at Kı¯lauea Volcano, Hawai‘i. This kind ofanalysis requires manual identification of characteristic spatio-temporal patterns, which is prac-tically cumbersome, inherently subjective, and informed by the experience of the analyst. Forinstance, which spectral properties distinguish non-eruptive from eruptive unrest is unclear. Conse-quently, to be able to objectively identify patterns and extract key information related to imminentor active volcanism, analysts are increasingly reliant on automated algorithms (e.g., Carniel, 2014;Cortes et al., 2015).Pattern recognition and machine learning methods provide a possible solution and are used ina wide range of disciplines (e.g., Kaski et al., 1998; Oja et al., 2002; Bishop, 2006). In particular,“unsupervised” methods imply that no a priori knowledge of patterns is necessary, i.e. the algorithmself-learns from the data (e.g. Bishop, 2006; Langer et al., 2009). In volcano monitoring, thisfeature is essential because the temporal evolution of patterns in monitoring time series is oftenunknown (e.g. Sparks et al., 2012). A good review of different, unsupervised feature extractionmethods and their application to volcano seismicity can be found in Orozco-Alzate et al. (2012)and Carniel (2014). Such studies have used Self-Organizing Maps (SOM) and other techniques todetect different types of seismicity (e.g., Carniel, 1996; Langer et al., 2009; Carniel et al., 2013a;Curilem et al., 2014), or link changes in time series from volcano monitoring with different eruptive423.2. Data and Preprocessingvents or type of eruptions (e.g., Esposito et al., 2008; Di Salvo et al., 2013). Several studies firstuse SOM to reduce the amount of data to be analyzed, and subsequently apply clustering algorithmsto obtain final groupings (e.g., De Matos et al., 2006; Ko¨hler et al., 2009; Messina and Langer,2011; Carniel et al., 2013a).SOM can generate a visual representation of the similarities and differences between patterns ina dataset (e.g., Esposito et al., 2008), require no a priori knowledge of patterns (e.g., Murtagh andHerna´ndez-Pajares, 1995), and can thus be useful for detecting distinctive spectral characteristicsof volcanic tremor. In fields such as oceanography or meteorology, it is common to evaluate patternrecognition techniques against each other, against other methods, and with synthetic data (e.g.,Reusch et al., 2005; Liu et al., 2006). In seismology, different methods including SOM have beentested against each other at individual volcanic settings (e.g., Langer et al., 2009; Cortes et al.,2015), and SOM performance has been tested with artificial data consisting of parameters fromthe time and frequency domains (e.g., Ko¨hler et al., 2009). However, to our knowledge no studiesapplying SOM combined with cluster analysis to volcanic tremor evaluate the functionality of SOMin spectral space with a synthetic dataset. Thus, the following key knowledge gaps persist:1. The performance of SOM against more standard techniques such as Principal ComponentAnalysis (PCA) has not been systematically evaluated with synthetic datasets of spectra.2. Appropriate benchmarking datasets closely aligned with real observations, and with knownpatterns and their occurrence in time do not exist (Orozco-Alzate et al., 2012).3. It is not clear that the features of interest (e.g., relative spectral power at different frequencies,occurrence and evolution of various spectral shapes in time) are captured by SOM, or hownoise affects the results. The limitations of the method in terms of its application to volcanoseismic spectra are thus unclear.Accordingly, in Section 3.2, we produce synthetic spectra on the basis of detailed manual extrac-tion of two characteristic spectral signatures during eruptive periods at Kı¯lauea Volcano, Hawai‘i(Unglert and Jellinek, 2015). Specifically, we address two questions:1. Can hierarchical clustering, a common approach to identify groupings in data used in pre-vious studies of volcano seismicity, applied to the results from PCA (Section 3.3) and SOM(Section 3.4) correctly identify the known spectra and their occurrence/evolution in time in atypical volcanic spectrogram?2. How do the clustering results differ between the two techniques, and what are the limitationsof each of the methods and of our synthetic dataset (Section 3.5)?3.2 Data and PreprocessingMany methods exist for classifying volcano seismicity in both the time and the frequency domains(e.g., Langer and Falsaperla, 2003; Ibs-von Seht, 2008; Curilem et al., 2009). However, Castro-433.2. Data and PreprocessingAHU−155˚15' −155˚10' −155˚05'19˚20'19˚25'0 5kmEast Rift ZoneArea of dike intrusions& eruptions, 2007 & 2011(a) (b)03datefrequency (Hz)  6/17 6/18 6/19 6/20 6/21 6/22/20072468-3x 104 nm/sPhase II (5)transitions (3,4,6)background (1)Phase I (2)101214Kīlauea: AHUdB−20 −10 0 10 20 30 40frequency (Hz)03/20 03/21 03/22 03/23/20095101505date-5x 103 nm/s Redoubt: RSOdB−20 −10 0 10 20 30 40(c) (d)end of eruption 08/21 08/25/2008frequency (Hz)51015010datedB0 10 20 30 40 50 60-10x 104 nm/s Okmok: OKWR08/23frequency (Hz)5 10 15spectral power (dB)0102030405060frequency (Hz)5 10 15spectral power (dB)-20-10010203040lead up to explosions on Mar 23Figure 3.1: (a) Location of station AHU and eruptions on Kı¯lauea Volcano, Hawai‘i. (b) Spec-trogram shows characteristic evolution of seismic data from background through an event phase(Phase I; see purple bars in seismogram indicating located earthquakes) to a tremor phase (Phase II),as discussed by Unglert and Jellinek (2015). White solid and dashed arrows point to periods usedas the model for our simplified synthetic dataset (Section 3.2.1). (c) Spectrogram from station RSOduring Redoubt 2009 eruption. Inset shows one spectrum from the beginning and the end of showntime period (dashed lines in spectrogram). (d) Spectrogram from station OKWR during Okmok2008 eruption. Inset shows one spectrum from the beginning and halfway through the shown timeperiod (dashed lines in spectrogram). Both (c) and (d) show different spectral shapes, as well as im-pulsive and emergent variations of those shapes over time, similar to Kı¯lauea. Our synthetic datasetis based on Hawai‘i, but captures the same spectral features observed at other volcanoes, regardlessof the exact temporal evolution or the underlying processes.443.2. Data and PreprocessingCabrera et al. (2014) found that classification utilizing entire spectra performs better than classifi-cation utilizing sets of other temporal and spectral parameters such as the mean amplitude or meanfrequency in a given time window. Furthermore, previous work shows that distinct spectral shapesand transitions between them may relate to the underlying physical processes (e.g., Aki et al., 1977;Benoit and McNutt, 1997; Maryanto et al., 2008; Unglert and Jellinek, 2015).To evaluate whether SOM or PCA are suitable for automated analysis of time varying spec-tral signatures, and more accurate and efficient than visual inspection of spectrograms, we create asynthetic dataset of volcano seismic spectra on the basis of the major spectral characteristics of seis-mic signals from Kı¯lauea Volcano, Hawai‘i between 2007–2011 (Fig. 3.1(a); Unglert and Jellinek(2015)). During this period, two dike intrusions and accompanying fissure eruptions in the EastRift Zone showed a phase of discrete, seismic events near the intruding dikes (Phase I, Figs. 3.1(b)and 3.2), followed by a phase of continuous tremor near the summit (Phase II, Figs. 3.1(b) and 3.2)with a stronger decrease of spectral power from low to high frequencies compared to Phase I (Un-glert and Jellinek, 2015). A prominent feature of Phase II is gliding of spectral lines (Unglert andJellinek, 2015). However, because the gliding was expressed at different frequencies during the twointrusions, and because it did not affect the overall character of Phase II, we do not include glidingspectral peaks in Phase II of our synthetic dataset. Such gradual variations in the frequencies of in-dividual spectral peaks are, in principle, similar to transitions over time from one phase to another,which are included in our synthetic dataset. We touch upon this subject again in Section 3.5.3.The eruptive phases at Kı¯lauea and their temporal variations are not representative of volcanoseismicity in general, but they capture some of the main features of pre- and syn-eruptive seismicityobserved in other settings such as Redoubt Volcano, (Fig. 3.1(c)) or Okmok Volcano, (Fig. 3.1(d)),such as different spectral shapes and impulsive and emergent variations of those shapes over time(e.g., Carniel et al., 1996; Neuberg, 2000; Ruiz et al., 2006; Curilem et al., 2009; Langer et al.,2009; Buurman et al., 2012)). The particular value of our dataset is that it enables reliable perfor-mance evaluation of SOM and PCA on well understood data that are drawn from well-establishedobservations.3.2.1 Synthetic SpectraTo create the three spectra, we choose three 5-minute windows of continuous seismic data corre-sponding to the background state, Phase I, and Phase II at station AHU from Kı¯lauea as describedabove (Figs. 3.1-3.2). Station AHU is situated between the inferred locations of Phase I and II (closeto the area of dike intrusion and below the summit, respectively) and showed both phases clearlyand with relatively similar strength. The data are demeaned, detrended, tapered, and Fourier trans-formed. The resulting spectra are then smoothed and subsampled with a 50 point moving average toobtain the trends of spectral power (Fig. 3.2(a)). For the tests in this study, we limit the frequenciesto 0.5–10 Hz unless otherwise indicated. The lower frequency limit is dictated by contamination ofvolcanic signals with low frequency (≤ 0.3 Hz) seismic noise from the ocean (McNamara and Bu-land, 2004; Bromirski et al., 2005), and by decreasing sensitivity of short period instruments below453.2. Data and Preprocessing2 4 6 8 10 12 14−40−30−20−100102030frequency (Hz)spectral power (dB)  backgroundphase Iphase II(a)(c)frequency (Hz) 123456789day1 2 3 4 5 6 7background (1)Phase I (2)Phase II w/ amplitude variations (5)transitions (3,4,6)1 2 3 4 5 6 7 8 9−40−30−20−1001020frequency (Hz)spectral power (dB)  noise 0.1noise 1.5no noise(b)(d)dayfrequency (Hz)  1 2 3 4 5 6 7123456789−30−20−100102030spectral power (dB)background (1)Phase I (2)Phase II w/ amplitude variations (5)transitions (3,4,6)Figure 3.2: Synthetic data setup. (a) Original spectra representing background, Phase I, andPhase II, respectively. Dashed vertical line indicates upper frequency limit for first part of thisstudy. Different frequency ranges will be discussed in Section 3.5.3. (b) Example for differentnoise levels: Background spectrum at noise levels 0, 0.1, and 1.5. (c) Spectrogram based on thethree representative spectra with phases and transitions between them, noise level 0.1. White solidand dashed arrows point to periods described in Section 3.2.1. Black vertical line indicates time forspectrum in (b). (d) Same spectrogram as in (c), but at noise level 1.5.1 Hz (Mark Product L-4 seismometers with a natural frequency of 1 Hz). The upper limit is chosento include the frequency range where the (non-normalized) spectra differ the most (Figs. 3.1(b) and3.2(a)). Different frequency bounds will be discussed in Section 3.5.3.The three spectra in Figure 3.2(a) capture the main differences between the three time periods:The background state has a relatively monotonic, steep decay of spectral power between 0.5–4 Hz,and flattens slightly at higher frequencies; Phase I and Phase II have increasing spectral power be-tween 0.5–1 Hz (stronger for Phase II), and lower, approximately linear slopes from 1 Hz towardshigher frequencies (compared to the background; Unglert and Jellinek, 2015). These features sug-gest differences in the underlying physical processes (Unglert and Jellinek, 2015). The strongerspectral power at low frequencies during Phase II compared to the background is, for example,explained by bubble cloud oscillations in a magma reservoir below Kı¯lauea’s summit, whereas therelatively even, strong contributions at all frequencies during Phase I result from discrete fractureevents related to dike intrusion (Unglert and Jellinek, 2015).On the basis of these natural spectra, we construct a synthetic spectrogram with a spectrumevery 15 minutes that consists of the following components:463.2. Data and Preprocessing1. Background (24 hours)2. Phase I (4 hours)3. Linear transition in time at each frequency from Phase I to background (4 hours)4. Linear transition in time at each frequency from background to Phase II (4 hours)5. Phase II (3 days)6. Linear transition in time at each frequency from Phase II to background (2.5 days)Phase II includes 100 spectra shifted to lower values, and 100 spectra scaled by 0.5. Becausethe spectral shape of Phase II is preserved during these periods, our aim is to classify them as onegroup. The transitions between the phases and the background represent the possible emergentonset or disappearance of signals such as volcanic tremor (Konstantinou and Schlindwein, 2002;McNutt and Nishimura, 2008).To investigate the effect of small variations in spectral power at each frequency, we add differentlevels of noise to the synthetic spectrogram (Fig. 3.2 (b), (c), and (d)). Noise level 0.1 indicates thatthe range of the noise (from minimum to maximum) is 10% of the mean spectral power value Smean,which is achieved by adding or subtracting a random value drawn from a uniform distributionbetween ±0.5 · 0.1 · Smean. This noise is not to be confused with “seismic noise”, which may havea specific shape in the frequency domain. Our white noise represents the temporal variability ofspectral power, affects the location of individual peaks, and may or may not mask the overall shapeof the spectrum.The resulting spectrograms have 672 spectra, i.e., observations in time, with 57 frequency sam-ples each (Fig. 3.2(c) and (d)).3.2.2 Preprocessing StepsThe characteristic feature in our dataset is the shape of the spectra, which relates to known differ-ences in source processes (Unglert and Jellinek, 2015). In contrast, differences in spectral ampli-tude can be readily distinguished in spectrograms and are not related to changing source processes.To only focus on source processes, the input spectra must consequently be normalized to removeany differences in amplitude. Typically, normalization is performed by demeaning spectral powerat each frequency and dividing it by its standard deviation (e.g., Langer et al., 2009). However,with such preprocessing, important information about the relative amplitude from one frequencyto another (e.g., Carniel, 2014; Unglert and Jellinek, 2015) gets lost. We therefore normalize ourinput data in the following way:1. For each spectrum, each spectral power value is divided by the sum of all absolute spectralpower values to account for spectra with similar shapes but scaled with respect to each other.2. Each spectrum is shifted to have a 0 dB median to remove differences between spectra withthe same shape that are shifted with respect to each other (Fig. 3.3(a)).473.3. Principal Component Analysis2 4 6 8 10−0.02−0.0100.010.020.03frequency (Hz)normalized spectral power (dB)  backgroundPhase IPhase IIdayfrequency (Hz)  1 2 3 4 5 6 7123456789−0.02−0.0100.010.020.030.04norm. spectral power (dB)(a) (b)1 234 5 6Figure 3.3: Normalized synthetic data used as input for pattern recognition algorithms. (a) Nor-malized model spectra representing background, Phase I, and Phase II, respectively. Note the lowerspectral power values compared to the originals (Fig. 3.2(a)). (b) Spectrogram based on the normal-ized spectra, noise level 0.1. Vertical, dashed white lines and small blue numbers indicate periodsof change described in Section 3.2.1.The amplitude variations introduced during Phase II disappear with these preprocessing steps (timeperiod 5, cf. Fig. 3.2(c) vs. Fig. 3.3), so all of the spectra can now be classified solely on the basisof their spectral shapes.3.3 Principal Component AnalysisThe basic idea of dimensionality reduction with PCA is to rotate the original, multidimensionalcoordinate system into a new coordinate system of mutually orthogonal vectors along the direc-tions of maximum variance. In our case the dimensions are the 57 frequency samples. Volcanoseismic applications of PCA and similar methods include Langer and Falsaperla (1996, 2003); DeLauro et al. (2005) and De Martino et al. (2005). For our purpose, PCA provides a simple, wellestablished method to go from many frequencies to a lower dimensional space where data can beclassified on the basis of a smaller number of dimensions. We apply a subsequent clustering al-gorithm to the results and use this as a benchmark to compare against the performance of SOM.Because the nomenclature for PCA concepts varies widely in the literature, we align our use ofterminology with Hsieh (2009): The directions of maximum variance are called modes or eigen-vectors, their coordinates in relation to the original coordinate system are called loadings, the new,rotated coordinate system is called Principal Component (PC) Space, and the projections of thespectra in PC space are called principal components.3.3.1 PCA and ClusteringSimilar to previous work by Langer and Falsaperla (2003) or Carniel et al. (2013b), the input datafor our MATLAB R© based PCA algorithm are the normalized synthetic spectrograms at differentnoise levels, starting at noise level 0.1. The fraction of the total variance explained by each mode(Fig. 3.4(a), with the total number of modes necessary to explain 90% of the variance summarized483.3. Principal Component Analysis100 101 10201020304050607080mode number% of varianceprincipal component 1-0.05 0 0.05principal component 2-0.06-0.04-0.0200.020.040.06principal component 1-0.05 0 0.05principal component 2-0.06-0.04-0.0200.020.040.06 cluster 1cluster 2cluster 32 4 6 8 10−0.02−0.0100.010.020.03frequency (Hz)norm. spectral power (dB)(a) (b) (c)(d) (e) (f)1 2 3 4 5 6 70.50.60.70.80.91daycos(θ)1 234 5 62 4 6 8 10−0.2−0.100.10.20.30.40.50.6frequency (Hz)eigenv. loadings (dB)  mode 1: 79.56%mode 2: 16.36%mode 3: 0.99%−0.3Figure 3.4: PCA results for noise level 0.1. (a) Percentage of variance explained by each mode.(b) Loadings for first three eigenvectors. Small numbers in legend indicate amount of varianceaccounted for by each mode. (c) Projection of observations in space spanned by principal com-ponents 1–2. Dashed circles indicate approximate cluster centers for three clusters, determined byvisual inspection. (d) Clustering of observations in PC space for three clusters from hierarchicalclustering, with clusters 1, 2, and 3 in blue, green, and yellow, respectively. (e) Reconstructedspectrum from center (median) of each cluster, from superposition of first three modes. (f) Time se-ries of angles between observed (synthetic) spectra and reconstructed spectrum (e) for each clusterwhen spectra are treated as vectors. Values close to 1 indicate strong alignment. More detail can befound in main body of text. Vertical, blue dashed lines and small numbers same as in Fig 3.3(b).in Table 3.1 for different noise levels) shows that the first two modes together explain 95.9% ofvariance: The first mode explains 79.6%, and the second 16.4%. Much of the remaining variance,expanded by the remaining modes, is probably due to contributions from noise. The first two tothree modes explain most of the variance for all noise levels (Section 3.3.2). We thus choose aconsistent but generic cut-off and only include the first three modes in any further analysis.Consistent with results from other applications of PCA (Liu et al., 2006; Hsieh, 2009), theeigenvectors for the first three modes (Fig. 3.4(b)) fail to reproduce the known patterns (Fig. 3.3(a)),except for few aspects (such as the decay of amplitude from 0.5 to 4 Hz for eigenvector 1). Toretrieve the actual frequency patterns, the data can be reconstructed as a superposition of the firstthree modes, i.e. the sum over the product between each eigenvector and its principal component.The principal components are shown in Figure 3.4(c) (note that only the first two components areshown). We apply clustering in the space spanned by the first three principal components to testwhether the resulting clusters will replicate the three known patterns in the data. This approach issimilar to clustering the reconstructed spectra based on the first three modes.To do this, we use an agglomerative hierarchical clustering algorithm (cf. Wu and Chow, 2004;Hastie et al., 2009; Jain, 2010). This clustering technique iteratively merges pairs of individual ob-servations on the basis of the squared Euclidean distances dij = ||Xi−Xj ||2 between observations493.3. Principal Component AnalysisTable 3.1: Quality measurements and clustering results for different noise levels determined byRMS value of cross correlation coefficient between reconstructed spectra, comparison betweenPCA and SOM. Columns from left to right are: Noise level, number of modes necessary to explain90% of the total variance, best cluster number k, misfit E (dB) for cluster number k, dimensionsof the SOM topology, quantization error QE (dB), topographic error TE, best cluster number kand misfit E (dB) as for PCA, and misfit E* (dB) for manual selection of three nodes from SOM(without clustering, see Fig. 3.8).PCA SOMNoise 90% var. k E Map size QE TE k E E*0.1 2 3 16e-4 19×7 42e-4 387e-4 4 23e-4 10e-40.5 35 3 41e-4 19×7 17e-4 283e-4 13 36e-41 44 3 91e-4 19×7 284e-4 238e-4 6 77e-41.5 46 3 122e-4 19×7 366e-4 223e-4 14 107e-42 47 5 135e-4 17×8 426e-4 193e-4 6 136e-44 48 24 190-4 13×10 553e-4 238e-4 25 200e-4i and j. The algorithm then successively combines these subclusters containing two observationseach into larger clusters using the same distance metric to assess similarity. We use Ward’s methodto form the clusters, which assures that at each formation of a larger cluster there is the minimumincrease in total within-cluster variance after merging. Ward’s method is known as the best hierar-chical clustering method (Gong and Richman, 1995) and is commonly used. The optimal clusternumber k must be determined from the resulting cluster structure. In this case, by visually inspect-ing Figure 3.4(c), we obtain a rough estimate for k = 3 clusters (a less subjective choice of clusternumber will be discussed later). Figure 3.4(d) shows the cluster memberships for this case in PCspace.To enable evaluation and interpretation of the three clusters, we extract the median value for thefirst three components in each of the three clusters, and reconstruct a representative spectrum foreach cluster by using the eigenvectors and the median principal components (Fig. 3.4(e)). Visually,the resulting spectra match the three known input spectra (Fig. 3.3(a)) well. We will discuss a morequantitative evaluation later.To examine the temporal evolution of our synthetic signal (Figs. 3.2-3.3) in terms of the threeclusters, we project the observed spectra Sn at each time step onto each of the reconstructed, repre-sentative spectra Rj . If each projection is normalized by ||Sn|| · ||Rj ||, the resulting value is equalto the cosine of the angle θ between the two vectors. In this time series (Fig. 3.4(f)), if cos(θ)→ 0,the vectors are approximately orthogonal and our reconstructed spectra do not capture any part ofthe data. Alternatively, cos(θ)→ 1 indicates strong alignment of the two vectors, and thus wesuccessfully represent the data by the reconstructed spectrum (e.g., cluster 3 shows good represen-tation of the data during day 1, confirming the visual assessment that it is similar to the background,Fig. 3.4(e)-(f)). The changes in time from one dominating cluster to the next generally agree withthe known changes from the synthetic input spectrogram during background, Phase I, and Phase II.Furthermore, during transitional time periods, when the spectra are known to gradually change from503.3. Principal Component Analysisone phase to another, one cluster slowly “decreases in importance” (i.e. the resemblance betweenthe observed spectra and the representative spectrum for this cluster decreases), whereas anotherone increases (e.g., during time period 6, the alignment between the observations and cluster 1 de-creases, while the alignment with cluster 3 increases, in accordance with the known change fromPhase II to background). This way of projecting the data overcomes the main drawback of showingthe results only as cluster indexes in time, where each observation is uniquely assigned one clusterindex (often referred to as “hard” or “crisp” clustering, Ko¨hler et al., 2009; Messina and Langer,2011) and which therefore cannot capture the gradual transitions from one pattern to another.To evaluate how closely the reconstructed cluster spectra match the known input for a givencluster number k, we introduce the following misfit metric. For each known input spectrum Si(Fig. 3.3(a)), we find the best-fitting reconstructed spectrum Sj (Fig. 3.4(e)) by identifying theminimum value of the RMS difference Dij between Si with all Sj . The misfit is determined asE = Σ3i=1(min3j=1(Dij)). For noise level 0.1, E = 0.0016 dB. The difference between maximumand minimum value of Phase I spectrum (i.e., the spectrum with the smallest range, Fig. 3.3(a)) isapproximately 0.03 dB, and E thus corresponds to less than ∼2% difference per spectrum relativeto this smallest range. An advantage of measuring the misfit between the reconstructed spectra andthe known input is that we can explicitly compare the results from our PCA analysis with the SOMmethod (Table 3.1), which we describe in detail in Section 3.4.One of the biggest challenges in clustering data is to find the optimal cluster number k (e.g.,Davies and Bouldin, 1979; Carniel et al., 2013a), which we set manually on the basis of the knowninput for illustrative purposes above. Previous studies have applied cluster evaluation measures inthe space where the clustering was done (i.e., the principal component space; e.g. Farzadi and Hes-thammer, 2007), for example by using a dendrogram (Fig. 3.5(a)), i.e., the tree-like visualization ofthe cluster structure from the hierarchical clustering (e.g., Carniel et al., 2013a). The dendrogramin Figure 3.5(a) shows 30 (arbitrarily numbered) subclusters on the x-axis (as opposed to reachingdown to the level of joining individual observations, which would be complicated to visualize),and the y-axis indicates the distance between the subclusters joined at any given level. The level atwhich these distances become relatively small further down the dendrogram is a common choice fora cut-off level to determine the optimum number of clusters (e.g., Marroquı´n et al., 2008; Hsieh,2009). In our case, the dendrogram shows that distances become much smaller for k = 2, 3 or 4(Fig. 3.5(a), dashed lines), thus not yielding a unique optimum number of clusters. This somewhatsubjective metric is one of the main shortcomings of the dendrogram applications (e.g., Carnielet al., 2013a).Whereas identifying the cluster number through the dendrogram only utilizes the distancesamong the clusters after each merging, our goal here is to find the minimum number of clusterswhose corresponding reconstructed spectra are the least similar each other. (Fig. 3.4(e)). We thusintroduce an independent metric that takes the reconstructed spectra into account. As shown for thecase of k = 3 from Figure 3.4, similar to McGreger and Lees (2004); Ruiz et al. (2006); Carnielet al. (2013a) we obtain pairwise Pearson’s cross-correlation coefficients ρ for all nc = k!/(2!(k −2)!) unique combinations of reconstructed spectra to estimate (dis)similarity (Fig. 3.5(a)). We then513.3. Principal Component Analysis5 10 15 20 25 300.10.120.140.160.180.20.220.24cluster number kC RMS(a) (b)252622242123181920 3 5 7 1 2 6 4 8 911103012131415162829172700.10.20.30.40.50.60.7distance (dB)arbitrary cluster numberk = 2k = 3k = 4Figure 3.5: Cluster evaluation diagnostics, noise level 0.1. (a) Dendrogram showing cluster struc-ture and distances between clusters. Only up to 30 subclusters (instead of all observations) areshown. The vertical positions of the solid horizontal bars linking different clusters indicate thedistance between those clusters. Dashed lines show possible cut off levels related to decreasingdistances between cluster below. (b) CRMS value for cross-correlation coefficient between uniquecombinations of reconstructed spectra from (a), for cluster numbers between 2–30. A large valuemeans that there is a lower correlation between the representative spectra, and thus that the similar-ity between the spectra for this cluster configuration is low.use the root-mean square (RMS) error of those correlation coefficients relative to a reference valueof 1 (perfect correlation)CRMS =√Σncn=1(ρn − 1)2nc(3.1)as a measure for the similarity between the patterns when clustering the data with this k. Wecalculate this CRMS value for a number of cluster configurations with k = 2 .. 30 (Fig. 3.5(b)).A smaller value indicates a higher overall correlation between the reconstructed spectra, and thuspotentially redundant information from this cluster structure compared to others. The resultingdistribution for CRMS has a maximum at k = 3, indicating a minimum in similarity, which agreeswith the known number of input patterns.Our approach is similar to that of Langer and Falsaperla (1996); Falsaperla et al. (1998) andLanger and Falsaperla (2003) in that we use spectral power as input to PCA. However, our nor-malization (pre-processing) is designed specifically to detect spectral patterns on the basis of theirshape, not their absolute amplitude. In addition, we apply cluster analysis in the lower-dimensionalPC space. Instead of determining the best number of clusters in principal component space, wedevelop a criterion based on the reconstructed spectral space. Furthermore, our approach uses theresults to reconstruct representative spectra in the original, spectral domain. Lastly, the methodol-ogy in Langer and Falsaperla (1996); Falsaperla et al. (1998), and Langer and Falsaperla (2003)was directly applied to real data, without the rigorous testing (i.e., benchmarking) with a controldataset we perform here.523.3. Principal Component Analysisprincipal component 1-0.05 0 0.05principal component 2-0.0500.055 10 15 20 25 300.080.10.120.140.160.180.20.22cluster number kC RMS1 2 3 4 5 6 70.30.40.50.60.70.80.91day1 234 5 6cos(θ)100 101 102051015mode number% of varianceprincipal component 1-0.05 0 0.05principal component 2-0.0500.05cluster 1cluster 2cluster 32 4 6 8 10−0.0100.010.02frequency (Hz)norm. spectral power (dB)(a) (b) (c)(d) (e) (f)Figure 3.6: PCA results for noise level 1.5. (a) Percentage of variance explained by each mode. (b)Projection of the observations in space spanned by principal components 1 and 2. (c) Evaluationmeasure for different cluster configurations, with the peak at k = 3 indicating the best clusternumber. (d)-(f) Same as in Figure 3.4.3.3.2 Performance of PCA and Clustering at Higher Noise LevelsWe next evaluate the sensitivity of our combined PCA and clustering algorithm to different levels ofwhite noise. Table 3.1 summarizes some parameters as well as the misfits, and Figure 3.6 shows theanalysis steps for the example case of noise level 1.5. Figure 3.2 shows that this noise level is higherthan what is expected from a real dataset (cf. Fig 3.1(b)). Much more of the variance is now carriedby the “noisy” higher modes (the first three modes carry only 21.1% of the variance, Fig. 3.6(a)),and the principal components do no longer follow the simple trajectories apparent for noise level 0.1(Fig. 3.6(b)). CRMS reaches its peak at k = 3, correctly indicating the number of known patternsdespite the increased noise level. This emphasizes the importance of performing the clustering inthe space of first few (in our case three) modes, regardless of how much of the total variance theyexplain. In PC space, clusters are determined on the basis of the relevant dissimilarity in termsof the spectra instead of the differences in the noise, which is mainly captured in the higher PCAmodes that we neglect. This procedure assures that, even for the noise level of 1.5, the clusteringcan successfully distinguish the relevant differences in the patterns from the “irrelevant” differencesintroduced by noise.The bottom row in Figure 3.6 summarizes the outcome of the clustering, the reconstructed spec-tra, and the temporal evolution for k = 3. The background, Phase I, and Phase II still form distinctclusters consistent with the original input spectra, albeit with reduced amplitudes (Figs. 3.3 and3.6(e)). However, because of the way we normalize the input, absolute amplitude information forcomparison between the different spectra cannot be obtained for any noise level, and the differenceis, thus, meaningless. For this noise level (1.5), the misfit E = 0.0122 dB, i.e., approximately 14%per spectrum. The main differences between the input spectra, e.g., the higher variability at various533.4. Self-Organizing Mapsfrequencies during Phase I and the average slopes of the spectra during the three time periods arestill captured, despite the higher level of noise. However, whereas the general trends of the temporalevolution are similar to the low noise case (Fig. 3.4(f) vs. Fig. 3.6(f)), the distinctions between theclusters become unclear.Table 3.1 shows that the misfit between the known and the reconstructed spectra increases withincreasing noise. The clustering algorithm shows a trend towards requiring more clusters (k > 3) toidentify the three known input patterns (according to CRMS). Our cluster evaluation criterion thusoverestimates the total number of clusters and consequently includes redundant patterns in additionto the known three input spectra.3.4 Self-Organizing MapsWe use the results of our PCA algorithm as benchmarks to evaluate the performance of SOM on thesame synthetic seismic dataset. For the SOM algorithm, we use a MATLAB R© based SOM toolboxby Vesanto et al. (1999, 2000) (freely available on http://www.cis.hut.fi/projects/somtoolbox/). TheSOM algorithm was introduced by Kohonen (1982, 1990). The basic idea is to cluster observations(in our case the spectra) onto a 2D topology of nodes (whose number has to be set) by finding theminimum Euclidean distance between each observed spectrum and the pre-assigned spectrum of agiven node. When this so-called best-matching unit (BMU) is identified, its spectrum, as well asthe spectra associated with surrounding nodes in a given radius around the BMU are updated tobe more similar to the data spectrum. When this process is done iteratively, the map “learns” themain patterns of the input data. On the final topology, neighboring nodes represent similar pat-terns/spectra, whereas dissimilar patterns are placed farther apart. Even though the SOM approachhas been commonly used as a clustering tool (i.e., clustering the data onto a 2-D map), its valuelies in its role as a discrete nonlinear PCA (Cherkassky and Mulier, 1998). Equivalent to represent-ing the multidimensional PC space by mutually orthogonal eigenvectors, the SOM approximates adataset in multidimensional space by a flexible grid (typically of two dimensions) of cluster centers.To examine the SOM results, we visualize the shape of the feature spectra in relation to theirlocation on the SOM topology (Fig. 3.7(a)), the relative distances between feature patterns of thenodes (smaller node size means a larger distance to the neighboring nodes, Fig. 3.7(b)), and theBMU for each observation in time (Fig. 3.7(c)). Both visualizations of the topology can be usedto determine which spectra are similar. For the temporal evolution, the y-axis refers to the numberof the map nodes, which are numbered first along the rows of the topology, and second along thecolumns (i.e., in this example node 20 is the node in the first row of the second column for the19×7 map, Fig. 3.7). The color contains the same information, and helps to visually determinewhich nodes are close to each other. Excellent resources exist with more details about the SOMalgorithm (e.g., Kohonen, 1990; Vesanto et al., 2000; Klose, 2006; Langer et al., 2009; Carniel,2014). Here, we apply the method combined with clustering in a way similar to previous volcanoseismic studies (e.g., Langer et al., 2009; Messina and Langer, 2011; Carniel et al., 2013a,b)) toevaluate its capability to capture the main features of our synthetic dataset.543.4. Self-Organizing Maps1 2 3 4 5 6 7020406080100120140dayBMU number1 234 5 6(a) (b)(c)Figure 3.7: Output from SOM algorithm, noise level 0.1. (a) Feature space with representativespectra shown on each node, with color coding for easy referencing. White nodes are “empty”, ie.,not associated with any data in the final map configuration. Three nodes outlined in bold indicatespectra manually chosen for Figure 3.8. Dashed black lines outline approximate grouping accordingto feature spectra, discussed in Section 3.4.2. (b) Same feature space, but with node size scaled bymean distance to neighbouring nodes (small nodes correspond to large distances, and vice versa).Dashed black lines outline approximate grouping according to distances, discussed in Section 3.4.2.(c) Temporal evolution of BMUs for each observation in time. Certain areas of the SOM topologyare only active at certain times. Vertical, blue dashed lines and small numbers same as in Fig 3.3(b).553.4. Self-Organizing MapsTable 3.2: Quality measurements and clustering results according to RMS value of cross correlationcoefficient between reconstructed spectra, for different SOM sizes at noise level 0.1. Columns fromleft to right are: Dimensions of the SOM topology, quantization error QE (dB), topographic errorTE, best cluster number k and misfitE (dB), and misfitE* (dB) for manual selection of three nodesfrom SOM (without clustering, see Fig. 3.8).Map size QE TE k E E*2×3 96e-4 0e-4 4 99e-4 99e-45×2 83e-4 253e-4 2 105e-48×3 63e-4 1012e-4 2 102e-411×4 53e-4 610e-4 6 42e-414×5 48e-4 565e-4 4 43e-416×6 44e-4 343e-4 4 33e-43.4.1 SOM Topology SizeFor a given dataset, many parameters can be modified within the SOM toolbox. To test the methodas it is often implemented, we chose values consistent with previous work (e.g., Langer et al.,2009, 2011; Di Salvo et al., 2013). In particular, we use hexagonal units on a sheet topology. Theautomatic training length calculation results in 3 iterations and a learning rate of 0.5 for the roughtraining phase, and 9 iterations and a learning rate of 0.05 for the fine tuning phase. Depending onmap size, the Gaussian neighbourhood radii are 2–3 and 1 for the two training phases, respectively.The only parameter where we do not choose the default is the initialization of the feature patternson the topology, because we found linear initialization (i.e., the initial SOM nodes lay on the planespanned by the two leading PCA eigenvectors) to yield slightly more reproducible results.In terms of our ability to recover the known phases (Fig. 3.3), one important parameter is thesize of the resulting 2D topology (e.g., Radic and Clarke, 2011). In particular, a smaller numberof nodes will result in broader generalizations of the patterns in the input data space. In contrast,larger SOM are able to capture finer variations in the input data space, which in our case representdifferences in the patterns due to the noise. Similarly, if there is noise in the data then patternsthat occur only a few times compared to the total length of the dataset may be easier to detect ona large SOM. The toolbox can determine the ideal size and shape (i.e., aspect ratio of the map) onthe basis of the dataset length (i.e., the total number of observed spectra) and the ratio of the twolargest eigenvalues for the dataset (Vesanto et al., 1999, 2000). For noise level 0.1 the best size asdetermined by the algorithm is 19×7. There are two measures for goodness of fit of a topology: Thequantization error QE (i.e., the mean RMS difference between each data spectrum and its BMU),and the topographic error TE (i.e., the fraction of the observations for which the first BMU and thesecond BMU are not neighboring nodes), both of which should be small. The more nodes the maphas the better it can fit the data (i.e., generally decreasing QE), but the trade off is that the likelihoodof overfitting increases (i.e., generally larger TE, Table 3.2).Figure 3.8 illustrates the difference in results for varying map sizes. We manually pick threerepresentative spectra from a small 2×3 topology (Fig. 3.8(a)), and from the feature space of the563.4. Self-Organizing Maps2 4 6 8 10−0.0100.010.020.03frequency (Hz)normalized spectral power (dB)node 132node 23node 1162 4 6 8 10−0.0100.010.020.03frequency (Hz)normalized spectral power (dB) node 6node 3node 1(a) (b)Figure 3.8: Three feature spectra from (a) a small 2×3 topology (inset), and (b) the SOM topol-ogy in Fig. 3.7. The nodes were chosen as the approximate centers of groups on the topologyrepresenting the three input spectra (Fig. 3.3), determined by eye. Whereas the smaller map can-not distinguish between Phase I and II, the larger map captures the differences related to the inputspectra well.original 19×7 topology (Figs. 3.7 and 3.8(b)) for comparison. The small 2×3 map shows fewervariations in spectral characteristics across the map topology, i.e., the variations of the input spectraare mostly averaged out (which leads to higher QE, Table 3.1), whereas the general shape with adecrease in spectral power from low to high frequencies is preserved. However, despite the factthat six nodes should theoretically be enough “groups” to account for the background and bothphases, in practice Phase I and Phase II are grouped by this small topology. Most likely, thisresult is related to Phase I appearing only for a relatively short amount of time and the patternis consequently averaged out. In contrast, the “ideal” 19×7 map as determined by the algorithmshows more subtle variations among the feature spectra. The presence of subtle variations for largermaps highlights the importance of map size: A large number of nodes is essential to capture spectralcharacteristics that may not be represented in many observations and are thus not carrying enoughweight to significantly influence the feature patterns (such as Phase I). We tested several topologysizes with the same aspect ratio but a smaller number of nodes (Table 3.2), which may be easier forgrouping. QE and TE indicate that the 19×7 topology is the ideal choice.The automatic size determination provided by the toolbox has been used for previous studies(e.g., Langer et al., 2011) and is our preferred method, mainly because it is automated and repro-ducible, in particular without a priori knowledge of the patterns. Because the resulting number ofnodes on the 19×7 SOM overestimates the known number of three patterns, we follow previousSOM studies (e.g. De Matos et al., 2006; Ko¨hler et al., 2009; Messina and Langer, 2011; Carnielet al., 2013a; Di Salvo et al., 2013) and apply clustering to the SOM topology, which we discuss inSection 3.4.2. This is different from reducing the number of nodes as discussed above, since clus-tering of the topology does not usually depend on the frequency of occurrence of each spectrum,but simply on the distance between the respective patterns of each node.573.4. Self-Organizing Maps3.4.2 Results and Clustering of SOM PatternsIn terms of the spectra, the biggest differences among patterns on the SOM appear between the topand the bottom half of the map (cyan, green, yellow vs. dark blue, red, purple; Fig. 3.7(a)), andbetween the 4–5 spectra at the top right corner and the rest (cyan and green vs. yellow; Fig. 3.7(a)).This division into three groups is partly confirmed by the visualization of the distances betweennodes on the topology (Fig. 3.7(b)). However, the larger distances between nodes for a large portionof the bottom half of the map (dark blue, purple, and orange area; Fig. 3.7(b)) suggests that fourgroups may also be a valid choice. This ambiguity is similar to the difficulties with dendrogramsdiscussed in Section 3.3.1 and indicates that it may be difficult to evaluate how nodes on the mapshould be grouped without a priori knowledge of the patterns or additional processing.On the timeline (Fig. 3.7(c)), the “harmonic” character stems from the mapping of the 2Dtopology onto the (1D) y-axis (i.e., on the 19×7 map node number 1 is adjacent to node number20, and so on). For example, during time period 5 all the variation in terms of BMUs is confinedto the top left corner of the topology (cyan and green), which consists of similar patterns that differmainly in their white noise level. In contrast, the transitional time periods (e.g., period 6) are shownas gradual changes in BMU from one area of the topology to another over time. This result indicatesthat dark blue, purple, and red nodes may be representative of this transitional time, and highlightsagain that grouping of patterns is particularly difficult if gradual transitions exist in the data.On the basis of these challenges, the large number of nodes necessary to capture short-durationphases (Section 3.4.1), and the similarity of spectral shapes in different areas of the map, we applythe same hierarchical clustering algorithm used for PCA (Section 3.3.1). In this case the clusteringis applied to SOM patterns that occur in the data, i.e. we exclude the nodes that never act as a BMUto any of the observed spectra. These “empty” nodes correspond to artificial patterns created solelyto “fill in” the gaps in the topology, and should not be considered as real patterns present in thedata (e.g., Liu et al., 2006). Following the same approach as for clustering the observations in PCspace, we cluster the SOM patterns for k = 2..30 and use the CRMS metric to identify the idealcluster number k (Equation 3.3.1). For noise level 0.1, the ideal k = 4 (Fig. 3.9(a)). For each of theresulting clusters we find the corresponding pattern by taking the median of all spectra associatedwith the nodes within that cluster (Fig. 3.9(b)–(c)), and plot the temporal evolution as done for thePCA results (Fig. 3.9(d)).Even at low noise, the best clustering structure according to CRMS is obtained for k = 4, notk = 3 as with PCA. Three out of identified four patterns correspond well to our three known pat-terns (E =0.0023 dB) which means that the clustering on SOM is able to identify the known setof patterns but only by additionally identifying a redundant pattern. Similar to the results fromclustering in PC space on data with noise level 2, the correct three pattens are identified for an over-estimated optimal number of clusters (k > 3). However, for clustering on SOM this overestimationoccurs already at noise level 0.1. Similarly, the clustering algorithm in combination with CRMSconsistently overestimates the ideal k on the SOM for higher noise levels. For noise level 0.5, forexample, where the ideal k = 13, 10 additional, redundant patterns are identified. Because of these583.4. Self-Organizing Maps0.60.70.80.911 2 3 4 5 6 7day1 234 5 6cos(θ)1 2 3 4 5 6 7 8 9−0.0100.010.020.03frequency (Hz)norm. spectral power (dB)  cluster 1cluster 2cluster 3cluster 40 5 10 15 20 25 300.050.070.090.110.13cluster number kC RMS(a) (b)(c) (d)Figure 3.9: Clustering of SOM topology, noise level 0.1. (a) Cluster evaluation measure, with peakindicating k = 4. (b) SOM topology with feature spectra, colored according to clustering. Emptynodes in white. (c) Final spectra, reconstructed from the median of all feature spectra included inrespective cluster. (d) Time series of angles between observed spectra and central spectrum for eachcluster. Values close to 1 indicate strong alignment. Vertical, blue dashed lines and small numberssame as in Fig 3.3(b).593.5. Discussion1 2 3 4 5 6 7 8 9−0.0100.010.020.03frequency (Hz)norm. spectral power (dB)  cluster 1cluster 2cluster 30.60.70.80.911 2 3 4 5 6 7day1 234 5 6cos(θ)(a) (b)Figure 3.10: Clustering of SOM topology, noise level 0.1, manual selection of k = 3. (a) Finalspectra, reconstructed from the median of all feature spectra included in respective cluster, withSOM topology colored according to clustering as inset. (b) Time series of angles between observedspectra and central spectrum for each cluster. Values close to 1 indicate strong alignment. Vertical,blue dashed lines and small numbers same as in Fig 3.3(b).redundant patterns that capture transitions and noise, the misfit for clustering on the SOM is lowerthan for PCA for the same noise levels (Table 3.1). Manually setting k = 3 for the hierarchical clus-tering for noise level 0.1 only partly reproduces the known phases and corresponding input spectra(Fig. 3.10). The misfit E = 0.0090 dB is still over 5 times larger than for clustering applied tothe PCA results. We further discuss manual selection of parameters in Section 3.5.2, and potentialimplications for our cluster evaluation criterion in Section 3.5.3.3.5 DiscussionIn the following, we discuss the main results of our work and the implications for applying the PCAand SOM methods to a synthetic dataset with spectral features (different spectral shapes with bothimpulsive and emergent variations over time) that can be observed at Kı¯lauea and other volcanoes.Because our work is aimed at recognizing distinctive spectral patterns we do not include a detaileddiscussion about the underlying mechanics which may not be unique and which are addressed innumerous other studies (e.g., Ripepe and Gordeev, 1999; Johnson et al., 1998; Chouet, 1986; Leet,1988; Julian, 1994; Neuberg et al., 2000; McNutt, 2005; Jellinek and Bercovici, 2011; Unglertand Jellinek, 2015). Here, we first give a summary of the steps necessary for each method (Sec-tion 3.5.1). We then discuss the limitations of the SOM method (Section 3.5.2), and the limitationsof the PCA method and our synthetic data (Section 3.5.3).3.5.1 Summary of Steps Taken for Each Method: Parameter ChoicesFor PCA, there are two important steps to reliably capture different spectral patterns:1. Examine variance graph to determine the number of modes to be used for further analysis603.5. Discussion(Figs. 3.4(a) and 3.6(a); three modes were kept here to enable comparison between the dif-ferent cases).2. Use CRMS (Figs. 3.5(b) and 3.6(c), Equation 3.3.1) to identify the optimal cluster number.By contrast, for SOM the following choices need to be made:1. Set parameters (including map size) for SOM algorithm.2. Either use CRMS (Fig. 3.9, Equation 3.3.1),3. or use visual inspection of patterns on SOM topology (Fig. 3.7(a)) to identify the best clusternumber.The comparison between the PCA and SOM cluster analyses of our synthetic spectral datasetindicates that each method has distinct advantages and pitfalls that we will discuss in the followingsections. Processing times for both methods were on the order of 100 seconds9. In general, ourPCA approach was more successful than SOM at reproducing the known number of input patternsat the same noise level in our synthetic dataset.3.5.2 Limitations of Typical Volcano Seismic SOM ApproachOur cluster evaluation criterion applied to the SOM topology gave k > 3 as the best clusternumber for all noise levels (Table 3.1), which is inconsistent with the three known input patterns(Fig. 3.3(a)). The three known patterns are identified on the SOM, but clustering cannot success-fully distinguish between those and other, redundant patterns. This lack of success demonstratesthat the clustering without any a priori information cannot correctly identify the number and appear-ance of the patterns from the data on the SOM. To overcome this impediment, an additional metriccould be introduced to direct the initial groupings around the cluster centers of interest. A type ofsupervised classification, rather than unsupervised clustering, might thus perform better for this ap-plication on SOM. The underperformance of clustering on SOM relative to clustering on PCA maybe related to the clustering on the SOM not accounting for some nodes being representative of onlyvery few spectra from the original dataset. Patterns carrying almost no variance may, thus, domi-nate the clustering, turning the original advantage of clustering not accounting for variance into adisadvantage. Furthermore, clustering on the SOM topology may be complicated by the fact thatit is based on the full spectrum (i.e., all 57 frequency samples), as opposed to the low-dimensionalPC space (i.e., 3 dimensions out of 57). Similarly, the clustering algorithm does not account for theposition of each node on the map topology, which is a crucial part of the information provided bySOM.Alternatively, nodes characteristic for the main patterns in the data can be manually selected onthe SOM topology (Fig. 3.8(b)). However, on the basis of ambiguities with respect to the optimal9On a 2 of 6 core/12 thread Intel R© Xeon R© CPU E5645 with 2.40 GHz (in effect 12 core/24 thread); 48 GB DDR3RAM; storage 6x4 TB raid 6 sequential benchmark ≈ 500 MB/s.613.5. Discussionnumber of clusters, and the associated subjective choices, we do not investigate this option further.Similarly, manual determination of cluster membership of each node is difficult and subjective, be-cause of the nature of gradual variations of spectral patterns across the SOM topology with changesat many frequencies (Fig. 3.7(a)).For different map sizes, k varies between 2–6 (Table 3.2), and is more consistent with the threeknown input spectra than for the automatically determined map size on average because of thelow noise level. This suggests that the size of the map topology influences the performance of theclustering algorithm. Running the SOM algorithm with a range of map sizes, and subsequentlyapplying the clustering to each topology may, thus, help to get a better estimate of the best k fora natural dataset with a generally unknown number of patterns. However, in some cases Phase Iand Phase II are combined into one cluster (2×3, 5×2 and 8×3), whereas in others the phases arecorrectly identified but with additional patterns related to the transitions between the phases (e.g.,11×4). Even with an exhaustive set of topologies, it is not clear how to determine the final bestanswer without any a priori knowledge.Our analysis suggests that the clustering methodology appears to be the main inhibiting factorfor SOM performance, even when applying the quantitative approach with our cluster evaluationmetric. Tests of the method with earlier versions of the synthetic dataset gave good clustering resultsin some cases, but not in others (for example, with the noise added to spectral amplitude insteadof power, resulting in a stronger variability at high frequencies where spectral amplitude/power arelow; results not shown). This highlights the strong dependence of the SOM topology and subse-quent clustering on the input dataset. Several modifications of the algorithm, including usage ofcross-correlation based clustering as suggested by Carniel et al. (2013a), and applying PCA to theSOM topology to cluster the nodes in the resulting lower dimensional space did not yield signif-icant improvement. Replacing hierarchical clustering with a different cluster algorithm may helpto alleviate the issues. For example, De Matos et al. (2006) apply k-means clustering to the SOMtopology for the analysis of waveforms to identify seismic facies in the subsurface. Their synthetictest shows good results (De Matos et al., 2006), but more detailed investigation is necessary toevaluate its performance when analyzing features in volcano seismic spectra. Alternatively, replac-ing traditional clustering algorithms with different ways of grouping the nodes may have a higherchance of success. In particular, any grouping algorithm should account for the information inher-ent in the SOM topology, which clustering methods typically neglect. Bauer et al. (2012) applygrouping of nodes by using the gradient of the distance matrix of the SOM topology to derive alithological model from inversion results of seismic and magnetotelluric data. Initial tests with asimilar method to group nodes on our SOM topology show that accounting for the topological re-lationships between the nodes may improve the results. Detailed investigation of this new methodis beyond the scope of this comparative study, and will be addressed in a future paper.However, SOMwithout clustering can be useful in providing an overview of patterns in the dataspace and their similarities and differences (Fig. 3.7). The temporal evolution of BMUs (Fig. 3.7(c))can be used to capture continuous transitions from one pattern to another. However, using the SOMoutput in this way may be subjective. Interpretation of similarity in color on the timeline, for exam-623.5. Discussionple, depends on the subjective perception of color differences (e.g., Rogowitz and Treinish, 1998;Borland and Taylor, 2007), and suffers from mapping the non-linear SOM topology onto a pre-scribed, typically linear, color scale. To navigate this challenge, Langer et al. (2009) apply PCA tothe SOM output, and assign red, green, and blue to the first three principal components respectively.Each feature pattern is then projected onto the three principal components, and the correspondingnode is given the corresponding mixture of red, green, and blue on the basis of the projections.Similarly, Langer et al. (2011) project the nodes onto the first two principal components for visu-alization of distances, and show the temporal evolution in combination with a separately obtainedcluster analysis. Whereas the additional PCA might help to better depict the distances betweennodes by using color, the subjectivity in color perception remains unaddressed. Furthermore, theirvisualization of the temporal evolution of BMUs relies on results from an independently obtainedcluster analysis in both studies, and may not be usable on its own.On the basis of these shortcomings, on the fact that previous studies (Langer et al., 2009, 2011)had to combine SOM, PCA, and cluster analysis, and on the potentially subjective choices that haveto be made, the question arises whether skipping the SOM step and using PCA and cluster analysisonly might yield characteristic volcano seismic spectra in a more efficient way. We thus focus theremainder of Section 3.5 on discussing the PCA approach and its application to our synthetic data.3.5.3 Limitations of our Synthetic Data and the PCA ApproachBecause of the way we construct the relatively short synthetic dataset, one could argue that the samefeatures could be identified by visual inspection of the spectrograms (e.g., Fig. 3.3). However, thetrue power of the PCA plus clustering approach is that the algorithm can extract the patterns in thesame way for much longer datasets with patterns that are not necessarily temporally grouped. Evenif a volcano is exhibiting anomalous signals for only a small period of time (such as Phase I, whichrepresents approximately 2% of the entire dataset), PCA will identify those signals if the varianceof the usual patterns is smaller than the difference between the anomalous and the more commonsignals.Our synthetic dataset, drawn from volcanic unrest at Kı¯lauea with features similar to othervolcanic settings (Fig. 3.1), is only one of many possible examples for a benchmarking case. Toevaluate whether the successful application of the PCA plus clustering method is only due to thenature of our synthetic data, we test a modified version of the dataset, where an additional pattern isadded to analyze four instead of three patterns in total. We test two cases, where (i) the additionalpattern corresponds to the Phase II spectrum flipped along a vertical axis in frequency space (noiselevel 0.1, Fig. 3.11), and (ii) the additional pattern is a modified version of Phase II that is not asdifferent from the other spectra compared to the previous case (Fig. 3.12). For the flipped Phase IIcase, the principal components now show an additional cluster of points (cluster 1, Fig. 3.11(c))relatively far removed from the observations from the original dataset. The shape of the originalprincipal components is still preserved (clusters 1–3, Figs. 3.4(d), 3.11(c) and 3.11(e)). Becauseour cluster evaluation criterion favors strong dissimilarity including anti-correlation between clus-633.5. Discussion100 101 1020102030405060708090mode number% of variance−0.2 −0.15 −0.1 −0.05 0 0.05−0.03−0.02−0.0100.010.020.03  principal component 1 principal component 2cluster 1cluster 22 4 6 8 10−0.02−0.0100.010.02frequency (Hz)norm. spectral power (dB)−0.2 −0.15 −0.1 −0.05 0 0.05−0.03−0.02−0.0100.010.020.03  principal component 1 principal component 2cluster 1cluster 2cluster 3cluster 42 4 6 8 10−0.02−0.0100.010.020.030.04frequency (Hz)norm. spectral power (dB)2 4 6 8 10−0.02−0.0100.010.020.030.04frequency (Hz)norm. spectral power (dB)  backgroundPhase IPhase IIPhase II flipped(a) (b)(c) (d)(e) (f)Figure 3.11: PCA plus clustering method applied to same synthetic dataset with flipped Phase IIpattern. (a) Known input spectra. Background, Phase I, and Phase II as before, with a flippedPhase II pattern added. (b) Percentage of variance explained by each mode. (c) Clustering ofobservations in PC space with k = 2 determined through CRMS. Note the similarity of the shapeof clusters 1–3 compared to the original dataset (Fig. 3.4(c)-(d)). (d) Reconstructed cluster spectrafor k = 2. (e)-(f) Same as (c)-(d) but for k = 4 (k chosen manually by visual inspection of (c)/(e)).643.5. Discussion−0.06 −0.04 −0.02 0 0.02 0.04−0.04−0.03−0.02−0.0100.010.02  principal component 1 principal component 22 4 6 8−0.0100.010.020.03frequency (Hz)  cluster 1cluster 2cluster 3cluster 4norm. spectral power (dB)0 5 10 15 20 25 300.080.10.120.140.160.180.2cluster number kC RMS2 4 6 8−0.0100.010.020.03frequency (Hz)norm. spectral power (dB)  backgroundPhase IPhase IIPhase II modified(a) (b)(c) (d)Figure 3.12: PCA plus clustering method applied to same synthetic dataset with modified Phase IIpattern. (a) Known input spectra. Background, Phase I, and Phase II as before, with a slightlymodified Phase II pattern added. (b) CRMS indicates best k = 4. (c) Clustering of observations inPC space with k = 4. (d) Reconstructed cluster spectra for k = 4.653.5. Discussionters (highest information gain), for this four-pattern case the peak is at k = 2, and the three originalspectra are combined into one large cluster (Fig. 3.11(c)-(d)). This shows that our clustering ap-proach only works in an automated fashion if the input patterns all are at comparable distancesrelative to each other in PC space (e.g., as is the case for our three original input spectra). In con-trast, for the four patterns that had comparable distances in PC space ((ii), Fig. 3.12) the clusteringapproach correctly identified k = 4 and reproduced the patterns.For case (i) that includes the flipped Phase II spectrum, the transitions between the three originalspectra add observations in the space between their respective cluster centers, further contributingto the spectra being combined into one cluster. However, in such a case visual inspection of thePCA space (e.g., Fig. 3.11(c) and (e)) can help to identify “subclusters” at different scales, andsubsequent manual adjustment of the cluster number to k = 4 can be used to reconstruct thepatterns corresponding to those lower level clusters (Fig. 3.11(f)). In contrast to manually selectingthe cluster number on the SOM topology, this approach works in PC space, because the decision ismade in the low dimensional PC space that can easily be visualized.The PCA plus clustering approach works well with our dataset because the data are normalizedto account only for their shapes. If some spectra in the dataset were to cover a much larger rangeof spectral power values than others (similar to the background vs. Phase I, only more extremethan shown in Fig. 3.2(a)), the normalization would remove these differences in range. However,as a trade off, this way the small variations of spectral power between different frequencies may beenhanced for spectra with a small total range of spectral power. For example, the small variations ofPhase I before the normalization (Fig. 3.2(a)) are amplified by the way we normalize each spectrum(Fig. 3.3(a)). Because this will be similar for spectra with similar shapes, we do not expect thiseffect to strongly influence the performance of our algorithm in a negative way. If a differentnormalization is chosen, amplitude differences may become important. Future studies should beconducted to investigate how different normalizations impact the performance of the algorithm.Table 3.1 indicates that our cluster evaluation criterion shows a slight dependence on the noisefor our PCAmethod (best k = 3 for all but the highest two noise cases for our three pattern dataset).To test the sensitivity of the clustering results to the choice of cluster evaluation criterion CRMS,we test a different criterion (Table 3.3) that obtains the RMS value of the RMS differences betweenthe reconstructed cluster spectra (consistent with Euclidean distances used for clustering in PCAspace). The resulting ideal cluster numbers are almost identical for the PCA approach for all casescompared to the cross-correlation criterion, indicating that the results are robust with respect toour cluster evaluation criterion. For the SOM approach the results are less similar, confirming thatcommon clustering algorithms may not be the ideal method to group patterns on the SOM.We do not suggest that our cluster evaluation criterion can replace other, more generally appli-cable criteria such as the Davies-Bouldin Index (Davies and Bouldin, 1979), but it appears to workwell in cases where the data can easily be reconstructed in a physically meaningful space such asspectra in the frequency domain.The small number of modes (three) used in our PCA approach is justified by the drop offin variance after modes 1–3 for most noise levels. However, this approach does not work if the663.5. DiscussionTable 3.3: Quality measurements and clustering results for different noise levels based on RMSvalue of RMS differences between reconstructed spectra, comparison between PCA and SOM.Columns from left to right are: Noise level, number of modes necessary to explain 90% of thetotal variance, best cluster number k, misfit E (dB) for cluster number k, dimensions of the SOMtopology, quantization error QE (dB), topographic error TE, best cluster number k and misfit E(dB) as for PCA.PCA SOMNoise 90% var. k E Map size QE TE k E0.1 2 3 16e-4 19×7 42e-4 387e-4 4 23e-40.5 35 3 41e-4 19×7 17e-4 283e-4 4 68e-41 44 3 91e-4 19×7 284e-4 238e-4 6 77e-41.5 46 3 122e-4 19×7 366e-4 223e-4 14 107e-42 47 6 128e-4 17×8 426e-4 193e-4 8 132e-44 48 24 190-4 13×10 553e-4 238e-4 25 200e-4explained variance has the same order of magnitude for all modes (Hsieh, 2009) (e.g., noise level 4,Table 3.1, where all modes explain a percentage of the variance on the order of 1%). We note thatthe method still performs well in cases where a relatively small amount of variance is explained bythe first three modes (e.g. noise level 1.5 with 21.1% of the variance, Section 3.3.2 and Fig. 3.6).However, the choice of the number of modes may not always work in the way shown here, whichmay result in SOM being the more successful method.As discussed in Section 3.2, we do not include gliding spectral lines in our synthetic dataset.However, these features are gradual, systematic variations in the change of spectral shapes overtime, and are thus similar to the transitions between the different phases. With the PCA approachthese transitions are captured by the time series of angles between the reconstructed and the ob-served synthetic spectra (Figs. 3.4(f) and 3.6(f)). However, the transitions implemented in oursynthetic dataset affect large parts of the spectrum. Given that frequency gliding at Kı¯lauea onlyinvolved a few individual peaks, it is questionable if their slow variations have enough weight tostrongly change the angles. In contrast, the SOM approach can show such transitions before theapplication of the clustering (Fig. 3.7(c)), which indicates that it may be better suited to capturegradual variations in time. However, from the time series from either method it is not clear what thenature of such continuous changes in time is (e.g., transition between phases vs. gliding), indicat-ing that spectrograms and/or seismograms have to be consulted after periods of interest have beenidentified with our automated algorithms.Our synthetic data were limited between 0.5–10 Hz as discussed in Section 3.2.1. To assesswhether the results depend on this frequency band we apply both the PCA and the SOM approachto the same dataset limited to an arbitrary range of different frequency bands (Table 3.4). Intu-itively, an increase in information in spectral space (i.e., a larger frequency range resulting in more“dimensions”) should improve the performance of a pattern recognition algorithm. This is partlyconfirmed by the decreasing misfits for an increasing upper frequency limit (Table 3.4). The idealcluster number k for PCA hovers around k = 3 for all frequency ranges. Both cases of k = 4 from673.5. DiscussionTable 3.4: Clustering results for different frequency bands based on RMS value of cross correlationcoefficients between reconstructed spectra for noise level 0.1, comparison between PCA and SOM.Columns from left to right are: Frequency range, best cluster number k and misfitE (dB) for clusternumber k from PCA, best cluster number k and misfit E (dB) from SOM.PCA SOMFrequ. (Hz) k E k E0.5–3 2 543e-4 4 156e-40.5–8 4 9e-4 4 47e-40.5–10 3 16e-4 4 23e-40.5–12 3 7e-4 9 9e-40.5–15 4 5e-4 12 9e-4the PCA approach recover parts of the transition between the two phases and the background as aseparate cluster, in addition to correctly identifying the three known input spectra. This separationof the transitions explains the lower misfit for 0.5–8 Hz compared to 0.5–10 Hz.In contrast, three out of five cases give k = 4 on the SOM, and the remaining two cases yieldk = 9 and k = 12. Even forcing k = 3 does not recover the known phases correctly. Most likely,the way the synthetic data are set up and normalized, Phase II and the background are seen as twoendmembers of the same continuous space on the SOM topology, whereas Phase I is separate, orPhase I and Phase II are combined. Grouping of Phase II and the background may be partly relatedto the long, gradual transition (time period 6). This result highlights the potential sensitivity of SOMto the normalization, which removes the amplitude differences between the phases and increasesthe similarity. Other methods of normalizing the data that give more weight to the amplitudes thanwe do here could be investigated further in future work.Lastly, previous studies have suggested that non-linear processes may underlie some of theobserved volcano seismic signals (e.g., Shaw and Chouet, 1988; Julian, 1994; Konstantinou andLin, 2004; Konstantinou et al., 2013). The question arises whether PCA as an inherently linearmethod (e.g., Hsieh, 2009) would be suitable to analyze data from such non-linear processes.Because our synthetic spectrograms were explicitly constructed from spectra (instead of first usingsynthetic waveforms to obtain the spectra), non-linearity can enter the analysis only during thetransitions from one phase to another (time periods 3, 4, and 6). Basic tests with exponentialinstead of linear transitions showed an equally good performance of the method. If, on the otherhand, a synthetic dataset were obtained by estimating spectral content from a seismic time seriesconstructed from nonlinear combinations of signal components, it is unclear how well our PCAplus clustering approach would work. However, in such a case, analyzing spectra from FourierTransforms (which is indirectly linked to our approach, since the characteristic spectra in Unglertand Jellinek (2015) were obtained by using FFTs) may not yield useful insight into the sourcemechanics (Julian, 1994; Konstantinou and Lin, 2004). To look explicitly for non-linear dynamics,an entirely different, bespoke synthetic data setup and analysis approach (e.g., Singular SpectrumAnalysis, Ghil et al. (2002)) needs to be designed and tested. Such a detailed analysis of non-lineareffects is beyond the scope of this work.683.6. Conclusions3.6 ConclusionsFor the first time, we (i) construct a synthetic dataset as a benchmark to (ii) evaluate the perfor-mance of SOM in combination with hierarchical cluster analysis similar to previous studies onvolcano seismic spectra, (iii) compare this method to PCA plus clustering, and (iv) introduce anew cluster evaluation criterion specific to the spectral space. The synthetic data are based onKı¯lauea Volcano, but the results are generally applicable to seismicity with similar spectral shapeselsewhere. Consequently, our main conclusions are:• For SOM, large topologies are necessary to capture spectral phases that last for a relativelyshort amount of time compared to the length of the dataset.• SOM can detect changes in spectral content, and can give a visually appealing overview ofthe data space on the SOM topology.• Further interpretation of the SOM results based on the map topology and temporal evolutionof BMUs is difficult and subjective.• Hierarchical clustering on SOM consistently overestimates the number of optimal clusters,and therefore fails to correctly identify the set of known patterns in the data without addingredundant patterns to the final set.• PCA in combination with our hierarchical cluster analysis shows consistently better perfor-mance and reproduces the known input spectra both at low and high noise levels well.In summary, where the goal is to detect a small number of distinct patterns, clustering in PCspace is our preferred method. By contrast, SOM (without clustering) is useful to give a directoverview of most characteristic patterns in the data. Our results show that it is crucial to evalu-ate the performance of different machine learning methods before implementing applications. Forexample, other clustering algorithms should be tested to investigate if they are more successfulon clustering SOM topologies. Without control data as we have produced, it may be difficult toevaluate the reliability of the algorithm, and to interpret the results. We suggest that, bearing inmind their individual strengths and weaknesses in relation to volcano seismic spectra, both PCA incombination with clustering and SOM on their own can be used to detect characteristic spectral pat-terns in volcano seismicity depending on the specific application. Future studies could test differentbenchmarking datasets. In particular, alternative approaches might involve constructing syntheticseismograms and converting them into the frequency domain. For SOM, more work beyond our di-rect comparison is necessary with respect to evaluating other clustering algorithms (e.g., k-means)than the ones presented here, and assessing non-traditional ways of grouping nodes on the SOMtopology.The ability to rapidly classify spectra of volcano seismic data without prior knowledge of thecharacter of the seismicity at a given volcanic system holds great potential for real time or near-real time applications, and thus ultimately for eruption forecasting. Several PCA/SOM (and other693.6. Conclusionsmachine learning) toolboxes already provide the necessary computational tools, and even graphicaluser interfaces exist (e.g., KKAnalysis, Messina and Langer, 2011). If monitoring records aresufficiently long (i.e. cover multiple eruptive cycles), the spectral signatures of the (potentially un-known) “background” state of a volcanic system, different stages preceding and during the eruptivecycle, or specific types of volcanic activity can be identified with PCA and SOM, and data could beadded in real time to detect changes critically indicative of an impending eruption very quickly.70Chapter 4Spectral Pattern Recognition RevealsDistinct Classes of Volcanic Tremor10SummarySystematic investigations of the similarities and differences among volcanic tremor at a range ofvolcano types may hold crucial information about the plausibility of inferred source mechanisms,which, in turn, is important for eruption forecasting. However, such studies are rare. We de-velop a tremor detection algorithm and identify over 12,000 hours of volcanic tremor on 24 stationsat Kı¯lauea, Okmok, Pavlof, and Redoubt volcanoes. We estimate spectral content over 5-minutetremor windows, and apply a combination of Principal Component Analysis (PCA) and hierarchi-cal clustering to identify patterns in the tremor spectra. Analyzing several stations from a givenvolcano together reveals different styles of tremor within individual volcanic settings. These typesinclude localized tremor signals related to processes such as lahars or dike intrusions that are onlyobserved on some of the stations within a network. Subsequent application of our analysis to acombination of stations from the different volcanoes reveals that at least four main tremor classescan be detected across all settings. Whereas a regime with a low frequency (1–2 Hz) ridge and asubsequent decay of spectral power towards higher frequencies is observed dominantly at volca-noes (Kı¯lauea, Okmok, Redoubt) with magma reservoirs centered at less than 5 km below sea level(b.s.l.), a steeper spectrum with a slightly more pronounced peak at 1–2 Hz is observed only in as-sociation with open vents (Kı¯lauea and Pavlof). A third regime with a peak at approximately 3 Hz isconfined to the two stratovolcanoes (Pavlof and Redoubt), and a fourth tremor type with a peak closeto 10 Hz occurs at Pavlof only and appears to be characteristic for lahars. These observations sug-gest that there may be generic relationships between the spectral character of the observed signalsand volcano characteristics such as magma viscosity, storage depths, and the physical properties ofvolcanic edifices. Similarities among the spectral patterns detected at stations 4 km and 8–10 kmdistance from the centers of volcanic activity, respectively, indicate that path effects do not stronglyinfluence spectral shapes at distances of a few kilometers from the inferred source of the signals. Onthe basis of these promising results, we suggest that further work on data from a larger sample anddiverse range of volcano types will be critical. In addition to revealing additional classes of tremorsignals in volcanic environments, such work will plausibly more completely identify fingerprints ofsource processes specific to volcano type, but independent of volcano location.10In preparation for submission.714.1. Introduction4.1 IntroductionVolcanic eruptions are often preceded and accompanied by a low-frequency (approximately 0.5–10 Hz) seismic signal called “volcanic tremor” (McNutt, 1992; Konstantinou and Schlindwein,2002; McNutt and Nishimura, 2008), hereafter referred to as “tremor”. Tremor can persist forminutes to weeks and its occurrence is often interpreted as a sign of an impending eruption (e.g.,D’Agostino et al., 2013; Chardot et al., 2015). The reliability of tremor as a forecasting tool is,however, uncertain, because the underlying physical processes remain unclear (Konstantinou andSchlindwein, 2002). A range of tremor observations in different locations suggests that such lowfrequency seismicity may be the expression of a variety of mechanisms (e.g., Chouet, 1986; Ju-lian, 1994; Benoit and McNutt, 1997; Ripepe and Gordeev, 1999; Neuberg et al., 2000; Lesageet al., 2006; Jellinek and Bercovici, 2011; Dmitrieva et al., 2013; Bean et al., 2014). However, sys-tematic investigations of similarities and differences among tremor properties in different volcanicsettings that could shed light on the general applicability of potential source processes are rare (e.g.,McNutt, 1994, 2004). Accordingly, we specifically address the following questions:(1) Within a given volcanic setting:(a) Are there tremor signals with distinct spectral signatures?(b) What are the spatio-temporal properties of such signals?(2) Among several volcanic settings:(a) Are there spectral properties of tremor that are common to several volcanoes?(b) Do observations of similarities of tremor properties among different settings relate to thedistinctive characteristics of the volcanoes (e.g., magma viscosity, edifice type, geometryof the plumbing system)?To identify such systematics we use pattern recognition to determine characteristic spectralshapes for tremor from four volcanoes with well-studied and strongly contrasting eruptions. In Sec-tion 4.2 we introduce each volcanic setting analyzed here. In Section 4.3, we develop an algorithmto detect volcanic tremor in continuous seismic data on individual stations (“single station detec-tion”) and outline the preprocessing steps to obtain corresponding tremor spectra. These spectra arethen analyzed with a recently developed pattern recognition approach that combines Principal Com-ponent Analysis (PCA) and hierarchical clustering (Section 4.4; Unglert et al., 2016)). Finally, wediscuss our observations, inferences, and potential implications for identifying and understandingunderlying physical processes in Section 4.5.4.2 Volcanic SettingsWe analyze data related to volcanic unrest from Kı¯lauea (2007–2011, USA), Okmok (2008, USA),Pavlof (2007 & 2013, USA), and Redoubt (2009, USA). All datasets are from permanent networks,and all times are in UTC.724.3. Data and PreprocessingKı¯lauea Volcano on the Big Island of Hawai‘i is an intraplate shield volcano erupting mostlybasaltic magmas (∼49-50 wt.% SiO2, Garcia et al., 1989, 1992; Global Volcanism Program,2013a). Our data include two time periods of dike intrusions and accompanying small fissureeruptions (19 Jun 2007 and 6-10 March 2011, Poland et al., 2008; Fee et al., 2011a; Orr et al.,2015), and a period of small explosive bursts during the formation of the summit lava lake in 2008(Wilson et al., 2008; Houghton et al., 2013). All three episodes of volcanic activity are part ofthe ongoing eruptive sequence with a Volcanic Explosivity Index (VEI) of 1 (Global VolcanismProgram, 2013a). A shorter version of the same dataset was analyzed extensively by Unglert andJellinek (2015). We thus use it as a benchmark for the pattern recognition algorithm by Unglertet al. (2016)) that has only been tested on synthetic data.Okmok, Pavlof, and Redoubt are part of the Aleutian chain, a volcanic arc related to subductionof the Pacific Plate below the North American and Bering Sea plates (e.g., Buurman et al., 2014).Okmok is a shield volcano with volcanic activity focused in a complex of two overlapping calderas(Global Volcanism Program, 2013b). Our data from permanent stations operated by the AlaskaVolcano Observatory span a large (VEI 4) phreatomagmatic explosive eruption between 12 Jul -19 Aug 2008 that produced dominantly andesite to basaltic andesite (∼51-57 wt.% SiO2) and aseries of lahars (Larsen et al., 2009, 2013, 2015).Pavlof Volcano is a stratovolcano close to the western end of the Alaska Peninsula with mostlyStrombolian to Vulcanian activity and andesite to basaltic andesite magmas (∼53-58 wt.% SiO2,Waythomas et al., 2008; Mangan et al., 2009; McGimsey et al., 2011; Waythomas et al., 2014).Two eruptions are included in our analysis: A VEI 2 eruption on the southeastern flank between14 Aug - 13 Sep 2007 (Waythomas et al., 2008), and a VEI 3 eruption on the northwestern flankbetween 13 May - 1 Jul 2013 (Waythomas et al., 2014). In addition to explosive activity and ashemission, both eruptions included lava fountaining, spatter flows, and lahars on the slopes of thecone (Waythomas et al., 2014).At Redoubt Volcano, an andesitic stratovolcano at the northeastern end of the arc, a VEI 3 erup-tive period between 15 Mar to approximately 1 Jul 2009 included phreatic and magmatic explo-sions, as well as the effusion and destruction of several lava domes and associated lahars (Schaefer,2011). Our data include a period of precursory seismicity (Schaefer, 2011; Power et al., 2013) inaddition to the main eruptive phases. The eruption produced mainly andesite with 57-63 wt.%SiO2 (Schaefer, 2011).4.3 Data and PreprocessingWe combine continuous, vertical component seismic data from short-period sensors from the per-manent networks at the volcanoes introduced in Section 4.2. All of the time periods include at leastone discrete eruptive event, or are part of an ongoing eruptive phase. We select these volcanoes onthe basis of data availability, the detection of volcanic tremor and to cover a large range of volcanotypes, magma compositions, and eruptive activity. We restrict our analysis to stations that recordedseismicity associated with the eruptive episodes approximately continuously without any technical734.3. Data and Preprocessingissues. We perform an instrument response correction to achieve a flat response between 0.5–15 Hz.4.3.1 Distinguishing Tremor from the BackgroundTo reduce the amount of data to be analyzed, we develop an algorithm to detect periods of vol-canic tremor. In our examples, we define tremor as elevated seismic amplitude compared to thebackground at each station, sustained over durations much longer than typical local earthquake du-rations (usually up to 10s of seconds, e.g., Go´mez M and Torres C, 1997; Ketner and Power, 2013).We choose a value of 5 minutes for the length of the time window, similar to studies of tectonictremor (e.g.,Wech and Creager, 2008). However, tests with shorter (3 minutes) and longer (10 min-utes) durations give qualitatively similar results. To identify high amplitudes, we take the followingapproach:1. Estimate median absolute background amplitude.2. Divide continuous seismic data into non-overlapping 5-minute windows.3. Compare median absolute amplitude over each window to median absolute background am-plitude.We introduce the no-overlap criterion to avoid counting tremor episodes twice. We use the medianin all cases to reduce the influence of a few large spikes within any given window. To determine themedian absolute background amplitude, we obtain the background spectrum (Fig. 4.1(a) and (c))by identifying the minimum spectral power value at each frequency over time (Vila et al., 2006).We then estimate the signal associated with this background spectrum by converting it back into thetime domain (Fig. 4.1(b) and (d)), where we take the absolute value of the signal and determine itsmedian.We compare the median absolute velocity amplitude of each 5-minute window of continuousseismic data to the median obtained from the background signal. If the median in the windowexceeds the background by a factor f it is recorded as initial detection. Tests with data from Kı¯laueaVolcano that were studied in detail byUnglert and Jellinek (2015) show that f = 150 is a reasonablechoice to detect tremor during known periods of activity.4.3.2 Removing Earthquake SignalsEach successful detection is then tested for the presence of earthquakes. We use two criteria:1. If the detection window includes the origin time of a local earthquake in the ANSS catalog itis excluded from the analysis.2. Criterion 1 is insufficient, because some earthquakes may not be recorded in the catalog. Wethus test each window for spikes that are larger than 6 standard deviations of the data withinthe corresponding window to exclude those events.744.3. Data and Preprocessing2 4 6 8 10 12 14−180−160−140−120−100−80−60−40−200frequency (Hz)spectral power (dB)AHU0 400 800 1200 1600−15−10−5051015time (s)velocity (nm/s)(c) (d)2 4 6 8 10 12 14−140−120−100−80−60−40−200frequency (Hz)spectral power (dB)OKWE0 400 800 1200 1600−30−20−100102030time (s)velocity (nm/s)(a) (b)Figure 4.1: Examples for background signal estimation. (a) Estimate for background spectrum,and (b) associated time domain signal at station OKWE (Okmok Volcano, USA). White dashedline indicates zero velocity, and red dashed line shows the median value of the absolute velocityamplitudes. (c) and (d) are same graphs for station AHU (Kı¯lauea Volcano, USA).09:20 09:25 09:30 09:35 09:40 09:45 09:50 09:55 10:00 10:05 10:10 10:15 10:20−4000−3000−2000−1000010002000300040005000timevelocity (nm/s)RSOtreshold for tremor detectionstart of final tremor windowcatalog earthquakestart of non-tremor windowsmall spikes(1) (2) (3) (12)(11)(10)(9)(8)(7)(6)(5)(4)Figure 4.2: Example seismogram showing different cases of our tremor detection, from Redoubtstation RSO on 25 Jan 2009. Windows (1)–(4) fall below our detection threshold, window (8)includes a catalog earthquake, and windows (9)–(10) include spikes. Only windows (5)–(7) and(11)–(12) are kept as final detections.754.3. Data and PreprocessingFigure 4.2 shows some of the different cases. Over the course of one hour, seismic amplitudesincrease above our tremor threshold (starting in time window (4), Fig. 4.2). Some windows are,however, excluded from detection because of the presence of known earthquakes (window (8),Fig. 4.2) or other spikes (windows (9)–(10), Fig. 4.2). Additionally, some windows have a non-zeromean (not shown), which may be related to transient problems with the instrument. We thus excludewindows with an absolute mean larger than an arbitrary threshold of 100. All steps above are doneseparately for each station, similar to the envelope based single station detection of tectonic tremorby Brudzinski and Allen (2007) or single station event detection by Ketner and Power (2013). Thedisadvantage of this single station approach is that local non-volcanic processes that only affect onestation (e.g., a particularly noisy site) may be included in the analysis. The advantage is that thealgorithm works even for locations with only one station. Furthermore, even if multiple stations areavailable, localized and weaker signals that may only be recorded on one station can be detected,which for our purposes outweighs the drawbacks of a detection algorithm that relies on individualstations.By using our tremor detection algorithm we identify 148,853 5-minute tremor windows on 24stations in total. Table 4.1 summarizes the results for the four different volcanoes.Table 4.1: Summary of volcanoes, stations, data time period, and number of tremor windows. Onlyoverall start and end dates for data periods are given, data gaps may exist in between. Asterisk (∗)denotes that more data were available, but not analyzed because of unresolved technical issues.Volcano Station Start End Tremor Win-dowsKı¯lauea AHU 2007/04/01 2011/03/11 38,473KNH 2007/04/01 2011/03/11 5,917OTL 2007/04/01 2011/03/11 38,059PAU 2007/04/01 2011/03/11 1,016STC 2007/04/01 2011/03/11 28,353Okmok OKAK 2008/07/05∗ 2008/09/08 3,807OKRE 2008/07/05∗ 2008/09/08 5,429OKSP 2008/07/05∗ 2008/09/08 1,059OKWE 2008/07/05∗ 2008/09/08 6,419OKWR 2008/07/05∗ 2008/09/08 4,239Pavlof HAG 2007/07/01 2013/08/07 164PN7A 2007/07/01 2007/10/31∗ 22PS1A 2007/08/21∗ 2013/08/07 1,689PS4A 2007/07/01 2010/08/07 1,788PV6 2007/07/01 2007/10/31∗ 447PVV 2007/07/01 2013/08/07 922Redoubt DFR 2009/02/01∗ 2009/06/03 256NCT 2009/02/01∗ 2009/06/03 204RDN 2009/01/01 2009/04/10∗ 472REF 2009/01/01 2009/04/10∗ 774764.4. Spectral Pattern Recognition4.3.3 Obtaining Tremor SpectraFor each tremor window we obtain a power spectrum, which is smoothed with a 50 point movingaverage and subsampled at the same interval to reduce the effect of individual peaks and to empha-size the overall trends in the spectra (Unglert et al., 2016)). Each spectrum is then scaled by itscumulative spectral power and aligned to achieve a 0 dB median to avoid bias in the results relatedto amplitude differences between spectra of the same shape (Unglert et al., 2016)). To account forvariations in the number of points per spectrum at different stations related to differences in their re-spective sampling rates, we linearly interpolate each spectrum and subsample between 0.75–12 Hzin steps of 0.25 Hz to include the most common tremor frequencies (McNutt and Nishimura, 2008)as far as the data allow. The final spectra are then used as input for our pattern recognition algorithmaimed at identifying characteristic patterns.4.4 Spectral Pattern Recognition4.4.1 OverviewWe analyze the spectra from the tremor windows obtained above to identify patterns in space andtime that may be common to several volcanic settings, specific to one volcano, or be observed atonly one location within a station network. We use an approach developed by Unglert et al. (2016)that combines Principal Component Analysis (PCA) and hierarchical clustering to obtain charac-teristic spectra and their temporal and spatial manifestation. In this section, we outline the mainsteps of the method, followed by a summary of the results. To visualize the theoretical conceptsbehind the methodology we refer to Figures 4.3 and 4.4 here, and explore the respective results inSection 4.4.2.PCA is a statistical technique for dimensionality reduction that enables us to identify groupingsof points in a space with fewer dimensions than the full spectral bandwidth of our observations.Following Unglert et al. (2016)), the frequency samples of the input spectra are treated as theoriginal coordinate system, which is rotated to find the mutually orthogonal directions of maximumvariance (modes; in order of decreasing variance, Fig. 4.3(a)). We then apply hierarchical clusteringto identify groupings of points on the basis of their Euclidean distances in the lower dimensionalPrincipal Component (PC) space defined by the first two modes alone. We choose the cut-off aftermode 2 as a consistent criterion for all cases because of the relatively small variance carried byhigher modes. The resulting clusters can be used to reconstruct spectra corresponding to the maingroupings in the data by superposing the first two principal components of each cluster center.To determine the ideal number of clusters k we use a criterion designed to identify the maximumof allCRMS,k =√Σncn=1(ρn − 1)2nc, (4.1)where ρn is Pearson’s correlation coefficient between the spectra of two clusters for all possiblenc unique combinations of clusters for a given k (Fig. 4.3(b)). CRMS,k ranges between [0..2] for774.4. Spectral Pattern Recognitionρ = [−1..1]. The maximum CRMS,k = 2 corresponding to ρ = −1 indicates the largest deviationfrom perfect correlation (ρ = 1), or lowest similarity between the spectral shapes of each cluster.This minimum correlation thus indicates maximally distinct clusters. The corresponding mediancluster spectra capture the main groupings within the full variety of observed spectra. In all ourcalculations k = 2..10 unless otherwise noted. Detailed descriptions and synthetic tests of themethod can be found in Unglert et al. (2016)).This analysis can be done (i) on data from one station only to identify the recurrence of similarprocesses over time; (ii) on data from a station network to identify spatio-temporal systematics ofcertain spectral patterns related to, for example the station location relative to volcanic activity;or (iii) on data from a combination of stations from different volcanoes to identify systematic dif-ferences or similarities among distinct volcanic settings. Because the temporal evolution at eachindividual station can also be obtained when analyzing the entire network, we focus on cases (ii)and (iii).For both analysis scenarios, there are several ways of visualizing the results. For each case,we show variance explained by each mode (Fig. 4.3(a))and the CRMS,k distribution to determinethe ideal number of clusters k (Fig. 4.3(b)). The clustering of observations (i.e., each spectrum intime) in PC space and the median of each cluster (Fig. 4.3(c)) is used to obtain the associated recon-structed spectrum for each cluster (Fig. 4.3(d)). Clusters are colored according to their position inPC space and their similarities in terms of spectral character. We then examine the occurrence of thedifferent clusters in space: In Figure 4.3(e), we show histograms with the number of observationsfrom a given cluster at each station, including a station map for reference. For each volcano, weorder the stations by approximate distance from their respective center of activity (small numbersnext to station names in histogram, Fig. 4.3(e)).For Kı¯lauea, because of the long spatial extent of the East Rift Zone with various active partsat different times during the eruptions in 2007, 2008, and 2011, our reference point is the summitvent. At Okmok, the center of activity is defined as the region in the caldera from which the 2008eruption originated. At Pavlof, we use the summit as our reference location, and at Redoubt wemeasure the distance from the approximate center of the summit crater11.At an individual station, the histogram can be used to compare the different clusters to each otherin terms of their numbers, and to determine the most common cluster(s). Similarly, the number ofdetections in each cluster can be compared between the different stations to investigate differencesdepending on the station location.To assess the temporal evolution of tremor properties and their timing relative to eruptive eventsit is useful evaluate time series of detection rates and the cluster that each detection is associatedwith (Fig. 4.4). For each station, we show the temporal evolution of the tremor detection rateas the number of detections per hour, which can reach a maximum of twelve 5-minute tremorwindows (black solid curves at the bottom of each panel). Conceptually, this metric is similar tomeasurements of average seismic amplitude in time (e.g., real time seismic amplitude measurement11We do not use the location of dome growth from the 2009 eruption because the exact source location of the precursoryhydrothermal phase may not be the same.784.4. Spectral Pattern Recognition−0.1 −0.05 0 0.05 0.1−0.05−0.04−0.03−0.02−0.0100.010.020.030.040.05  principal component 1 principal component 21234567891011cluster0 5 10 15 2000.050.10.150.20.25cluster number kC RMS100 101 102010203040506070mode numberpercentage of variance explained(a) (b)(c)1 2 3 4 5 6 7 8 9 10 11020040060080010001200140016001800119427325610213454 55611685 160548detections in each clusterKNH (12.1 km)1 2 3 4 5 6 7 8 9 10 1100.511.522.5 x 1043 172 28583320478110010 326 0 10 208detections in each clusterOTL (2.1 km)1 2 3 4 5 6 7 8 9 10 11020004000600080001000012000140001 388794881291625031139120 297684detections in each clusterSTC (16.5 km)1 10−0.01−0.00500.0050.010.0150.020.0250.030.0350.04frequency (Hz)normalized spectral power (dB)  cluster 1cluster 2cluster 3cluster 4cluster 5cluster 6cluster 7cluster 8cluster 9cluster 10cluster 112 3 4 5 6 8(d)1 2 3 4 5 6 7 8 9 10 1100.511.52 x 10488195180 6881206148421 154641494643detections in each clusterAHU (4.1 km)1 2 3 4 5 6 7 8 9 10 110100200300400500151390 149417 2120875460detections in each clusterPAU (7.7 km)(e)AHUKNHOTL PAU STC−155˚15' −155˚10'5 km19˚20'19˚25'East Rift Zonedike intrusions & eruptions, 2007 & 2011summit calderaFigure 4.3: PCA and clustering results for network analysis at Kı¯lauea, 2007, 2008, and 2011.(a) Variance explained by each mode. Grey shaded area indicates modes excluded from furtheranalysis. (b) Cluster evaluation by examining cross-correlation coefficients indicates best clusteringfor k = 11. (c) Clustering of observations in space spanned by first two modes. Asterisk withincluster indicates location of median used to reconstruct spectra. (d) Reconstructed spectra for eachcluster. (e) Number of tremor detections associated with each cluster at each station, includingstation map. Stations ordered from West to East, with increasing distance from Kı¯lauea’s summit(small number next to station name).794.4. Spectral Pattern Recognitionor RSAM, Murray and Endo, 1989). As we show in the following sections, the detection rates area simple and useful proxy for tremor activity.05/13 05/27 06/10 06/24/20071234567891011OTL (West)0.950.960.980.720.970.960.9312/hrintrusion start intrusion enderuptionstart & endcluster number05/13 05/27 06/10 06/24/20071234567891011AHU0.990.980.980.960.990.9112/hrcluster number05/13 05/27 06/10 06/24/20071234567891011timeSTC (East)0.980.960.990.990.960.9312/hrcluster number05/13 05/27 06/10 06/24/20071234567891011PAU0.970.960.940.950.980.9712/hrcluster number05/13 05/27 06/10 06/24/20071234567891011KNH0.970.980.950.400.980.940.970.960.8712/hrcluster number(a) (b)(c) (d)(e)Figure 4.4: Clustering time series for network analysis at Kı¯lauea, 2007. Stations (a) OTL, (b)AHU, (c) PAU, (d) KNH, and (e) STC, ordered from West to East. For each station, colored timeseries shows best cluster (values between 1–11). Small offset from cluster number shows alignmentbetween cluster spectrum and actual spectrum observed at the time, where the colored dashed lineindicates perfect alignment. Mean alignment cos(φ) for each cluster shown as colored numberon the right of each time series. Black line at the bottom of the cluster time series shows tremordetection rate at each station, with horizontal dotted line indicating the maximum of twelve tremorwindows detected during the preceding hour. Vertical dotted lines indicate important dates. Formore details see main body of text.Furthermore, we introduce the angle between two spectral vectors (i.e., a measure of their or-thogonality) as a quantitative measure for the similarity of each observed spectrum S with thecorresponding cluster spectrum R by measuringcos(φ) =S ·R||S||||R|| . (4.2)Each detection is then slightly offset from the level of its associated cluster by a value of 0.5 ·cos(φ). The dashed colored line slightly above each cluster level indicates a perfect alignment of0.5 · cos(0◦) = 0.5. The offset from this line can thus be used to assess how representative a givencluster is for the actual observation at the time. The mean value of cos(φ) over all times indicateshow well a given cluster represents its associated spectra at each station, and is shown as colorednumber on the right of the time series. In addition, to evaluate the temporal evolution of eachspectral pattern relative to eruptive activity, for example, we indicate the timing of important eventsas vertical dotted lines (Fig. 4.4).In summary, with these metrics it is possible to assess the number and character of spectral804.4. Spectral Pattern Recognitionpatterns as well as their manifestation in space and time. We summarize the results from the analysisof each station network individually in Section 4.4.2, and from the combined analysis of one stationfrom each of the different volcanic settings in Section 4.4.3.4.4.2 PCA for Multiple Stations at Individual SettingsTo explore processes occurring at different locations on individual volcanoes, we apply our tech-nique to station networks at Kı¯lauea, Okmok, Pavlof, and Redoubt, respectively. By analyzing ourdata in the space of the first two modes, we account for 80.6% of the variance at Kı¯lauea, 76.0% atOkmok, 79.0% at Pavlof, and 70.6% at Redoubt. The differences in variance may indicate differ-ent levels of white noise, where more noise results in a decrease in variance explained by the firstfew modes because of even contributions of the noise to all modes/dimensions (cf. Unglert et al.,2016)).Kı¯laueaTo evaluate the success of our pattern recognition approach, we first analyze data from five stationsat Kı¯lauea between 2007–2008 and fromMarch 2011 that each record distinct tremor signals relatedto volcanic unrest (Unglert and Jellinek, 2015). On the basis of the first two modes in PC space,CRMS,k indicates k = 10. Because this value corresponds to the maximum of the range tested(k = [2..10]) and can thus not reliably be identified as a local maximum, we extend the range of kup to 20 and obtain the ideal k = 11 (Fig. 4.3).This ideal k = 11, the proximity of the clusters in PC space, and the similarity of the overallshapes and alignment of individual peaks of the different cluster spectra (Fig. 4.3(b)–(d)) indicatethat the clusters are mainly representing end members and stages of different regimes, rather thancompletely independent patterns. Because of the similarities of their individual frequency peaksand spectral slopes, we qualitatively divide the clusters into three categories:1. The green regime includes clusters 1, 2, 9, 10 with relatively steep slopes of spectral powerdecaying from low to high frequencies.2. The blue regime includes clusters 4, 5, 6 with slightly flatter slopes compared to the greengroup.3. The red regime includes clusters 7, 8, 11 with a ridge (or broad peak) of spectral powerbetween 1–4 Hz and a decay towards higher frequencies.In addition to the three regimes, cluster 3 is treated independently because it has features from boththe red and the blue regimes. In Figure 4.3(e), the number of detections per cluster and stationsshows that the blue and green regimes are dominant in the West, whereas the red regime appearsmostly in the East.Figures 4.4, 4.5, and 4.6 show the presence/absence of the 11 different characteristic spectra ateach station in time. We summarize the results for each time period separately.814.4. Spectral Pattern RecognitionDuring May and June 2007, the westernmost station OTL shows no large amount of detectionsup to the beginning of the Father’s Day intrusion on 17 June 2007 (Fig. 4.4(a)). Tremor detectionrates gradually increase over approximately 1 day, and then stay close to the maximum until 4 daysafter the onset of the intrusion, when they rapidly drop to zero over the course of 2 hours. Thespectra accompanying these high detection rates are dominantly from the blue regime, but alsoinclude detections from the red regime. The only other significant tremor activity at OTL occursduring a short spike of detection rates around 26 June.At STC, the easternmost station, the results differ strongly (Fig. 4.4(e)). Tremor detection ratesare consistently high before the intrusive episode, and drop rapidly with the onset of the intrusion.Whereas at STC the red regime is dominant, the same time period at KNH (Fig. 4.4(d)) is markedmostly by clusters from the green regime. The detection rates at KNH are slightly lower than atSTC, and fluctuate on a timescale of hours to days.None of the other stations further West towards OTL show consistent pre-intrusion detections(Fig. 4.4(b)–(c)). However, after the onset of the Father’s Day intrusion on 17 June 2007, all ofthe western stations exhibit several days of tremor detections that generally persist after the endof the eruption and the cessation of intrusion (Fig. 4.4(a)–(c)). Tremor rates appear to decreasewith increasing distance from OTL during the intrusion. Most associated spectra belong to theblue regime, but also include contributions from the green and red regimes. Cluster 3 (purple) isobserved for two days (not directly) following the small eruption on 19 June 2007 (Poland et al.,2008; Fee et al., 2011b) at KNH (Fig. 4.4(d)).2008 200912345678910110.940.960.720.930.980.970.980.960.95OTL (West)12/hrdegassing burstscluster number2008 200912345678910110.970.990.910.980.960.980.980.990.990.98AHU12/hrcluster number2008 20091234567891011PAU0.970.950.940.980.9712/hrcluster number2008 20091234567891011KNH0.970.960.870.950.940.980.980.9712/hrcluster number2008 200912345678910110.930.930.670.960.940.990.990.960.98timeSTC (East)12/hrcluster number(a) (b)(c) (d)(e)Figure 4.5: Clustering time series for network analysis at Kı¯lauea, 2008. For caption see Figure 4.4.Throughout the rest of 2007 and 2008 (Fig. 4.5), tremor with characteristic spectra similar tothe pre-intrusion tremor in 2007 appear at stations STC (red regime, Fig. 4.5(e)) and KNH (green824.4. Spectral Pattern Recognitionregime, Fig. 4.5(d)), the two easternmost stations. Whereas PAU is marked by low detection rates(Fig. 4.5(c)), high detection rates occur at OTL and AHU in the West (Fig. 4.5(a)–(b)), closest to thesummit. The predominant clusters there belong to the green and blue regimes, with no systematicchanges over time. Detections at AHU generally correspond to detections at OTL, with slightlyhigher detection rates at OTL compared to AHU. Similarly, STC and KNH show detections at thesame time, with higher rates at STC compared to KNH (Fig. 4.5(d)–(e)). There appears to be norelationship between any of the characteristic spectra and the degassings bursts (Fee et al., 2010)during this time period.In 2011, no significant episodes of pre-intrusion tremor detections are observed at any station(Fig. 4.6). However, after the onset of the intrusion, just before 6 March 2011 (Lundgren et al.,2013; Orr et al., 2015), tremor mostly belonging to the blue and red regimes is observed at stationsOTL through KNH (Fig. 4.6(a)–(d)). These stations show a trend of spectra increasingly evolvingfrom blue to red over time, where stations further East show earlier occurrences of spectra belongingto the red regime than stations in the West. Tremor at OTL and AHU persists after the end of theeruption (Fig. 4.6(a)–(b)). Station STC is dominated by the blue regime and cluster 3, with thefirst detection directly at the time of the onset of intrusion, and the beginning of nearly continuousdetections (Fig. 4.6(e)) just after the start of the fissure eruption early on 6 March 2011 (Orr et al.,2015). Both at STC in 2011 and KNH in 2007, cluster 3 appears to be less well aligned on averagewith the observed spectra than the other clusters (cos(φ) ∼0.4, Figs. 4.4(d) and 4.6(e))). Otherwisecluster 3 only occurs a few times at station OTL during all three time periods.03/06 03/07 03/08 03/09 03/10/20111234567891011OTL (West)0.720.930.980.970.9512/hreruption start eruption endintrusionstartcluster number03/06 03/07 03/08 03/09 03/10/201112345678910110.970.950.960.940.970.97PAU12/hrcluster number03/06 03/07 03/08 03/09 03/10/201112345678910110.960.950.940.960.980.980.97KNH12/hrcluster number03/06 03/07 03/08 03/09 03/10/201112345678910110.990.910.980.960.980.98AHU12/hrcluster number03/06 03/07 03/08 03/09 03/10/20111234567891011timeSTC (East)0.930.670.980.3612/hrcluster number(a) (b)(c) (d)(e)Figure 4.6: Clustering time series for network analysis at Kı¯lauea, 2011. For caption see Figure 4.4.834.4. Spectral Pattern RecognitionOkmokFigure 4.7 shows the PCA results for the five stations analyzed at Okmok Volcano during the 2008eruption. Our cluster evaluation criterion (Unglert et al., 2016)) suggests k = 6 as the ideal numberof clusters (Fig. 4.7(b)). However, CRMS,k only varies slightly among the different numbers ofclusters, and is generally low (CRMS,k = [0.02..0.05] from full possible range [0..2]), indicatingstrong correlations among the corresponding spectra. Similar to Kı¯lauea, the observations in thespace of the first two principal components form a relatively dense cloud without clear separationsbetween the different clusters (Fig. 4.7(c)). The reconstructed spectra are consequently relativelysimilar to each other (Fig. 4.7(d)), representing a continuum rather than independent, clearly sep-arated clusters. We divide them into a blue regime (clusters 3–6) with increasingly steeper slopesgoing from dark to light blue, and a green regime (clusters 1–2) with a ridge of high spectral powerbetween 1–4 Hz on the basis of common spectral peaks.Histograms of the total number of detections show that clusters 3 and 6 (dark blue) are morecommon close to the eruption site (< 10 km) than further away (Fig. 4.7(e)). In addition, the greenregime seems to occur at close and intermediate range (up to ∼ 10 km). In contrast, clusters 4 and5 (lighter blue) are observed mostly at stations further away (> 15 km).The temporal evolution of tremor detections and cluster memberships (Fig. 4.8) show thattremor is almost exclusively confined to the time of the eruption. Detection rates start to decrease atthe beginning of August, in particular at the stations furthest away from the eruption site (OKAK,OKSP, Fig. 4.8(d)–(e)), and go to zero at the end of the eruption on 19 Aug 2008 (Larsen et al.,2015). There are no systematic variations in terms of the temporal (dis-)appearance of the differentclusters. For example, no particular spectrum is associated with the period of higher detection ratesin July compared to the lower rates in August, or vice versa.PavlofAt Pavlof, our data include two different eruptions (Section 4.2). Figure 4.9 shows the results forthe combined PCA and cluster analysis. CRMS,k (Fig. 4.9(b)) has a maximum at k = 3. The largerabsolute values (up to 1.33) indicate that the reconstructed spectra are more distinct than they areat Kı¯lauea and Okmok. The observations in PC space (Fig. 4.9(c)) form at least three dispersedgroups, and the spectra corresponding to each of the three clusters show distinct characteristics:Cluster 1 (blue) has a ridge at relatively high frequencies (8–9 Hz), cluster 2 (purple) has a lowfrequency ridge (1–2 Hz) with a gentle decay towards higher frequencies, and cluster 3 (pink)exhibits a low frequency peak (1–2 Hz) with a steeper decay compared to cluster 2. This steeplydecaying cluster 3 spectrum appears to occur mostly on the stations towards the Southeast of thevolcano, whereas the gently decaying cluster 2 spectrum is observed at all stations to some extent.The high frequency cluster 1 regime is observed most often at station PVV.PN7A and HAG have very few detections during the 2007 eruption (Fig. 4.10), so the followingsummary will focus on the remaining three stations. There are no high tremor detection ratespreceding the 2007 eruption. Instead, tremor is detected almost exclusively during the eruption at844.4. Spectral Pattern Recognition−0.06 −0.04 −0.02 0 0.02 0.04 0.06−0.02−0.0100.010.02 principal component 1 principal component 2123456cluster−0.00500.0050.010.0150.020.0250.03frequency (Hz)normalized spectral power (dB) cluster 1cluster 2cluster 3cluster 4cluster 5cluster 61 102 3 4 5 6 81 2 3 4 5 6020040060080010001200140016001800618116516270 4816detections in each clusterOKWR (6.4 km)1 2 3 4 5 6050010001500200025000 469662362430detections in each clusterOKAK (16.8 km)01 2 3 4 5 601002003004005006001 0 17140577318detections in each clusterOKSP (23.8 km)1 2 3 4 5 605001000150020002500300028731318101 2 561081detections in each clusterOKRE (10.1 km)1 2 3 4 5 60500100015002000250030003500400056 3636430 92642detections in each clusterOKWE (9.6 km)100 101 102010203040506070mode numberpercentage of variance explained2 3 4 5 6 7 8 9 100.020.0250.030.0350.040.0450.05cluster number kC RMS(a) (b)(c)(e)OKWEOKWROKREOKSPOKAK−168˚30' −168˚00'53˚20'53˚30'5 km(d)Figure 4.7: PCA and clustering results for multistation analysis at Okmok, 2008. (a) Varianceexplained by each mode. Grey shaded area indicates modes excluded from further analysis. (b)Cluster evaluation by examining cross-correlation coefficients indicates best clustering for k = 6.(c) Clustering of observations in space spanned by first two modes. Asterisk within cluster indicateslocation of median used to reconstruct spectra. (d) Reconstructed spectra for each cluster. (e)Number of tremor detections associated with each cluster at each station, including station map.Stations ordered by increasing distance from eruption.854.4. Spectral Pattern Recognition07/05 07/19 08/02 08/16 08/30/20081234560.890.990.990.97timeOKAKcluster number12/hr07/05 07/19 08/02 08/16 08/30/20081234560.970.960.940.960.970.97timeOKREcluster number12/hr07/05 07/19 08/02 08/16 08/30/20081234560.970.890.980.980.97timeOKSPcluster number12/hr07/05 07/19 08/02 08/16 08/30/20081234560.970.970.980.980.99timeOKWEcluster number12/hr07/05 07/19 08/02 08/16 08/30/20081234560.970.950.970.970.98timeOKWReruption start eruption endcluster number12/hr(a) (b)(c) (d)(e)Figure 4.8: Clustering time series for network analysis at Okmok, 2008. For caption see Figure 4.4.all stations (Fig. 4.10). At PV6 and PS1A, the most common spectrum is the gently decaying regime(cluster 2, Fig. 4.10(a) and (d)). In contrast, at PVV, the high frequency ridge regime (cluster 1)is most commonly observed (Fig. 4.10(c)). Consistent with these differences in the predominantclusters, the angle between the observations at PVV and cluster 1 is lower than the angle for thesame cluster at the other stations where a few instances of this cluster are observed, indicating thatcluster 1 is a better representation of the observations at station PVV (cos(φ) ∼ 0.5 or φ ∼ 60◦, vs.cos(φ) < 0 or φ > 90◦ at all other stations). Similar to the observation of a distinct cluster at PVV,the detection rates at PV6 and PS1A show a slow increase in the amount of tremor detections fromthe onset of the eruption until early September (Fig. 4.10(a) and (d)), whereas the detection rates atPVV (Fig. 4.10(c)) show five pulses surrounded by a few hours to days of slightly lower detectionrates that do not follow the same temporal evolution as at the other stations.The detections during the 2013 eruption show two main pulses of high tremor rates maintainedfor a few hours to days (Fig. 4.11), one shortly after the onset of the eruption, and one during thefinal culminating eruptive phase (Waythomas et al., 2014). Similar to 2007, the gently decayingspectrum (cluster 2) is the most common tremor type during the eruption and observed at all sta-tions. Larger amounts of detections associated with the steeply decaying spectrum (cluster 3) areonly observed at stations PVV and PS1A (Fig. 4.11(a) and (c)). The high-frequency ridge regimeis not observed to a significant extent at any station during 2013, and the few occasions show largeangles between the cluster spectrum and the actual observed ones.864.4. Spectral Pattern Recognition−0.1 −0.05 0 0.05 0.1−0.06−0.04−0.0200.020.040.06  principal component 1 principal component 2123cluster2 3 4 5 6 7 8 9 1000.20.40.60.811.21.4cluster number kC RMS100 101 1020102030405060mode numberpercentage of variance explained(a) (b)(c)−0.0100.010.020.030.04frequency (Hz)normalized spectral power (dB)  cluster 1cluster 2cluster 31 102 3 4 5 6 8(d)PV6PVVPN7APS1AHAGPS4A−162˚30' −162˚00' −161˚30'55˚20'55˚30'5 km1 2 3020040060080010001200140023141373detections in each clusterPS1A (9.5 km)1 2 3020040060080010001200140016001800817791detections in each clusterPS4A (8.3 km)1 2 305010015020025030035040045004470detections in each clusterPV6 (4.3 km)1 2 30102030405060708044 4575detections in each clusterHAG (11.1 km)1 2 30100200300400500600284114524detections in each clusterPVV (8.1 km)1 2 30246810121416181741detections in each clusterPN7A (6.8 km)(e)Figure 4.9: PCA and clustering results for network analysis at Pavlof, 2007 and 2013. For captionsee Figure 4.7874.4. Spectral Pattern Recognition07/11 07/25 08/08 08/22 09/05 09/19 10/03 10/17/2007123timeHAG0.8112/hrcluster number07/11 07/25 08/08 08/22 09/05 09/19 10/03 10/17/2007123−0.160.700.97timePN7A12/hrcluster number07/11 07/25 08/08 08/22 09/05 09/19 10/03 10/17/2007123timePS1A−0.140.590.9812/hrcluster number07/11 07/25 08/08 08/22 09/05 09/19 10/03 10/17/20071230.94timePV612/hreruption start eruption endcluster number07/11 07/25 08/08 08/22 09/05 09/19 10/03 10/17/2007123timePVV0.540.860.9712/hrcluster number(a) (b)(c) (d)(e)Figure 4.10: Clustering time series for network analysis at Pavlof, 2007. For caption see Figure 4.4.05/01 05/15 05/29 06/12 06/26 07/10 07/24/2013123−0.040.960.94timePS4A12/hrcluster number05/01 05/15 05/29 06/12 06/26 07/10 07/24/2013123−0.060.810.97timeHAG12/hrcluster number05/01 05/15 05/29 06/12 06/26 07/10 07/24/2013123−0.140.590.98timePS1A12/hrcluster number05/01 05/15 05/29 06/12 06/26 07/10 07/24/20131230.540.860.97timePVV12/hreruption start eruption enderuption hiatuscluster number(a) (b)(c) (d)Figure 4.11: Clustering time series for network analysis at Pavlof, 2013. For caption see Figure 4.4.884.4. Spectral Pattern RecognitionRedoubtThe variance explained by the first two modes at Redoubt in 2009 is slightly smaller (Fig. 4.12(a))than at Kı¯lauea, Okmok, and Pavlof. The observations can be clustered with an ideal k = 7(Fig. 4.12(b)). In PC space, the observations form one big cloud that is less dense and showsclearer separation of the clusters than at Okmok, for example (Fig. 4.12(c) vs. Fig. 4.7(c)). Withinthis cloud, the clusters capture several regimes, whose differences with respect to each other appearto be stronger than at Kı¯lauea and Okmok (Fig. 4.12(c)). This pattern is confirmed by the differentreconstructed spectra (Fig. 4.12(d)). We divide the clusters into three main categories:1. The red regime includes clusters 1, 2 and 7 and has a low-frequency (1–5 Hz) plateau ofrelatively high spectral power with peaks around 3–5 Hz.2. The dark blue regime includes cluster 5 and has a narrow ridge between 1–2 Hz, from wherespectral power decays gently towards higher frequencies.3. The light blue regime includes cluster 6 and has the same ridge as in the dark blue regime, butless well defined. In addition, the light blue regime shows shows a kink in the slope around5 Hz.4. The green regime includes clusters 3 and 4 and shows an even narrower ridge around 2 Hzcompared to the blue regimes, with a steeper decay of spectral power from just above 2 Hztowards higher frequencies.In terms of absolute numbers of detections, the red and the light blue regimes become lesscommon with increasing distance from the volcanic edifice (Fig. 4.12(e)). In contrast, the dark blueand the green regimes are more common further away from the summit of the volcano.The temporal evolution reveals two main phases of tremor detections (Fig. 4.13). During thefirst phase, between late January and late February 2009 approximately one month before the onsetof the eruption, a large number of detections coincides with a known period of elevated seismicamplitudes (Buurman et al., 2012; Power et al., 2013). This precursory phase shows the highestdetection rates at station REF (Fig. 4.13(a)), and decreases in terms of detection rates with increas-ing distance from volcano. Only few detections (Fig. 4.13) accompany the time period between theonset of the phreatic and the magmatic explosive phases of the eruptions in mid-March 2009 (fordetails about the eruptive phases see e.g., Bull and Buurman, 2012). The subsequent magmatic ex-plosive phase shows consistent detections at most stations. After the cessation of explosive activity,no notable tremor detections occur during dome growth.Spectra from the blue and the red regimes are observed during the precursory phase with de-creasing frequency of occurrence for each spectrum with increasing distance from the summit(Figs. 4.12(e) and 4.13(a)–(c)). During the magmatic explosive phase, all tremor types are observedat one or more stations. Whereas the red regime tends to be confined to stations close to the volcano(Fig. 4.13(a)–(b)), the green regime is observed mostly at larger distances (Fig. 4.13(c)–(d)), in linewith the trend observed in Figure 4.12(e).894.4. Spectral Pattern Recognition−0.06 −0.04 −0.02 0 0.02 0.04 0.06−0.06−0.04−0.0200.020.040.06 principal component 1 principal component 21234567cluster1 2 3 4 5 6 70204060801001206841102450detections in each clusterDFR (12.3 km)001 2 3 4 5 6 70204060801001201406137498 4detections in each clusterNCT (12.3 km)001 2 3 4 5 6 7020406080100120140160180125622063169 150detections in each clusterRDN (4.1 km)1 2 3 4 5 6 7050100150200250300812331 032282145detections in each clusterREF (3.9 km)100 101 102051015202530354045mode numberpercentage of variance explained−0.00500.0050.010.0150.020.025frequency (Hz)normalized spectral power (dB)  cluster 1cluster 2cluster 3cluster 4cluster 5cluster 6cluster 71 102 3 4 5 6 82 3 4 5 6 7 8 9 100.10.110.120.130.140.150.160.170.180.190.2cluster number kC RMS(a) (b)(c) (d)RDNREFNCTDFR−153˚00' −152˚30'60˚20'60˚30'60˚40'5 km(e)Figure 4.12: PCA and clustering results for network analysis at Redoubt, 2009. For caption seeFigure 4.7904.4. Spectral Pattern RecognitionFeb Mar Apr May Jun 200912345670.860.960.950.870.93timeNCTJan12/hrprecursorendphreaticphase magmaticphase startexplosivephase endcluster numberprecursoronsetJan Feb Mar Apr May12345670.960.960.790.970.960.960.97timeRDNJun 2009cluster number12/hrJan Feb Mar Apr May12345670.960.970.860.960.940.98timeREFJun 2009cluster number12/hrFeb Mar Apr May Jun 200912345670.950.970.970.95timeDFRcluster numberJan12/hr(a) (b)(c) (d)Figure 4.13: Clustering time series for network analysis at Redoubt, 2009. For caption see Fig-ure 4.4. Note event labels in (d) instead of (a) to avoid cluttering.4.4.3 PCA for Comparison Between Volcanic SettingsTo investigate similarities and differences among the volcanic settings, we apply the pattern recogni-tion algorithm to a combined dataset with one station from each of the four volcanoes. To minimizecomplications related to differences in travel path length of the signals from their source to the seis-mometer, we base our station choice on the distance from the center of volcanic activity. Applyingthe reference center points for each volcano defined in Section 4.4.1, we generate two groups ofstations at approximately equal distances from their respective volcanic centers:• The first subset of stations (proximal: 4 km distance) includes AHU (Kı¯lauea, ∼4.1 km),PV6 (Pavlof, ∼4.3 km) and REF (Redoubt, ∼3.9 km). The closest station at Okmok fromthe network approach in Section 4.4.2 is located at over 6 km distance, and is thus excludedfrom the analysis.• The second subset of stations (distal: 8–10 km distance) includes PAU (Kı¯lauea, ∼7.7 km),OKWE (Okmok,∼9.6 km), and PVV (Pavlof, ∼8.1 km). Unfortunately, none of the Redoubtstations analyzed in Section 4.4.2 is at a comparable distance even when considering thelarger spread of distances compared to the first group.The results from these two subsets of stations are summarized in the following sections. Be-cause the number of detections at Kı¯lauea station AHU is at least one order of magnitude higherthan for the stations from the other volcanoes, and because there are no significant, systematic vari-ations in the data from AHU and PAU between July 2007–December 2008 (Fig. 4.5), we restrictthe data from the Kı¯lauea stations to May–June 2007, March–April 2008, and the week around theintrusion in 2011. This shorter dataset includes 12,676 detections for AHU and 929 detections forPAU.914.4. Spectral Pattern RecognitionProximal Tremor Properties: 4 km DistanceFigure 4.14 summarizes the PCA and clustering results for the proximal stations. The first twomodes explain 78.5% of the variance (Fig. 4.14(a)), similar to the individual networks. As in Sec-tion 4.4.2, we extend the range of k up to 20. The resulting distribution shows k = 16, whichis larger than the values obtained in any of the individual network analyses. Clustering the ob-servations with k = 16 in PC space (Fig. 4.14(c)) and reconstructing the corresponding spectra(Fig. 4.14(d)) reveals similarities among the majority of patterns, suggesting that k = 16 may betoo large. In such a case where the ideal k is ill-defined, the automated algorithm requires interven-tion (Unglert et al., 2016)). The first local maximum of CRMS,k occurs for k = 3 (Fig. 4.14(b)) andwe thus hypothesize that k = 3 is more appropriate and can capture the main patterns. In supportof this value, the points in Figure 4.14(c) appear to form three main clouds, which agrees with theoccurrence of three main distinct spectral shapes in Figure 4.14. These observations indicate thatour estimated k = 3may be a good choice that qualitatively reproduces the essential features buriedin the results for k = 16.Manually setting k = 3 and subsequent application of the clustering algorithm (Fig. 4.15)confirms the patterns visually determined for k = 16 (cf. Fig. 4.14). The observations in PC space(Fig. 4.15(a)) are clustered in a way very similar to the three main groups visible in Figure 4.14(c),and the corresponding spectra capture the same main features detected with k = 16. We thus focuson the manually adjusted k = 3 for the following summary and interpretation.The three spectra in Figure 4.15(b) are a spectrum with a relatively steep decay from low to highfrequencies (cluster 3), a spectrum with a low frequency ridge at approximately 1 Hz (cluster 1),and a spectrum with a narrower peak close to 3 Hz (cluster 2). The peaked cluster 2 spectrumappears to occur mostly at Pavlof and Redoubt, whereas the other two are both relatively commonat Kı¯lauea (Fig. 4.15(c)).The temporal evolution of the clusters at each station for this configuration is shown in Fig-ure 4.16. With this smaller number of clusters compared to the individual network analyses (Sec-tion 4.4.2), the variations of the observations at AHU are captured by two clusters only (clusters 1and 3). Whereas cluster 1 dominates during both intrusions (2007 and 2011, Fig. 4.16(a) and (c)),cluster 3 is the dominant spectrum during 2008 (Fig. 4.16(b)). This spectrum is observed almostexclusively at Kı¯lauea with over 10,000 detections, compared to 4 and 10 detections at Pavlof andRedoubt, respectively (Fig. 4.15(c)). In contrast, cluster 2 is only observed at Pavlof and Redoubt,which both also show occurrences of cluster 1 (Fig. 4.16(d)–(e)). Whereas cluster 2 is dominant atPavlof and during the precursory tremor phase at Redoubt, cluster 1 appears predominantly duringthe eruptive phase at Redoubt. To investigate whether those differences are related to the distance orlocation of the stations relative to the volcanic centers, we analyze the distal stations in the followingsection.924.4. Spectral Pattern Recognition−0.00500.0050.010.0150.020.0250.030.0350.04frequency (Hz)normalized spectral power (dB) cluster 1cluster 2cluster 3cluster 4cluster 5cluster 6cluster 7cluster 8cluster 9cluster 10cluster 11cluster 12cluster 13cluster 14cluster 15cluster 161 102 3 4 5 6 8−0.05 0 0.05−0.04−0.03−0.02−0.0100.010.020.030.040.05 principal component 1 principal component 224681012141613579111315cluster0 5 10 15 200.060.080.10.120.140.160.18cluster number kC RMS100 101 1020102030405060mode numberpercentage of variance explained(a) (b)(c) (d)Figure 4.14: PCA and clustering results for combined analysis, for proximal stations (4 km). (a)Variance explained by each mode. Grey shaded area indicates modes excluded from further analy-sis. (b) Cluster evaluation by examining cross-correlation coefficients indicates best clustering fork = 16. (c) Clustering of observations in space spanned by first two modes. (d) Reconstructedspectra for each cluster. Similarities among the 16 spectra in (d), point clouds in (c), and first lo-cal maximum of CRMS,k for k = 3 (additional dotted circle in (b)) suggest alternative option forchoosing k, with corresponding results shown in Figure 4.15. For details see main body of text.934.4. Spectral Pattern Recognition−0.06 −0.04 −0.02 0 0.02 0.04 0.06−0.06−0.04−0.0200.020.040.06 principal component 1 principal component 2123cluster1 2 3050100150200250300350400450184254detections in each clusterPV61 2 305010015020025030035040045050029546910detections in each clusterREF1 2 30200040006000800010000120002248010428detections in each clusterAHU−50510152025x 10−3frequency (Hz)normalized spectral power (dB)  cluster 1cluster 2cluster 31 102 3 4 5 6 8(a) (b)(c)Figure 4.15: Clustering results for combined analysis, for proximal stations (4 km), for 3 clusters.(a) Clustering of observations in space spanned by first two modes. Asterisk within cluster indicateslocation of median used to reconstruct spectra. (b) Reconstructed spectra for each cluster. (c)Number of tremor detections associated with each cluster at each station.Distal Tremor Properties: 8–10 km DistanceFor the distal stations, the first two PCAmodes explain 80.2% of the variance (Fig. 4.17(a)). CRMS,kreveals the ideal k = 3 (Fig. 4.17(b)), which corresponds to the manually adjusted value for theclose range stations. The three clusters are well separated in PC space (Fig. 4.17(c)), and thecorresponding reconstructed spectra capture distinct spectral shapes (Fig. 4.17(d)). Cluster 2 (blue)is similar to cluster 1 from the proximal stations (blue, Fig. 4.15(b)), with a plateau of high spectralpower that falls off above 2 Hz. Cluster 3 (orange) has the same steep decay of spectral powerfrom approximately 2 Hz to higher frequencies that can be observed in cluster 3 from the proximalstations (orange, Fig. 4.15(b)), but with a pronounced peak in the 1–2 Hz band, and a distinctflattening of the curve above 6 Hz. Cluster 1 (purple) is similar to cluster 2 from the proximalsubset (red, Fig. 4.15(b)), with increased spectral power at higher frequencies than the other twocluster spectra, but its peak is shifted even further to the right to approximately 9–10 Hz comparedto station subset 1.Cluster 1 is observed almost exclusively at Pavlof station PVV (Fig. 4.17(e)). A similar, albeitslightly weaker trend is observed for the steeply decaying cluster 3 spectrum, which occurs over 600times at Pavlof, compared to 52 and 0 detections at Kı¯lauea and Okmok, respectively (Fig. 4.17(e)).Those settings are dominated by cluster 2.The temporal evolution (Fig. 4.18) also shows similarities to the more proximal stations (Fig. 4.16).Kı¯lauea station PAU is dominated by cluster 2 during the intrusions (Fig. 4.18(a) and (c)), the same944.4. Spectral Pattern RecognitionJan Feb Mar Apr 20091230.930.940.95timeREFcluster number12/hrprecursoronsetprecursorendphreaticphasemagmaticphase startexplosivephase end06/16 06/17 06/18 06/19 06/20 06/21 06/22 06/23/2007123timeAHUcluster number0.970.9912/hrintrusion enderuptionstart & endintrusionstart03/01 03/15 03/29 04/12 04/26/2008123timeAHUcluster number0.970.9912/hrdegassing bursts03/05 03/06 03/07 03/08 03/09 03/10 03/11/20111230.970.99timecluster numberAHU12/hreruption start eruption endintrusionstart07/22 08/05 08/19 09/02 09/16/20071230.850.960.65timePV6cluster number12/hreruption start eruption end(a) (b)(c) (d)(e)Figure 4.16: Clustering time series for combined analysis, proximal stations (4 km). For eachstation, colored time series shows best cluster (values between 1–3). Small offset from clusternumber shows alignment between cluster spectrum and actual spectrum observed at the time, wherethe colored dashed line indicates perfect alignment. Mean alignment cos(φ) for each cluster shownas colored number on the right of each time series. Black line at the bottom of the cluster time seriesshows tremor detection rate at each station, with horizontal dotted line indicating the maximum oftwelve tremor windows detected during the preceding hour. Vertical dotted lines indicate importantdates. For more details see main body of text.954.4. Spectral Pattern Recognition−0.1 −0.05 0 0.05 0.1−0.06−0.04−0.0200.020.040.06  principal component 1 principal component 2123cluster1 2 3010020030040050060070028522615detections in each clusterPVV1 2 301000200030004000500060007000063860detections in each clusterOKWE1 2 30100200300400500600700800900187652detections in each clusterPAU−0.00500.0050.010.0150.020.0250.03frequency (Hz)normalized spectral power (dB)  cluster 1cluster 2cluster 31 102 3 4 5 6 82 3 4 5 6 7 8 9 1000.511.5cluster number kC RMS100 101 10201020304050607080mode numberpercentage of variance explained(a) (b)(c) (d)(e)Figure 4.17: PCA and clustering results for combined analysis, for distal stations (8–10 km). (a)Variance explained by each mode. Grey shaded area indicates modes excluded from further analy-sis. (b) Cluster evaluation by examining cross-correlation coefficients indicates best clustering fork = 3. (c) Clustering of observations in space spanned by first two modes. Asterisk within clusterindicates location of median used to reconstruct spectra. (d) Reconstructed spectra for each cluster.(e) Number of tremor detections associated with each cluster at each station.964.5. Discussionas the equivalent spectrum at AHU from the proximal stations (Fig. 4.16(a) and (c)). Similarly,cluster 3 is the only spectrum observed in 2008 (Fig. 4.18(b)). In agreement with the relativelysmall differences between the spectra from the network analysis at Okmok (Figs. 4.7 and 4.8), sta-tion OKWE is marked by cluster 2 only (Fig. 4.18(d)). Whereas the 2007 eruption at Pavlof showsmostly cluster 1 spectra at PVV, the detections during the 2013 eruption at the same station belongdominantly to cluster 3 (Fig. 4.18(e)–(f)).07/05 07/19 08/02 08/16 08/30/20081230.99timeOKWEcluster number12/hreruption start eruption end03/05 03/06 03/07 03/08 03/09 03/10 03/11/2011123−0.320.960.96timePAUcluster number12/hreruption start eruption endintrusionstart03/01 03/15 03/29 04/12 04/26/2008123timePAU0.96cluster number12/hrdegassing bursts06/16 06/17 06/18 06/19 06/20 06/21 06/22 06/23/2007123timePAU0.960.96cluster number12/hrintrusion enderuptionstart & endintrusionstart07/22 08/05 08/19 09/02 09/16/2007123timePVVcluster number0.710.890.9712/hreruption start eruption end05/01 05/15 05/29 06/12 06/26 07/10 07/24/20131230.710.890.97timePVVcluster number12/hreruption start eruption enderuption hiatus(a) (b)(c) (d)(e) (f)Figure 4.18: Clustering time series for combined analysis, distal stations (8–10 km). For captionsee Figure 4.16.4.5 DiscussionOur pattern recognition approach shows interesting results both for the individual network analysesand the investigation of common patterns between the different volcanic settings. In the followingsections, we first discuss the observations related to distinct spectral patterns at each of the locationsindividually (Sections 4.5.1–4.5.4). Next, we explore the implications of the results for our tremordetection algorithm (Section 4.5.5). Last, we discuss similarities and differences between tremor atdifferent volcanic settings the basis of the multi-setting analysis and the lessons learned in terms ofour approach (Section 4.5.6).4.5.1 Kı¯lauea: 2007, 2008, 2011Several of our observations at Kı¯lauea confirm the results obtained through manual analysis byUnglert and Jellinek (2015). In particular, we confirm the presence of pre-intrusion tremor in974.5. Discussion2007 at the eastern stations (Fig. 4.4(d)–(e)). Furthermore, syn-intrusion tremor in 2007 and 2011dominant at the western stations near the summit (Figs. 4.4(a)–(c) and 4.6(a)–(c)) is consistent withthe second phase of continuous tremor observed by Unglert and Jellinek (2015). A lack of changesin spectral character associated with the more explosive degassing bursts at the summit lava lakein 2008 (Fig. 4.5), and the lack of any pre-intrusion signals in 2011 (Fig. 4.6) were also observedby Unglert and Jellinek (2015). The absence of high tremor detection rates in the early phasesof the intrusions is expected because of the findings that the first phase of seismicity consists ofdiscrete events (Unglert and Jellinek, 2015), which our detection algorithm excludes from analysis(Section 4.3.2).The similarity of detection rates during all years at the two western and the two eastern stations,respectively, where the westernmost (OTL) and easternmost stations (STC) show the highest rates,confirms that potentially shallow processes at the summit and in the East Rift Zone (Fig. 4.3(e)) cangenerate different, localized seismicity patterns (Unglert and Jellinek, 2015).At any given time, several clusters are observed at individual stations, almost simultaneously(e.g., several clusters within blue regime at station OTL in 2008, Fig. 4.5(a)). Similarly, differentstations show different clusters that appear to coincide in time (e.g., red regime at STC before 2007intrusion vs. green regime at KNH during the same time period, Fig. 4.4(d)–(e)). These resultssuggest that the same processes can be expressed in different ways at one station, or at two stationslocated relatively close to each other. In addition, because the clusters are not well separated inPC space (Fig. 4.3(c)), and because the changes from one cluster spectrum to the next in somecases appear to capture small variations in the slope without altering the main spectral shapes, wesuggest that k = 11 does not correspond to the actual number of independent processes. Instead,the large number of clusters may represent different stages or end members of only a few processesactive concurrently. The spectra associated with the clusters within each of the three main regimesmostly differ in terms of their spectral slopes, but share common frequency peaks. This suggeststhat the systematic differences between stations may relate to path and location effects, where agiven process generates slightly different spectra depending on the distance between the stationto the source, for example. Similarly, the near simultaneous occurrence of different clusters atindividual stations may stem from small fluctuations of the underlying source process. We discussthese observations in more detail in Section 4.5.6.Among the 11 clusters obtained for Kı¯lauea, we do not include cluster 3 (purple) in the threemain regimes (Section 4.4.2). This omission is related to its spectral character that appears to bein-between the blue and the red regimes (Fig. 4.3(d)), to its generally poorer alignment with theobserved spectra compared to the other clusters (Figs. 4.4, 4.5, and 4.6), and to its occurrencemostly confined to stations KNH (2007) and STC (2011) (Figs. 4.4(d) and 4.6(e)). Unglert andJellinek (2015) attribute a localized signal at STC in 2011 to a shallow source potentially directlyrelated to magma flow dynamics of the ongoing fissure eruption. Because cluster 3 is observed atSTC in 2011 (Fig. 4.6(e)) and KNH in 2007 (Fig. 4.4(d)), where STC is closest to the eruption sitein 2011 and KNH in 2007, respectively, it is possible that this eruption related source process isactive at those stations close to the eruptive fissures. However, a more detailed view of the temporal984.5. Discussionevolution (Fig. 4.19) relative to the start and end times of the intrusions and eruptions reveals thatthe cluster 3 signal is detected after the end of the main intrusion period and after the short eruptionat KNH (Fig. 4.19(a)). Similarly, the corresponding signal at STC starts earlier but persists afterthe end of the eruption (Fig. 4.19(b)). There is a systematic initial decrease of alignment betweenthe observed spectra and the typical cluster 3 pattern, followed by a shorter increase in alignmentat both stations, which, together with the previous similarities, indicates a common source process.The manual analysis by Unglert and Jellinek (2015) did not allow such detailed investigation ofthese signals. The new observations provide improved constraints on plausible source mechanism,and imply that processes directly related to the surface expression of the eruption as suggested byUnglert and Jellinek (2015) (e.g., lava spattering Patrick et al., 2011b) cannot fully explain ourobservations.06/19 06/20 06/21 06/22 06/23/200723456timeKNHeruption start & endintrusion endcluster number03/05 03/06 03/07 03/08 03/09 03/10 03/11 03/12/20112345timeeruption start eruption endintrusion start STCcluster number(a)(b)Figure 4.19: Zoom into temporal evolution of main clusters during intrusions at Kı¯lauea in (a) 2007at KNH, and (b) 2011 at STC. Vertical level of observations indicates cluster number. Small offsetshows alignment between cluster and observed spectra, where +0.5 is perfect alignment (horizontaldashed lines above cluster level), and -0.5 indicates 180◦ difference between vectors.4.5.2 Okmok: 2008The generally consistent and high detection rates throughout the eruption are in agreement withother work on this dataset (Haney, 2010). Despite an increase in ash production at the beginning ofAugust (Larsen et al., 2015) tremor detection rates showed no significant increase at the same time,a result previously noted by Larsen et al. (2009). In fact, detection rates decreased at the stationsfurther away from the eruptive vent around that time.994.5. DiscussionSimilar to Kı¯lauea, the cluster spectra at Okmok resemble each other (Fig. 4.7(d)). However,in contrast to Kı¯lauea, there are no significant systematic changes between the different regimesin terms of their timing relative to the eruption (Fig. 4.8). There are several possible explanationsfor this behaviour. The observed spectral shapes can look similar if (i) the observed tremor is theexpression of only one main source process, that is slightly time-dependent, or if (ii) the volcanicedifice acts as a filter, which restricts all tremor spectra to have similar characteristic shapes, regard-less of the underlying process(es). The differences in terms of relative contributions of the clustersat different locations (Fig. 4.7(e)) that do not appear to be reflected in temporal differences do notallow to distinguish between these two scenarios.Another possibility (iii) is that the main differences between the spectra lie outside of the fre-quency band analyzed here. A change of the source location of very-long period (VLP) tremor(<0.5 Hz) during the eruption occurred on 2 Aug 2008 (Haney, 2010). We do not observe a changein spectral character at the same time (Fig. 4.8). However, if the movement of the VLP tremorsource is accompanied by a change in spectral characteristics, these would naturally be strongest inthe VLP band, i.e., below our lower frequency limit, and we would not expect to observe a temporalchange in our analysis.Our higher frequency band (0.75–12 Hz) is generally more prone to path effects than the lowerfrequencies (e.g., Haney, 2010), and a combination of all three processes may thus have someinfluence on our results.As a final remark, several lahars occurred during the Okmok eruption and may be detected byour algorithm and have a specific spectral signature. However, the exact timing of these flows isunknown because they were observed only indirectly in their deposits during intermittent visits tothe island (Larsen et al., 2015). Ash isopachs from the eruption at Okmok reveal the thickest ashdeposits in the southeast quadrant of the island (Larsen et al., 2015), which may indicate that laharsare most likely to develop in that area. None of the stations used for our analysis are situated close tothose deposits (Fig. 4.7(e)), so it is possible that localized signals cause by lahars exist but cannot bedetected by our stations. We thus cannot determine whether lahars may be related to specific spectraat Okmok. Similarly, a lack of variations in the temporal evolution of clusters combined with poorknowledge of the exact timing of other syn-eruptive processes makes it difficult to associate any ofthe observed spectra with processes occurring during the eruption.4.5.3 Pavlof: 2007, 2013Detection rates at Pavlof (Figs. 4.10 and 4.11) agree well with previous studies which report thetemporal evolution of RSAM over the course of the 2007 and 2013 eruptions (McGimsey et al.,2011;Waythomas et al., 2014). The only exception is station PVV in 2007 (Fig. 4.10(c)), where de-spite the large number of detections the temporal evolution of the detection rates differs significantlyfrom the other stations. In addition, the dominant cluster is cluster 1 (Fig. 4.10(c)), which appearsonly very infrequently at other stations or times. The 2007 eruption occurred on the Southeast flankand lava flows as well as over 40 lahars were directed downwards towards PVV (Waythomas et al.,1004.5. Discussion2008; Global Volcanism Program, 2013c). Taken together, these observations suggest a relationshipbetween the directionality of the eruption and the differences between PVV and the other stations.Indeed, the first detection of cluster 1 at PVV occurs on 16 Aug 2007 at 15:30. This tremor signalcoincides with the detection of the first lahar of the 2007 eruption at the same station (Waythomaset al., 2008). The peaks in detection rates around 17 Aug and 25 Aug at PVV (Fig. 4.10(c)) coin-cide with the observation of multiple lahars during those times. It is, thus, possible that the cluster 1signature is directly related to the shaking induced by the flow of material down the slopes of thevolcano.Alternatively, a subsurface process prior to lahar generation could be responsible for the ob-served signal. However, because lahars were occurring on the southeastern flank, and becausecluster 1 is not observed at any other station, we suggest that the former scenario is more likely.Waythomas et al. (2008) report that tremor typically preceded the lahars by 11-25 minutes. If thetremor is related to the onset of the lahar higher on the volcano, this time period implies a signaltraveling at 20–46 km/h towards PVV (8.5 km distance from the summit, neglecting the relativelysmall contribution to travel time from seismic wave velocities), which is similar to lahar speedsobserved at Popocate´petl Volcano, Mexico (Mun˜oz-Salinas et al., 2007) and thus makes a surfacesignal scenario likely. Additional data from other eruptions could help to distinguish between thetwo mechanisms. The 2013 eruption was directed towards the Northwest, but stations PN7A andPV6 situated in that area were unfortunately not operating during the time (Waythomas et al., 2014).Regardless of the exact mechanisms (surface vs. subsurface), on the basis of our observations wethus suggest that the differences between clusters 2–3 vs. cluster 1 stem from the fact that cluster 1is related to the lahars on the flanks of the volcano. Our algorithm not only detects the differences intemporal evolution between the different stations, but also provides a specific spectrum associatedwith the “anomalous” tremor process.4.5.4 Redoubt: 2009Our detection rates at Redoubt agree with previously identified periods of increased seismic am-plitudes (Buurman et al., 2012). Most detections are observed on the station closest to the summit(REF), in particular during the precursory phase (Fig. 4.13(a)). The precursory tremor has been at-tributed to activation of the shallow hydrothermal system (Power et al., 2013). This shallow sourceexplains the localization of the signals. Power et al. (2013) and Buurman et al. (2012) observedlarge variations in the spectral character of volcanic tremor during this period preceding the erup-tive phases. Similarly, a mostly coherent period of detections belonging to the red regime in midFebruary 2009 is sometimes interspersed with spectra from the blue regime, which are also associ-ated with a small amount of detections before, between, and after the different precursory/eruptivephases (Fig. 4.13(a)).Whereas the hydrothermal phase is mostly visible on REF (Fig. 4.13(a)), we observe syn-eruptive detections also on stations further away (Fig. 4.13(b)–(d)). The similarities in terms oftiming of detections at the different stations suggest that the same process(es) cause detections1014.5. Discussioneverywhere, despite the differences in best matching clusters (Fig. 4.13).The summit crater at Redoubt, from where the 2009 eruption originated, opens up to the Northflank of the volcano into the Drift River valley (Schaefer, 2011). All our stations except REF arelocated in the same direction. Between 23 March and 4 April 2009 several pyroclastic flows andlahars accompanied dome growth and collapse as well as repeated explosions (Schaefer, 2011; Bulland Buurman, 2012). There is some indication that lahars tend to be accompanied by seismic sig-nals with spectra from the blue regime at stations RDN and DFR, but a clear relationship cannotbe identified and not all lahars coincide in time with our detections. Because of the multitude ofprocesses occurring during the explosive phase, our detections switch on and off, and change fromone cluster to another over short time intervals, which makes identifying explicit relationships tothe eruptive events during the highly energetic explosive phase difficult. If the detections duringthe explosive phase are not directly associated with energetic lahars that come close to most sta-tions, then the question remains why those detections are visible at all stations, in contrast to theprecursory phase that appeared to come from localized processes at the summit. If the precursorsstem from shallow processes related to the hydrothermal system, the mechanics underlying the de-tections during the explosive phase must either be stronger or deeper for them to be detected manykilometers away from their source.4.5.5 Implications for Tremor Detection AlgorithmThe detections from our algorithm mirror the temporal evolution of RSAM at Pavlof (McGimseyet al., 2011; Waythomas et al., 2014) and at Redoubt (Buurman et al., 2012; Power et al., 2013), aswell as the known evolution of seismicity at Kı¯lauea (Unglert and Jellinek, 2015). These matchessuggest that our amplitude-based algorithm accurately identifies tremor signals. Furthermore, thedetection parameters informed by known characteristics of the data at the Kı¯lauea (Section 4.3)capture time periods of elevated tremor amplitudes also for other settings.05/04 12:00 05/05 12:00 05/06 12:00 05/07 12:00 05/08/200924681012detections per hourRSOtimeFigure 4.20: Detection rates at station RSO during several days in May 2009. High rates are mostlikely related to earthquake swarm activity.However, because of the nature of our algorithm we detect signals that may not be related to1024.5. Discussionvolcanic tremor in its definition as a continuous seismic signal, which we illustrate below. Becauseof a station outage around the time of the main eruptive phase at Redoubt, station RSO is excludedfrom our pattern recognition analysis. However, the data from RSO produce valid detections atother times that can be analyzed in terms of detections in order to assess our algorithm. One ofthose periods is a pulse of detections in early May 2009 (Fig. 4.20), which we attribute to a swarmof small, closely spaced earthquakes. This swarm included peak rates of over 660 earthquakesper hour (Ketner and Power, 2013), resulting in up to 55 earthquakes per 5-minute window. Itis thus not surprising that this swarm resembles tremor from the perspective of our detection al-gorithm. These detections highlight a potential drawback of our method, which detects not onlytremor but also discrete earthquakes if they become closely spaced or overlap in time. However,in some volcanic settings including Soufrie`re Hills Volcano and Redoubt, individual low-frequencyearthquakes closely spaced in time merge into tremor (Neuberg et al., 2000; Hotovec et al., 2013).Consequently, it may be desirable to detect such closely spaced individual events as tremor. If, incontrast, such events should be excluded from any tremor analysis a detailed investigation identi-fying them is required so that event origin times can be included in the tremor detection algorithm(Section 4.3.2). We refer the reader to previous work on this topic for more details about how to de-tect similar events within swarms or earthquakes buried in other signals (e.g., Green and Neuberg,2006; Ketner and Power, 2013).Another “anomalous” signal that was detected by the algorithm are the potential lahar signaturesat Pavlof station PVV in 2007 (Fig. 4.10). If these signals are suspected to come from such surfaceprocesses, they should ideally be excluded from the analysis where the goal is to detect volcanictremor only, which is a limitation of our detection methodology. However, our pattern recognitionapproach is able to clearly recognize the differences between the lahars and most of the other signalsat Pavlof, so it would be easy to remove those events before proceeding with any further analysisrelated to tremor. This result shows that in addition to our detection methodology informing thepattern recognition approach, the process can also work in reverse. The PCA and clustering methodcan inform any processing following the detections by isolating specific signals in a case where theanalysis of the overall similarities and differences between patterns is not the main goal. In contrast,several lahars are observed at Redoubt (e.g., on camera) but are not necessarily detected by ourtremor detection algorithm. This lack of detections may be related partly to the threshold set by ouralgorithm. A possible way to test this hypothesis could be to introduce a variable detection thresholddepending on station distance from the suspected center of activity. Further test are required todetermine if this variation of our algorithm helps to detect the lahars at Redoubt.4.5.6 Joint Analysis: Lessons LearnedThe combined analysis of stations from each of the volcanic settings for the two different stationsubsets reveals interesting results. The lower cluster numbers (k = 3) give simplified, but consis-tent results compared to the individual network analysis (pattern recognition among several stationswithin one setting, Section 4.4.2). For example, the Kı¯lauea stations both show similar spectra that1034.5. Discussionpersist consistently throughout the intrusions in 2007 and 2011, and a different spectral signatureduring the times of degassing bursts in 2008 (Figs. 4.16(a)–(c) and 4.18(a)–(c)), in agreement withthe results from the network analysis and the results by Unglert and Jellinek (2015). Similarly,at Okmok the combined analysis reveals no changes in spectral shape during the 2008 eruption(Fig. 4.18(d)), consistent with the results from the network analysis at Okmok. During the 2007eruption at Pavlof, a narrowly peaked spectrum relative to the other clusters is observed at PV6(Fig. 4.16(d)), whereas PVV is marked by the high frequency peak spectrum of cluster 1, whichis not observed in significant amounts at other times or stations (Fig. 4.18(e)). Last, the tempo-ral evolution of clusters from the combined analysis at Redoubt suggests peaked spectra (∼3 Hz)during the precursor phase at REF, followed by spectra with a low frequency plateau during theeruptive phase (Fig. 4.16(e)). This confirms the results obtained by analyzing the Redoubt networkindividually.Proximal vs. Distal Tremor PropertiesSpectra from all four individual network analyses have steeper decays of spectral power from low tohigh frequencies with increasing distance from the inferred source location (indicated as shades ofthe same color within the regimes of spectra obtained for each setting). Because our normalizationscales each original spectrum by its cumulative spectral power (Section 4.3.3, Unglert et al., 2016)),such differences in slope still relate to differences in the amplitude of the spectral power curvesin the original data. A steeply decaying spectrum is a property of lower overall spectral power,and spectra with flatter slopes are indicative of higher overall spectral power. This relationshipindicates that, as expected, the same spectral shape can be observed at the same time at differentstations, with spectral power decreasing (i.e., steepening of slopes) with increasing distance fromthe inferred source location.Whereas for the distal (8–10 km) stations our algorithm gives a clear peak at k = 3 (Fig. 4.17(b)),the proximal results (4 km) show that CRMS,k has several local maxima. This behaviour indicatesthat the sensitivity to the range of k tested, and that more clusters than the three discussed here maybe required to fully explain the data.The agreement between the network analysis and the combined approach for the manually ad-justed k = 3 in this case, however, suggest that the obtained spectra are meaningful representationsof the data. Comparing Figures 4.14(d) and 4.15(b) shows that the larger number of clusters inFigure 4.14 is related to the differences in slopes, with the main three patterns clearly visible inboth Figures 4.14(d) and 4.15(b). The trend towards higher cluster numbers in CRMS,k for theproximal stations compared to distal stations and the implied larger variability in terms of overallspectral power thus raises a question of whether this result is related to the shorter distance to thesource of volcanic activity for subset 1. Together with the differences in detection rates discussedin the previous sections, the larger variability in spectral power (manifested in different spectralslopes after our normalization) confirms an intuitive result: Whereas various stages of the samespectral fingerprint (i.e., similar spectral shape) can be detected closer to the center of activity, only1044.5. Discussionthe strongest phases are detected at stations further away. Because the overall patterns for the twostation subsets are relatively similar in their character and timing, we suggest that they stem fromthe same underlying processes, implying that the length (and possibly nature) of the travel paths ofthese signals do not influence their spectral character. Similar to observations by previous studies(e.g., Sherburn et al., 1999), Bean et al. (2008) and Bean et al. (2014) have recently shown the in-fluence of the seismic wave path on the characteristics of volcanic low frequency seismicity, whichmay be misinterpreted as effects of the source mechanics if the recording seismometers are morethan 500 m away from the source. Because our stations are all at least a few kilometers away fromtheir source, our work does not dispute this result. However, we can conclude from our results thatsimilar qualitative changes to tremor spectra do not occur at larger distances in our data.Volcano Intercomparison and Some Implications for Source MechanismsThe identification of systematic similarities and differences in the properties of volcanic tremoramong volcanoes globally is the main motivation behind this work. With only four volcanoesanalyzed, we cannot conclusively address this goal. However, our results reveal some trends thatcan be tested in future work, and illustrate the value of such a global comparison, which we discussbelow.  cluster 1cluster 2cluster 34 km 1 2 329546910detectionsREF1 2 3184254PV6detections1 2 328522615PVVdetections1 2 3063860OKWEdetections1 2 32248010428AHUdetections1 2 3187652PAUdetections48 50 52 54 56 58 60 62 64wt % SiO2KilaueaOkmokPavlofRedoubt−1005altitude a.s.l. (km)−5depth of magma storagesummit altituderange of compositions cluster 1cluster 2cluster 38-10 km shield volcanoes stratovolcanoesFigure 4.21: Summary of tremor types in relation to volcano and eruption characteristics. Top panelshows dominant composition during data period, summit altitude above sea level (a.s.l.) as proxyfor volcano type, and inferred depths of magma storage region(s) for each volcano. Bottom panelshows histogramsFigure 4.21 summarizes some of the characteristics of each the volcanoes that may influencethe similarities and differences revealed by our pattern recognition algorithm. Many tremor mech-1054.5. Discussionanisms that have been suggested in the literature depend on magma viscosity or rheology (e.g.,Ripepe and Gordeev, 1999; Johnson and Lees, 2000; Jellinek and Bercovici, 2011; Thomas andNeuberg, 2012). Ripepe and Gordeev (1999), for example, predict a relationship between magmaviscosity and tremor peak frequency. In lieu of direct estimates of viscosity or rheology, we usemagma SiO2 as a proxy (e.g., Gonnermann and Manga, 2007; Takeuchi, 2015) and categorize thefour volcanoes according to their edifice type including summit altitude (Fig. 4.21). In addition,we show estimates for magma storage depths. Below these essential volcano characteristics, eachpanel shows the histograms at a particular volcano for the clusters identified through analysis of thestations at 4 km (Fig. 4.21, top row) and 8–10 km distance (Fig. 4.21, bottom row), respectively,with the corresponding spectra on the right for comparison. The blue spectrum is observed at allvolcanoes and stations to some extent. By contrast, the other types occur at certain volcanoes only.For example, we only observe the purple spectrum at Pavlof, whereas the red spectrum appears atPavlof and Redoubt (both stratovolcanoes) and is absent at Kı¯lauea.At Pavlof, both the network analysis and the combined approach reveal the presence of a spec-trum that is almost exclusively confined to station PVV during a period of lahar activity duringthe 2007 eruption. We suggest that these flows down the slopes of the volcanic edifice cause theobserved signals (Section 4.5.3).The combined analysis shows that the red spectrum from the proximal stations (4 km) is com-mon to the precursory phase in 2009 at Redoubt and the 2007 eruption at Pavlof (Figs. 4.16(d)–(e)and 4.21). The seismicity at Redoubt during that time when no eruptions occurred has been pre-viously explained as activation of the shallow hydrothermal system (e.g., Power et al., 2013). AtPavlof, however, a similar signal is observed at several stations, albeit with the peak at slightly lowerfrequencies around 1–2 Hz (Fig. 4.10). Whereas no details about the presence of a hydrothermalsystem at Pavlof are included in recent conceptual models of the region (Emmons Lake VolcanicCenter, Mangan et al., 2009), phreatomagmatic eruptions have been recorded at Pavlof (e.g., Mc-Nutt, 1987a). This observation in combination with its persistent ice and snow cover (Waythomaset al., 2014) may suggest the presence of shallow groundwater or the interaction of erupted materialwith surface water. Both Pavlof and Redoubt are at the higher end of the range of magma SiO2 con-tent of the volcanoes sampled in our work (Fig. 4.21 and Section 4.2), and form tall stratovolcanoeswith summits over 2,500 m above sea level. In particular, similarities in the structure of their edi-fices and the presence of water may inform explanations of why this spectrum (cluster 2) is commonto both volcanoes. Alternatively, processes related to the higher silica content, and thus potentiallyincreased effective viscosity relative to the other two settings (e.g., Jellinek and Bercovici, 2011;Dmitrieva et al., 2013) may drive the observed signal.Interestingly, the blue spectrum observed at Redoubt during the eruptive phase is also observedat Kı¯lauea during the dike intrusions, and at Okmok during the 2008 eruption, both at 4 km (clus-ter 1) and 8–10 km (cluster 2) distance (Figs. 4.16(a) and (c), 4.16(a), (c), and (d) and 4.21). Allthree volcanoes are inferred to have part of their magma storage centered between 0–5 km belowsea level (b.s.l.) (Fig. 4.21; Poland et al., 2009; Masterlark et al., 2010; Grapenthin et al., 2013). Incontrast to Kı¯lauea, Okmok, and Redoubt, the corresponding spectrum is observed for less than 3%1064.5. Discussionof all detections at Pavlof (Fig. 4.21), which is not known to have a magma reservoir at comparabledepths (Lu and Dzurisin, 2014). It is thus possible that the manifestation of this spectrum relates toprocesses related to magma storage at a few kilometers depth. Unglert and Jellinek (2015) argued,for example, that tremor spectra during the intrusions at Kı¯lauea in 2007 and 2011 reflected, in part,the dynamics of bubble clouds in magma flowing through a vertically and laterally complex magmaplumbing system. However, assuming the observed spectrum is related to the same source processat all three volcanoes, mechanisms that are insensitive to the geometry of the magmatic plumbingsystem but relate specifically to magma rheology (e.g., magma wagging, Jellinek and Bercovici,2011, or frictional faulting of high viscosity magma, Dmitrieva et al., 2013), are unlikely expla-nations for these detections. Instead, the geometry of the magma storage system may play a keyrole in explaining the observation of this blue spectrum at three volcanoes with strong differencesin their magma rheology and eruptive processes.The last characteristic spectrum from our combined analysis is cluster 3 (orange) for the proxi-mal stations. This cluster is similar to cluster 1, which may indicate an effect of the overall spectralpower of the original spectra. In this case, tremor during the degassing bursts in 2008 at Kı¯lauea maybe explained by the same process as tremor during the intrusions (Figs. 4.16(a)–(c) and 4.18(a)–(c)).Alternatively, if the cluster 3 at the proximal stations reflects distinct mechanisms comparedto cluster 1, it is interesting to note that cluster 3 from the distal stations has a similar character(Fig. 4.21), which may indicate that the same processes are observed on the proximal and the distalstations. For both station subsets, this cluster is associated with tremor at Kı¯lauea during 2008(Figs. 4.16(c) and 4.18(c)). The processes accompanying the degassing bursts at Kı¯lauea are relatedto the formation of the open vent at Kı¯lauea’s summit (Fee et al., 2010; Patrick et al., 2011b). Inaddition, the spectrum associated with cluster 3 is observed at Pavlof, where eruptions are typicallyaccompanied by lava fountaining (Waythomas et al., 2014) and which is considered an open ventsystem (e.g., Mangan et al., 2009). During the 2013 eruption at Pavlof, the phases of increasedtremor detections coincide with phases of lava fountaining and explosive activity (Fig. 4.18(f),Waythomas et al., 2014), whereas a phase in early June 2013 dominated only by explosions doesnot show accompanying tremor. We thus suggest that the observed cluster 3 spectra may be causedby processes related to the presence and/or formation of an open vent, or the presence of shallow(less than a few 100 meters) magma.In summary, our results show that different types of tremor with distinct spectral features exist.Systematic occurrence of these tremor classes in relation to a variety of volcano characteristics suchas magma storage depth or properties of the volcanic edifice indicate that certain volcanoes mayhave common tremor mechanisms. The notion that each volcano requires its own, unique processesdriving volcanic tremor (e.g., Konstantinou and Schlindwein, 2002) may thus need reassessment.Implications for Pattern Recognition ApproachThe results for the pattern recognition analyses that include data from Kı¯lauea, which we use as abenchmark, confirm that our approach can successfully detect different spectral shapes and identify1074.6. Conclusionstheir spatial and temporal characteristics. As discussed in Unglert et al. (2016)), the algorithm isnot suited to detect signals such as gliding spectral lines, which are observed during the intrusiontremor in 2007 and 2011 at Kı¯lauea (Unglert and Jellinek, 2015). In detecting such gliding signals,automated pattern recognition cannot replace more traditional methods such as visual inspectionof spectrograms. However, that we were able to identify additional systematics that had not beenrecognized through exhaustive manual analysis (Section 4.5.1) shows the value of our approach,which is well suited to determine systematic similarities and differences among many thousands ofspectra at any desired level of detail (for example, detailed analysis of one cluster over only fewdays on Kı¯lauea, Fig. 4.19, vs. large scale multi-setting analysis of the main three patterns overmultiple eruptive periods for the stations at close range, Fig. 4.21).For the multi-setting approach and for all cases of the station network analyses except Pavlof,we combined a relatively large number of clusters k as determined by CRMS,k into a smaller numberof regimes, within which spectra share common spectral peaks. This decision has two implicationsfor our algorithm:1. As discussed in Section 4.5.6, the normalization suggested by Unglert et al. (2016)) allowsamplitude differences to enter the algorithm, albeit at a reduced magnitude. Such ampli-tude differences lead to different slopes of spectra with otherwise similar frequency peaks.Whereas it is relatively easy to visually group the corresponding spectra, further work maybe desirable to reduce the effects and yield a more automated solution.2. The ideal number of clusters is determined by CRMS,k (Unglert et al., 2016)). This criterionmostly tends to favor larger cluster numbers than visual inspection would suggest. Theselarger numbers may be impractical to analyze further from an interpretational point of view.It is unclear to what extent this overestimation of k is related to the CRMS,k criterion, or thenormalization discussed above.The joint analysis of the close range stations (Section 4.4.3), however, shows that even betweenvalues of k close to extreme ends of the full range evaluated here (k = 3 vs. k = 16 for a rangeof [2..20]), the resulting spectral patterns are qualitatively similar, and only differ in terms of smalldetails that may or may not be desired for any interpretation. This result suggests that, even thoughit is useful to have a quantitative criterion to guide the decision on the ideal number of clusters, thefinal choice of a local maximum in CRMS,k might only affect the level of detail, but not the overallinterpretation.4.6 ConclusionsWe develop a single station detection algorithm for volcanic tremor on the basis of amplitudescompared to a defined background signal. We use this algorithm to detect tremor with seismicnetworks on four different volcanoes over the course of seven eruptive episodes in total. For eachof the resulting tremor detections we estimate spectral content and apply a pattern recognition1084.6. Conclusionsapproach that combines PCA and hierarchical clustering to, for the first time, investigate systematicsimilarities and differences (i) between tremor recorded on multiple stations at one volcano, and (ii)between tremor recorded at one station each from the different volcanic settings. Our results yieldthe following conclusions:1. Our tremor detection algorithm successfully detects tremor as confirmed by published analy-ses of the seismicity at the different volcanoes.2. Periods of tremor-like signals (such as shaking induced by lahars, or intense earthquake activ-ity that resembles tremor) are also detected by our algorithm, and may be reliably identifiedand excluded from further analysis if desired.3. Our pattern recognition approach applied to the individual station networks reveals that dif-ferent localized tremor signals can be detected and distinguished within a network, and thatsignals observed at all stations mostly differ in their strength, which depends predominantlyon the distance of the station with respect to the inferred source location.4. Our pattern recognition approach applied to the combination of stations from the differentvolcanoes reveals that at the proximal and distal locations we investigate (4 km vs. 8–10 km),spectra show similar shapes, suggesting that path effects do not significantly affect frequencycontent.5. We show that at least four different tremor types can be observed across the four volcanic set-tings, and that there may be relationships to common physical characteristics among some ofthe volcanoes, such as magma viscosity, the presence of magma reservoirs at certain depths,or the existence of an open vent and related shallow activity.Further work with datasets from a larger sample of volcanoes of differing types is necessary toreliably and more fully identify systematic similarities and differences among the tremor propertiescharacteristic of volcanic unrest. However, our results indicate that a global comparison of volcanictremor carried out on the basis of its spectral content is a promising avenue to constrain underlyingmechanics that are both generically distinctive of the class of volcanic system or specific to a givenvolcano.109Chapter 5Concluding RemarksThe main goal of this thesis was to systematically investigate and rigorously characterize similaritiesand differences in volcanic tremor properties from a variety of volcanoes. In particular, establish-ing the extent to which spectral properties of tremor are independent of the specific features of agiven volcano, or vary among volcanoes of differing class, is a major step forward to constrainingplausible source mechanisms. In carrying out this research, I identified several critical knowledgegaps, which led to the publications in Chapters 2, 3, and 4. I rephrase these challenges from theintroduction (Chapter 1):• Few studies systematically investigate the temporal evolution of tremor properties over mul-tiple eruptions.• No simple metric exists to characterize tremor properties across multiple volcanic settings.• No algorithms exist to make pattern recognition in tremor datasets inherently objective andtime-efficient.With the aim of producing a careful global comparison, my work systematically addresses thesegaps. I summarize the main outcomes of the three parts of my research (Chapters 2, 3, and 4) andthe decisions that lead to each subsequent research avenue in Section 5.1. In Section 5.2, I revisit thehypotheses formed in Chapter 1. Finally, I provide an outlook towards future work in Section 5.35.1 Summary of Work and Context for Each PublicationIn Chapter 2, I undertook a comparison of volcano seismicity at Kı¯lauea Volcano over three differenteruptive periods. The main goal was to identify an optimal way to characterize tremor in relation toother types of seismicity, and to explore the variety and evolution of seismic signals over more thanjust one eruption. A further goal was to provide explicit and restrictive constraints on tremor sourcemechanisms related to similarities and differences among the eruptive periods. For the first time, Iidentified two phases of seismicity that are characteristic for dike intrusions at Kı¯lauea. Whereasthe first phase is marked by discrete events and appears to be directly associated with the intrusionof magma in the shallow crust, the second phase is comprised of continuous tremor that lasts forseveral days. In contrast, tremor during a period of degassing bursts from Kı¯lauea’s summit ismore similar to the background seismic signal. Previously, low-frequency seismicity at Kı¯lauea,including tremor as observed during the intrusions, has been attributed to processes related to, forexample, the presence of the lava lake at Kı¯lauea’s summit (Fee et al., 2010; Patrick et al., 2011b),1105.1. Summary of Work and Context for Each Publicationor lava spattering during fissure eruptions (Patrick et al., 2011a). Because the lava lake did notexist at the time of the first of the two intrusions, and because the observed Phase II tremor didnot directly coincide in time with the eruptions, my research showed that such mechanisms cannotaccount for the characteristic intrusion tremor. That I was able to exclude a number of processes aspotential candidates for volcanic tremor at Kı¯lauea confirms that a comparison of tremor propertiesover multiple eruptive cycles is a promising approach and potentially a critical step to systematicallycomparing tremor from a range of volcanic settings. In addition, the tremor observed during theperiod of degassing bursts from the summit compared to the intrusion tremor differs mostly in theshape of their respective spectra, which resulted in the decision to use spectral shape as metric forthe nature of volcanic tremor.Following the results from Chapter 2, the next step was to determine the best algorithm toidentify different spectral shapes to be able to repeat the analysis from Kı¯lauea at other volcanoes.Because the manual approach from Chapter 2 is both subjective and time consuming for analyzingthe long time series of seismic data typical for volcanic unrest, my goal in Chapter 3 was to developan automated and largely unsupervised pattern recognition algorithm. In addition, I decided togenerate a synthetic dataset based on the different spectral properties of seismicity observed inHawai‘i to be able to assess the performance of the final algorithm. Self-Organizing Maps (SOM)(Kohonen, 1982, 1990) had been applied in a volcano seismic context before (e.g., Esposito et al.,2008;Messina and Langer, 2011; Carniel et al., 2013b), and initial tests on the Kı¯lauea data yieldedpromising results. However, it became clear that to properly interpret the different patterns on theSOM topology, either a priori knowledge about the expected patterns, or additional supervisedprocessing is required. As shown in Chapter 3, in the subsequent comparison of SOM againstPrincipal Component Analysis (PCA), a more established and widely used technique, both methodswere followed by hierarchical clustering to test whether the known spectral patterns can be retrievedreliably. Surprisingly, PCA combined with our cluster evaluation criterion and the hierarchicalclustering method gave consistently better results than the SOM approach on the same dataset.Further testing revealed that clustering of the map topology may not always work in the intendedstraightforward way. Whereas the question of a solution to this problem will be the topic of futurework, I identified that PCA, in combination with clustering, is a successful approach to identifypatterns in long time series of spectra. This methodology thus enabled me to rapidly classify tremorspectra from several volcanic settings.Building on the success of the PCA and clustering approach in Chapter 3, in Chapter 4 I de-veloped an algorithm to detect tremor signals in continuous time series of seismic data from well-studied eruptive periods at Kı¯lauea, Okmok, Pavlof, and Redoubt, i.e., volcanoes that express arange of edifice type, magma compositions, and eruptive styles. I applied the methodology de-veloped in Chapter 3 to the time series of spectra from tremor detections from all stations at eachvolcano individually, and to the combined detections from one station from each of the settings.The results revealed that path effects do not significantly alter spectral shapes at distances of a fewkilometers between our stations and the inferred signal sources. Furthermore, I identified four dis-tinct classes of tremor signals, that may be related to volcano characteristics such as specifics of the1115.2. Revisiting the Hypothesesplumbing system or eruptive style.In summary, the main contributions of my work to the study and understanding of volcanictremor are:(1) A thorough characterization of seismicity associated with dike intrusions at Kı¯lauea, includingvolcanic tremor.(2) A detailed discussion of the constraints on the mechanics underlying volcanic tremor providedby assessing observations over several eruptions, shown on the example of Kı¯lauea.(3) A rigorous investigation of the performance of two approaches for pattern recognition witha carefully constructed synthetic dataset of spectra with features that are applicable to manyvolcanoes.(4) A systematic analysis of similarities and differences among tremor from four distinct volcanicsettings as an avenue towards a global comparison, including the identification of several tremortypes that may be related to volcanic controls.5.2 Revisiting the HypothesesIn Chapter 1, I listed four hypotheses as the basis of my work. Below, I reassess each of thehypotheses in light of the findings of Chapters 2, 3, and 4:(i) Tremor is an expression of volcanic processes, which are also expressed in other monitoringparameters.My results in Chapters 2 and 4 indicate explicit relationships between volcanic processes, andseismic and other types of monitoring. At Kı¯lauea, volcanic tremor coincides in time withstrong deformation during dike intrusions (Poland et al., 2008; Lundgren et al., 2013), andmay be linked to magma flow through a magma reservoir. At Okmok and Pavlof, tremoris observed almost exclusively during eruptions. Whereas at Okmok there appears to be nodirect relationship between the strength of the eruption (measured through ash productionfrom explosive activity, Larsen et al., 2015), periods of lava fountaining at Pavlof (Waythomaset al., 2014) coincide in time with the observation of high tremor detection rates. Furthermore,visual observations of lahars at Pavlof (Waythomas et al., 2008) are accompanied by volcanictremor. At Redoubt, tremor preceding the 2009 eruption is accompanied by high levels ofgas emissions (particularly CO2, Werner et al., 2012) and increased glacial melting rates,indicating an activation of the shallow volcanic system (Bleick et al., 2013). All of thesecases show a relation between the occurrence of tremor and volcanic processes. The types ofmonitoring parameters that correlate with tremor vary between different settings, which maysuggest different types of volcanic tremor, or may be related to certain types of monitoringonly available for some settings.1125.2. Revisiting the Hypotheses(ii) Volcanic tremor expresses itself in a variety of temporal, spatial, and spectral properties. Theseproperties are distinct for different types of tremor.Related to (i), there are instances of tremor recorded only on a few stations within a networkat any given time. For example, the temporal evolution of tremor properties at Kı¯lauea differsbetween the western and the eastern end of the East Rift Zone (Chapters 2 and 4), where pre-intrusion tremor is only observed in the East. Similarly, tremor signals in one location that arenot accompanied by tremor detections at other stations, are sometimes associated with distinctspectra (Chapter 4). The variety of these properties can thus be attributed to different types ofvolcanic tremor.(iii) The complexity of tremor properties, in combination with other monitoring parameters, canbe mapped into a parameter space based on the volcanic and tectonic context to identify char-acteristic “fingerprints”.In Chapter 4, I show that the spectra associated with different types of tremor observed in thefour volcanic settings may be related to volcano characteristics such as magma storage depthor edifice structure. This relationship suggests that it is possible to develop a parameter spacethat maps tremor spectra in relation to the volcanic context where they are observed, and thatthe plausible source mechanisms for the tremor fingerprints may be identified. For example,the detection of a common spectrum at two snow-covered strato volcanoes (Pavlof and Re-doubt) at different times relative to eruptions may indicate that the process driving this signalis related to the presence of shallow groundwater and/or properties of the edifice. Similarly,a common spectrum observed at Kı¯lauea, Okmok, and Redoubt (with varying eruptive stylesand magma properties) suggests that mechanisms related to the depth of magma storage mayexplain the common signal, whereas magma rheology is not likely to be a major controllingfactor. Taken together, these observations indicate that tremor does not necessarily have toshow different properties from one volcano to the next, and that the analysis of common be-haviour is promising. I do not have enough datasets to assess the contribution of tectoniccontrols yet, but my thorough comparison of pattern recognition algorithms in Chapter 3 hasprovided the necessary tool for this question to be addressed in future studies.(iv) If plausible source mechanisms are identified for different tremor fingerprints, volcanic tremormay be reliably used for eruption forecasting.This last hypothesis remains unaddressed. However, I identified spectral fingerprints for atleast four different types of volcanic tremor in Chapter 4, and have provided a preliminaryparameter space for the four volcanic settings studied here. To reliably assess whether therelationships I observe in this initial case study are valid globally, a larger sample of differentvolcanoes is necessary.1135.3. Outlook5.3 OutlookThe identification of at least four types of volcanic tremor and the relationships to volcanic controlsdetected in four volcanic settings hold promising implications.Previous investigations of tremor across multiple volcanic settings have typically summarizedthe observation of different tremor properties without identifying potential links to the characteris-tics of the volcanoes from which the observations originate (e.g., Konstantinou and Schlindwein,2002). Few studies have identified relationships between tremor properties and other observables,such as amplitude versus explosivitiy or cross sectional area of the vent (e.g.,McNutt, 1994;McNuttand Nishimura, 2008). However, such studies may fail to identify distinct correlations if differenttypes of tremor are not recognized and are instead analyzed together. For example, tremor prop-erties from signals that likely originate from magma reservoirs at a few kilometers depth, such asthe tremor observed during dike intrusions at Kı¯lauea (Chapters 2 and 4), would not be expected toshow a relationship to vent size. In contrast, such a relationship may exist for tremor associated withopen vents such as the signals observed during lava fountaining at Pavlof and the degassing burstsduring formation of the lava lake at Kı¯lauea (Chapter 4). If these two signals are not identified asdifferent types and subsequently analyzed separately, the reservoir tremor may mask a correlationbetween open vent tremor properties and vent size, and the underlying mechanisms will not be rec-ognized. Identifying different tremor types, as shown here, is thus crucial to reliably determine theprocesses driving volcanic tremor.Konstantinou and Schlindwein (2002) summarize tremor observations from many locations,and, similar to many authors, support the notion that tremor sources vary from one volcano to thenext. My results show that this concept is certainly true to some extent: The temporal evolution andspatial characteristics of tremor differ between Kı¯lauea, Okmok, Pavlof, and Redoubt (Chapter 4).However, whereas some spectral fingerprints are unique to certain settings, others are observed atseveral volcanoes. My results indicate that there are systematic similarities among tremor signalsfrom different volcanoes. This important outcome, in turn, suggests that several volcanic settingsshare one or multiple common tremor source mechanisms.There are two key steps towards confirming the relationships suggested by my results, andtowards uniquely determining tremor source processes:1. Apply my approach to data from a larger sample of volcanic settings to confirm the differenttypes of volcanic tremor and their relationship to volcanic controls.2. Analyze each tremor type independently with respect to potential control parameters depend-ing on the relationships to the volcanic settings where each type is observed, such as vent size(McNutt and Nishimura, 2008) for suspected open vent tremor.Furthermore, additional work could investigate optimal network design on the basis of the obser-vation of certain types of tremor. Additionally, future studies could identify an appropriate metricto characterize tremor in the time domain (e.g., spasmodic vs. continuous, Chapter 1), which couldthen be applied to recognize time domain patterns within one spectral tremor class, or to identify1145.3. Outlookthe corresponding time domain expression of each spectral type of tremor. 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Icount color figures versus black-and-white figures in the first 5 articles listed online in the Journalof Geophysical Research – Solid Earth, for the April issues of 1981, 1991, 2001, and 2011, andthe October issues of 1984, 1994, 2004, and 2014. To avoid bias related to a lack of color figuresbecause of printing costs, only html versions are counted from 2004 onwards, the first year inmy sample for which html was available (journals often allow color figures in the online versionsof articles at no additional cost). Subfigures are not counted separately, and any supplementarymaterial is ignored. Any figure that has at least one color other than shades between black andwhite is counted towards color figures. Bias might come from the small sample size and from onlyconsidering one journal. Additionally, certain topic areas might be grouped together in the table ofcontents of an issue, and be more likely to include either mostly color figures, or mostly black-and-white figures on the basis of the respective research field. Yet, these biases are unlikely to remove orreverse the trend of increasing total numbers (left) and percentage (right) of color figures (Fig. A.1).When multiple datasets or variables are shown in one figure, the use of color allows to effec-tively add a dimension to our perception. For example, if a set of points are defined by their x- andy-coordinates, and a measurement m is taken at each point, the value of this measurement can eitherbe displayed in a 3D perspective view as a third axis z, or it can be visualized with color in a plane(2D) graph. For higher dimensional datasets, for example, point coordinates x, y, z plus measure-ment m, the point coordinates alone require a 3D graph, and the color can be used to display thevalue of m at each point.In studies of volcanic tremor, one of the most common applications of color maps is to displayspectrograms, i.e., the temporal evolution of frequency content of seismic data (e.g., Benoit andMcNutt, 1997; Thompson et al., 2002; Custodio et al., 2003; Lesage et al., 2006; Almendros et al.,2012; Cusano et al., 2015, and many more). The x- and y-coordinates are time and frequency,respectively, and color is used to visualize spectral power or amplitude at each point in time foreach frequency. Unfortunately, the choice of color map has a strong influence on which features ofthe data are emphasized. Furthermore, many of these colored spectrograms are not accompanied by137A.1. Challenges with Color Maps        0102030405060708090100percentage of figures  Apr 1981Oct 1984Apr 1991Oct 1994Apr 2001Oct 2004Apr 2011Oct 2014black & whitecolour        0102030405060number of figures  Apr 1981Oct 1984Apr 1991Oct 1994Apr 2001Oct 2004Apr 2011Oct 2014black & whitecolour(a) (b)Figure A.1: Color use in geoscience publications, (a) in total numbers and (b) in percent.a color scale (e.g., Fig.1.2, or Lesage et al., 2006; Almendros et al., 2012) on which the viewer can,for example, quantitatively assess differences in spectral power between different frequencies. Theviewer thus has to rely solely on their perception of the colors in the map for interpretation. Moststudies with colored spectrograms use a rainbow color map, which, for example, was the defaultcolor map in MatLab R© before version R2014b, and in many other software packages (Borland andTaylor, 2007). It has been shown, that many standard rainbow color maps (including the previouslymentioned MatLab R© default “jet”) suffer from a number of challenges:1. Lightness on rainbow color maps generally does not change monotonically. However, atsmall spatial scales, for example in a figure with many small variations, the human percep-tion is mostly sensitive to lightness as opposed to color (e.g., Mullen, 1985; Stone, 2012).Rainbow color maps do not work well for visualization of data at small spatial scales.2. Similarly, rainbow color maps do not follow perceptual ordering like purely luminance basedcolor maps do (Borland and Taylor, 2007). Figure A.2 shows a rainbow series of 4 squaresderived from 4 evenly spaced samples of the MatLab R© color map “jet”. The top row followsthe rainbow ordering from blue to red. The second row shows the same colors converted togreyscale. Whereas the blue and red square have the same luminance, the cyan and yellowsquares are slightly different from each other. The third row shows a better ordering of thesquares in terms of their luminance, and the fourth row shows the equivalent order in colorspace, which appears counter intuitive based on the wavelength spectrum of the colors.3. The transition from one hue to the next along a rainbow color map can introduce sharp, ar-tificial contrasts that may be interpreted as strong contrasts in the data (e.g., Rogowitz andTreinish, 1998). In addition, some color variations are not easily perceived, and thus appar-ently cover a larger range of data values compared to others.138A.2. Some Ideas for ImprovementFigure A.2: Ordering issues for rainbow color maps. First row shows ordering of squares based onrainbow color map, second row shows conversion to grey scale. Third row shows reordered squaresbased on grey scale/luminance, and fourth row translates the new order back to color space. Formore discussion see main body of text.A.2 Some Ideas for ImprovementA.2.1 Using Line Graphs Instead of ImagesWhen color figures were expensive or simply not available in scientific publishing, many authorsutilized alternative ways to display the same information. A simple way to convey temporal vari-ation in spectral content of seismic data is to show a series of spectra taken from different timewindows (Fig. A.3). When these spectra are plotted at a slight offset from each other, and there areenough spectra over time, this can create the 3D effect shown in Figure A.3(b). An actual 3D graphviewed at an angle could further improve this type of visualization. A disadvantage is that, depend-ing on the level of noise, the scaling, and the number of spectra, visualization of the temporallychanging spectral information may be messy and difficult to interpret.A.2.2 Greyscale Color MapsAn alternative to simple line graphs is to show spectrograms with greyscale color maps. Figure A.4shows an example for a greyscale spectrogram from Sherburn et al. (1998). Note that no legend orscale bar for the different shades of grey exist, which makes interpretation more subjective. Anotherexample can be seen in Figure 1.2. With greyscale color maps, luminance changes monotonically,and thus no “ordering” issues arise.However, a challenge persists: The perceived “middle” grey level does not align with the centerof the scale for most standard vendor greyscale maps. Bespoke color maps (including greyscale)139A.2. Some Ideas for Improvement5x10-2 cm1298765431011121 2 3 4 5 2007/092007/122008/032008/062008/092008/122009/032009/062009/092009/1210.2 0.4 0.6 0.8 frequency (Hz)frequency (Hz)(a) (b)Figure A.3: Line graph spectrograms. (a) Tremor spectrogram over 120 seconds from LangilaVolcano, Papua New Guinea, recorded between 1977 and 1986 (Mori et al., 1989). Numbers nextto spectra indicate 10 second window number. Reproduced with permission from Elsevier. (b)Spectrogram for VLPs from over 2 years at Kı¯lauea (Dawson et al., 2010). Note the lack of a scalefor the spectra. Reproduced with permission from Wiley.Time (s)Frequency (Hz)2 4 6 8 10 12 14 16 184812162024Figure A.4: Greyscale spectrogram from a volcanic earthquake, recorded on White Island, NewZealand, in February 1992 (Sherburn et al., 1998). Greyscale is achieved by displaying differentpoint densities. Reproduced with permission from Elsevier.140A.2. Some Ideas for Improvementare thus necessary.A.2.3 Perceptually Uniform Color MapsFigure A.5 shows a spectrogram with a variety of features from Kı¯lauea at station OTL with threedifferent color maps. The top image uses the MATLAB R© standard “jet”, which results in an appar-ent sharp contrast between spectral power values around 10–15 dB (blue to cyan), and then againaround 25–30 dB (green to yellow to orange). Whereas the range perceived as mostly uniform bluespans more than 10 dB, the range perceived as cyan only covers up to roughly 5 dB. Furthermore,the lightness gradient between cyan and yellow is very low, which may result in masking of fea-tures in the data (Kovesi, 2015). Similar imbalances with the other colors may cause some parts ofa given dataset to appear more prominent than others. In order to avoid these issues, Kovesi (2015)designed a series of perceptually uniform color maps, where flat spots as well as sharp artificial con-trasts are minimised. For full details of these implementations see Kovesi (2015). Using a better,more perceptually uniform rainbow color map for the spectrogram (Fig. A.5, second spectrogram)shows that the apparent strong change from high to low spectral power and back to high values be-tween Phases I and II is partly an artifact of the color map used in the top spectrogram. Despite thisimprovement, the second rainbow color map still suffers from a reversal of the lightness gradientfrom yellow to red (see discussion in Section A.1 and Fig. A.2). A color map based on only onecolor with a constant lightness gradient can help to alleviate this issue (Fig. A.5, third spectrogram).This approach is equivalent to using a suitable greyscale map.In summary, all of the approaches mentioned above have their own advantages and disadvan-tages. There is no unique “best” choice. Instead, the most suitable option depends on the type anddistribution of data to be visualized. However, most studies agree that the default rainbow colormap, that MATLAB R© and other software packages (used to) have built-in, is the least desirableoption, and a better choice can almost always be made. At the very least, any data visualization thatuses color (including greyscale) should have a legend so that the perceived colors can be referencedagainst numerical values.141A.2. Some Ideas for Improvement02 x 104 frequency (Hz) 12345678frequency (Hz) 12345678date 3/6 3/7 3/8frequency (Hz) 12345678dB010203040dB010203040dB010203040Figure A.5: Spectrogram from Hawai‘i at station OTL during intrusion in 2011 with different colormaps. For description of the data see Fig. 2.5. Spectrogram panels show (from top to bottom)MATLAB R© color map “jet”, a rainbow color map implementation and a linear blue color mapimplementation by Kovesi (2015). The second and third color maps are designed to be more per-ceptually uniform. Figure modified from Chapter 2, reproduced with permission from Wiley.142

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