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Time domain studies of short period teleseismic P phases Basham, Peter William 1967

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TIME DOMAIN STUDIES OP SHORT PERIOD TELESEISMIC P PHASES by PETER WILLIAM BASHAM B.A.Sc. University of B r i t i s h Columbia, 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of Geophysics We accept t h i s thesis as conforming to the required standard University of B r i t i s h Columbia September, 1967 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and S t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my Depar tment o r by h.iJs r e p r e s e n t a t i v e s . It i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l no t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . P. W. Basham D e p a r t m e n t o f Geophysics The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada Date September 14, 1967 i ABSTRACT Porty-one seismic events recorded on the plains of western Alberta are subjected to a detailed study i n the time domain. A "P-detection" time-varying p o l a r i z a t i o n f i l t e r i s described and applied to the events to detect segments of strong P motion i n the f i r s t 25 seconds of the P phase coda. On seismograms of 23 events, 12 of which have reported depths shallower than 40 km, pP phases have been i d e n t i f i e d ^ sP phases have been i d e n t i f i e d on 9 of the events. Considering estimated accuracies of observed and calculated pP-P times, assigned f o c a l depths are accurate to within -15 km. A varying upper c r u s t a l structure i s found to make a similar contribution to the v e r t i c a l components of the P phase f o r stations at separations up to 160 km. The r a d i a l components at these stations are similar only during time segments of strong P motion. The d i s s i m i l a r i t y i n other time segments of the r a d i a l components i s a t t r i -buted to d i f f e r e n t amplitudes and time-delays f o r PS converted phases generated at c r u s t a l layer interfaces. The largest PS converted phase, with amplitude up to about 1.5 that of P, i s generated at the base of the sediments. i i A small number of PS converted phases generated at the base of the crust have been identified. i i i TABLE OP CONTENTS CHAPTER I INTRODUCTION 1-1 The AINA Seismic Project 1 1- 2 Scope of the Present Study 2 CHAPTER II DATA ACQUISITION 2- 1 instrumentation 5 2-2 The F i e l d Program 7 2-3 Events Recorded 11 2- 4 D i g i t a l Records 15 CHAPTER III PRELIMINARY FILTERING AND ROTATION 3- 1 Bandpass F i l t e r i n g 16 3-2 Seismogram Rotation about the V e r t i c a l Component 17 3- 3 Seismogram Rotation about the Transverse Component 22 CHAPTER IV DETECTION OF RECTILINEAR MOTION 4- 1 Cross-correlation F i l t e r Functions 25 4-2 Normalized and Phase Selective F i l t e r s 33 4-3 General Discussion of F i l t e r Response 35 4-4 Selection of Appropriate Processor 37 4-5 Description of P-Detection (P-D) Processor 40 4-6 Results of P-D Processing 42 i v CHAPTER V GENERAL RECORD CHARACTER 5-1 Strength and Character of Onset 47 5-2 E f f e c t s of the Source Radiation Pattern 47 5-3 Some Observed Radiation Pattern E f f e c t s 52 5-4 Duration of the P Phase 57 5- 5 Period of Motion 60 CHAPTER VI COMPARISON OP STATION RECORDS 6- 1 Introductory Remarks 63 6-2 Comparison of V e r t i c a l Records 64 6-3 Comparison of Radial Records 72 6- 4 Significance of Results 76 CHAPTER VII SECONDARY SOURCE PHASES 7- 1 introductory Remarks 85 7-2 Amplitude Considerations 88 7-3 Crustal Columns at the Source 91 7-4 The Path of pP Above the Source 93 7-5 Picking and Timing Secondary Phases 96 7-6 Summary of pP Results 100 7-7 Summary of sP Results 103 7- 8 Other Possible E a r l y - A r r i v i n g Phases 105 CHAPTER VIII SOURCES OP PHASE DISTORTION 8- 1 Introductory Remarks 111 8-2 Times and Amplitudes of Lo c a l l y Generated SV 112 8-3 Examples of Lo c a l l y Generated SV 117 8-4 Examples of Transverse Motion 123 V CHAPTER IX SUMMARY AND CONCLUSIONS 9-1 Summary , 128 9-2 Conclusions 130 CHAPTER X SUGGESTIONS FOR FURTHER RESEARCH 10-1 Bandpass and Po l a r i z a t i o n F i l t e r i n g 134 10-2 pP and Focal Depth Assignment 135 10-3 PS Converted Phases 136 REFERENCES 137 APPENDIX A THE LANCZOS NUMERICAL FILTER 140 APPENDIX B LISTING OF FORTRAN IV SUBROUTINE "REMODE" 143 v i LIST OP TABLES TABLE I Description of Stations 10 TABLE II Summary of Earthquake Locations and Other Pertinent Data 12 TABLE III R.M.S. Amplitude Signal/Noise Ratios 66 TABLE IV Errors i n pP-P Time Resulting from Assumption of V e r t i c a l Reflection 95 TABLE V Summary of pP-P Calculations 101 TABLE VI Summary of sP-P Calculations 104 TABLE VII Wavelengths of Compressional Waves i n the Layers of the Alberta Crust 115 TABLE VIII V e l o c i t y Ratios i n the Alberta Crust 115 v i i LIST OP FIGURES FIGURE 1 FIGURE 2 FIGURE 3 FIGURE 4 FIGURE 5 FIGURE 6 FIGURE 7 FIGURE 8 FIGURE 9 FIGURE 10 FIGURE 11 FIGURE 12 FIGURE 13 Laboratory layout of FM magnetic tape re c o r d i n g seismograph. 6 Displacement s e n s i t i v i t y of record-i n g system at 6 db a m p l i f i e r input attenuator s e t t i n g . 8 A l b e r t a recording l o c a t i o n s 9 8 l p o i n t bandpass f i l t e r 18 Seismogram r o t a t i o n : (a) about v e r t i c a l component, (b) about t r a n s -verse component. 20 Example of r o t a t i o n of h o r i z o n t a l motion i n t o r a d i a l and transverse components. 21 E p i c e n t r a l d istance vs. angle of incidence of P wave at the base of the c r u s t ( a f t e r Ichikawa, personal communication). 23 D e t e c t i o n of P and SV motion by product of v e r t i c a l and r a d i a l com-ponent of motion. 26 Sample f i l t e r f u n c t i o n s and cor-responding response f u n c t i o n s f o r input s i n u s o i d s . 32 H a l f - c y c l e cosine f u n c t i o n i l l u s t r a t -i n g approximate response of normalized REMODE processors. 38 An example of the e f f e c t of the P-Det e c t i o n Processor. 43 An example of an event w i t h strong P motion which does not require P-Detect i o n Processing f o r i d e n t i f i c a t i o n . 45 An example of the P-D processor detect-i n g a common secondary phase i n d i s -s i m i l a r s i g n a l s . 46 v i i i FIGURE 14 FIGURE 15 FIGURE 16 FIGURE 17 FIGURE 18 FIGURE 19 FIGURE 20 FIGURE 21 FIGURE 22 FIGURE' 23 FIGURE 24 FIGURE 25 FIGURE 26. FIGURE 27 T h e o r e t i c a l P wave displacement p a t t e r n ( r i g h t ) f o r each of three mechanism f o r c e systems: (a) s i n g l e couple, (b) double couple, and (c) double d i p o l e ( a f t e r Stevens, 1966). O r i e n t a t i o n s of source P r a d i a t i o n p a t t e r n s which w i l l produce: (a) strong P and weak pP, (b) weak P and strong pP, and (c) strong P and strong pP. Two New B r i t a i n events w i t h opposite r a d i a t i o n p a t t e r n e f f e c t s . Two North A t l a n t i c earthquakes showing weak onset r e l a t i v e to secondary a r r i v a l . E f f e c t s ' of f o c a l depth and c r u s t a l type on appearance of P phase. Average period of 20 seconds of P motion vs. e p i c e n t r a l d i s t a n c e . VERT components of three s i m i l a r events. VERT components of three events d i s t o r t e d by n o i s e . VERT components of two near events w i t h d i s t i n c t d i f f e r e n c e i n s i g n a l c h a r a c t e r , VERT components of two s i m i l a r near events. RAD components of f o u r s h o r t - p e r i o d events. RAD components of three long-period events. Sedimentary columns under A l b e r t a r e c o r d i n g s i t e s showing P v e l o c i t i e s i n km/sec. Ex t r a p o l a t e d c r u s t a l s t r u c t u r e under A l b e r t a s i t e s ( a f t e r Cumming and Kanasewich, 1966) showing P and S ray paths. 49 51 55 56 59 62 65 68 69 71 74 75 78 80 ix FIGURE 28 FIGURE 29 FIGURE 30 FIGURE 31 FIGURE 32 FIGURE 33 FIGURE 34 FIGURE 35 Precambrian basement under recording area (after Garland and Burwash, 1959). 83 Four c r u s t a l columns used f o r c a l c u l a t -ing pP-P and sP-P delay times (after Menard, 1967). Thicknesses i n km are shown on the l e f t and P v e l o c i t i e s i n km/sec on the right of each layer. W, the water depth, was determined from bathometric maps f o r each event. Simulated pP path above the source. High qua l i t y P-D records showing secondary phases a r r i v i n g at an iden-t i c a l time on two stations. Three events with PcP a r r i v i n g about 5 seconds aft e r P. Three events with multiple secondary a r r i v a l s . Examples of possible PS^ phases. V e r t i c a l - r a d i a l p a r t i c l e motion plots of P phases. Each plot con-tains 2.4 seconds of motion. The beginning of each plot i s denoted by a heavy dot. 6 i s the approxi-mate angle of incidence at the surface. 120 92 95 98 106 108 118 FIGURE 36 Horizontal onset o r b i t a l motion. 125 X ACKNOWLEDGEMENTS The author would l i k e to thank Dr. R.M. E l l i s f o r many valuable discussions during the AINA Seismic Project i n Ottawa and throughout the research f o r t h i s thesis at the University of B r i t i s h Columbia. Dr. E l l i s also gave a c r i t i c a l appraisal of the manuscript. Gratitude i s expressed to Dr. K. Whitham, Chief, Seismology D i v i s i o n , Observatories Branch, Department of Energy, Mines, and Resources f o r stimulating discussions, to Dr. R.W. Yole, Department of Geology, Carleton University f o r providing the geological information, and to Dr. J.A. Jacobs, Head of the Department of Geophysics, University of B r i t i s h Columbia f o r the use of departmental f a c i l i t i e s . The author i s indebted to the A r c t i c Institute of North America f o r extending f i n a n c i a l support during educational leave. This research was sponsored by the A i r Force Office of S c i e n t i f i c Research, Office of Aerospace Research, United States A i r Force under AFOSR Grant AF-AFOSR-702-67 to the A r c t i c I n s t i t u t e of North America. 1 CHAPTER I INTRODUCTION 1-1 The AINA Seismic Project In 1962 the A r c t i c I n s t i t u t e of North America received from the A i r Force Office of S c i e n t i f i c Research/ United States A i r Force, a grant to undertake a project e n t i t l e d "Effects of Location of Seismograph Stations on the Records Obtained". This constituted a part of the United States Department of Defense, Advanced Research Projects Agency's program "Vela Uniform", the program undertaken to improve the c a p a b i l i t y of d i s t i n g u i s h i n g underground nuclear explosions from natural earthquakes. This project w i l l be referred to as the "AINA Seismic Project" throughout t h i s thesis. The broad aim of the AINA Seismic Project was to examine seismograms from the stations of the Canadian seismo-graph network, to define station to station and earthquake to earthquake differences,. and to search f o r an explanation of any differences which may be found. The ultimate aim was to determine l o c a l e f f e c t s i n s u f f i c i e n t d e t a i l to allow t h e i r removal from the seisinogram; t h i s would enable a study to be made of seismic 2 signals from a distant source without the added complications due to cr u s t a l layering at the recording s i t e . The p r i n c i p a l early work of the AINA Seismic Project has been reported i n two papers: ichikawa and Basham (1965) and Utsu (1966). These dealt with u n i f i e d magnitude residuals and spectral analysis studies of P,phases using data hand-d i g i t i z e d from photographic seismograms. The second phase of the project used data automatically d i g i t i z e d from records of a s p e c i a l l y constructed seismograph system operated at four locations i n Alberta. The seismograph system has been described by Bancroft and Basham (1967), who also present d e t a i l s of the v i r t u a l l y simultaneous d i g i t i z a t i o n of the three components of motion of the events recorded. The Alberta Experiment was designed to test pro-cedures f o r detecting the e f f e c t i n the short-period range of the crust f o r a seismic recording area where the upper crust was geologically simple and well defined. At the time of writing, a report on the results of frequency analysis of the events of the Alberta Experiment (see Section 2-3) i s i n preparation by R.M. E l l i s and the present author ( E l l i s and Basham, 1967). 1-2 Scope of the Present Study The work undertaken f o r t h i s thesis was a detailed study of the Alberta Experiment events, r e s t r i c t e d to the time 3 domain, and directed toward answering the question: what i s the nature and o r i g i n of the seismic signals which contribute to the short-period recording of a teleseismic event within about 25 seconds of the onset of the P phase? This question i s pertinent to c r u s t a l e f f e c t studies and to the fundamental problem of seismogram composition. As an aid to i d e n t i f i c a t i o n of the types of seismic wave motion present on the seismograms, a l l events have been processed with a s p e c i a l l y designed time-varying p o l a r i z a t i o n f i l t e r . This processor, denoted "P-Dn, for P-detection, i s an adaptation of the REMODE processor developed by a group of researchers at the Seismic Data Laboratory, Teledyne, i n c . (Mims and Sax, 1965, G r i f f i n , 1966a and 1966b, and Sax, 1966). Passage of P motion by the P-D processor i s dependent on i t s amplitude and degree of r e c t i l i n e a r i t y ; a l l motion which Is predominantly of S type i s rejected. Before presenting the p r i n c i p a l r e s u l t s of these studies, the i d e n t i f i c a t i o n of wave motion i n the P wave coda, two chapters are presented i n which general seismogram appearance i s considered. The f i r s t , Chapter V, deals with the features of a P phase which constitute i t s general character; the second, Chapter VI, gives a comparison of P phase records at various p a i r s of stations at which they were recorded. The P-D processor detects much strong P motion 4 within the 25 second P phase coda of most of the events. Most of t h i s signal energy can be attributed to secondary source phases, i . e . , phases which arise i n the general earth-quake source region but which are delayed varying amounts and arrive at a distant station a f t e r the main P wave. The strongest phases of t h i s type are pP, which i s a r e f l e c t i o n of the main P wave from the surface of the earth above the source, and sP, which i s a r e f l e c t i o n from the surface as P of the source-generated S wave. pP phases have been t e n t a t i v e l y i d e n t i f i e d on 23 of the 40 earthquake seismograms i n the s u i t e . Twelve of these earthquakes had reported f o c a l depths shallower than 40 km. In addition, sP phases have been i d e n t i f i e d on 9 of the same seismograms. These and other r e s u l t s of the study of secondary source phases are described i n Chapter VII. Although the detection of P motion by the P-D processor i s dependent on the r e c t i l i n e a r i t y of the P o r b i t a l motion, v e r t i c a l - r a d i a l p a r t i c l e motion diagrams of the P phase exhibit a high degree of e l l i p t i c i t y . The source of the e l l i p t i c i t y can be ascribed to PS converted phases gene-rated within the crust near the recording station. The strongest PS converted phase i s found to be that r e s u l t i n g from P to SV conversion at the interface bet-ween the sedi-ments and the c r y s t a l l i n e basement rock. This and other sources of d i s t o r t i o n of the P phase away from i t s r e c t i -l i n e a r i t y are discussed i n Chapter VIII. 5 CHAPTER II DATA ACQUISITION 2-1 Instrumentation For purposes of recording short-period seismological data, a slow-speed FM magnetic tape recording seismograph (Bancroft and Basham, 1967) was assembled by the AINA Seismic Project s t a f f i n cooperation with the personnel of the Seismo-logy Divi s i o n , Observatories Branch, Department of Energy, Mines, and Resources. Because t h i s seismograph system was used to c o l l e c t the data discussed i n t h i s thesis, f o r purposes of completeness a b r i e f description of the instrumentation w i l l be given here. A laboratory layout of the seismograph i s shown i n Figure 1. Frequency-modulated signals are written by a slow-speed (3/32 ips) IRIG standard magnetic tape recorder on 7-track tape. Using 10 1/2 inch reels of 1.0 mil tape the recording period Is 5.3 days. Three components of seismic ground motion are detected by seismometers with a natural frequency of 0.5 Hz, amplified with phototube-galvanometer amplifiers with a natural frequency of 5 Hz, and presented to the recorder at two gain l e v e l s separated by 12 db. The Figure 1. Laboratory layout of FM magnetic tape recording seismograph. 7 seismic signals require 6 tape tracks; the seventh i s used to record time signals. Overall gain Is set with the ampli-f i e r input attenuators. A sample 6 db l e v e l (amplifier Input attenuation) displacement s e n s i t i v i t y curve f o r the system i s shown i n Figure 2. As each component amplifier has a s l i g h t l y d i f -ferent o v e r a l l gain, and may be set at a d i f f e r e n t Input attenuation, a normalization factor can be applied during playback to standardize a l l signals to the response shown i n Figure 2. The inverse of the curve of Figure 2 can be applied to any signal when actual ground displacement i s required. 2-2 The F i e l d Program During the period June to October, 1965, two of the seismograph systems described In section 2-1 were operated at four s i t e s i n western Alberta. The recording s i t e s , Leduc, Warburg, Alder F l a t s , and Rocky Mountain House are shown on the map i n Figure 3 by name abbreviation and station number. The l o c a t i o n and s i t e description of each station i s given i n Table I. One system was operated throughout the entire recording period at Leduc. The other system was operated successively f o r approximately 6 week periods at Warburg, Alder F l a t s , and Rocky Mountain House. The Leduc s i t e i s on sandstone and shale bedrock 8 Figure 2. Displacement s e n s i t i v i t y of recording system at 6 db amplifier input attenuator setting. s RECORDING SITES MAJOR HIGHWAYS 0 50 100 I i 1 (KILOMETERS) A A ALD (3) WAR (2) \ \ EDMONTON I / I \ LED (1) / A RMH (4) / I \ \ CALGARY s B.C. *. ALBERTA v . Figure 3 . Alberta recording locations. 10 TABLE I DESCRIPTION OP STATIONS STATION NAME LEDUC (LED) STATION NUMBER LATITUDE 53° 13 ! N LONGITUDE 1139 21» W SITE DESCRIPTION University of Alberta seismograph vault, 8 miles east of Leduc town. WARBURG (WAR) 53° 10' N 114° 19' W Concrete basement of vacant house within Warburg town.. ALDER FLATS (ALD) 52° 56' N 114° 57f W Concrete basement of vacant house within Alder F l a t s town. ROCKY MOUNTAIN HOUSE (RMH) . 52° 24' N 114° 57' W Concrete f l o o r of vehicle garage 3 miles northwest of Rocky Mountain House. 11 of the Edmonton (Upper Cretaceous) formation. The Warburg, Alder F l a t s , and Rocky Mountain House s i t e s are, respectively, on approximately 10, 100, and 30 feet of unconsolidated d r i f t and s o i l above the shale and sandstone of the Paskapoo (Tertiary) formation. Geophysical surveys and well logs provide good control of the sedimentary section In the recording area. Further d e t a i l s of the t o t a l c r u s t a l section w i l l be given i n a l a t e r chapter. 2-3 Events Recorded During any five-month period many s i g n i f i c a n t earth-quakes occur throughout the world. Compared to many of the world seismograph stations the recording stations were se i s -mically quiet s i t e s ; seismic background noise hear 1 Hz was approximately 20 millimicrons peak-to-peak at each of the four stations. A number of earthquakes occurred during the recording period which were large enough to over-load the FM tape and were, therefore, unusable. Many small events were detected but were not s u f f i c i e n t l y above the background noise to constitute good qua l i t y records. Forty-one events were chosen as suitable f o r analysis; these consisted of 40 earthquakes and the nuclear explosion LONG SHOT. A summary of the event locations and other pertinent data i s given In Table I I . The f i r s t two columns of Table II give the event number and the number of the second station on which i t was TABLE II SUMMARY OP EARTHQUAKE LOCATIONS AND OTHER PERTINENT DATA 12 EVENT SECOND REGION LATITUDE LONGITUDE DEPTH DATE TIME MAGNI- A NUMBER STATION (KM) Y M D H M S TUDE (deg) 1 2 Aleutians +52.6 +173.2 ' 25 65 06 09 13 26 52 5.6 42 2 2 Aleutians +51.8 +174.1 35 65 06 11 02 37 35 5.5 42 3 2 N. Chile -20 .3 - 68.9 103 65 06 12 18 50 11 5.8 83 4 2 Hokkaido +41.9 +143.4 32 65 06 13 07 06 14 5.7 64 5 2 Aleutians +52.3 +172.0 54 65 06 19 06 33 13 5.5 43 6 2 Oregon +42.8 -126.0 33 65 06 20 18 04 36 5.6 13 7 2 S. Alaska +56.6 -152.9 36 65 06 23 11 09 15 5-7 23 8 2 S. Alaska +56.6 -152.8 25 65 06 23 12 23 22 6.0 22 9 2 Bouvet I s l . -54.5 + 5.6 33 65 06 27 09 45 48 5.9 139 10 2 S. Alaska +60.3 -141.2 12 65 06 27 11 08 56 5.3 17 11 2 Aleutians +51.7 +176.5 60 65 06 30 08 33 32 6 . 0 41 12 N. Atlantic +52.9 - 34.2 33 65 07 05 08 31 59 5.7 45 13 2 Greece +38.7 + 22.6 28 65 07 06 03 18 44 5.9 81 14 3 Solomons - 9.7 +159.8 23 65 07 17 07 20 31 6.4 95 15 3 Aleutians +53.3 +170.4 26 65 07 21 17 52 31 5.7 43 16 3 New B r i t a i n - 5.3 +151.7 47 65 08 05 00 07 50 6.3 97 17* 3 New Hebrides -15.4 +166.9 26 65 08 11 03 40 56 6.3 96 18 3 New Hebrides -15 .3 +167.2 33 65 08 11 22 31 49 6.4 96 19 3 New B r i t a i n - 5.3 +152.2 41 65 08 12 12 57 10 5.9 96 20 3 N. Chile - 1 9 . 0 - 69.1 129 65 08 20 09 42 49 6 . 0 82 21 3 F i j i -22.9 -176.3 77 65 08 20 21 21 51 6 .2 93 22 3 Mexico +15.9 - 9 6 . 2 12 65 08 24 00 56 21 5.5 40 23 3 Mexico +16.2 - 9 6 . 2 31 65 08 24 01 01 01 5.6 39 TABLE II (CONTINUED) 13 EVENT SECOND REGION LATITUDE LONGITUDE DEPTH DATE TIME MAGNI-" A NUMBER STATION (KM) Y M D H M s TUDE (deg) 24 3 S. Alaska +59.4 - 1 4 5 . 6 19 65 08 24 13 12 19 5 . 4 18 25 4 S. Alaska +57.5 -152.1 25 65 09 08 03 26 21 5 . 6 22 26 4 S. Alaska +55.7 -155.4 33 65 09 08 11 16 34 5 . 4 24 27 4 Cent. Am. + 6.5 - 8 4 . 4 27 65 09 09 10 02 25 5 .5 52 28 4 New B r i t a i n - 5 . 3 +153.0 67 65 09 11 06 53 02 6 .3 96 29 4 New B r i t a i n - 6 .3 +151.6 48 65 09 12 08 40 13 6 . 2 98 30 4 C a l i f o r n i a +40 .4 -125.7 33 65 09 16' 04 10 23 5 . 6 15 31 4 S. Alaska +59.5 - 1 4 5 . 1 22 65 09 18 20 46 39 5 . 3 1.8 32 4 China Sea +29.1 +128.2 197 65 09 21 01 3.8 30 6 . 0 82 33 4 N. Atlantic +40 .7 - 50 .0 23 65 09 21 03 26 37 5 . 3 44 34 4 Aleutians +51.9 +175.5 41 65 09 27 05 09 13 5.5 41 35 4 S. Alaska +59.7 - 1 4 3 . 4 19 65 09 30 23 47 4 1 4 . 8 13 36 4 Kuriles +49 .5 +156.5 33 65 10 03 14 45 27 5 . 9 53 37 4 Aleutians +51.4 -173.9 43 65 10 08 16 32 32 5 . 2 36 38 4 Aleutians +51.6 -173.8 32 65 10 20 11 15 11 5 .4 36 39 4 Cent. Am. +12.5 - 87.4 70 65 10 20 23 54 30 5 .4 46 40 4 Missouri +37.5 - 91 .0 22 65 10 21 02 09 31 5 . 2 22 41 4 Long Shot +51.4 +179.2 1 65 10 29 21 00 00 6 .0 40 The station 1 d i g i t a l seismogram of event 17 was not available. The wrong section of the analog record had been d i g i t i z e d . 14 recorded; a l l of the events were recorded at st a t i o n 1. Through-out the text and on the I l l u s t r a t i o n s a l l events w i l l be referred to by event and station number! fo r example, 17-3 i s event 17 recorded on station 3 . The location, o r i g i n time, and u n i f i e d magnitude are those given by the United States Coast and Geodetic Survey (U.S.CG.S.) " Preliminary Determination of Epicenters" cards. As the maximum station separation (1-4) i s l e s s than 2° , the epicentral distances ( A ) i n Table II are accurate to within 1° f o r any p a r t i c u l a r station. An event i s defined to be teleseismic i f i t occurs within the epicentral distance range 20° to l 8 o ° . The Atomic Weapons Research Establishment (A.W.R.E.)(1965), i n studies related to nuclear explosion detection, define a narrower range "source window" which extends from 30° to 90° epicentral distance. It i s through t h i s "window" that the source can be "seen" almost undisturbed by the transmission path between the source and the recorder. At distances l e s s than 30° the signal i s disturbed by the c r u s t a l and upper mantle shadow and t r a n s i t i o n zones, and at distances greater than 90° by the core shadow and t r a n s i t i o n zones. Twenty-one of the events i n Table II f a l l within t h i s "source window", 11 at smaller distances, and 9 at larger distances. Eight of the events occurred i n a continental environment, the remainder i n an oceanic or t r a n s i t i o n a l oceanic-continental environment. Three events have reported depths greater than 100 km, 7 have depths between 45 and 77 km, and 15 the remaining 31 are shallower than 43 km. 2-4 D i g i t a l Records These 4 l events, each with a recording at two stations, were available to t h i s study i n d i g i t i z e d form on d i g i t a l mag-netic tape. The d i g i t i z i n g procedure and tape format has been described by Bancroft and Basham (1967). The d i g i t i z i n g rate was 16.6 samples per second y i e l d i n g a Nyquist frequency of 8 . 3 Hz. Eleven minutes of the three components of seismic information plus the time track have been retained f o r each event at each of the two stations, beginning approximately 1 minute p r i o r to the P a r r i v a l time. The d i g i t i z a t i o n was done on the Department of Energy, Mines, and Resources CDC 3100 computer. A l l computing for t h i s thesis was done on the University of B r i t i s h Columbia IBM 7044 computer. 16 CHAPTER III PRELIMINARY FILTERING AND ROTATION 3-1 Bandpass F i l t e r i n g E l l i s and Basham (1967) have shown that the P wave signal energy In the recording passband (see Figure 2) f o r these events i s concentrated i n the frequency band between 0 . 3 and 2.5 Hz. It i s shown i n Chapter V by a study of the period of P phase motion that the dominant period can vary considerably among events within t h i s equivalent frequency range. Many of the events are contaminated by background noise at both sides of t h i s frequency band. At the low frequency end there are the well-known oceanic microseisms with periods between about 3 and 10 seconds. At the high frequency end of the band there i s considerable contamination of many of the events by c u l t u r a l noise. Although Leduc i s the most is o l a t e d s i t e (see Table I) there are occasional bursts of noise from farm machinery and a l o c a l road i n the area. Each of the other three s i t e s i s i n close proximity to moderately heavy vehicular t r a f f i c which contributes noise i n t h i s band. The frequency of t h i s c u l t u r a l noise i s generally 17 3 to 4 Hz. For a production processing run (P-detection to be described in Chapter IV) i t was desirable to use a single bandpass f i l t e r on a l l events before Input to the processor. The bandpass f i l t e r BP-1, whose response i s shown in Figure 4, was used for this purpose. This i s an 8 l-point symmetrical f i l t e r of the Lanczos type (Lanczos, 1957) with corners at 0.25 and 2.0 Hz. A general discussion of the Lanczos f i l t e r i s given In Appendix A. The f i l t e r does not completely eliminate either the high or low frequency noise but was considered the best general f i l t e r for the production run. 3-2 Seismogram Rotation about the Vertical Component A plane P wave i s a compressional wave with dis-placement rectilinear In the direction of propagation. When such a wave enters obliquely a horizontally layered crustal system i t w i l l undergo reflection and refraction and generate reflected and transmitted P and SV waves at each interface. A l l Incident displacement i s in a plane containing the vertical direction and the direction of the great-circle azimuth of approach. The interface boundary conditions require that a l l P and SV displacements generated during passage through a horizontally layered crust must remain in this same plane. Although this i s often far from true in practice, i t i s useful to rotate the three recorded components so that a l l signals accountable in terms of plane P wave propagating through a 18 FREQUENCY (Hz) Figure 4 8l point bandpass f i l t e r response. 19 h o r i z o n t a l l y layered crust are represented on two components, the v e r t i c a l and r a d i a l , the r a d i a l being the horizontal d i r e c t i o n of the g r e a t - c i r c l e azimuth. Theoretically, no signal remains on the transverse hori z o n t a l . This rotation about the v e r t i c a l d i r e c t i o n i s accomplished as shown i n Figure 5(a). The r e s u l t i n g r a d i a l and transverse components are given by the rel a t i o n s R - — C O S OC — E sin »C and T =• W s i n =>C - E Cos oC where oc i s the g r e a t - c i r c l e azimuth from the station to the epicenter measured clockwise from north. N i s the recorded north-south component defined as posit i v e toward the north and E i s the recorded east-west component defined as posit i v e toward the east. This y i e l d s the convention of R being positive away from the epicenter and T posit i v e toward the r i g h t . An example of the e f f e c t of t h i s rotation i s shown i n Figure 6 f o r event 10-1 . Shown are the three o r i g i n a l components and the rotated r a d i a l and transverse. The onset pick i s shown by a broken v e r t i c a l l i n e through each of the components. It can be seen i n Figure 6 that most of the horizontal signal energy i s retained by the r a d i a l component and very l i t t l e retained by the transverse. The transverse i s not s i g n i f i c a n t l y above the background noise u n t i l a slow buildup of energy occurs 15 or 20 seconds after the onset. 20 Figure 5 . Seismogram rotation: (a) about v e r t i c a l component, (b) about transverse component. B'lgure 6 . Example of r o t a t i o n of h o r i z o n t a l motion Into r a d i a l and transverse components. 22 This transverse energy w i l l be discussed i n some d e t a i l i n Chapter VIII. It w i l l be seen there that many events show considerably more transverse energy than does t h i s event. 3-3 Seismogram Rotation about the Transverse Component The specialized f i l t e r s to be described i n Chapter IV require that the signal energy be approximately equally d i s -tributed between the v e r t i c a l and the r a d i a l components. This i s accomplished as shown i n Figure 5(b) by rotating the v e r t i c a l and r a d i a l components about the new transverse component so that each i s 45° away from a specified angle of incidence of the P a r r i v a l f o r the p a r t i c u l a r event. The rotated v e r t i c a l and rotated r a d i a l as described i n Figure 5(b) are given by the r e l a t i o n s VERT = Z C O S ( T T / 4 - i ) + N cosoc sin (7r/4 - i ) + E sinot sin(ir/ 4 - i ) RAD = Z sin (7r/4 - i ) - N cost*. C O S ( T T / 4 - i ) - E sinoCcos (Tr/4 - i ) where i s the azimuth and i the angle of incidence. These re l a t i o n s give the doubly rotated VERT and RAD i n terms of the recorded components. The angle of incidence used i n these c a l c u l a t i o n s i s the angle at the base of the crust. A curve of t h i s angle versus epicentral distance, after Ichikawa (personal communication), i s shown i n Figure J. As the approach path steepens during passage'through the crust (see Figure 27) , use of the angle of incidence at the base of the crust rather than the apparent angle ,of emergence 23 Figure 7. E p i c e n t r a l distance vs. angle of incidence of P wave at the base of the crust (after Ichikawa, personal communication). 24 at the surface has the effect of retaining proportionally more of the signal on VERT than on RAD. This does not make a s i g n i f i c a n t difference to the signal processing described i n Chapter IV. A l l but the nearest events are at epicentral d i s -tances greater than 20° (see Table I I ) , hence the angles of incidence given on Figure 7 w i l l be smaller than 45°. The effect of rotation about the transverse w i l l generally be the addition of v e r t i c a l signal energy to the r a d i a l component rather than visa versa. 25 CHAPTER IV DETECTION OP RECTILINEAR MOTION 4-1 Cross-Correlation F i l t e r Functions An important c h a r a c t e r i s t i c of P and SV seismic signals i s t h e i r r e c t i l i n e a r p o l a r i z a t i o n ; both are i n the vertical-azimuthal plane, but P i n the d i r e c t i o n of propaga-t i o n and SV orthogonal to t h i s d i r e c t i o n . Using the v e r t i c a l and r a d i a l seismograms, operators can be designed which use the r e c t i l i n e a r p o l a r i z a t i o n of the signals compared with e l l i p t i c a l and random p o l a r i z a t i o n of noise to enhance the seismic signals. The simplest operation of t h i s type uses the d i f -ference i n phase relations between the v e r t i c a l and r a d i a l components to dis t i n g u i s h P from SV. This i s a simple motion product operator described i n the diagram and accompanying table i n Figure 8. Forming the zero-lag cross-correlation between the v e r t i c a l and r a d i a l component, usually with some smoothing process, the product i s posit i v e f o r a P wave and negative f o r an SV wave. This operation i s e a s i l y accomplished with data i n either analog or d i g i t a l form. Shimshoni and Smith (1964) describe two non-linear 26 S U R F A C E S I G N S OF COMPONENTS P H A S E z R ZXR +P + + - P - - + +SV - -- S V + — — Figure 8. Detection of P and SV motion b y product of v e r t i c a l and r a d i a l component of motion 27 processes which u t i l i z e p o l a r i z a t i o n f o r signal enhancement. One process uses the product of the time-averaged cross-product and the two components of the o r i g i n a l signal to amplify a l l r e c t i l i n e a r l y polarized signals i n the seismo-gram. The output trace amplitude at each point i s simply the Input trace amplitude multi p l i e d by a time varying constant. The second process f i t s e l l i p s e s to the p a r t i c l e t r a j e c t o r i e s and displays the parameters of the e l l i p s e s as functions of time to separate the r e c t i l i n e a r l y polarized waves and to obtain a rough estimate of t h e i r angle of incidence. A class of more general p o l a r i z a t i o n f i l t e r s , c o l l e c t i v e l y c a l l e d "REMODE" (for r e c t i l i n e a r motion detec-tion) has recently been developed by a group of researchers at Teledyne Inc.; Mims and Sax (1965), G r i f f i n (1966a, 1966b), Sax (I966). These REMODE f i l t e r s are based on the following concept. When a large P or SV phase arrives at a recording s i t e , i t s p a r t i c l e motion orbi t w i l l be more r e c t i l i n e a r than e l l i p t i c a l or random, i f the segments of the rotated v e r t i c a l and r a d i a l components containing the phase are cross-correlated, the even part of the cross-correlation function w i l l be large r e l a t i v e to i t s odd part. When the even part of the function i s used as a f i l t e r on the same segments of the components, the f i l t e r w i l l pass with least attenuation the frequency band f o r which p a r t i c l e motion i s most r e c t i l i n e a r . A cross-correlation function i s defined f o r a segment of record as 28 t + w/2 c(T) - z(t)r(t +T) dt t - w/2 where t Is the time at the center of the record segment, w Is the segment width, and T i s the lag interval . z(t) and r(t) are the rotated ver t ica l and radial input traces. To determine C(T) i n ideal l imit ing cases, consider z(t) and r(t) when they are unit-amplitude sinusoids with a phase difference of 9. Equation (1) becomes which, after integration and simplification, becomes The sinusoidal motion w i l l be purely rect i l inear when 0=0, and purely c ircular when 6 = ir/2. Prom equation (2) the cross-correlation function for rect i l inear motion becomes t + w/2 t - w/2 CREC ^ ^ = 1 / / 2 [ s l n w s i n 2 t ] s i n T + 1/2fw - sin w cos 2t j cos X 29 and the cross-correlation function for c i r c u l a r motion becomes CCIR ^ ) = 1 /' 2 [ s l n w s i n 2 t ] 0 0 3 ^ + 1/2 £ sin v/ cos 2t-w j^ sin T- (4) These are functions which re t a i n the window length and record time as parameters. If w i s large compared to unity then s x / s i n w s i n 2t w " | s i n w cos 2t and C R E C (T) ^ | cos T (5) and C C I R (V -| sin T . (6) Thus, fo r a long window length the r e c t i l i n e a r c r o s s - c o r r e l a t i o n function i s a cosine (even) and the c i r c u l a r c ross-correlation function i s a sine (odd). Now consider using the even parts of these two cr o s s - c o r r e l a t i o n functions (equations (5) and (6)) as f i l t e r s f o r the input sinusoids. The even part of the c i r c u l a r function i s i d e n t i c a l l y zero and the input sinusoid w i l l be attenuated completely. Convolution of the even part of the r e c t i l i n e a r function, i . e . , the entire C R E^ (T)> with one of the input sinusoids w i l l y i e l d an amplified sinusoid as output. In the intermediate case of a phase difference-0 < Q < TT/2, or the more p r a c t i c a l case where the input sinusoids are distorted by additional random motions, the cross-correlation function w i l l contain both even and odd parts, the even part predominating i f the motion i s more 30 nearly r e c t i l i n e a r , the odd part predominating i f the motion i s more nearly c i r c u l a r . The even part of a general C(T ) as i t varies continually along the records would be an appropriate time varying f i l t e r f o r passing motion i n proportion to the degree of r e c t i l i n e a r i t y . However, i t i s computationally more e f f i c i e n t to use a s l i g h t l y d i f f e r e n t function. The procedure adopted by the Teledyne researchers for the REMODE processor ( G r i f f i n , 1966a) was to use an even function which has the form of equation (5) when the motion i s i d e a l l y r e c t i l i n e a r . This i s accomplished by defining a cross-correlation function f o r positive lags as °t,w ( + T > -t + w/2 z ( t ) r ( t +T)dt, t - w/2 and by making the function even by r e f l e c t i n g the p o s i t i v e -lag c o r r elations into negative lags by imposing the condition Ct,w ( -?> = Ct,w ( + ? ) . The f i l t e r function i s then defined as (2)£tjW (V) - c t ^ w ( T ) , where the prescript, ( 2 ) , denotes the Teledyne designation for REMODE 2, and the subscripts t and w denote dependence of the f i l t e r function on the record time and window length respectively. For the case of input in-phase sinusoids 31 equation (7) w i l l be i d e n t i c a l to equation ( 3 ) , and f o r w >> 1 equation (9) w i l l be i d e n t i c a l to equation ( 5 ) . When the Input sinusoids are out-of-phase (9 - TT/2) the procedure of equation (8 ) , by r e f l e c t i n g the sine function (equation (6)) about the point V = 0, would place a TT phase s h i f t at the center of the f i l t e r function. Such a f i l t e r function would reject motion having the same period as the c i r c u l a r input sinusoids. To demonstrate the response of , +. , T ( T ) f o r \d) i>, w i n - and out-of-phase sinusoids, and to carry the procedure one step closer to the p r a c t i c a l case, ( g ) ^ t w ^ ^ a n d i t s frequency response have been calculated f o r a p a r t i c u l a r data sample i n t e r v a l , window length, and t o t a l lag length. The r e s u l t s of these computations are shown i n Figure 9 . The input sinusoids with 16 sample points per cycle are shown on the top of Figure 9 . The r e c t i l i n e a r motion i s shown with in-phase sinusoids and the c i r c u l a r motion with R lagging Z by w/2. The r e c t i l i n e a r and c i r c u l a r f i l t e r functions shown i n the center of Figure 9 were computed using the d i g i t a l equivalents of equations (7 ) , (8 ) , and (9) with w = 20 sample i n t e r v a l s and maximum "V = 12 sample i n t e r v a l s . This value of w, being greater than one period (2TT), conforms generally to the requirements f o r equations (5) and (6) but Is not long enough f o r the f i l t e r functions to take the exact form of equations (5) and ( 6 ) . A maximum lag of only s l i g h t l y more than half of the window length i s used so that the f i l t e r functions r e t a i n a s i g n i f i c a n t Figure 9. Sample f i l t e r functions and corresponding response functions for input sinusoids. 33 contribution from the input signals at the larger lags. Because of the r e g u l a r i t y of the sinusoidal inputs, the para-meter t does not appear i n t h i s computation; the f i l t e r func-tions are the same at any point i n the record. The e f f e c t that these f i l t e r s w i l l have on the input traces i s well demonstrated by t h e i r cosine transform response functions which are shown at the bottom of Figure 9. For input sinusoids of frequency f the r e c t i l i n e a r f i l t e r has a gain of 80 and the c i r c u l a r f i l t e r a gain of 1.2 at a frequency of f . Therefore, i f the input records contained successive portions of i n - and out-of-phase motion, the i n -phase ( r e c t i l i n e a r ) sections would be amplified by a f a c t o r of about 65 r e l a t i v e to the out-of-phase ( c i r c u l a r ) sections. The f i l t e r responses also demonstrate the necessity of narrow bandpass f i l t e r i n g of experimental input signals. Because of the f i l t e r function truncation, the corresponding response function has large side lobes. For the case of input sinusoids shown i n Figure 9, which can be considered as experimental signals passed by an i n f i n i t e l y narrow band-pass f i l t e r , the r e c t i l i n e a r detection e f f e c t applies only within a small range of the input frequency. 4-2 Normalized and Phase Selective F i l t e r s The response of ( 2 ) ^ t w f ^ ) ' t h e R ^ 0 0 2 2 f i l t e r , depends on the amplitudes of, and the phase difference between, the input signals. The dependence on amplitude can be eliminated 34 by normalizing the f i l t e r function by time-varying estimates of the average power in the input signals, over the same time window as used In the cross-correlation estimates. The normalization factors are determined from zero-lag auto-correlations as t + w/2 t + w/2 I z 2(t)dt I r 2 ( t ) d t (10 and the normalized f i l t e r function becomes where the prescript, (3), i s the Teledyne designation for REMODE 3. The response of the f i l t e r function (3)fEt depends only on the phase difference between the input signals. Some discussion of the form of this response i s given in Section 4-3. The polarity convention for a l l seismograms i s such that the zero-lag cross-correlations between z and r compo-nents w i l l have positive values for P phases and negative values for SV phases (see Figure 8). The Teledyne f i l t e r s REMODE 2A and 3A are modified versions of REMODE 2 and 3 which reject SV motion by setting the f i l t e r functions to zero whenever the zero-lag cross-correlations are negative. The REMODE 2A and 3A f i l t e r functions can, therefore, be given by the relations 35 ( 2 A ) 5 t , w ^ ) " [ ( 2)It,w^) f 0 r Ct,w(°) * 0 0 f o r C t j W ( 0 ) < 0 and (3A)$t>w(T) = r ( 3 ) l t , w ( T ) f o r c t f W ( 0 ) > 0 1 0 f o r C t ) J O ) ± 0 These unnormalized and normalized phase selective f i l t e r s could equally well be defined to reject P rather than SV motion by setting the f i l t e r functions to zero when the zero-lag c r o s s - c o r r e l a t i o n was p o s i t i v e . 4-3 General Discussion of F i l t e r Response The response of the REMODE 2 f i l t e r has been shown i n Figure 9 f o r two ide a l l i m i t i n g cases, pure in-phase and out-of-phase input sinusoids. A f i l t e r function defined by equations ( 7 ) , (8) and (9) with z(t) and r ( t ) as rotated v e r t i c a l and r a d i a l components of an experimental seismogram w i l l be d i f f e r e n t at every point along the record. Although such a f i l t e r cannot be defined a n a l y t i c a l l y i t i s important to gain some understanding of i t s response i n the p r a c t i c a l application. G r i f f i n (1966a), i n an examination of the case of i n f i n i t e window lengths, assumes that ^g)5"t w^ "^  ^ s e n o u& n l i k e the even part of the general CCC) that the response of 36 the even part of C ( T ) w i l l be representative of the response o f (2)5t w^^* G r i f f i n presents the following discussion. Let z. (t) and r. (t) be two transient functions representing T'O ^o segments of two components of a seismogram within some time window centered on t , and l e t t h e i r c ross-correlation func-o' t i o n be defined + oo z. (t) r. (t +T)dt, lo ^o (15) - o o If the two record segments have Fourier transforms Z t 0 ^ C 0 ^ exp [ i (J)z (co , t Q ) j and Rt (c*>)| exp[ i(|) r(co, t o ) ] then C. ( T ) has a Fourier Transform given by 2ir Z t Q(w)| |R t o(oo)| e x p [ i ( ( ( ) r ( c o , t Q ) -(|>z(w, t Q ) ) ] (16) The r e a l part of (16) w i l l be the transform of the even part of C. ( f ) l n equation ( 15) . Therefore, the frequency response °^ (2)i&t w^^) w i l l have the form of 2TT |z t o(co)||R t (CO)| cos[<)>r(co, t Q ) -4>z(co, t Q ) ] , i . e . , i t i s both amplitude and phase dependent. Frequency components of the input signals w i l l be passed i n proportion to the cosine of the phase difference between z. (t) and r. ( t ) . When the f i l t e r function i s normalized with a function 37 similar to equation (10) the response of ^ ) ^ t w^^ w i l l have the form of cos[4> r(co, t Q ) -4> z(co, t Q ) ] . (17) G r i f f i n (1966a) presents a graph of the r a t i o of input to output amplitudes versus the phase difference between the two input records f o r a narrowly bandpass f i l t e r e d teleseism processed with REMODE 3A. The graph shows considerable s i m i l a r i t y to the cosine function, (17)« A half cycle of such a cosine function i s shown i n Figure 10. The response i s +1 and -1 f o r phase differences of 0 and 180 degrees respectively, i . e . , the f i l t e r w i l l pass pure P and pure SV with unit gain. The response is. +1/2, 0, and -1/2 f o r phase differences of 60, 90, and 120 degrees respectively. The e f f e c t of SV re j e c t i o n shown by equation (14) i s represented by the broken l i n e i n Figure 10. The REMODE 3A processor simply has zero response f o r phase differences between 90 and 180 degrees. A Fortran IV subroutine with options to process a two-component time series according to REMODE 2, 2A, 3, or 3A i s shown i n Appendix B. The e x p l i c i t form of the ca l c u l a t i o n used i n t h i s subroutine i s described i n Section 4 - 5 . 4-4 Selection of Appropriate Processor The f i r s t h a l f minute after the onset of a t e l e -38 0 40 80 120 160 PHASE DIFFERENCE BETWEEN Z AND R INPUT SIGNALS (DEGREES) Figure 10. Half-cycle cosine function i l l u s t r a t i n g approximate response of normalized REMODE processors. 39 seismic P phase should contain p r i n c i p a l l y P type motion. As can be seen i n the one seismogram that has been pre-sented (Figure 6 ) , and w i l l be seen on many to follow, the seismic energy i s usually well d i s t r i b u t e d over t h i s i n t e r v a l . It was decided to use a normalized version of the REMODE processor, i . e . , normalized according to the average power i n the input traces, to enhance the stronger signal sections i n the record i n t e r v a l . I t would be expected that there would be more signal i n t h i s i n t e r v a l that tends toward r e c t i l i n e a r ! t y than signal which does not. A REMODE 3 pro-cessor would, therefore, pass more signal than i t would reject, and would pass equally P and SV signals of equal amplitude and r e c t i l l n e a r i t y . One would have to return to the Z and R input signals to decide on the basis of phase re l a t i o n s alone which part of the input was SV. By using a REMODE 3A processor, P i s passed i n amounts proportional to i t s r e c t i l l n e a r i t y and t o t a l energy, and a l l SV motion i s attenuated completely. Strong SV motions can then be detected by noting which portions of the signal were rejected, and which were distinguishably out-of-phase on the input records. A REMODE 3A type pro-cessor, designated "P-Dn f o r P-Detection, was used i n a pro-duction run f o r the 41 events i n t h i s study. The P-D processor i s described In d e t a i l i n the next section. 40 4-5 Description of the P-Detection (P-D) Processor As described i n section 4 - 1 , the basic processor i s REMODE 2. Applying to a seismogram the f i l t e r described by equations ( 7 ) , (8 ) , and (9 ) , the output i n d i g i t a l form can be described by -rLW2 L _ MhLW2-L 7 i = k - L W 2 1 = 1 j = K-LW2 for the z component, and M - L W 2 L _ K + L W 2 - L V 7 -f o r the r component, with the following variable d e f i n i t i o n s k = sample index z^ = k t h rotated v e r t i c a l sample •f" Vi r k = k rotated r a d i a l sample rz = cross-product of the q^ h rotated r a d i a l p , q sample with the (q + p - l ) s t rotated v e r t i c a l sample p = lag number LW2 = 1/2 the window length L = maximum lag gPz^. = k^ h v e r t i c a l output sample gPr^ = k t h r a d i a l output sample 41 Using the normalizing factor from equation (10), K + L W 2 7 U K ^ 2 U K (19) the normalized output i s given by and 3P*k " <*"k " # \ 3 P rk -<T k" ^ k (20) for the vertical and radial output respectively. Using the procedure shown in equation (14), the f i n a l output becomes (P-D VERT) k = 3 P z k • s o for rz for r z k ^ k > 0 < 0 and (21) (P-D RAD)k - 3 P r k = 0 for r z k ^ k > 0 for r z k ^ k < 0, where the designation P-D (for P-Detection) i s given to the fi n a l output. Equations (18) to (21) are used in subroutine "REMODE" shown in Appendix B. Half a minute of signal starting approximately 5 seconds before the onset of P was processed for each of the events liste d in Table II using the P-D processor with a window length of 20 sample intervals and L = 12. The second 42 ha l f minute was processed f o r those events with f o c a l depth greater than 100 km. The window length and L were chosen as suitable a f t e r some experiments on seismograms varying these values. The dominant periods of motion were 1 to 2 seconds. With data d i g i t i z e d at 16.6 samples per second, the window length of 20 sample i n t e r v a l s was a compromise f o r a production run. Throughout the text and on a l l i l l u s t r a t i o n s the components w i l l be referred to as VERT and RAD f o r the doubly rotated v e r t i c a l and r a d i a l Input signal's respectively, and P-D VERT and P-D RAD f o r the P-D processed v e r t i c a l and r a d i a l output signals respectively. 4-6 Results of P-D Processing A few examples of the re s u l t s of P-D processing w i l l be shown here to demonstrate some of the more important e f f e c t s . Others w i l l be shown i n some of the following chapters as i l l u s t r a t i o n s f o r p a r t i c u l a r topics. Figure 11 gives a comparison of the appearance of the input and output records. The VERT record shows two strong signal bursts, the primary P and another approximately 15 seconds l a t e r . As can be seen from the phase r e l a t i o n s on VERT and RAD, the f i r s t burst Is r e l a t i v e l y pure P motion, and i s passed strongly on P-D VERT and P-D RAD. The second burst i s strong on VERT but weaker and distorted on RADj only half of one cycle of t h i s burst i s passed strongly by the 44 processor. The processor e l i m i n a t e s completely a l l other motion on the records. An important e f f e c t shown i n Figure 11 i s the enhancement of the i n i t i a l onset of the two strong s i g n a l b u r s t s . Figure 12 i s included to i l l u s t r a t e that strong P motion does not req u i r e P-D processing f o r I d e n t i f i c a t i o n . The VERT and RAD records are superimposed and the area bet-ween the t r a c e s shaded to emphasise t h e i r s i m i l a r i t y . From the coincidence and in-phase r e l a t i o n of the VERT and RAD components a l l of the energy i n the seismogram can be iden-t i f i e d as r e l a t i v e l y pure P. That t h i s i s true i s shown by the abundant energy r e t a i n e d on P-D VERT and P-D RAD. The a b i l i t y of the P-D processor to detect a common secondary phase at two s t a t i o n s when the seisinograms are not s i m i l a r i s shown i n Figure 13. The two s t a t i o n records are a l l i g n e d on the onset p i c k . The strongest P-D VERT energy burst appears at an i d e n t i c a l time (13 seconds a f t e r onset) on both of the s t a t i o n records. Although passage of t h i s phase i s based p a r t l y on the r a d i a l components which are not shown i n Figure 13, the appearance of the VERT records does not suggest the presence of a s i n g l e strong phase common to the two s e i sinograms. The a b i l i t y of the processor to detect such phases i s used to i d e n t i f y pP and sP phases which are discussed i n Chapter V I I . Figure 12. An example of an event w i t h strong P motion which does not require P-Detection processing f o r i d e n t i f i c a t i o n . Figure 13. An example of the P-D processor d e t e c t i n g a common secondary phase In d i s s i m i l a r s i g n a l s . 47 CHAPTER V GENERAL RECORD CHARACTER 5 - 1 Strength and Character of Onset Experienced seismologists can often look at a t e l e -seismic P phase and, without the benefit of other information, categorize the earthquake as distant or near, deep or shallow, continental or oceanic, etc. This judgement i s made on the basis of the "character" of the P phase. The term "character" i s not e a s i l y defined i n t h i s context but includes such things as the frequency of the o s c i l l a t i o n s , the degree of sinusoidal r e g u l a r i t y of the o s c i l l a t i o n s , the time of duration of strong motion, the strength of the onset r e l a t i v e to l a t e r a r r i v i n g signals, and the time of a r r i v a l of l a t e r a r r i v i n g signals. Some of the parameters of an earthquake which appear to con-t r i b u t e to t h i s general record character w i l l be discussed i n t h i s chapter on the basis of the appearance of the P phase of some of the events i n Table I I . 5 - 2 E f f e c t s of the Source Radiation Pattern For many large earthquakes source mechanism solu-tions can be determined which y i e l d information on the stress 48 system acting i n the f o c a l region. For a summary of the theory and procedure see, f o r example, Stevens (1966). There are believed to be three p r i n c i p a l types of force systems the single couple, the double couple, and the double dipole. These three force systems are shown schematically on the l e f t side of Figure 14. Each w i l l produce an i d e n t i c a l i n i t i a l displacement pattern i n the P wave. This quadrantal displacement pattern i s shown on the right of Figure 14. A p a i r of orthogonal planes i n t e r s e c t i n g i n the focus are oriented such that there i s a separation of areas of com-pressional P f i r s t motion (away from the focus and defined as positive) and d i l a t a t i o n a l P f i r s t motion (toward the focus and defined as negative). The P f i r s t motion on these "nodal" planes i s zero. The orientation of the force systems, and hence of the radiatio n patterns, w i l l depend on the tectonics of the source area and can i n general be con-sidered to have a random d i s t r i b u t i o n . This f i r s t motion displacement pattern expresses i t s e l f as an azimuthal v a r i a -t i o n on world-wide station records; the observed d i s t r i b u t i o n enables the determination of the orientation of the nodal planes. Each of the t h e o r e t i c a l force systems leads to a th e o r e t i c a l f a u l t i n g model f o r the earthquakes, one of the nodal planes being the f a u l t plane and the other orthogonal to i t . An additional feature of f a u l t i n g i s the azimuthal v a r i a t i o n which expresses i t s e l f not only i n a f i r s t motion pattern but also i n a v a r i a t i o n of signal amplitude and shape with azimuth. 49 A (b) (c) Figure 14. Theoretical P wave displacement pattern (right) for each of three mechanism force systems: a) single couple, (b) double couple, and c) double dipole (after Stevens, 1966). 50 On the world-wide scale of azimuthal v a r i a t i o n f o r such an earthquake mechanism, the entire recording area of western Alberta would v i r t u a l l y constitute a single point. Although there w i l l be no observable variations among stations due to the nodal plane orientations, there i s an ef f e c t related to the source radiat i o n pattern which would be common to a l l four stations. The main P wave i s often c l o s e l y followed by a r e f l e c t i o n (pP) from the earth's surface almost d i r e c t l y above the source, the P to pP time separation being dependent on the depth of the source. The complexity of these secondary source phases w i l l be discussed i n Chapter VII. The strength of a pP phase on a seismogram i s often as great and sometimes greater than that of the primary P phase. On some seismo-grams pP may be e n t i r e l y absent. In Figure 15 i t i s shown how appropriate orientation of the P displacement pattern can cause differences i n the r e l a t i v e strength of P and pP. In Figure 15 P Is shown leaving the source region i n c l i n e d to the v e r t i c a l at an angle ( i ) of 30° . As the ray path w i l l t r a v e l an approximately symmetrical path from the source to the station, t h i s P w i l l arive at the base of the crust below the recording station at an angle of i n c i d -ence of approximately 30° . As the depth of the source i s small compared to the t o t a l t r a v e l path, the minimum time path of pP w i l l be very similar to that of P, and pP w i l l , therefore, r e f l e c t from the surface at a point almost d i r e c t l y SURFACE (a) (b) (c) Figure 15. Orientations of source P radiation patterns which w i l l produce: (a) strong P and weak pP, (b) weak P and strong pP, and (c) strong P and strong pP. . 52 above the source. A detailed discussion of the point of r e f l e c t i o n of pP i s given i n Section 7-4. pP, during i t s upward path i s shown on Figure 15 s l i g h t l y i n c l i n e d to the v e r t i c a l . The P and pP rays are shown p a r a l l e l leaving the source region; because of the scale of the drawings t h i s has the e f f e c t of d i s t o r t i n g the equality of angles of incidence and r e f l e c t i o n of pP at the surface. The t h e o r e t i c a l P wave displacement pattern from Figure l4 has been superimposed on these ray paths i n three d i f f e r e n t orientations. In Figure 15 (a) i t i s oriented to produce maximum P displacement and minimum pP displacement, i n Figure 15(b) the opposite, and i n Figure 15(c) P and pP of approximately equal strength. Although, because of the complexity of pP type phases and of source mechanisms them-selves, t h i s i s a gross over-simplification, i t i s believed that some of these radiat i o n pattern e f f e c t s appear on seismo-grams of some of the earthquakes of Table I I . 5-3 Some Observed Radiation Pattern E f f e c t s If an earthquake i s shallower than about 80 km i t s pP phase w i l l arrive within about 25 seconds of the primary P phase. The P-D process was run on t h i s length of record and the output p l o t s normalized according to the maximum amplitude i n the output record. The P-D VERT records, therefore, show the r e l a t i v e strength of primary P and secondary source phases f o r earthquakes shallower than 80 km. pP and P 54 EVENT NUMBERS (SEE TABLE II) strong onset, weak secondary 14, 16, 22, 23, 29, 39 weak onset, strong secondary 2, 11, 12, 19, 27, 28, 33, 34 strong onset, strong secondary 1, 4, 5, 13, 15, 17, 18, 21, 36, 37, 38 To demonstrate the c r i t e r i o n of "weak" and "strong" signals, and to show how the P-D processor emphasizes the comparison, two New B r i t a i n earthquakes with apparently opposite radiation pattern e f f e c t s are shown i n Figure 16. The two events, 19-1 and 29-1 are all i g n e d on the a r r i v a l pick. The r e l a t i v e strengths of the onset and secondary are apparent on the VERT records, but emphasized on the P-D VERT records. 19-1 shows no P-D VERT motion at the onset, but 2 cycles of secondary motion at about 15 seconds. 29-1 shows 3 strong cycles of onset motion, but no secondary motion. Both North A t l a n t i c earthquakes, events 12 and 33, show weak onset r e l a t i v e to the secondary motion. The VERT and P-D VERT records f o r 12-2 and 33-4 are shown i n Figure 17. The P-D VERT records show very strong secondaries; at 16 seconds f o r 12-2 and 8 seconds f o r 3 3 - 4 . On the basis of the time of a r r i v a l of event 12 secondary, the f o c a l depth f o r t h i s event has been adjusted to 45 km (see Table V and accompanying t e x t ) . Figure 16. Two New B r i t a i n events with opposite radiation pattern e f f e c t s . 1 2 - 2 DEPTH 33 KM 35-4 DEPTH 23 KM I VERT i ONSET 5 SEC V Figure 17. Two North A t l a n t i c earthquakes showing weak onset r e l a t i v e to secondary a r r i v a l . 57 Sykes (1967) gives mechanism solutions f o r ten earthquakes occurring on fracture zones that intersect the North A t l a n t i c ridge. The mechanism of each of the earth-quakes i s characterized by predominant s t r i k e - s l i p motion on a steeply dipping plane. Using the fracture zone map of Heezen and Tharp (1965) i t i s found that event 12 i s on a large fracture zone, event 33 i s not. There remains the p o s s i b i l i t y that event 33 i s associated with a smaller f r a c -ture zone not shown on the large scale map of Heezen and Tharp. The P r a d i a t i o n patterns shown i n Figures 14 and 15 are cross sections through the focus i n the plane of the force system, and are representative of a point source. For a steeply dipping f a u l t plane, figures of the type shown i n Figure 15 would contain the plane of the radiation pattern perpendicular to the plane of the paper. Therefore, t h i s type of rad i a t i o n pattern cannot be drawn i n the same plane as the P and pP rays. Although i t might be assumed that events 12 and 33 have mechanism solutions similar to the ten earth-quakes studied by Sykes, because of t h i s d i f f i c u l t y i t cannot be shown that a steeply dipping f a u l t i s (or i s not) consistent with weak onset signals r e l a t i v e to strong secondaries. Of possible significance i s that the two North A t l a n t i c quakes shown i n Figure 17 may have a similar mechanism orientation. 5-4 Duration of the P phase pP phases f o r earthquakes at depths greater than 100 km are well separated on the seismogram from the primary 58 P a r r i v a l . As pP i s , except i n special circumstances, the only strong phase which arri v e s within a minute of P f o r teleseismic events, i t i s e a s i l y recognized and an approximate depth f o r the event e a s i l y calculated by assuming a v e l o c i t y f o r i t s extra two-way t r a v e l path to the surface. For shallow earthquakes (say, 30 km), pP w i l l follow the primary P phase very c l o s e l y and may overlap and Interfere with the main P signal burst. For very shallow events, f o r example, under-ground nuclear explosions at depths of 1 or 2 km (large earth-quakes seldom have depths shallower than about 10 km), pP phases w i l l be inseparably mixed with the primary P signal on the seismogram. Therefore, the depth of an event strongly governs the complexity and duration, i . e . , part of the "character", of the f i r s t a r r i v i n g signals on a seismogram. An i l l u s t r a t i o n of t h i s e f f e c t i s given i n Figure 18 which shows VERT records f o r 4 d i f f e r e n t events. The portions of each record which, on the basis of P-D VERT, i s strong P i s shown shaded on Figure 18. Event 32 was 197 km deep and shows about 3 cycles of regular motion with a duration of about 9 seconds. pP f o r event 32 arrives 52 seconds aft e r the onset and i s not shown i n Figure 18. Event 4 l , which i s the nuclear explosion LONG SHOT, has about 6 seconds of higher frequency and more ir r e g u l a r motion. Both events 32 and 41 show low signal l e v e l a f t e r the i n i t i a l burst. Events 13 and 4 on Figure 18 have reported depths of 28 and 32 km respectively. Event 13 occurred i n a continental environ-ment (Greece) and event 4 i n a t r a n s i t i o n a l oceanic-continental 3 2 - 1 VERT 4 1 - 1 VERT 1 3 - 1 VERT —y D E P T H 1 9 7 K M A D E P T H 1 KM D E P T H 28 KM ( C O N T I N E N T A L ) D E P T H 3 2 m (OCEANIC) Figure 1 8 . E f f e c t of f o c a l depth and c r u s t a l appearance of P phase. C r u s t a l ^ P e °n 60 environment (Hokkaido); both show strong signal over the entire 25 second record, including more than one contribu-t i o n of strong P type motion. Although pP i s the dominant phase which contributes to the signal after the primary P, the seismograms are com-pl i c a t e d further by additional phases generated both at the source and i n the crust near the recording station. Some of these e f f e c t s w i l l be discussed i n Chapters VII and VIII. 5-5 Period of Motion Another factor contributing to the character of the P phase i s the period of the o s c i l l a t i o n s . The varia-tions i n period of o s c i l l a t i o n that can occur i s well demonstrated by the four events shown i n Figure 18. The domi-nant period i n the strong motion of 32-1 Is about 3 seconds whereas i n 13-1 i t i s about 1 second. The periods of motion i n 4 l - l and 4-1 are more variable. In a search f o r c o r r e l a t i o n between the period of P motion and other hypocentral parameters, the average period was determined f o r the f i r s t 20 seconds of the VERT station 1 record f o r each of the events. E l l i s and Basham (1967) show that the dominant period of motion f o r a p a r t i -cular event can vary from station to station, depending on the c r u s t a l transfer function. By studying the periods at one station only It i s assumed that variations i n the c r u s t a l 61 transfer function among events w i l l not be great. The r e s u l t s of the period measurements are shown i n Figure 19 where period i s plotted versus epicentral distance using d i f f e r e n t symbols for each of 3 f o c a l depth ranges. There i s not a strong dependence of period of motion on either epicentral distance or f o c a l depth, although the events with epicentral distance between 80 and 100 degrees, taken as a group, show s l i g h t l y longer periods than the nearer events. There i s a d i f f e r e n t i a l attenua-t i o n of P waves with period, the shorter periods being more strongly attenuated, as the waves t r a v e l through the earth. This phenomena i s probably causing the above e f f e c t . Also the shorter periods may be r e l a t i v e l y more attenuated f o r shallow events than f o r deep events because of the greater density of small scale inhomogeneities i n the upper layers of the earth. A dependence of period of motion on depth of focus i s not seen i n Figure 19. Most of the v a r i a t i o n i n period of P phase motion among events i s probably attributable to variations i n source functions. It should be remembered however, that the selsmograms being used here have passed through the recording system response shown i n Figure 2 and do not represent true ground motion, l e t alone true source motion. CO g 2 o o w co o H 1 PS w . 0 FOCAL DEPTHS V h < 20 KM O 21 < h < 41 • h > 42 KM o 7 m • O C D o o o • vj_l O O O • o V 20 30 40 50 60 70 EPICENTRAL DISTANCE (DEGREES) 80 ro 90 100 Figure 19. Average period of 20 seconds of P motion vs. e p i c e n t r a l distance. 63 CHAPTER VI COMPARISON OP STATION RECORDS 6-1 I n t r o d u c t o r y Remarks The p r i n c i p a l o b j e c t i v e of frequency domain st u d i e s of P phases by E l l i s and Basham (IQ67) and others has been to determine i f the r e l a t i v e frequency content of h o r i z o n t a l and v e r t i c a l P s i g n a l s i s i n agreement wit h the wave spectra p r e d i c t e d t h e o r e t i c a l l y from knowledge of the c r u s t a l l a y e r i n g . I f good agreement could be found the procedure would provide a method of (a) deter-mining l o c a l c r u s t a l s t r u c t u r e from the P phase records of any s i n g l e seismograph s t a t i o n , and (b) removing l o c a l e f f e c t s from the record to study source s i g n a l s undisturbed by c r u s t a l c o m p l e x i t i e s . To date the method, broadly termed " c r u s t a l deconvolutlon", has been r e l a t i v e l y s u c c e s s f u l at the longer periods, say greater than 10 seconds, but not at shorter periods (authors c i t e d by E l l i s and Basham, 1967). I f a P phase has a frequency content which i s dependent on the l o c a l c r u s t a l c o n d i t i o n s , some v a r i a b i l i t y among s t a t i o n s should appear i n the time domain records. 64 A search f o r t h i s v a r i a b i l i t y has been made on the records of events of the A l b e r t a Experiment. 6-2 Comparison of V e r t i c a l Records When the VERT records f o r the s t a t i o n p a i r s f o r the 41 events are superimposed some events can be c l a s s i f i e d as having s i m i l a r VERT records at the two s t a t i o n s , and others as having d i s s i m i l a r VERT records. When the VERT records are s i m i l a r they are remarkably so. The three events shown i n Figure 20 demonstrate t h i s s i m i l a r i t y . A t o t a l of 26 p a i r s of VERT components are s i m i l a r to approxi-mately the degree shown f o r the events i n Figure 20. Of the remaining 14 events (event 17 omitted), one or both VERT components are d i s t o r t e d by noise (12 events) or show a d i s t i n c t d i f f e r e n c e i n VERT s i g n a l character (2 eve n t s ) . In Table I I I are l i s t e d the s i g n a l - t o - n o i s e r a t i o s f o r a l l events determined from the r.m.s. amplitudes of the f i r s t 8 seconds of unrotated v e r t i c a l s i g n a l and the preceding 8 seconds of background n o i s e . The noise and s i g n a l s e c t i o n s were f i l t e r e d w i t h a f i l t e r s i m i l a r to BP-1 i n Figure 4 p r i o r to the S/N c a l c u l a t i o n . As would be expected, the 11 events w i t h noise d i s t o r t i o n have low S/N r a t i o s on one or both s t a t i o n s i n Table I I I . However, many of the 26 events showing s i m i l a r VERT components have S/N r a t i o s . l o w e r than 2.0 on one or both s t a t i o n s ; three of the events i n Figure 20, 12-1, 12-2, and 22-3, have S/N ! 65 Figure 20. VERT components of three s i m i l a r events. 66 TABLE I I I RMS AMPLITUDE SIGNAL/NOISE RATIOS STATION STATION EVENT 1 2 3 EVENT 1 . 4 1 2.9 2.3 25 6.8 13.5 2 5.2 5 .4 • 26 3 . 0 2.4 3 10.6 5.9 27 3 . 5 5 . 2 4 2.9 2.0 28 2. 2 1.1 5 6.3 8 . 3 29 1. 3 1.8 6 3.7 4 .4 30 7. 5 5.0 7 5.1 6.7 31 2. 7 2.8 8 1.1 2.0 32 19. 3 17.6 9 7.8 5 . 4 33 1. 1 3.1 10 2.3 5 .4 34 4.5 1.6 11 4 . 2 2.2 35 1. 7 1.7 12 2.0 2.1 36 6.9 2.4 13 11.9 8 . 0 37 4 . 1 1.4 14 38 1. 2 0.9 6.2 1.8 39 3 . 6 3.0 15 8.5 7.7 4o 9 . 8 4 .1 16 3.4 3.6 41 8 . 4 2.4 17 - 1.2 18 1.6 1.0 19 4 . 0 2.9 20 23.3 8.5 STATION MEAN S/N 21 5 . 3 1.2 1 5.1 22 4 . 6 1.9 2 4 . 6 23 5.3 2.3 1 6.6 24 3.9 4 . 0 3 3.3 1 5.1 4 4.1 67 r a t i o s near 2.0. Three examples of events showing noise d i s t o r t i o n on the VERT records are shown i n Figure 21. Comparing the events of Figure 21 w i t h those of Figure 20, the approxi-mate noise l e v e l throughout the records can be judged by the c l e a r n e s s of onset of the s i g n a l ! events 2 and 12 i n Figure 20 show a very c l e a n onset, whereas a l l events i n Figure 21 show onset d i s t o r t i o n . When background noise contaminates these events i t s frequency band i s u s u a l l y very near to that of the s i g n a l and cannot be e l i m i n a t e d by the f i l t e r BP-1. However, some of the u n f i l t e r e d records contained excessive long and short pe r i o d noise which passed the f i l t e r i n s u f f i c i e n t amounts to contaminate the VERT records; the s t a t i o n - p a i r s i m i l a r i t y of these would be improved by a s l i g h t l y narrower bandpass f i l t e r . The general sources of background noise were o u t l i n e d i n S e c t i o n 3-1• In that s e c t i o n i t was stated that s t a t i o n 1 was the q u i e t e s t of the four s i t e s . An approximate measure of the background noise l e v e l at the fou r s t a t i o n s i s shown i n the t a b l e of average S/N r a t i o s f o r the three s t a t i o n p a i r s i n Table I I I . For each s t a t i o n -p a i r group of events s t a t i o n 1 has a s l i g h t l y higher S/N r a t i o . The two events showing a d i s t i n c t d i f f e r e n c e i n VERT s i g n a l which i s not a t t r i b u t a b l e e n t i r e l y to noise contamination are shown i n Figure 22. Both of these are Figure 21. VERT components of three events d i s t o r t e d by-noise. 69 OREGON COAST DEPTH 33 KM 6-1 A 13 DEG 5 SEC ' CALIFORNIA COAST Figure 22. VERT components of two near events with d i s t i n c t difference i n signal character. 70 near events on the P a c i f i c coast of United S t a t e s . Event 6 has a d i f f e r e n c e i n s i g n a l amplitude throughout the f i r s t h a l f of the 25 second record, and a r e l a t i v e s h i f t i n phase throughout the second h a l f . Event 30 shows amplitude and phase d i f f e r e n c e s throughout the record. With e p i c e n t r a l d i s t a n c e s of 13 and 15 degrees f o r events 6 and 30 r e s p e c t i v e l y , n e i t h e r i s t e l e s e l s m i c (as defined i n S e c t i o n 2-3). However, there are four southern Alaska events (10, 24, 31, and 35) which are not t e l e s e l s m i c but which show remarkably s i m i l a r VERT compo-nents on the s t a t i o n p a i r s . I t may then be assumed that the degree of d i f f e r e n c e i s i n some manner r e l a t e d to the azimuth of approach. There are f i v e events w i t h e p i c e n t r a l d i s t a n c e s s l i g h t l y l a r g e r than 20 degrees. Two i n southern Alaska (7 and 25) having s i m i l a r s t a t i o n - p a i r VERT compo-nents, two i n southern Alaska (8 and 26) with noise d i s -t o r t i o n , and one i n M i s s o u r i (40) with noise d i s t o r t i o n . For comparison w i t h the d i s s i m i l a r near events i n Figure 22, two s i m i l a r southern Alaska near events are reproduced i n Figure 23. The phases which c o n s t i t u t e the P s i g n a l f o r events of t h i s e p i c e n t r a l d istance range (13 to 24 degress) are not w e l l understood. I t i s w i t h i n t h i s distance range that P n and P^ (the wave r e f r a c t e d below a low v e l o c i t y d i s c o n t i n u i t y i n the mantle) t r a v e l time curves I n t e r s e c t (see, f o r example, Lehmann, 1962), but the time d i f f e r e n c e 71 SOUTHERN ALASKA DEPTH 12 KM 10-1 A 17 DEG Figure 23. V E R T components of two s i m i l a r near events. 72 between P and P w i l l depend on a number of other factors n r including the f o c a l depth of the event, the thickness and ve l o c i t y structure of the crust, and the v e l o c i t y structure of the upper mantle. In addition there can be amplitude shadow zones caused by reversals i n sign of the v e l o c i t y -depth gradient below the Moho, and further complexity due to a r r i v i n g secondary pP and sP type phases. Eecause of the generally complex tectonic regions traversed by seismic waves from Oregon, C a l i f o r n i a and Alaska to central Alberta, the character variations d i s -cussed above and i l l u s t r a t e d on Figures 22 and 23 are more l i k e l y associated with a complex t r a v e l path than with e f f e c t s l o c a l to the stations. 6-3 Comparison of Radial Records The RAD records show a generally higher back-ground noise contamination than do the VERT records. This i s because both microseismic and c u l t u r a l noise have a greater proportion of t h e i r displacement i n horizontal plane, and because of the low horizontal signal l e v e l f o r phases a r r i v i n g at a steep angle of incidence. The lower general S/N r a t i o of RAD components makes comparison of station p a i r s of RAD signals more d i f f i c u l t . RAD records f o r only those events with epicentral distances between about 35 and 55 degrees were compared i n t h i s study. This range was chosen f o r two reasons: 73 f i r s t l y , the d i s t a n t events have a s i g n i f i c a n t c o n t r i b u t i o n of v e r t i c a l energy i n the RAD component due to the r o t a t i o n about the transverse, and secondly, there may be complica-t i o n s i n RAD records f o r the near events of a type discussed i n the previous s e c t i o n . There are 16 events i n the 35 to 55 degree e p i -c e n t r a l d istance range, but 9 of these have RAD records contaminated by n o i s e . The remaining 7 RAD p a i r s d i v i d e i n t o two c o n t r a s t i n g groups, 4 w i t h r e l a t i v e l y s h o r t - p e r i o d motion, and 3 w i t h r e l a t i v e l y long-period motion. The f o u r s h o r t - p e r i o d p a i r s are shown i n Figure 24, and the three long-period p a i r s i n Figure 25. Some of these RAD records have a f a i r l y high noise content, although not enough to d i s g u i s e the s i g n a l content. Event 5-1 on Figure 24 has some long-period noise but the s i g n a l i s strong enough to dominate the record. Events 22-3 and 23-3 on Figure 25 show some sh o r t - p e r i o d noise, but not enough to d i s t o r t the long-period s i g n a l . I t i s seen on Fi g u r e s 24 and 25 that when long-and s h o r t - p e r i o d RAD motion has s i m i l a r amplitude r e l a t i v e to the background noise, the long-period s i g n a l shows greater s i m i l a r i t y on the s t a t i o n p a i r s of records than does the short-.perlod s i g n a l . Those segments of the records which, on the b a s i s of the P-D RAD records, are s t r o n g l y r e c t i l i n e a r P s i g n a l are designated by a ! fP w on Fi g u r e s 24 and 25. At a l l of these s e g m e n t a n d f o r only these Figure 24. RAD components of f o u r s h o r t - p e r i o d events. Figure 25. RAD components of three long-period events. 76 segments, are the RAD records of the stations strongly coincident. This i s i n contrast to the VERT components which re t a i n a s i m i l a r i t y on the station p a i r s throughout the entire record (see Figures 20 and 23). 6-4 Significance of Results Some important conclusions can be drawn from t h i s comparison of station records. The remarkable s i m i l a r i t y of VERT components (for distances greater than 20 degrees, and when no noise contamination i s present) i s highly s i g n i f i c a n t i n terms of the e f f e c t of the c r u s t a l structure on records obtained at a station. The differences i n station-pair RAD records when a strong P signal i s not present i s related to S wave generation i n the c r u s t a l layers. The f i r s t of these topics (VERT s i m i l a r i t y ) w i l l be discussed here, the second (RAD differences) w i l l be included i n a more detailed discussion of phase d i s t o r t i o n i n Chapter VIII. The Alberta experiment, during which the events of t h i s study were recorded, was s p e c i f i c a l l y planned to test the hypothesis that variations i n c r u s t a l c h a r a c t e r i s t i c s beneath stations w i l l be evident i n the short-period P phases of teleselsmic events. Previous studies (ichikawa and Basham, 1965, and Utsu, 1966) had indicated that the most dominant e f f e c t i n the short-period range could be expected from the upper few kilometers of the crust. It 77 was f o r t h i s reason that A l b e r t a w i t h a w e l l defined s e d i -mentary s e c t i o n was chosen as a reco r d i n g s i t e . The s t a t i o n s were l o c a t e d i n a l i n e perpendicular to the s t r i k e of the r e g i o n a l trend (see Figure 3) to y i e l d a maximum v a r i a t i o n i n sedimentary s e c t i o n t h i c k n e s s f o r a s t a t i o n spacing up to about 160 km. The se'dlmentary column under each of the four r e c o r d i n g s i t e s i s shown i n Figure 26. The columns were constructed from a v a i l a b l e deep w e l l c o n t r o l and isopach maps. Each sedimentary sequence i n the columns i s l a b e l l e d w i t h the P v e l o c i t y i n km/sec determined from continuous v e l o c i t y l o g s from 12 deep w e l l s near the l i n e of s e c t i o n . The c r u s t a l r e f r a c t i o n prof i l e \ nearest to the recor d i n g area was that of Richards and Walker (1959). The r e c o r d i n g l i n e with a shot p o i n t at each end was 140 km long and o r i e n t e d approximately north-south w i t h the center p o i n t about 40 km northeast of Calgary. The p r o f i l e was not long enough to d e l i n e a t e the Mono and intermediate boundaries at any point except near the center of the l i n e . ..^  The only other r e f r a c t i o n p r o f i l e i n the A l b e r t a area i s that of Cumming and Kanasewich (1966) between Sw i f t Current, Saskatchewan and Vulcan, A l b e r t a . The western end of t h i s p r o f i l e i s approximately 200 km southeast of the r e c o r d i n g area. The i n t e r p r e t e d c r u s t a l s t r u c t u r e on the western end of t h i s p r o f i l e i s used f o r the recording area, on the assumption that I t can be extrapolated along POST ALBERTA ALBERTA BLAIRMORE JUR AND MISS WABUMUM WOODBKND BEAVERHILL LK. ELK PT. CAMBRIAN PRE .CAMBRIAN RMH 3 . 3 3.6 4 . 4 5.6 6.0 ^ 1 ^ 5 . 3 4 . 3 6.1 ALD WAR 3.0 2.7 / y / ' s 3.2 3.5 3.7 4.9 5.2 3.8 4.5 S.3 4.8 5.8 4.7 / / / / / / y 4.3 4 .Q 6.1 S . 2 4.6 6.1 <y LED 2.6 2.9 iL9_ - V 5 . 2 4.1 6.1 Figure 26. Sedimentary columns under A l b e r t a recording s i t e s showing P v e l o c i t i e s i n km/sec. 79 the regional s t r i k e . This c r u s t a l section, which i s shown i n Figure 27, i s not s u f f i c i e n t l y well defined to allow further i n t e r p o l a t i o n to y i e l d a d i f f e r e n t c r u s t a l column under each of the recording stations. As the incident P wave propagates through these c r u s t a l layers, r e f l e c t e d and refracted P and SV waves are generated at each interface, the amplitude of these con-verted waves depending on the contrast i n acoustic impedance across the i n t e r f a c e . Acoustic impedance depends on wave ve l o c i t y and medium density, and v e l o c i t y i s usually assumed to be a l i n e a r function of density i n the v e l o c i t y range of i n t e r e s t here. Therefore, i t can be assumed that the converted wave amplitudes w i l l depend on the v e l o c i t y con-t r a s t across the i n t e r f a c e . References to the numerous investigators who have studied the t h e o r e t i c a l problem of the p a r t i t i o n of energy incident at an e l a s t i c interface and the amplitudes of the r e s u l t i n g r e f l e c t e d and refracted waves are given by Costain et a l (1963). The Incident angle used i n the seismogram rotation described i n Section 3-3 was the angle at the base of the crust. The steepening of the ray path as i t propagates through the crust i s shown i n Figure 27. It can be seen In the table accompanying Figure 27, f o r example, that an angle of incidence, i , at the Moho of 18° w i l l steepen to 10.7° (6) at the surface; an I of 42° w i l l steepen to e of 23 .8° . Figure 27. Ext r a p o l a t e d c r u s t a l s t r u c t u r e under A l b e r t a s i t e s ( a f t e r Cumming and Kariasewich, 1966) showing P and S ray paths. 81 For events i n the "source window" i w i l l be between 20 and 40 degrees (see Figure 7 ) , therefore, 9 w i l l be between about 11 and 23 degrees. I t i s apparent then that the greatest proportion of the displacement of dir e c t or converted P waves w i l l be recorded at the sur-face i n the v e r t i c a l component, the greatest proportion of converted SV displacement i n the r a d i a l component. Relating t h i s to the simi l a r station-pair VERT records discussed i n Section 6-2, I t i s concluded that a teleselsmic event contributes almost i d e n t i c a l amounts of dir e c t and converted P motion to each of the stations, and, i f there are s i g n i f i c a n t amounts of converted P motion, i t arrived at an i d e n t i c a l delay time at each station (within the time resolution of the records shown). The v e r t i c a l t r a v e l time of dir e c t P through, f o r example, stat i o n 1 sediments i s about 0.8 seconds; through station 4 sediments i t i s about 1.1 seconds. A converted P a r r i v i n g l a t e r would have to spend part of i t s t r a n s i t time as converted SV or as a multiple r e f l e c t i o n among some of the layers. In order to arrive at each of the stations at delay times d i f f e r e n t enough to be distinguishable on the records shown (say 0.5 seconds) the converted P would lose almost a l l of I t s energy i n the delaying process. Without more detailed Information on the gross c r u s t a l structure under each of the stations, i t i s not possible to determine whether si m i l a r e f f e c t s i n the gross crust could produce s u f f i c i e n t amplitude and time-delayed converted P to make 82 a distinguishable difference to the VERT records on the station p a i r s . The s i m i l a r i t y of VERT records, however, suggests that such an e f f e c t does not occur. The general conclusion to be reached i s that although the c r u s t a l columns, and p a r t i c u l a r l y the sedi-ments, under the four stations may be d i f f e r e n t , to the v e r t i c a l component of a P phase i n the period range d i s -cussed here they appear i d e n t i c a l . Some additional information concerning the ray paths through the Alberta crust i s presented i n Figure 27 to show the scale of c r u s t a l I r r e g u l a r i t i e s required to a f f e c t a teleselsmic P phase. These are the distances i n a horizontal d i r e c t i o n between a point d i r e c t l y beneath the s t a t i o n and the point where d i r e c t P crosses the base of the Moho (XP), where d i r e c t P crosses the base of the sediments (XP 1), and where P to SV conversion would occur at the Moho (XS). Values of XP, XP«, and XS are l i s t e d In the table of Figure 27 f o r six d i f f e r e n t angles I. I r r e g u l a r i t i e s at Moho depth would have to be situated within a c i r c l e of radius about 25 km to a f f e c t a t e l e -seismic phase a r r i v i n g at an Alberta station. The radius of a s i m i l a r c i r c l e at basement depth would be about 1.3 km. The available information on the basement structure under the recording area, a f t e r Garland and Burwash (1959), i s shown i n Figure 28 . This basement geology was determined from gravity measurements, magnetic p r o f i l e s , and p e t r o l o g l c a l 83 F i g u r e 28. Precambrian basement under rec o r d i n g area ( a f t e r Garland and Burwash, 1959). 84 studies of basement well samples. There were no well samples available i n the western portion of the map of Figure 28, so the geology represents an interpretation of the geophysical measurements alone. The important feature would appear to be the contact between gneissic and g r a n i t i c rock passing around the ALD and WAR stations. But, considering the scale of basement i r r e g u l a r i t i e s discussed i n r e l a t i o n to XP' on Figure 27 and the required amplitude and delay times of converted phases, i t i s u n l i k e l y that t h i s feature would have a noticeable e f f e c t on the records. If the feature extended to considerable depth i n the basement the incoming ray might pass through i t . However, nothing i s observed on the records which can be s p e c i f i c a l l y cor-related with the contact. 85 CHAPTER VII SECONDARY SOURCE PHASES 7-1 Introductory Remarks It has been indicated i n some of the foregoing chapters that complexity i n the P phase "coda" r e s u l t s from l a t e a r r i v i n g secondary source phases. The most dominant of these secondary phases i s pP, the r e f l e c t i o n of the i n i t i a l compressional pulse from the surface of the earth above the source. Other secondary phases can be generated near an earthquake source. Theoretical f a u l t -ing models indicate (A.W.R.E., 1965) that, at the source, shear waves w i l l contain more energy than compressional waves. That t h i s i s true i n practice i s shown by the greater proportion of shear energy on records made near an earthquake source. The source-generated shear waves are strongly attenuated a f t e r t r a v e l l i n g teleselsmic d i s -tances, and, because of lower v e l o c i t i e s , w i l l arrive of the order of a few minutes aft e r the primary P. However, they are p a r t i a l l y converted into compressional waves at the surface and at other e l a s t i c d i s c o n t i n u i t i e s above the source. The i n i t i a l compressional wave i t s e l f w i l l be p a r t i a l l y r e f l e c t e d at e l a s t i c d i s c o n t i n u i t i e s near 86 the source. These converted and ref l e c t e d waves w i l l follow the main P signal to the recording station, and, because of time spent traversing extra paths near the source, w i l l arrive at l a t e r times contributing to an extended and complex P coda. The delay time of these secondary source phases w i l l depend;on the depth of the earthquake. The delay times, p a r t i c u l a r l y of pP which i s the strongest and hence most e a s i l y recognized of the secondary phases, are the most useful c r i t e r i a i n assigning accurate depths to the deeper earthquakes. Because the pP signal w i l l overlap and i n t e r -fere with the P signal f o r shallow events, pP i s not e a s i l y enough recognized to allow i t s use i n depth cal c u l a t i o n s of earthquakes shallower than about 50 km. Accurate determination of the f o c a l depth of the shallower events i s of p r a c t i c a l importance to the detection of underground nuclear explosions. The majority of earth-quakes occur at depths greater than 10 kmj the detonation of explosions i s l i m i t e d to shallower depths. Therefore, the number of natural earthquakes that might be mistaken fo r explosions' would be greatly reduced i f depths could be dependably measured to - 5 km. Depths of the shallower events reported by U.S.C.G.S. often represent a judgment, or are restrained to "normal" (33 km), with an estimated accuracy of 25 km. Consequently, a number of researchers have attempted to i d e n t i f y pP phases on seismograms of shallow 87 events and thereby a s s i g n to them more accurate f o c a l depths. G r i f f i n (1966a) describes the a p p l i c a t i o n of REMODE 2 A and 3A processors (see se c t i o n s 4-1 and 4 - 2 ) to seismograms to enhance secondary depth phases. Those phases which were c l e a r l y evident on unprocessed records were made d i s t i n c t l y c l e a r e r by processing. For events which showed no s i g n of a depth phase on the unprocessed records, no enhancement was obtained by process i n g . G r i f f i n r e p o r t s considerable improvement i n depth phase d e t e c t i o n u s i n g a more s e l e c t i v e processor, REMODE 5 , which has not been discussed i n Chapter IV. Using REMODE 5, r e c t i l i n e a r waves whose apparent angle of incidence d i f f e r s from a s p e c i f i e d angle can be attenuated as much as d e s i r e d . T h i s , i n e f f e c t , r e q u i r e s a f o c u s i n g of the processor at an apparent angle of incidence determined from the v e r t i c a l and r a d i a l s i g n a l amplitudes f o r each event. Howell et a l (1967) describe a process whereby a seismogram i s convolved w i t h an optimum inverse f i l t e r . The f i l t e r i s designed such that i t s c o n v o l u t i o n w i t h an e n t i r e seismogram, c o n s i s t i n g of primary event, p l u s secondary events, p l u s noise, should y i e l d the primary seismogram only, thereby s i m p l i f y i n g that p o r t i o n of the o r i g i n a l seismogram which contained secondary s i g n a l s . Howell et a l report that the technique i s u s e f u l i n i d e n t i f y -i n g secondary phases, but f i n d s many pulses besides pP and 88 does not always f i n d pP. The P-Detection processor described i n Chapter IV was applied to the events i n t h i s study to detect which portions of the P coda were r e l a t i v e l y pure P motion, which portions were P phases more-or-less distorted by shear motions, and which portions were r e l a t i v e l y pure SV motion. It became apparent that very strong P signals could be recognized i n the P coda of many of the events as d i s t i n c t secondary a r r i v a l s . On the unprocessed records of the deeper events these could be e a s i l y i d e n t i f i e d as pP. On most of the shallower event records the signal l e v e l remained high over most of the half-minute record length, but clear a r r i v a l s of s p e c i f i c secondary phases could not be discerned. The P-D processor, by enhancing r e c t i l i n e a r P motion, enabled many secondary phases a r r i v i n g at the station as compressional waves to be accurately timed. See, f o r example, Figures 11, 12, and 13. In a l l , pP phases have been t e n t a t i v e l y i d e n t i f i e d f o r 23 events, and sP phases f o r 9 events. It has been possible to adjust the f o c a l depth reported by U.S.C.G.S. fo r some of these events. 7-2 Amplitude Considerations Before presenting the res u l t s of the i d e n t i f i c a -t i o n of secondary source phases, a discussion w i l l be given of the amplitudes that can be expected f o r the secon-dary phases r e l a t i v e to the primary P phase. 89 The wave propagating upward from the source w i l l s t r i k e the surface i n c l i n e d to the v e r t i c a l at an angle depending on the f o c a l depth and epicentral distance. Assume, f o r the purpose of determining r e f l e c t i o n c o e f f i -cients, that the angle (8) Is 5 degrees. Ewing et a l (1957, p. 30-31) present the square root of the r a t i o of re f l e c t e d to incident energy f o r P and SV waves incident on the free surface of a homogeneous and i s o t r o p i c half space. For Poisson's r a t i o equal to 1/4 and 9 = 5 ° the above r a t i o i s O.98 f o r incident P re f l e c t e d as P and 0.30 f o r incident SV r e f l e c t e d as P. In theory, then, pP can contain v i r t u a l l y the same amount of energy as P, and sp about 1/10 of that amount. But, i f the source generates more shear than compressional energy, as seems to be the general case, the r e l a t i v e strength of sP could be considerably larger. Wu and Hannon (1966) have calculated r e f l e c t i o n c o e f f i c i e n t s f o r PP as functions of the frequency of the input signal and angle of incidence. Assuming an incident plane wave at the bottom of three d i f f e r e n t c r u s t a l models, the r e f l e c t i o n frequency response was computed using the Haskell-Thompson matrix method. Reflection c o e f f i c i e n t s applicable to pP (assuming the upward-going wave can be considered plane f o r shallow focus pP phases) appear on the graphs of Wu and Hannon at the smaller angles of Incid-ence. Values applicable to t h i s study appear at the 90 appropriate frequency. Using 0=5® and a frequency of 0.5 Hz, the r a t i o of incident to r e f l e c t e d P displacement i s greater than 0.9 f o r each of the three c r u s t a l models; average central U.S. structure, average oceanic structure, and Peru-Altiplano structure. Wu and Harmon (1966) also present synthesized PP signals computed on the basis of a delta function input and passing the output through a simulated 30-100 (seismo-meter-galvanometer periods) seismograph. In addition to the main pulse which r e f l e c t s from the surface, two addi-t i o n a l i d e n t i f i a b l e pulses are apparent on the synthetic records; a strong, repeated, multiple r e f l e c t i o n set up by the Incident wave i n the water layer of the oceanic c r u s t a l model, and a weak e a r l y - a r r i v i n g pulse which i s a r e f l e c t i o n from the base of the c r u s t a l models. Although the frequency range of the signals i n these synthetic records i s f a r below that of the events of t h i s study, the r e l a t i v e amplitudes of these additional signals i s generally applicable. An additional factor to be considered i n a d i s -cussion of amplitudes that can be expected f o r secondary source phases i s the radiatio n pattern e f f e c t discussed i n Section 5-2. If the rad i a t i o n pattern i s as strong as the re s u l t s of Section 5-3 suggest, the amplitude of secondary phases r e l a t i v e to primary P can vary considerably. 91 7-3 Crustal Columns at the Source If the delay time of pP and sP aft e r P can be accurately determined from a seismogram the assignment of accurate f o c a l depth to the earthquake requires knowledge of the v e l o c i t y structure of the earth between the source and the surface. Modern travel-time tables do not include l i s t s of pP-P or sP-P times versus epicentral distance and f o c a l depth. Gutenberg and Richter (1936) do present such a table but i t Is based on t h e i r average velocity-depth information (Gutenberg and Richter, 1935) and i s applicable only to f o c a l depths greater than about 100 km. The re-l a t i v e error from assumption of an average velocity-depth r e l a t i o n w i l l be greater f o r shallower earthquakes. Since earthquakes occur within a diverse assort-ment of geological environments, few of which have struc-tures known to an accurate degree, some source-to-surface v e l o c i t y structure must be assumed f o r each event. In t h i s study, f o r purposes of comparing observed pP-P and sP-P times with reported f o c a l depths, four d i f f e r e n t c r u s t a l sections a f t e r Menard (1967) were chosen as representative types. The four c r u s t a l columns are shown i n Figure 29 with layer thicknesses i n km l a b e l l e d on the l e f t side and P v e l o c i t i e s i n km/sec on the right side of each layer. The " t y p i c a l ocean" (T.O.) and " t y p i c a l continent" (T.C.) are those given by Menard. The "simple i s l a n d arc" (S.I.A.) 92 T.O. TYPICAL OCEAN S.I.A. SIMPLE ISLAND ARC C.I.A. COMPLEX ISLAND ARC T.C. TYPICAL CONTINENT T.O. w 1.5 1.0 4 . 5 6 .7 5 . 0 8 .1 S.I.A. C.I.A. T.C. W 1.5 1.0 3.5 5 . 0 1.5 2.2 2.9 4 . 0 7.0 7 .8 w 1.0 2.0 6.0 1.5 2.1 3 .9 6 .6 33 .0 8 . 0 Figure 29. Four c r u s t a l columns used f o r c a l c u l a t i n g pP-P and sP-p delay times (after Menard, 1967). Thicknesses i n km are shown on the l e f t and P v e l o c i t i e s i n km/sec on the right of each layer. W, the water depth, was determined from bathometric maps f o r each event. 93 i s Menard's Aleutian Basin structure and the "complex is l a n d arc" (C.I.A.), Menard's Yucatan Basin structure. The water depth (w) f o r the oceanic models was determined fo r each event i n an oceanic environment from bathometric maps f o r the p a r t i c u l a r epicenter. With epicenters accurate to a few tenths of a degree i n lati t u d e and longitude, the water depths are believed to be accurate to about 1 km. Although the 4 c r u s t a l columns are average ones and cannot be expected to exactly represent the crust above any of the events, the r e s u l t i n g errors i n pP-P time ca l c u l a t i o n s w i l l not be large. Two-way t r a v e l time error due to erroneous water depth w i l l be about 1 second. If a f o c a l depth Is 30 km and the water depth 3 km, the v e r t i c a l pP-P time f o r T.O. would be 11.1 seconds, for S.I.A., 13.3 seconds, and f o r C.I.A., 12.2 seconds. Assuming the crust Is well enough represented by one of these models to halve the error, the t o t a l expected error i n calculated pP-P time w i l l be about 2 seconds, 1 second from an inaccurate water layer and 1 second from inaccurate s o l i d layers. 7-4 The Path of pP Above the Source In the cal c u l a t i o n s of t h i s chapter i t w i l l be assumed that pP r e f l e c t s from the surface d i r e c t l y above the source, i . e . , tra v e l s a v e r t i c a l path, r e f l e c t i n g 94 from the surface at the epicenter. In practice the re-f l e c t i o n point w i l l be some distance toward the recording station from the epicenter. Using a simulated pP path shown i n Figure 30, a measure of the errors involved i n assuming v e r t i c a l r e f l e c t i o n f o r various depths and e p i -c e n t ral distances i s shown i n Table IV. It i s assumed i n Figure 30 that i f P leaves the source at an angle I, pP has an angle i of incidence and r e f l e c t i o n at the surface and leaves the source depth at an angle i . The material between the source at depth h and the surface has a constant compressional v e l o c i t y of oc= 8.5 km/sec. If pP r e f l e c t e d v e r t i c a l l y from the sur-face i t would have a t r a v e l time, t , given by the equation t = |£ + t< ( A , h), o oc O ' where t 1 i s the P t r a v e l time from a source at depth h to o a s t a t i o n at epic e n t r a l distance A . If pP t r a v e l s the i n c l i n e d path to the surface I t w i l l have a t r a v e l time given by t, = g , + t' ( A - D, h). 1 oCcos x o v ' The values of t - t, l i s t e d i n Table IV are the differences o 1 i n pP time between a v e r t i c a l r e f l e c t i o n path and t h i s simulated i n c l i n e d path. It i s seen i n Table IV that these time errors have a range from 0.6 to 5.7 seconds f o r the values of A 95 1^  • A to station ( t 0 ) (t,) Figure 30. Simulated pP path above the source. TABLE IV ERRORS IN pP-P TIME RESULTING FROM ASSUMPTION OF VERTICAL REFLECTION A (deg) h (km) i (deg) (Min:Sec) h (Min:Sec) (sec) 30 25 40 6:14.9 6:13.7 1.2 56 25 30 9:45.9 9:43..8 2.1 88 25 20 12:56.9 12:56.3 0.6 30 60 40 6:21.1 6:18.4 2.7 56 60 30 9:49.1 9:46.3 2.8 88 60 20 13:01.1 13:00.0 1.1 30 100 40 6:29.5 6:23.8 5.7 56 100 30 9:54.5 9:51.1 3.4 88 100 20 13:07.5 13:05.0 2.5 96 and h chosenj the smaller errors are f o r large A and small h, the larger errors f o r small A and large h. These values of t - t, are over-estimates of the error. This i s because o 1 the value of cc f o r the true earth i s not constant but generally decreases toward the surface, with the re s u l t that the up-going ray, to t r a v e l a minimum time path, w i l l bend toward the v e r t i c a l thereby decreasing the value of D from that assumed i n the calc u l a t i o n s of Table IV. I t i s assumed then that except f o r the worst case (large h and small A ), the error r e s u l t i n g from the assumption of v e r t i c a l r e f l e c t i o n f o r pP w i l l be les s than 2 seconds. Since the actual pP-P time w i l l be smaller than the time difference assuming a two-way v e r t i c a l path from source to surface, use of observed pP-P times i n c a l c u l a t -ing the v e r t i c a l distance w i l l r e s u l t i n an under-estimate of the f o c a l depth. Using a reported f o c a l depth, the two-way v e r t i c a l path time w i l l be an over-estimate of the pP-P time. 7-5 Picking and Timing Secondary Phases I d e n t i f i c a t i o n of secondary phases was made on the basis of a strong and sharp a r r i v a l on the P-D VERT and P-D RAD records at an i d e n t i c a l time delay on the records of both stations. Although t h i s c r i t e r i o n was used throughout, the general q u a l i t y of P-D records varied considerably. An example of high q u a l i t y P-D records 97 i s shown i n Figure 31 f o r event 18. When aligned on the primary P pulse, the f i r s t strong downward motion, the records show two strong secondaries a r r i v i n g at i d e n t i c a l times on both stations. In addition, there i s evidence of two weaker secondaries, one about 5 seconds a f t e r the primary P and the other about 7 seconds aft e r the second strong secondary. An example of lower q u a l i t y records can be seen i n Figure 13 f o r event 26. Although t h i s event shows no strong primary P and shows miscellaneous bursts of signal throughout the P-D records, the onset of a strong secondary appears at an almost i d e n t i c a l time at both stations. It can be seen on a number of examples of records shown that a small precursory signal often precedes the onset of strong primary P motion. On event 4 i n Figure 11, event 13 i n Figure 12, and event 29 i n Figure 16 t h i s delay time of the primary P a r r i v a l i s 1 to 1.5 seconds. Some events exhibit a strong Impulsive primary P onset with no precursor. These e f f e c t s are the azimuthal expression of the orientations of source P wave displacement r a d i a t i o n patterns. At the period of wave motion being considered here, the displacement pattern probably a f f e c t s only the f i r s t half cycle of onset motion. The reader w i l l , no doubt, note that t h i s appears contradictory to the d i s -cussions of rad i a t i o n pattern e f f e c t s i n Section 5 - 3 . In that section i t was concluded that the absence of a l l strong P (or pP) motion, not only of the f i r s t half cycle, Figure 31. High qua l i t y P-D records showing secondary phases a r r i v i n g at an i d e n t i c a l time on two stations. 99 could be attributed to the radiatio n pattern. This c o n f l i c t w i l l be l e f t unresolved, but i s probably related i n some way to more complex source e f f e c t s than were discussed i n Chapter V. However, since measurements of secondary phase delay times were made on P-D VERT records, when strong primary P signals were present the measurements were most e a s i l y made between the onset of the strong primary and the onse/t of a strong secondary; when strong primary P was absent, the measurement was made between the a r r i v a l pick and the onset of the secondary. This procedure could contribute an error of about 1 second to the pP-P and sP-P times. A second possible source of timing error i s i n the secondary onset as displayed on the P-D VERT records fo r the shallower events. The secondary phase arrives amid the coda of the primary P. Although the P-D pro-cessor i s su r p r i s i n g l y successful In enhancing the secon-dary there are suggestions that the f i r s t half cycle of the secondary of some events may be lo s t due to d i s t o r t i o n from the P coda. For example, the P-D VERT records of event 4 i n Figure 11 and event 12 i n Figure 17 show a considerably reduced f i r s t half cycle of the secondary. If t h i s half cycle i s l o s t on some of the events, an addi-t i o n a l timing error of about 1 second can r e s u l t . 100 7-6 Summary of pP Results On 23 events (events 17 and 4 l are omitted from t h i s discussion) the P-D processor detected at least one secondary a r r i v a l at an i d e n t i c a l time(s) on the records of both stations. The single secondary, or one of the multiple secondaries, of each of these events was i n t e r -preted as being pP. On 10 events one or both of the sta-tions showed secondary signal but, because of d i s t o r t i o n by background noise or the i n a b i l i t y of the P-D processor to enhance the signal, clear secondaries could not be i d e n t i f i e d at a coincident time on both records. Of the remaining 6 events, 5 exhibited no strong secondary motion and one i s discussed as a special case i n Section J-Q. A summary of observed and calculated pP-P times i s given i n Table V f o r the 23 events exh i b i t i n g pP phases. The presence or absence of a strong primary P onset i s designated YES or NO In the second column. The t h i r d column Is the f o c a l depth f o r the event reported by U.S.C.G.S., the fourth i s the ocean water depth determined f o r the ep i -center from a bathometric map, and the f i f t h i s the type of c r u s t a l column used i n c a l c u l a t i o n of the pP-P time (see Figure 2 9 ) . The calculated pP-P times i n Table V are the two-way v e r t i c a l t r a v e l times of a compressional wave between the surface and the source (at the reported f o c a l depth) using the appropriate crust and water layer model. The observed pP-P times were determined as described i n TABLE V SUMMARY OF pP-P CALCULATIONS CVENT STRONG ONSET REPORTED DEPTH (KM) WATER DEPTH (KM) CRUST TYPE pP-P TIME (SEC) CALC OBS. . OBS-CALC ADJUSTED DEPTH (KM) 1 YES 25 1 S»I o A o 9.9 8.5 - 1 . 4 2 NO 35 3 3 © I • A« 14 .4 11.4 - 3 . 0 23 3 YES 103 0 T © C c 28.1 27.4 - 0 . 7 5 YES 54 1 S e X o A e 17.1 12 .5 - 4 . 6 36 6 NO 33 4 T.O. 12.9 16.3 +3.4 47 8 NO 36 0 S o J e A » 11.5 9 . 6 -1 .9 : 9 YES 33 l T.O. 9 . 6 6 .0 - 3 . 6 18 11 NO 60 l S.I.A. 18.6 18.6 0 . 0 12 NO 33 2 T.O. 10.8 15.7 +4.9 45 13 YES 28 0 T.C. 9 . 2 9 .5 +0.3 16 YES 47 0 C . I. A. 13.3 13.4 +0.1 18 YES 33 2 C.I.A. 12.0 13.0 +1.0 19 NO 41 0 C.I.A. 11.8 11.3 - 0 . 5 20 YES 129 0 T»C c 34.5 33.1 - 1 . 4 21 YES 77 4 T.O. 22.5 19.8 - 2 . 7 66 26 NO 33 1 S.I.A. 11.7 11.2 - 0 . 5 27 NO 27 2 T.O. 9 . 3 4 . 8 - 4 . 5 9 28 NO 67 0 C.I.A. 18.3 18.4 +0.1 31 NO 22 1 T.O. 6.9 4 .7 - 2 . 2 13 32 YES 197 1 C « I o A e 51.8 51.5 - 0 . 3 33 NO 23 4 "T.O. 10.4 11.4 +1.0 34 NO 41 1 S.I.A. 13.3 12.0 - 1 . 3 39 YES 70 0 T.O. 17.5 17.0 - 0 . 5 102 Section 7-5. The assumption of v e r t i c a l r e f l e c t i o n f o r pP discussed i n Section 7-4 would r e s u l t i n the calculated pP-P time i n Table V being too large, and observed-minus-calculated residuals being negative. Most of the obs-calc residuals i n Table V are negative, suggesting that the assumption of v e r t i c a l r e f l e c t i o n does contribute s i g n i f i -cantly to the residuals. Event 6 with a residual of +3.4 seconds has A = 1 3 ° . In view of the discussion of near events i n Section 6-2, the pick of the pP phase i t s e l f may be i n question. Event 12 with a residual of +4.9 seconds has A = 4 5 ° . This i s probably an event with a large error i n the reported f o c a l depth. Since the observed and calculated pP-P times are estimated to be accurate to about 2 seconds and U.S.C.G.S. reported depths are accurate to ^25 km, i t i s appropriate to adjust the f o c a l depths of those events with large residuals. Depths were adjusted f o r a l l events i n Table V with time residuals larger than 2.0 seconds so that the new depth agreed with the observed pP-P time (again assuming v e r t i c a l r e f l e c t i o n ) f o r the appropriate c r u s t a l modelj these adjusted depths are l i s t e d i n the l a s t column i n Table V. Care must be taken i n assigning accuracy to these adjusted depths because, f o r example, 1 km of erro-neous water depth i s equivalent to about 6 km of mantle material. However, considering a l l of the error estimates 103 discussed above, the adjusted depths, and those not requiring adjustment, are probably accurate to within about 15 km. 7-7 Summary of sP Results sP phases w i l l appear on the records delayed a f t e r pP a time approximately equal to the difference between one-way compressional and shear t r a v e l times from the source to the surface. If a phase was observed on the P-D com-ponents at approximately t h i s delay time aft e r pP, i t was i d e n t i f i e d as sP; t h i s occurred on 9 events. The observed and calculated sP-P times f o r these events are l i s t e d i n Table VI, along with the absolute difference between observed and calculated time. If the f o c a l depth was adjusted (Table V) the calculated sP-P time i n Table VI was based on the adjusted depth. When the source c r u s t a l model contained an oceanic water layer i t was assumed that sP r e f l e c t e d not from the surface, but from the base of the water layer. A l l but two of the events i n Table VI have time residuals of 2.0 seconds or smaller, suggesting that f o r these events the pick of sP i s correct. Events 9 and l8 which have large residuals In Table VI, and a number of others requiring further consideration are discussed i n the following section. 104 TABLE VI SUMMARY OF sP-P CALCULATIONS EVENT SP-P TIME (SEC) OBS-CALC CALC OBS 3 38.2 37.7 0.5^  5 a 15.6 17.5 1.9 9 ft 7.9 12.0 4.1 13 12.6 14.0 1.4 16 18.3 19.7 1,4 18 12.8 18.5 5.7 21 * 25.3 25.0 0.3 28 25.1 23.1 2.0 31 % 8.1 10.0 1-9 Calculated time based on adjusted depth. 105 7-8 Other Possible E a r l y - A r r i v i n g Phases For a number of the events i n Tables V and VI the picking of pP and/or sP may be erroneous because of the p o s s i b i l i t y that other phases may be a r r i v i n g within the 25 second record length. Some events show separate phases i n addition to those picked as pP and sP. For c e r t a i n epicentral distances and f o c a l depths the phase PcP w i l l arrive very soon aft e r P. There are three events with conditions such that, on the basis of Jeffreys-Bullen t r a v e l times (Travis, 1965), PcP w i l l a rrive 5 or 6 seconds aft e r P. The VERT and P-D VERT records of one station f o r each of these events (13, 20, and 32) are shown i n Figure 32. Event 13 has a f o c a l depth of 28 km; pP and sP picks f o r i t l i s t e d i n Tables V and VI are shown by arrows on the P-D VERT record i n Figure 32. Events 20 and 32 are deep, 129 and 197 km respectively; only the onset P motion i s shown i n Figure 32 fo r these events. These three events are among the few which show more than one cycle of strong onset motion. The Jeffreys-Bullen PcP-P times f o r these events are 6.3, 5.3, and 4.7 seconds f o r events 13, 20, and 32 respectively. It i s probable that the extension of onset motion r e s u l t s from a contribution from PcP, but the overlap with P masks the a r r i v a l . Three events whose late a r r i v i n g phases might be Interpreted as something other than secondary source 106 F i g u r e 32o Three events w i t h PcP a r r i v i n g about 5 seconds a f t e r P. 107 phases are shown i n Figure 3 3 . The P-D VERT record of event 5-2 shows three strong secondaries la b e l l e d A, B, and C i n Figure 3 3 . pP and sP for t h i s event l i s t e d i n Tables V and VI were phases B and C respectively. This required an adjustment of f o c a l depth from the reported 5 4 km to 3 6 km. The U.S.C.G.S. depth was no doubt deter-mined on the basis of event C being pP; observed and calculated pP-P times would then agree quite w e l l . I f t h i s i s true, what inter p r e t a t i o n can be given to phases A and B? The epicentral distance for event 5 i s 4 3 degrees. None of the common phases except pP and sP w i l l arrive within the record length shown. One alternative i s to interpret event 5 as a double shock. Considering the amplitude of phase C r e l a t i v e to phases A and B, one possible explanation i s as follows, phase C i s pP cor-responding to the f i r s t a r r i v i n g P phase from a source of f o c a l depth 5 4 km, while phase B i s pP corresponding to the second P phase, A, from a source at a much shallower depth. There are a number of other p o s s i b i l i t i e s one could imagine, Including the one o r i g i n a l l y given on Tables V and VI with phase A interpreted as a second source shock P phase with no strong accompanying pP or sP. The phases l a b e l l e d A and B on event 9 i n Figure 3 3 were interpreted as pP and sP respectively i n Tables V and VI. This i s quite l i k e l y i n error. Interpreting phase A as pP required depth adjustment from 3 3 km to 1 8 km, and Figure 3 3 . Three events w i t h m u l t i p l e secondary a r r i v a l s . 109 then i n t e r p r e t a t i o n of phase B as sP and using the adjusted depth resulted i n a sP-P time residual of 4 . 1 seconds. The important parameter concerning t h i s event i s i t s large epicentral distance, 139 degrees) the f i r s t a r r i v i n g phase, therefore, i s PKP. This distance i s very near the "focus" on the PKP tr a v e l time curve, the point at which two PKP phases t r a v e l l i n g d i f f e r e n t paths through the earth arrive at the same time. A summary of e a r l i e r work and d e t a i l s of some recent theories concerning t h i s complicated phe-nomena are given by Bolt (1964). No further discussion w i l l be given here except to say that phases A and B on event 9 i n Figure 33 are more l i k e l y complex PKP type phases than pP and sp phases. The three secondary phases on event 3 5 . i n Figure 33 (they appear equally strong and at i d e n t i c a l times on station 1) were not interpreted as secondary source phases. The epicentral distance f o r t h i s event i s 13 degrees, and the l a t e r a r r i v i n g phases are probably related to the complications f o r near events discussed i n Section 6 - 2 . Event l 8 which has the largest sP-P time r e s i -dual In Table VI requires further consideration. This event has remarkably similar P-D VERT and P-D RAD records on the station pair and was used as an i l l u s t r a t i o n of t h i s i n Figure 31 . sP i s • s u s p i c i o u s l y strong but no other i n t e r p r e t a t i o n seems reasonable. There i s some long-110 period noise on the VERT and RAD records which may be masking portions of some of the phases r e s u l t i n g i n the large sP-P time r e s i d u a l . Apart from the events discussed i n t h i s section, upon which more than one inter p r e t a t i o n of the l a t e r a r r i v i n g phases may be placed, the P-D processor i s seen to be quite successful i n enhancing pP and sP phases. As w i l l be discussed i n Chapter X, further improvements can probably be made by appropriate adjustments i n f i l t e r -ing and P-D processing. i I l l CHAPTER VIII SOURCES OF PHASE DISTORTION 8-1 Introductory Remarks The P-D processor passes P motion i n proportion to i t s amplitude and degree of r e c t i l i n e a r i t y . From some of the P-D records shown i n foregoing chapters the impression might be gained that one does see strongly r e c t i l i n e a r P signals at the surface of the Alberta crust. It w i l l be shown i n t h i s chapter that these P signals have, i n f a c t , o r b i t a l motions which exhibit a high degree of e l l l p t i c i t y . Considering the approach angles of these P phases discussed i n Section 6-4, the greater proportion of compressional displacement w i l l appear on the recorded v e r t i c a l component, the greater proportion of c r u s t a l generated SV on the r a d i a l component. However, i t was shown on Figures 24 and 25 that the r a d i a l component of a strong P phase w i l l predominate over the SV motion on the r a d i a l records, and, although the SV motion i s also present on these record segments, the combined v e r t i c a l and r a d i a l P signal i s strong enough to be passed by the 112 P-D processor. But, as w i l l be shown i n Section 8-3, the P phase i s always highly e l l i p t i c a l because of the SV contribution. I t was stated i n an e a r l i e r section that, i n theory, a l l signal i n the seismogram record lengths d i s -cussed here i s confined to the v e r t i c a l and r a d i a l com-ponents, with no signal remaining i n the rotated transverse component. The degree to which the Alberta seisraograms conform to t h i s theory w i l l be discussed i n Section 8-4. A discussion w i l l also be given concerning the dependence of the amount of transverse motion on the general period of motion. 8-2 Times and Amplitudes of L o c a l l y Generated SV Before presenting some examples of d i s t o r t i o n of P phases by l o c a l l y generated SV and transverse :signals, consideration w i l l be given to the time delays and ampli-tudes which can be expected f o r SV generated i n the Alberta crust. A notation f o r PS converted waves used by Costain et a l (1963) w i l l be used here. Designation of layer numbers f o r the f i v e layers of the gross Alberta crust are shown c i r c l e d to the right of the layers i n Figure 27* they are numbered from 1 f o r the sediments to 5 f o r the mantle. A converted wave, PS n, enters the layered system as a P wave, Is converted to SV at the interface between the n + 1 and n layer and propagates the remaining distance to the surface as SV. Calculations of actual SV converted wave ampli-tudes i n the Alberta crust would be arduous and w i l l not be attempted here, instead, a number of comments given by Costain et a l ( 1 9 6 3 ) and Cook et a l ( 1 9 6 2 ) (the same group of authors i n each case) i n detailed summaries of previous investigations of SV converted waves are reproduced here. (1) It i s supposed that PS converted waves are formed i f the thickness of the layer i s greater than the wavelength of the compressional wave. ( 2 ) Strong PS converted waves are found on only those sei sinograms with wave periods 2 seconds or l e s s . ( 3 ) The periods of PS converted waves are not usually noticeably d i f f e r e n t from those of compressional waves found on the same records. (4) Whenever a wave changes i t s character the converted waves show larger decreases i n amplitudes than the pure longitudinal waves, and one may suppose, therefore, that the most favorable dynamic conditions f o r the converted waves are those i n which they change only once. (5) For the most favorable boundary conditions the amplitudes of the converted waves w i l l t h e o r e t i c a l l y be only s l i g h t l y smaller than the amplitude of the corresponding P wave. 114 (6) The amplitudes of the various PS converted wave a r r i v a l s increase with successively increasing depth to the interface where the conversion took place, provided the interface v e l o c i t y r a t i o s (upper/lower) continually decrease with depth. (7) Amplitudes of some PS converted waves are found to be at least twice the value of the corresponding longitudinal wave. It i s noted that these large amplitudes are to a c e r t a i n extent i n contradiction with calculated amplitude values and may be a t t r i -buted to a " p a r t i a l screening and weakening" of the pure longitudinal wave. These comments, some of which w i l l prove applicable to the Alberta seismograms, w i l l be referred to i n t h i s chapter by statement number. Table VII showing the wavelengths of compressional waves i n the Alberta crust i s presented with reference to Statement 1. The layer thicknesses and compressional v e l o c i t i e s are from Figures 26 and 27. The c a l c u l a t i o n was made f o r the sedimentary layer under both Leduc and Rocky Mountain House using approximate mean v e l o c i t i e s fo r the entire sedimentary column. Because of the varia-t i o n i n period of motion (see Figure 19) , wavelengths have been calculated f o r periods of 1.0 and 2.0 seconds using the simple rel a t i o n s h i p : wavelength = v e l o c i t y x period. I t w i l l be shown (Section 8-3) that SV i s generated at the base of the sediments. Therefore, Statement 1 i s 115 TABLE V I I WAVELENGTHS OP COMPRESSIONAL WAVES IN THE LAYERS OP THE ALBERTA CRUST. LAYER LAYER THICKNESS (KM) COMPRESSIONAL VELOCITY (KM/SEC) 1 (LED) 2.7 (4 .5) 1 (RMH) 4 . 4 (5 .0) 2 13 6.1 3 22 6.5 4 7 7.2 WAVELENGTH (KM) T = 1.0 SEC T = 2.0 SEC 4.5 5 . 0 6.1 6.5 7 .2 9 . 0 10.0 1 2 . 2 13.0 1 4 . 4 TABLE V I I I VELOCITY RATIOS IN THE ALBERTA CRUST INTERFACE LAYERS VELOCITY RATIO 1/2 (LED) 0.74 1/2 (RMH) 0.82 2/3 0.94 3/4 0.90 4/5 O .87 116 not generally v a l i d here, i . e . , PS converted waves are formed f o r layer thicknesses somewhat smaller than the wavelength of the compressional wave. The v e l o c i t y r a t i o s i n the Alberta crust are shown i n Table V I I I . The highest v e l o c i t y contrast (lowest rati o ) i s at the base of the sediments. Statement 1 notwithstanding i t i s probably t h i s interface which i s most favorable to the generation of converted SV waves, i . e . , PS-j_ should be a strong phase. Below the 1/2 interface the layering conforms to the requirement of Statement 6, i . e . , the v e l o c i t y r a t i o s decrease with depth. On t h i s basis then PS^ should be another strong converted phase. Because of the high v e l o c i t y r a t i o s at interfaces 2/3 and 3/4, converted phases PS 2 and PS^ w i l l not be con-sidered. There are some low v e l o c i t y r a t i o s within the sedimentary column (see Figure 26) but, because of the thinness of the layers, PS converted phases generated within the sediments w i l l not be considered. Attention i s now turned to the time delays of PS-^  and PS^ a f t e r P. The shear wave v e l o c i t i e s In the c r u s t a l layers (p) are shown on the right-hand edge of the layers i n Figure 27. On the basis of approximate average v e l o c i t i e s i n the LED and RMH sediments the PS^P times w i l l be about 0 . 5 and 0 . 7 seconds f o r LED and RMH respectively. Using the shear v e l o c i t e s shown i n Figure 27 the PS^-P time f o r the Alberta crust w i l l be about 5 . 2 117 seconds with a few tenths of a second v a r i a t i o n f o r d i f -ferent angles of incidence and d i f f e r e n t stations. The onset P motion has a duration of a few seconds, depending on the period of motion and other fa c t o r s . With PS-^ -P times of about half a second, the PS 1 phase with a period similar to that of P (see Statement 3) w i l l be almost e n t i r e l y coincident with the onset P motion. If t h i s onset motion (now containing both P and PS-^ dies away within 5 seconds, the PS^ phase should be observed following i t very c l o s e l y . 8-3 Examples of L o c a l l y Generated SV When attempting to i d e n t i f y PS 1 and PS^ phase motion, which may be very small and often superimposed on P motion, care must be taken to use records with very low background noise l e v e l . This also applies to the signals to be discussed i n Section 8 - 4 . The entire suite of records was searched f o r evidence of the presence of PS^ phases. The SV motion was i d e n t i f i e d as described i n Section 4 - 4 , i . e . , as motion which was completely rejected by the P-D processor but which was of s u f f i c i e n t amplitude and re g u l a r i t y to be distinguishably out-of-phase on the VERT and RAD components. The six examples found are shown i n Figure 34. Three, events 16-1, 19-1, and 22-1 , show one cycle of clear SV type motion 5 or 6 seconds a f t e r the P a r r i v a l ; these 118 119 segments have been la b e l l e d as PS^ In Figure 34. Three others, events 23-1, 32-1 (P phase), and 32-1 (pP phase) show l e s s d i s t i n c t SV motion which i s r e a l l y only an out-of-phase d i s t o r t i o n of the in-phase P motion; these seg-ments have been l a b e l l e d with a question mark i n Figure 34. In none of the other events could SV motion be i d e n t i f i e d at the appropriate time as well as shown i n the examples of Figure 34. This was generally due to background noise contamination or to a longer duration of the primary P phase. On the basis of these r e s u l t s the amplitude of PS^ i s judged to be approximately 0.2 to 0.3 that of P. Four representative sets of v e r t i c a l - r a d i a l P phase p a r t i c l e motion plots are shown i n Figure 35. These plots were constructed from bandpass f i l t e r e d (BP-1, Figure 4) o r i g i n a l v e r t i c a l and singly-rotated r a d i a l (see Figure 5(a)) seismograms. Seven plots, each showing 2.4 seconds of motion, consisting of two preceding background noise p l o t s and f i v e signal plots are shown f o r each event. The t o t a l signal represented i s then 12 seconds. A heavy dot i s shown at the beginning of each separate plot so that the o r b i t a l motion can e a s i l y be followed throughout the 12 seconds of sign a l . Here the general e l l i p t i c i t y of the P motion, even at the very onset of the signal, i s s t r i k i n g l y apparent. Although only four events with good signal-to-noise l e v e l are shown i n Figure 35, t h i s i s a feature 120 Figure 35. V e r t i c a l - r a d i a l p a r t i c l e motion plots of P phases. Each plot contains 2.4 seconds of motion. The beginning of each plot i s de-noted by a heavy dot. 6 i s the approximate angle of incidence at the surface. 121 common to a l l events. The f i r s t three signal p l o t s cor-respond generally to the P signal burst. In events 10-1 and 13-2 the signal l e v e l remains high i n the l a s t two plot s ; the reasons f o r t h i s can be seen i n Figure 6 f o r event 10 which was very shallow and exhibits long duration of P motion, and i n Figure 32 f o r event 13 which has pP a r r i v i n g at approximately 9 seconds (within the fourth signal p l o t ) . The d i s t o r t i o n of the primary P motion away from r e c t i l i n e a r i t y toward e l l i p t i c i t y i s interpreted as due to the presence of strong PS^ motion (with the possible addition of some motion due to PS,, and PS gene-rated within the sediments, although t h i s i s u n l i k e l y i n •v view of the discussions i n Section 8 - 2 ) . The angle of incidence (0) at which the signal approaches the surface, determined f o r these events from Figure 7 and the table i n Figure 27, i s shown i n Figure 35 . The greater degree of e l l i p t i c i t y exhibited f o r events with the greater angle 6 i s a generally observed feature. This i s i n agreement with a t h e o r e t i c a l PS^/P^ amplitude curve presented by Costain et a l (1963) f o r a si m i l a r c r u s t a l model. In t h e i r model P^ i s the P wave which i s incident on the bottom of the model, and the PS-^/P^ ampli-tude r a t i o has a maximum at i = 60 degrees, and drops to zero at I = 0 . On the basis of the re s u l t s shown a judgement can be made of the PS,/P amplitude r a t i o . PS-./P f o r 122 events 13-1 and 16-1 i s about 0.2, f o r event 10 about 0. 6, and f o r event 24 about 1.5. The l a t t e r value appears to be an example of the phenomena mentioned i n Statement 7 i n Section 8-2. It should be noted that the effeets of the free surface have not been accounted f o r i n the o r b i t a l motion p l o t s of Figure 35. The general conclusions should remain the same, however, with the amplitudes of both P and PS being approximately halved (see Costain et a l , 1963). The p a r t i c l e motion i n the larger amplitude plo t s of Figure 35 forms e l l i p s e s which are quite regular. This i s an i n d i c a t i o n that the period of SV signal form-ing the horizontal t r a j e c t o r y i s very nearly equal to the period of the P signal forming the v e r t i c a l trajectory, 1. e., these events are i n general agreement with Statement 3 i n Section 8-2. Event 13-2 i n Figure 35 diverges s l i g h t l y from t h i s trend, p a r t i c u l a r l y i n the 2^  to 4 signal plot, where the P motion describes 1 1/2 to 2 cycles while the SV describes l e s s than 1 cycle, i . e . , the period of SV i s s l i g h t l y longer than that of P. The PS^ phase seen on event 16-1 i n Figure 34 i s also apparent i n Figure 35, where event 16-1 exhibits mainly horizontal (SV) motion i n the l a s t two signal p l o t s . 123 8-4 Examples of Transverse Motion One transverse seismogram has been shown pre-viously, event 10-1 i n Figure 6. The gradual buildup of transverse signal over the 30 second record i s a general feature of the events of t h i s study. This i s a commonly observed phenomena which becomes more dominant as the frequency band becomes higher. For example, i n high-frequency r e f r a c t i o n seismology transverse signals similar i n amplitude to the v e r t i c a l and r a d i a l signals are not uncommon (A.M. Bancroft, personal communication). At the other end of the seismic body wave frequency band, f o r example i n teleseismic seismology, transverse d i s t o r t i o n s of t h i s type are seldom observed f o r signal periods greater than about 10 seconds (Key, 1967). This, and other types of signals which cannot be explained i n terms of the transmission of plane waves through horizontal layering have been termed "sig n a l -gene rated-noise 11 . It i s generally believed to be due to scattering ( i . e . , r e f l e c t i o n , r e f r a c t i o n , and d i f f r a c -tion) by the e l a s t i c and density d i s c o n t i n u i t i e s commonly present at shallow depths i n the crust of the earth. The shorter wavelengths (higher frequencies) can "see" these small inhomogeneities, the longer wavelengths (longer periods) cannot. Key (1967) by applying v e l o c i t y - f i l t e r i n g techniques to array records was, i n addition, able to i d e n t i f y dominant topographic features within about 100 km 124 of the station as sources of signal-generated-noise (probably surface waves). It i s u n l i k e l y that similar e f f e c t s are occurring at the Alberta s i t e s where the topographic r e l i e f i s usually very small. E l l i s and Basham (1967) have presented and discussed a number of examples of transverse signal-generated-noise on the Alberta records i n r e l a t i o n to the problems of c r u s t a l deconvolutlon; no further discussion w i l l be given here. Before leaving t h i s topic, however, a number of examples of a puzzling, but possibly related, phenomena w i l l be presented. This concerns the d i s t o r t i o n of the horizontal r e c t i l l n e a r i t y of the P signal immediately at i t s onset on some of the events. Although, because of the low signal l e v e l , the horizontal motion i s usually d i s -torted by background noise, on some of those events with high horizontal signal-to-noise r a t i o the horizontal o r b i t a l motion exhibits a high degree of e l l i p t i c i t y . Six examples of the horizontal o r b i t a l motion of the P onset are shown i n Figure 36 . These have been constructed from bandpass f i l t e r e d (BP-1, Figure 4) north-south and east-west components. Each plot shows 3 . 0 seconds of onset motion beginning at the a r r i v a l pick f o r the p a r t i -cular event. The d i r e c t i o n of approach of the P phase i s shown by a large arrow near each p l o t . Figure 36. Horizontal onset o r b i t a l motion. 126 A clue to the source of e l l l p t i c i t y of the horizontal o r b i t a l motion may be found i n the epicentral distance ( A ) which i s shown f o r each event i n Figure 36. Events with the larger epicentral distances exhibit a greater degree of e l l l p t i c i t y than do the nearer events. Much of the horizontal motion, p a r t i c u l a r l y f o r the distant events where the signal i s a r r i v i n g almost v e r t i c a l l y , r e s u l t s from the PS converted phases (PS^ f o r the case of onset motion). N i a z i (1966) i n a study of deviations of apparent azimuth due to r e f r a c t i o n at a t i l t e d i n t e r -face showed that the azimuth deviation f o r a p a r t i c u l a r dip and v e l o c i t y contrast depends on the azimuth but i s larger f o r the smaller angles of incidence, i . e . , f o r larger A ' s . An SV wave incident on an i n c l i n e d interface at some azimuth d i f f e r e n t from the dip d i r e c t i o n w i l l have i t s p o l a r i z a t i o n d i r e c t i o n shifted out of the v e r t i c a l plane. The projection of the r e c t i l i n e a r motion on to a horizontal plane (say, the surface) w i l l then be e l l i p -t i c a l , the semi-minor axes of the e l l i p s e s being larger f o r larger A" s<> The dip of the Alberta sediments i s less than 1° toward the SSW. The gross crust i s not well enough known to determine a possible dip on the Moho. and i n t e r -mediate interfaces, although i t might be expected that the crust would thicken s l i g h t l y toward the root of the Rocky Mountains. The e l l i p s e s with the larger semi-minor axes shown i n Figure 36 would require dips of the order 127 of 1 0 ° . Although such dips cannot be postulated f o r the Alberta crust, E l l i s and Basham (1967) do observe azimuth deviations f o r some of the events as large as 1 5 ° . The azimuth deviations, i f interpreted e n t i r e l y i n terms of dipping interfaces, would also require dips of the order of 1 0 ° . Niazi (1966) does report l o c a l i z e d Moho. dips of about 8° under Arizona. Recently Kanasewich and Clowes (1967) have reported dips of 20° on a r e f l e c t i n g horizon at a depth of 30 km i n southern Alberta. An additional contributing factor to e l l i p t i c a l t r a j e c t o r i e s during onset would be the generation of SH by small scale inhomogeneities at the interfaces or within the upper layers. 128 CHAPTER IX SUMMARY AND CONCLUSIONS 9-1 Summary The events recorded during the Alberta Experiment have been subjected to a detailed study i n the time domain using both v i s u a l observation and p o l a r i z a t i o n f i l t e r i n g of the records to i d e n t i f y the types of seismic motion present i n the P phase and about 25 seconds of i t s coda. A P-detection p o l a r i z a t i o n f i l t e r of the REMODE class has been designed and shown successful i n enhancing segments of the records containing strong P motions. The p r i n c i p a l findings can be summarized as follows. 1. The general appearance of a P phase at a distant station depends on the nature of the source of the event. Although the more distant events show s l i g h t l y longer period wave motion, most of the v a r i a t i o n i n period among events i s probably related to variations i n source functions. The length of duration of strong signal a f t e r the P onset depends on the depth of focus of the event, the main contribution to extended strong motion r e s u l t i n g from early a r r i v i n g secondary phases f o r the shallow events. 2. The P displacement radiat i o n pattern of a f a u l t -129 type earthquake mechanism governs the pP/P amplitude r a t i o . Appropriate orientations of the displacement pattern can, i n theory, explain much of the observed pP/P amplitude r a t i o s . 3 . Except f o r those events distorted by background noise a l l station p a i r s of v e r t i c a l records of teleselsmic events show very similar wave motion throughout the 25 second P coda. 4 . The station p a i r s of r a d i a l records show a general s i m i l a r i t y only i n those record segments containing strong P motion. 5 . pP phases have been i d e n t i f i e d f o r 23 of the 40 earthquakes. On the basis of observed pP-P times and using source c r u s t a l columns of Menard (1967), the f o c a l depth of 8 of these events has been adjusted. The adjusted depths and those not requiring adjustment are believed to be accurate to better than -15>km. 6. sP phases have been i d e n t i f i e d on 9 events. 7. The PS^ converted phase has been observed at the calculated time following six strong P phases. The PS^/P amplitude r a t i o i s found to be between 0 . 2 and 0 . 3 . 8. SV motion, and p a r t i c u l a r l y the PS 1 converted phase, i s present on a l l records of the sui t e . The PS^/P amplitude r a t i o s are observed to vary between 0 . 2 and 1 . 5 . The strongest PS^ phases appear on the records of the nearest events. 9 . Transverse motion attributed to scattering by 130 c r u s t a l inhomogeneities appears as a slow buildup on a l l seismograms. 10. Some events have unidentified transverse motion d i s t o r t i n g the horizontal p a r t i c l e t r a j e c t o r i e s very soon a f t e r the P onset. 9-2 Conclusions Conclusions which relate to three f i e l d s of seismology can be drawn from the r e s u l t s of t h i s study. These three f i e l d s are: c r u s t a l deconvolution i n the short period range, distinguishing underground explosions from natural seismic events, and the fundamental problem of P coda composition. During the Alberta experiment recordings were made of teleseismic events over a varying c r u s t a l section. E l l i s and Basham (1967) show the numerous d i f f i c u l t i e s inherent i n r e l a t i n g the t h e o r e t i c a l response of the c r u s t a l layering at each station to observed P phase spectra. The r e s u l t s of Chapter VI suggest that, within the resolution of v i s u a l inspection of the seismograms of t h i s suite, the d i f f e r e n t c r u s t a l layering beneath each of the four stations makes a very similar contribution to the v e r t i c a l component of the recorded signal f o r teleseismic events. The r a d i a l components of the recorded signals show considerable v a r i a t i o n among the stations. The major contribution to the r a d i a l differences can be 131 r e l a t e d to d i f f e r e n t amplitudes and d i f f e r e n t time-delayed SV waves generated w i t h i n the c r u s t a l l a y e r i n g . This alone, however, does not e x p l a i n the frequency domain d i f f i c u l t i e s because the t h e o r e t i c a l t r a n s f e r f u n c t i o n used takes i n t o account a l l P and SV r e f l e c t e d and r e f r a c t e d waves generated w i t h i n the assumed c r u s t a l model. But two other f a c t o r s which have been observed here i n the time domain may complicate the frequency domain s t u d i e s . The f i r s t i s the excessive amplitude of some PS converted phases which i s not p r e d i c t e d t h e o r e t i c a l l y ; t h i s w i l l c o n t r i b u t e p r i n c i p a l l y r a d i a l motion which i s not included i n the h o r i z o n t a l t r a n s f e r f u n c t i o n . The second f a c t o r i s the presence of larg e amplitude pP and sP phases f o r the shallow events w i t h i n the record segment used i n the frequency domain c a l c u l a t i o n . Although the e x t r a compres-s i o n a l phases themselves should not c o n t r i b u t e d i f f i c u l t i e s (they w i l l make an a d d i t i v e c o n t r i b u t i o n to both components of the t r a n s f e r f u n c t i o n ) , each w i l l have i t s associated PS converted phases making c o n t r i b u t i o n s discussed as f a c t o r one. In a d d i t i o n , i f the frequency-analysed record segment contains a strong pP or sP phase near the end of the segment the complete wave t r a n s f e r may not be represented In the segment, i . e . , some important r e v e r b e r a t i o n s and r e f r a c t i o n s which w i l l be Included i n the t h e o r e t i c a l record w i l l be omitted from the experimental record. I f the depth of occurrence of a l l seismic events could be determined a c c u r a t e l y the problem of d i s t i n g u i s h i n g 132 underground explosions from earthquakes would be greatly s i m p l i f i e d . The accuracy of f o c a l depth assignment (-15 km) fo r shallow events discussed i n Chapter VII i s an improve-ment of significance to explosion detection studies. Most underground explosions have been, and i n the future probably w i l l be, detonated on land masses, either islands or continents. This means that the error due to estimated ocean depth discussed i n Section 7-3 w i l l not apply. Further, the c r u s t a l column at the source, p a r t i c u l a r l y f o r continental epicenters, w i l l be known to a higher degree of accuracy than those used i n Chapter VII. Careful attention to these d e t a i l s might improve the accuracy of calculated pP-P times to within ^ 0 . 5 seconds. The observed pP-P times were assumed accurate to within -2 seconds. Improvements i n the P-detection processor (suggestions f o r which w i l l be made i n Chapter X) may bring these l i m i t s down to about ^0.5 seconds. If these l i m i t s of accuracy were attainable f o c a l depths of earthquakes e x h i b i t i n g pP phases could be determined to within -5 km, an accuracy s u f f i c i e n t to d i s t i n g u i s h a l l but the very small earthquakes from under-ground explosions. However, there i s a t h e o r e t i c a l con-sideration which has not been discussed here. In dealing with pP, consideration has to be given to the curvature of the wave front f o r the upward passage of the compressional wave from a shallow source. If the plane wave assumption i s not v a l i d i n the frequency range of the recording the amplitude of pP phases may be greatly reduced. 133 PS converted waves have been u t i l i z e d f o r c r u s t a l studies by a number of Russian and American researchers (see Cook et a l , 1962) using both explosive and natural seismic sources. In theory the thickness of a single c r u s t a l layer can be determined by observing the difference i n time of the a r r i v a l of the primary P wave and the a r r i v a l of the PS converted wave, provided the compressional v e l o c i t y i n the layer i s known approximately. The Alberta records were shown In Chapter VIII to be composed i n part of large amplitude PS converted phases, which suggests the f e a s i b i l i t y of similar studies i n Alberta and else-where using teleseismic recordings. The d i f f i c u l t y In accurately timing the PS converted phases shown i n Figures 34 and 35 would be the l i m i t i n g f a c t o r . PS^ i s often weak and distorted by the coda of the primary P signal burst; PS^, although strong, i s completely superimposed on the primary P s i g n a l . Careful observation of p a r t i c l e motion t r a j e c t o r i e s might enable accurate timing of the PS con-verted phases. 134 CHAPTER X SUGGESTIONS FOR FURTHER RESEARCH 10-1 Bandpass and P o l a r i z a t i o n F i l t e r i n g P r i o r to each of the studies reported i n t h i s thesis the records were bandpass f i l t e r e d using BP-1 shown i n Figure 4. On many of the events the f i l t e r was not s u f f i c i e n t l y narrow to eliminate a l l of the background noise. If further studies are to be conducted using the records of the Alberta Experiment i t i s suggested that a group of bandpass f i l t e r s be designed f o r app l i c a t i o n to the records as required. In some cases to provide good signal records the pass band may have to be very narrow, but only signal which i s inseparable from the noise w i l l be l o s t . The P-D p o l a r i z a t i o n f i l t e r described i n Chapter IV requires much addit i o n a l study. The e f f e c t on the output of varying the window length and maximum l a g should be considered i n more d e t a i l . Considerable Improvement i n processing might be made i f an optimum window length and maximum lag were chosen on the basis of the dominant period of motion i n each event. The t h e o r e t i c a l response of a l l 135 of the p o l a r i z a t i o n f i l t e r s i n the REMODE class requires further consideration. The REMODE 5 f i l t e r with variable selectivity-has not been discussed i n Chapter IV but t h i s f i l t e r may prove to be the most useful i n the REMODE c l a s s . The Important difference between i t and the P-D processor i s i t s a b i l i t y to detect r e c t i l i n e a r signals a r r i v i n g from within a narrow arc. The most important suggestion for further research to appear i n t h i s chapter i s that the REMODE 5 be programmed and applied to the events of the Alberta Experiment or others of similar q u a l i t y . 10-2 pP and Focal Depth Assignment Improvement i n signal q u a l i t y using the suggested changes i n bandpass and p o l a r i z a t i o n f i l t e r i n g would no doubt enable i d e n t i f i c a t i o n of pP phases to be made on some of the events considered too noisy i n t h i s study. Application of a REMODE 5 type processor might improve the pP-P timing accuracy to an extent which would enable con-siderable improvement i n f o c a l depth assignment to the shallower earthquakes. The possible improvement i n f o c a l depth determination suggested i n Section 9-2 should be attempted using a suite of shallow earthquakes from a continental or oceanic region with a well defined c r u s t a l structure. 136 10-3 PS Converted Phases PS converted phases make a s i g n i f i c a n t contribu-t i o n to seismograms of teleselsmic events. The importance of these events on the Alberta records has not been adequately explored; the observed amplitudes i n p a r t i c u l a r should be compared to t h e o r e t i c a l l y expected values. P a r t i c l e motion pl o t s showing PS^ motion have been presented f o r four of the quietest events (Figure 35). PS^ motion of similar amplitude i s present on a l l events, although some of the events w i l l require narrow bandpass f i l t e r i n g to remove background noise. The Alberta records are available i n d i g i t a l form and provide the opportunity of studying PS converted phases f o r a wide range of e p i -c e n t r a l distances. 137 REFERENCES Atomic Weapons Research Establishment, The d e t e c t i o n and r e c o g n i t i o n of underground expl o s i o n s , A s p e c i a l report to the United Kingdom Atomic Energy A u t h o r i t y , December , 1965. Bancroft, A.M., and P.W. Basham, An FM magnetic tape rec o r d i n g seismograph, Pub. Dom. Obs., 35, 199-217, 1967. B o l t , B.A., The v e l o c i t y of seismic waves near the earth's center, B u l l . Seism. Soc. Am., 54, 191-208, 1964. Cook, K.L., S.T. Algermlssen, and J.K. Cos t a i n , The s t a t u s of PS converted waves i n c r u s t a l s t u d i e s , J.G.R., 67, 4769-4778, 1962. C o s t a i n , J.K., K.L. Cook, and S.T. Algermissen, Amplitude, energy, and phase angles of plane SV waves and t h e i r a p p l i c a t i o n to ea r t h c r u s t a l s t u d i e s , B u l l . Seism. Soc. Am., 53, 1039-1074, 1963. Cumming, G.L., and E.R. Kanasewich, C r u s t a l s t r u c t u r e i n western Canada, F i n a l report f o r AFCRL-66-519, Department of Ph y s i c s , U n i v e r s i t y of A l b e r t a , June, 1966. E l l i s , R.M., and P.W. Basham, C r u s t a l c h a r a c t e r i s t i c s from short p e r i o d P waves ( p r o v i s i o n a l t i t l e ) , i n pr e p a r a t i o n , 1967. Ewing, W.M., W.S. Jardetzky, and F. Press, E l a s t i c waves i n l a y e r e d media, McGraw-Hill, 1957. Garland, G.D., and R.A. Burwash, Geophysical and p e n o -l o g i c a l study of the Precambrian of c e n t r a l A l b e r t a , Canada, B u l l . Am. Assoc. Pet. Geol., 43, 790-806, 1959. G r i f f i n , J.N., A p p l i c a t i o n and development of p o l a r i z a t i o n (REMODE) f i l t e r s , Seismic Data Laboratory Report No. l 4 l , E a r t h Sciences D i v i s i o n , Teledyne, Inc., A p r i l , 1966a. 138 G r i f f i n , J.N., REMODE signal/noise tests i n polarized noise, Seismic Data Laboratory Report No. 162, Earth Sciences Division, Teledyne, Inc., September, 1966b. Gutenberg, B., and C F . Richter, On seismic waves, Gerlands B e i t r . z. Geophys., 45, 28O-36O, 1935-Gutenberg, B., and C F . Richter, Materials f o r the study of deep-focus earthquakes, B u l l . Seism. Soc. Am., 26, 341-390, 1936. Heezen, B.C., and M. Tharp, Tectonic f a b r i c of the Atl a n t i c and Indian Oceans and continental d r i f t , P h i l . Trans. Roy. Soc. London, A, 258, 90-106, 1965. Howell, B.F., P.M. Lavin, R.J. Watson, Y.Y. Cheng, and J.L. L i n , Method f o r recognizing repeated pulse sequences i n a seismogram, J.G.R., 72, 3225-3232, 1967. Ichikawa, M., and P.W. Basham, Variations i n short-period records from Canadian seismograph stations, Can. J. Earth S c i . , 2, 510-542, 1965. Kanasewich, E.R. and R.M. Clowes, Geophysical invest i g a t i o n of the earth's crust and upper mantle i n Alberta (abstract), Physics i n Canada, 23, 106. Key, F.A., Signal-generated-noise recorded at the Eskdalemuir seismometer array station, B u l l . Seism. Soc. Am., 57, 27-37, 1967. Lanczos, c , Numerical analysis, Pitman, 1957. Lehmann, I., The t r a v e l times of the longitudinal waves of the Logan and Blanca atomic explosions and th e i r v e l o c i t i e s i n the upper mantle, B u l l . Seism. Soc. Am., 52, 519-526, 1962. Menard, H.W., Tr a n s i t i o n a l types of crust under small ocean basins, J.G.R., 72, 3061-3073, 1967. Mims, C.H., and R.L. Sax, Re c t i l i n e a r motion detection (REMODE), Seismic Data Laboratory Report No. 118, Earth Sciences Divis i o n , Teledyne, Inc., March, 1965. N i a z i , M., Corrections to apparent azimuths and travel-time gradients f o r a dipping Mohorovicic discontinuity, B u l l . Seism. Soc. Am., 56, 491-509, 1966. Richards, T.C, and D.J. Walker, Measurement of the thickness of the earth's crust i n the Alberta plains of western Canada, Geophysics, 24, 262-284, 1959-139 Sax, R.L., F e a s i b i l i t y of l i n e a r p o l a r i z a t i o n measurements for detecting and measuring seismic body waves, Seismic Data Laboratory Report No. 163, Earth Sciences Divisi o n , Teledyne, Inc., September , 1966. Shimshoni, M., and S.W. Smith, Seismic signal enhancement with three-component detectors, Geophysics, 29, 664-671, 1964. Stevens, A.E., S-wave f o c a l mechanism studies of the Hindu Kush earthquake of July 6, 1962, Can. J . Earth S c i . , 3, 367-387, 1966. Sykes, L.R., Mechanism of earthquakes and nature of f a u l t i n g on the mid-oceanic ridges, J.G.R., 72, 2131-2153, 1967. Travis, H.S., Interpolated Je f f r e y s and Bullen seismologlcal tables, Technical Report No. 65-35, The Geotechnical Corporation, May, 1965. Utsu, T., Variations i n spectra of P waves recorded at Canadian A r c t i c seismograph stations, Can. J . Earth S c i . , 3, 597-621, 1966. Wu, F.T., and W.J. Hannon, PP and c r u s t a l structure, B u l l . Seism. Soc. Am., 56, 733-747, 1966. 140 APPENDIX A THE LANGZOS NUMERICAL FILTER Ideally, one would l i k e a numerical f i l t e r which, i n the frequency domain, i s i n f i n i t e l y sharp. For example, fo r a low-pass f i l t e r the desired response, Y ( f ) , i s I l l u s t r a t e d i n the following diagram, - f - f N - f . 1/2 Y(f) 0 XC N +f where f ^ i s the Nyquist frequency and f^ i s the corner frequency of the low-pass f i l t e r . The time domain f i l t e r function, W(t), i s given by the Fourier transform of Y ( f ) , i . e . , + 00 , - c W(t) = j* Y(f) e i c , 5 t df = 1/2 j e i w t df. - 0 0 " f C This reduces to W(t) = sin 27rf ct 2rE (Al) 141 which i s the " d i f f r a c t i o n function". If the f i l t e r function, W(t), i s truncated to a f i n i t e length with a "boxcar", ri p p l e s (Gibbs o s c i l l a t i o n s ) w i l l appear on the correspond-ing response, Y ^ ( f ) . Lanczos* (1957) devised a method by which the Gibbs o s c i l l a t i o n s can be smoothed. Consider the expansion of an even function A(f) i n the i n t e r v a l (-ir, ir), i . e . , l e t f N = *  = TES ' then A t = ^ and 2irft = 2TrfkAt = fk , where k i s the time sample index. Truncating the expansion at n terms with a length "C= n A t y i e l d s n A n ( f ) =XIak C O S k f ( A 2 ) k=-n where a^ ., the expansion c o e f f i c i e n t s , are given by TT 1 a k —TT Since A n ( f ) i s A(f) truncated at n terms, the r i p p l e remain-ing on A n ( f ) w i l l be due to the highest order term, i . e . , the Lanczos, C , Numerical Analysis, Pitman, 1957. I I 142 n t h term. If A f i s the "period" of the n t h term ri p p l e then A f = % . Therefore, i f A (f) i s to be smoothed, i t should be smoothed ' n v ' 2ir . over the i n t e r v a l A f = -=JJ . The smoothed frequency-response i s given by f + w ^ ) - f e J M 5 ) d ? ' (A3) Substituting (A2) into (A3), integration and s i m p l i f i c a t i o n y i e l d s n a, s i n k n k k^ K~-n L K n cos kf, i . e . , the c o e f f i c i e n t s In the expansion of A n ( f ) when multip l i e d by a second d i f f r a c t i o n function become the c o e f f i c i e n t s i n the expansion of A n ( f ) . This smoothing process can be applied to the low-pass f i l t e r . I f W(t) given by (Al) i s truncated at T = n A t , the ri p p l e on Y Q (f) w i l l have a "period" of A f =-§-^* Putting (Al) i n d i g i t a l form, i . e . , t = k A t , and defining f c i n unit s of a f r a c t i o n of the Nyquist frequency, f R , the f i l t e r function which w i l l produce a smoothed frequency response Y Q ( f ) w i l l be given by 143 s i n irkf. K ( s i n k A t ) 2-irkAt TTA^ k < n (A4) That i s , the o r i g i n a l d i f f r a c t i o n function, (Al), i s truncated with the center lobe of another d i f f r a c t i o n function. response of a f i l t e r constructed from the convolution of a high-pass and a low-pass f i l t e r function, both designed on the basis of equation (A4). The Gibbs oscillations on the corners are almost non-existent and the f i r s t side lobe r i s e s to about 1 per cent of the peak. function center lobe can be used to produce a smoothed frequency response. For example, the center lobe of ft both a Hamming and Harming window have been tested. Both Hamming and Harming truncation produce s l i g h t l y l e s s sharp cut-off than the Lanczos truncation, but have a smaller f i r s t side lobe. In any p a r t i c u l a r a p p l i c a t i o n the corner sharpness requirement should be weighed against the side lobe height to decide which truncation function should be used. The bandpass f i l t e r shown In Figure 4 i s the Truncating functions other than a d i f f r a c t i o n f o r d e f i n i t i o n s see, f o r example, Blackman, R.B., and J.W. Tukey, The measurement of power spectra, Dover, 1959. 144 APPENDIX B L I S T I N G OP FORTRAN IV SUBROUTINE "REMODE" SUBROUTINE REMODE (LAGS,LWIN,NTOT,Z,R,FZ,PR,KEY) C C GENERAL ROUTINE FOR REMODE 2, 2A, 3, 3A C C RESTRICTED TO 610 DATA POINTS PER SERIES AND C 15 CROSS-CORRELATION LAGS C C LAGS = NUMBER OF LAGS C LWIN = WINDOW LENGTH IN SAMPLES C NTOT = TOTAL NUMBER OF DATA POINTS PER SERIES C Z VERTICAL INPUT SIGNAL C R RADIAL INPUT SIGNAL C F Z VERTICAL OUTPUT SIGNAL C FR RADIAL OUTPUT SIGNAL C C KEY DETERMINS TYPE OF REMODE F I L T E R — C KEY=1 REMODE 2 C KEY=2 REMODE 2A C KEY=3 REMODE 3 C KEY=4 REMODE 3A C DIMENSION Z ( 6 l O ) , R ( 6 l O ) , F Z ( 6 l O ) , P R ( 6 l O ) , R R ( 6 l O ) , Z Z ( 6 l O ) , 1RZ(15,610) DO 10 L=1,LAGS NT=NT0T-L+1 K=L-1 DO 10 1=1,NT J=K+I 10 R Z ( L , I ) = R ( I ) £ Z ( J ) LEND=NTOT-LAGS LW2=LWIN/2 GO TO (30,30, 20, 2 0 ) , KEY 20 L2=LEND+LW2 DO 25 I=LAGS,L2 Z Z ( l ) = Z ( l ) f t Z ( l " 25 R R ( I ) = R ( l ) f t R ( l ! 30 DO 70 II=LAGS,LEND SUM=0. J3=H+LW2 J1=II-LW2 145 GO TO (34,33,34,33),KEY 33 IF (RZ(1,II).GE.O.) GO TO 34 FZ(II ) = 0 . FR(II ) = 0 . TO TO 70 34 GO TO (37,37,35,35),KEY 35 Zl=0. t R 1 = 0 . D O 36 J - I I , J 3 Z l - Z l - f Z Z (J) 36 R1=R1+RR(J) SIG=SQRT(1./(Z1&R1)) 37 DO 40 K=J1,J3 40 SUM=SUM+RZ(1,K) SZ=Z(ll)ftSUM SR=R(II)ftSUM LLL=LAGS-1 DO 60 1=1, LLL 12=11-1 13=11+1 SSZ=Z(I2)+Z(I3) SSR=R(I2)+R(I3) 11=1+1 J2=J3-I RED=0. DO 50 J= J 1 , J 2 50 RED=RED+RZ(I1,J) SZ=SZ+SSZfiRED 60 SR= SR+ S SRitRED GO TO ( 6 5 , 6 5 , 6 6 , 6 6 ) ,KEY 65 FZ(II)=SZ FR(II)=SR GO TO 70 66 FZ(II)=SZ/SIG FR(II)=SR/SIG 70 CONTINUE I1=LAGS-1 I2=LEND+1 DO 80 1=1,11 FZ(I ) = 0 . 80 FR(I ) = 0 . DO 90 I=I2,NT0T FZ(I ) = 0 . 90 FR(I ) = 0 . RETURN END 

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