A TWO-COMPONENT ARCTIC AMBIENT NOISE MODEL by MICHAEL VICTOR GREENING B.Sc., University of Victoria, 1983 M.Sc., University of Victoria, 1987 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Oceanography We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 1994 ©Michael Victor Greening, 1994 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. (Signature) C) (2 Department of ! A The University of British Columbia Vancouver, Canada Date DE-6 (2/88) 25, 19C/ PH ‘ Supervisors: Dr.P.Zakarauskas and Dr.P.H .LeBlond Abstract Short term Arctic ambient noise spectra over the frequency band 2 - 200 Hz are presented along with a two component noise model capable of reproducing these spectra. The model is based on the measured source spectrum and the spatial, temporal and source level distributions of both active pressure ridging and thermal ice cracking. Modeled ambient noise levels are determined by summing the input energy of the distributions of ice cracking and pressure ridging events and removing the propagation loss. Measurements were obtained on a 22-element vertical array along with a 7-element horizontal array deployed beneath the Arctic pack ice in 420 meters of water. Over 900 thermal ice-cracking events were detected in approximately 2 hours of data col lected over several days during April 1988. The source directivity for events beyond 40 wavelengths range was found to be accurately represented by a dipole with an approximate 3 dB increase above the dipole directivity pattern near 60° - 65° caused by the leaked longitudinal plate wave. A technique for measuring the bottom re flectivity function by correcting the bottom reflection of a thermal ice crack for the measured directivity is presented. The spatial distribution of thermal ice-cracking events is consistent with a uniform distribution. Source levels were measured from 110 to 180 dB//pPa /Hz at 1 m with the distribution of all events approximating a 2 linearly decreasing function on a log-dB scale of the number of events versus source 11 level. Near the end of the data collection period, measurements from a nearby active pressure ridge were obtained. Evidence is presented that the infrasonic peak observed near 10 Hz in Arctic ambient noise spectra may result from a frequency dependent propagation loss acting on the source spectrum of pressure ridging. Both modeled and measured ambient noise spectra show that ice cracking may dominate the spring-time ambient noise to frequencies as low 40 Hz. Below 40 Hz, the ambient noise is dominated by a single or few active pressure ridges at ranges of tens of kilometers. Above 40 Hz, the ambient noise is dominated by a large distribution of thermal ice-cracking events with over 50% of the total noise level produced by events within 6 km range and over 80% produced by events within 30 km range. 111 A Two- Component Arctic Ambient Noise Model Table of Contents ABSTRACT ii TABLE OF CONTENTS iv LIST OF TABLES vii LIST OF FIGURES viii ACKNOWLEDGEMENTS xvii CHAPTER 1 1 INTRODUCTION 1.1 Objective 1 1.2 Approach and Contents 2 REVIEW OF SOURCE AND PROPAGATION CHAPTER 2 6 MODELS 7 2.1 Plate Waves 2.2 Dilatational Point Source 14 2.3 Horizontal and Vertical Point Force 16 2.4 Propagation Model 21 iv Table of Contents CHAPTER 3 DATA COLLECTION 34 3.1 Environment and Instrumentation 34 3.2 Source Detection and Description 36 CHAPTER 4 ARCTIC AMBIENT NOISE MEASUREMENTS CHAPTER 5 PRESSURE RIDGING .. 58 69 5.1 Spatial Distribution 69 5.2 Source Spectrum 70 5.3 Propagation Loss 71 5.4 Modeled Pressure Ridge Noise 75 CHAPTER 6 THERMAL ICE CRACKING 92 6.1 Spatial Distribution 93 6.2 Source Directivity 94 6.3 Source Spectrum 105 .6.4 Source Level Distribution 106 6.5 Modeled Thermal Ice-Cracking Noise 115 V Table of Contents CHAPTER 7 MODELED AMBIENT NOISE 148 CHAPTER 8 SUMMARY 154 157 REFERENCES APPENDIX A SEABED REFLECTIVITY FUNCTION vi 164 List of Tables 3-I Cross correlation of the number of detected ice-cracking events per 42 minute with environmental conditions. 4-I Mean and variance of measured environmental conditions and the 63 number of detected ice-cracking events per minute for the four classes of detected power spectra. 4-TI Cross correlation between the measured ambient noise levels at 10 64 Hz and 200 Hz with the measured environmental conditions and the number of detected ice-cracking events per minute. 5-I Parameters of ice and bottom layers used for propagation loss mod- 78 eling in Safari. 6-I Mean, variance and skewness of the distribution of the value of m in the sinm8 model of source directivity as a function of range and frequency. vii 119 List of Figures 2-1 Longitudinal (symmetric) and Flexural (antisymmetric) modes in a free 27 plate. 2-2 Dispersion curves for first three symmetric and antisymmetric modes in 28 a free plate for a Poisson’s ratio of 0.34. 2-3 Coordinate system used for a pair of horizontal point forces F applied at 29 the inner surface of a cylindrical cavity with radius a and height h. 2-4 Vertical directivity predicted from a pair of horizontal point forces applied 30 at the surface of 6 m thick ice for frequencies of 50, 100, 150 and 200 Hz. 2-5 Vertical directivity predicted from a vertical point force applied at the 31 surface of 6 m thick ice for frequencies of 50, 100, 150 and 200 Hz. 2-6 Vertical directivity predicted from both horizontal and vertical point forces applied at the surface of 3 m thick ice for frequencies of 50, 100, 150 and 200 Hz. vii’ 32 2-7 Vertical directivity predicted from both horizontal and vertical point 33 forces applied at the surface of 9 m thick ice for frequencies of 50, 100, 150 and 200 Hz. 3-1 a) Air temperature, d) wind speed, b) solar radiation, e) wind direction, and c) barometric pressure, 43 f) current speed for several days during time of experiment. 3-2 Measured sound speed profile along with the profile used for analysis 49 such as range finding, propagation loss estimation and vertical source angle estimation. 3-3 Array configuration. A linear equispaced vertical array with a 12 m 50 hydrophone spacing and the first hydrophone 18 m below sea level is used along with a low redundancy L shaped horizontal array with 7 hydrophones at 102 m depth. 3-4 Time series of received acoustic pressure for an ice-cracking event at 51 480 m horizontal range. 3-5 Time series of received acoustic pressure for an ice-cracking event at 52 3150 m horizontal range. 3-6 Number of detected ice-cracking events per minute for each of the 53 two-minute ambient noise recordings. 3-7 Time series of an event (or events) with distinct modal properties such as changing amplitude and phase with depth. ix 54 3-8 Time series of an ice-cracking event at 400 m horizontal range which 55 shows a leaked longitudinal plate wave arrival preceding the direct arrival. 3-9 Time series of the received acoustic pressure of three hydrophones in 56 the vertical array for two minutes during a nearby (approximately 2 km range) active ridge building event. 3-10 Time series of the received acoustic pressure of three hydrophones in 57 the vertical array for one minute during a time of active thermal ice cracking but several days prior to the ridge building event shown in Fig. 3-9. 4-1 Average ambient noise spectra and standard deviation for four classes of measured noise. 65 a) Class 1. Strong infrasonic peak at 8 Hz with little or no thermal ice cracking. b) Class 2. Strong infrasonic peak at 8 Hz with some thermal ice cracking. c) Class 3. Weaker and broader infrasonic peak at 4 Hz with some thermal ice cracking. d) Class 4. Very intense thermal ice cracking with no noticeable infrasonic peak. 5-1 Received spectral level of a typical pulse within the ridge building 79 event. 5-2 First 3 modes at 100 Hz in water 420-rn deep with a sound speed profile as shown in Fig. 3-2. Note that the modes are trapped near the surface resulting in propagation loss that is dependent on spreading and ice interaction. x 80 5-3 First 3 modes at 20 Hz in water 420-rn deep with a sound speed profile 81 as shown in Fig. 3-2. For this low a frequency, the modes are no longer trapped near the surface (as in Fig. 5-2) resulting in bottom interaction which in turn increases the propagation loss. 5-4 Propagation loss determined using the wave model SAFARI for a 82 source at 0.2-rn depth in 7-rn thick ice for water 420-rn deep and depth averaged over all hydrophones in the vertical array. 5-5 Propagation loss determined using the normal modes model KRAK- 83 ENC with Burke-Twersky scattering for water 420-rn deep and depth averaged over all hydrophones in the vertical array. An average of 11.5 keels per kilometer with keel depths of 5.3 m and keel half widths of 11.9 rn is used. 5-6 Received spectra of 3 ice-cracking events at different ranges when all 84 multiple arrivals including direct path, bottom reflection, under-ice reflection, etc. are used. 5-7 Resulting ambient noise spectra produced by distant ridge building 85 events using the environmental conditions given in Table 5-I to deter mine propagation loss. 5-8 Resulting ambient noise spectra produced by a ridge building event at 86 90 km range for sources at varying depths in the ice. 5-9 Resulting ambient noise spectra produced by a ridge building event at 90 km range for different levels of ice absorption. xi 87 5-10 Resulting ambient noise spectra produced by a ridge building event at 90 km range for different shear wave characteristics in the bottom. Ambient noise for different bottom shear wave speeds. 88 a) b) Ambient noise for different bottom shear wave absorptions. 5-11 Resulting ambient noise spectra produced by distant ridge building 90 events using the normal modes model KRAKENC with Burke-Twersky scattering. 5-12 Propagation loss as a function of frequency and total water depth for 91 a source at 200 km range. 6-1 Spatial distribution of all detected events about the vertical array. 120 6-2 Comparison of the vertical directivity of a pair of horizontal point 121 forces with the sin tm8 model. 6-3 Comparison of the vertical directivity of a vertical point force with the 122 sinmO model. 6-4 Vertical directivity of an ice-cracking event at 450 m range which fits 123 the sin tm 8 model very well. 6-5 Vertical directivity of an ice-cracking event at 300 m range which shows a small fluctuating pattern about the best fit to the model sin 8. tm xli 124 6-6 Vertical directivity of an ice-cracking event at 500 m range which does 125 not fit the sin 6 model. m 6-7 Normalized distribution of the directivity index m for all events within 126 2000 m range and with at least a 3 dB signal to noise ratio. 6-8 Normalized distribution of the directivity index m for one octave fre- 127 quency bands centered at 48 Hz, 96 Hz and 145 Hz. Distributions of m are given for all events less than approximately 40 wavelengths in 6-8a and for all events greater than this range but less than 2000 m in 6-8b. 6-9 Vertical directivity of an ice-cracking event at 300 m range showing 129 little or no dependence on frequency. 6-10 Vertical directivity of an ice-cracking event at 450 m range showing 130 strong dependence on frequency. 6-11 Vertical directivity of an ice-cracking event at 1150 m range showing 131 dependence on frequency. 6-12 Vertical directivity of an ice-cracking event at 140 m range showing an excess in pressure level of 1 dB source angle of 60° 6-13 - - 132 2 dB above the sinmO model at a 65°. Synthetically generated time series for an ice-cracking event at 500 m range and 5.5 m depth in 6 m thick ice. xiii 133 6-14 Vertical directivity of a synthetically produced ice crack at 500 m range 134 and 5.5 m depth in 6 m thick ice with a compressional absorption in the ice of 0.2 dB/wavelength. 6-15 Vertical directivity of a synthetically produced ice crack at 500 m range 135 and 0.25 m depth in 6 m thick ice with a compressional absorption in the ice of 0.2 dB/wavelength. 6-16 Vertical directivity of a synthetically produced ice crack at 500 m range 136 and 0.25 m depth in 6 m thick ice with a compressional absorption in the ice of 2.0 dB/wavelength. 6-17 Vertical directivity of a synthetically produced ice crack at 2000 m 137 range and 0.25 m depth in 6 m thick ice with a compressional absorp tion in the ice of 2.0 dB/wavelength. 6-18 Received power spectrum of the hydrophone at 150 m depth as a func- 138 tion of time for the event shown in figure 3-8. 6-19 Source spectral level of a typical ice-cracking event. 139 6-20 Detection threshold function indicating the probability of detecting an 140 event of a given received level. 6-21 Distribution of received levels of all detected events. 141 6-22 Median number of events per square kilometer per minute per 1 142 .iPa 1 dB// / 2 Hz at 1 m source level interval versus source level. xiv 6-23 The measured and modeled normalized distributions of received levels for all detected events over the range interval 0 6-24 - 143 1 km. The measured and modeled normalized distributions of source ranges 144 for all detected events. 6-25 Modeled thermal ice cracking noise. 145 6-26 Required range to model 80% (within 1 dB) of the total noise produced 146 from all thermal ice cracking events out to a range of 200 km. 6-27 Required range to model 50% (within 3 dB) of the total noise produced 147 from all thermal ice cracking events out to a range of 200 km. 7-1 Comparison of two component noise model to average ambient noise and standard deviation of real noise, a) Modeled noise for ridge of level +3 dB at 70 km range with thermal ice cracking at -8.2 dB and local ice cracking at -3 dB; versus class 1 real data from Fig. 4-la. b) Modeled noise for ridge of level +3 dB at 70 km range with thermal ice cracking at +0.4 dB and local ice cracking at +0 dB; versus class 2 real data from Fig. 4-lb. c) Modeled noise for ridge of level -5 dB at 40 km range with thermal ice cracking at -3.0 dB and local ice cracking at +0 dB; versus class 3 real data from Fig. 4-ic. d) Modeled noise for ridge of level -5 dB at 40 km range with thermal ice cracking at +5.3 dB and local ice cracking at +4 dB; versus class 4 real data from Fig. 4-id. xv 150 A-i Polar plot of the pressure level for a single event arriving at the array 173 along both the direct arrival and bottom reflected paths for the octave band centered at 96 Hz and corrected for spherical spreading loss. A-2 Scatter plot of the pressure level ratio between the bottom-reflected 174 arrivals and that extrapolated from the direct arrival, using a sinmO function corrected for spherical spreading losses, as a function of graz ing angle at the bottom. A-3 Sound pressure ratio between the measured direct arrivals above and that extrapolated from angles below 300, 3Q0 175 using a sin6 directivity function corrected for the spherical spreading losses, as a function of source angle, for all 30 events that fit the criteria of pg. 159. A-4 Averaged and plus and minus one-standard-deviation pressure level 176 ratios between the bottom-reflected arrivals, and that extrapolated from the direct arrival, using a sin6 directivity function corrected for the spherical spreading losses, as a function of grazing angle at the bottom. A-5 Sound pressure ratio between the bottom-reflected arrivals and that extrapolated from the direct arrival, using a sin e directivity function tm corrected for the spherical spreading losses, as a function of grazing angle at the bottom, for a few individual events. xvi 177 Acknowledgements I would like to thank all the members of my supervisory committee for their assistance in the research and preparation of this thesis. I would like to especially thank Pierre Zakarauskas for his guidance in this work and for being a friend and golfing partner. The financial support provided by Jasco Research Ltd., Datavision Computing Services Ltd. and especially Defence Research Establishment Pacific is gratefully acknowledged. The announced closure of Defence Research Establishment Pacific at the end of this thesis came as a surprise to many and it will be sorely missed among the scientific community. Finally, my deepest thanks and love go to my spouse, Cynthia Lane, who always believed in me and supported me and this work in every way. As everything in our lives, this thesis is a result of our work together. xvii Chapter 1 Introduction 1.1 Objective The study of ocean acoustics is valuable in many diverse fields such as fishing, oil exploration, weather prediction, navigation and ship detection. In the open ocean, ambient noise is generated mainly by wind, precipitation and distant shipping. Thus, knowledge of the ambient noise can be used directly in measuring weather or indirectly in designing sonar systems which can detect signals in a noisy background. In the ice covered Arctic, ambient noise is generated mainly by thermal ice cracking, ridging or grinding of ice, wind blown snow, impacting waves or melting icebergs. Thus, ambient noise measurements in the Arctic can be used directly for determining ice properties such as breakup or indirectly by aiding in the design of sonar systems. Due to the increase in mineral exploration and military use of the Arctic, it is apparent that the study of ice generated noise is very important. It is generally assumed that the underwater ambient noise below 1000 Hz in the ice-covered Arctic is produced by the summation of many discrete sources, which are usually attributed to either thermal ice cracking or active ridge building. 14 How ever, most previous studies of underwater Arctic acoustic noise have examined either individual source mechanisms or the ambient noise levels separately. This thesis de velops a two component noise model, incorporating both thermal ice cracking and active pressure ridging as source mechanisms, which is capable of reproducing the 1 low frequency ambient noise spectra. The model is based on the measured source spectrum, directivity and the spatial, temporal and source level distributions of thermal ice cracking along with measure ments and estimates of these parameters for active pressure ridging. Modeled ambient noise levels are determined by summing the input energy of the distributions of ice cracking and pressure ridging events and removing the propagation loss. The model also examines the short term variability of the ambient noise and relates this to environmental conditions. Finally, the model reveals the relative importance of each source term over the frequency band examined and the spatial and strength distributions of individual events which sum to give the ambient noise. This last result is an important factor in many sonar applications as it reveals whether the ambient noise is produced at close or far range. 1.2 Approach and Contents In concept, the approach of the two component ambient noise model is rel atively simple. The ambient noise spectrum over the frequency band 2 - 200 Hz is assumed to be produced by thermal ice cracking and active pressure ridging. Thus, by summing the acoustic field generated by the distribution of these events, the ambient noise can be reproduced and the relative contributions of each noise source at the re ceiver can be determined. In practice however, this procedure becomes very difficult. A source and propagation model must first be combined which is capable of repro ducing the measured field of a single event at any range. One requires knowledge of 2 the source characteristics along with accurate estimates of the impulse response of the ice and the associated propagation loss due to refraction, absorption and boundary interaction. The fields produced by all events which occur over a given time inter val must then be summed to produce the resulting ambient noise. This summation requires knowledge of the distribution of events in space, time and strength. Chapter two introduces the theoretical source and propagation models used to represent an event occurring in a floating ice sheet. The source model used is a purely dilatational point source (monopole) in the ice. Although a vertical or horizontal point force may be more representative of a thermal ice crack, the dilatational point source was found to be an adequate representation of an ice-cracking event for the low frequencies examined in this thesis. The propagation model used was a full wavefield technique which solves the four dimensional partial differential wave equation by applying a series of integral transforms to reduce the problem into a series of ordinary differential equations separated in depth. This model was chosen because it takes full account of elastic properties in the ice and bottom and because it is applicable to both close and far range. Another advantage of the source and propagation models chosen is the ease of combining these models together. The use of this combined source and propagation model will be justified in chapters five, six, and seven by comparing the modeled fields with measurements. Chapter three describes the experimental setup and the identification and de scription of individual thermal ice-cracking and pressure ridging events. A set of 69 two-minute samples of ambient noise were collected on both vertical and horizon tal arrays suspended beneath the ice. Individual transient events were detected by threshold clipping and by looking for unlikely groupings of local peaks. It was found 3 that the acoustic mode dominated the energy received in the water from ice cracks, with only occasional contributions due to the leaked longitudinal plate wave. Ambient noise measurements are shown in chapter four. These measurements are divided into four distinct classes by examining the power spectra. Each class is compared to both environmental conditions and the measured rate of thermal ice cracking. These classes are shown in chapters five, six and seven to depend on the overall level or rate of thermal ice cracking and the distance to the dominant active pressure ridge. Chapter five describes active pressure ridging and its role on the ambient noise. The spectrum of a single ridging event is shown along with an estimate of the spatial distribution of active pressure ridges. The large separation between active pressure ridges prompted an investigation of the received power from a single event at varying range. It was found that the received power from a single event could accurately reproduce the infrasonic peak in ambient noise spectra. Chapter six describes thermal ice-cracking events and their role on the ambient noise. The source spectrum and directivity of individual events is shown and com pared to measurements by other authors and to results from the theoretical source models (dilatational point source, vertical point force and horizontal point force) in troduced in chapter two. The source spatial, temporal and strength distributions are calculated from over 900 detected events and these are used to model ambient noise levels produced by thermal ice cracking. Appendix A shows how the bottom reflectivity function can be calculated by extending the directivity measured from the direct arrival of a thermal ice-cracking event to the bottom reflected arrival. 4 Chapter seven shows how the summation of the large distribution of thermal ice cracking events along with a single or few active pressure ridging events at varying ranges can reproduce the ambient noise measurements. Finally, chapter eight summarizes the results and conclusions of this thesis along with several interesting features of thermal ice cracking and active pressure ridging observed along the way. 5 Chapter 2 Review of Source and Propagation Models This chapter gives a brief review of the theoretical source and propagation models used to represent an event occurring in a floating ice sheet. This chapter is included to give the reader an understanding of the mathematics involved and to predict the type of waves expected in the water from a source in the ice. The purpose of this thesis is not to develop a theoretical source or propagation model which will explain the physical principles involved in Arctic noise generation or propagation but is rather to measure the characteristics of individual noise events and combine them with a propagation model to reproduce the Arctic ambient noise. In doing so, existing source and propagation models developed by other authors are used. For the source model, we are interested mainly in what type of field the model produces in the water and if this is a realistic representation of the measured fields created by real events. For the propagation model, we are interested in how well the model represents reality and reproduces measured effects along with how easily it may be used for different sites. Results of the theoretical models are compared to measurements. 6 2.1 Plate Waves We start with a model presented by Press and Ewing 5 which gives solutions for plane waves propagating in a floating ice sheet. Although this model does not examine waves radiated into the water in the near field of a source, it serves as a useful starting point for determining the types of waves which may exist in the ice or radiate into the water in the far field of a source imbedded in the ice. For purposes of this work, the far field of the source is meant as being at a range distant enough that the radiated waves in the ice may be represented by plane waves. This problem was originally examined by Press and Ewing to determine if elastic waves transmitted in the ice could be used to find the thickness and mechanical strength of the ice and for position fixing and long range signaling. The model consists of an infinite ice plate of thickness 2ff floating on an infinite half-space of water below with the atmosphere represented as a vacuum above. We are considering plane waves so Cartesian co-ordinates are used with the x-axis at the mid-plane of the ice and parallel to the direction of propagation and the positive z-axis vertically downward. A solution is sought which satisfies both the wave equations in the ice and water along with the boundary conditions at the ice/vacuum and ice/water interfaces. 7 The governing wave equations in the ice and water are: 2i &(P1 1 1 72j 8t = 1 2 at2 = 0, = 0, 1624,2 2 2 v at where 1 represents the ice, 2 represents the water, (2.1) is the bulk compressional wave speed in the ice, f3 is the bulk shear wave speed in the ice, v 2 is the speed of sound in water and 4, and are the scalar and vector displacement potentials defined by: (2.2) i=Vq5+Vx&. Note that 4, represents the irrotational component of the displacement field (compres sional waves) while & represents the incompressible component of the displacement field (shear waves). Inviscid fluids do not support shear waves and thus 2 = Then for a system with the x-axis parallel to the direction of propagation, 0. y 6 ô/ = 0, and equation 2.2 becomes: — U V w — — 64, ax 6z 84, = az a üx (2.3) The result is two uncoupled problems with the particle displacements in the x and z directions depending only on 4, and y direction depends only on 4,,, and while the particle displacement in the The particle displacements in the x and z directions produce the dilatational, or P wave and the vertically polarized shear, or SV wave while the particle displacement in the y direction produces the horizontally 8 polarized, or SH wave. Note that the particle displacement in the y direction contains only a shear component and theoretically should not generate waves in the water. For this reason, the SH wave will not be examined further. It should be noted though that current research has found that strong SH waves generated by rubbing ice plates 6 It has produce a pure tone signal near 800 Hz which can be measured in the water. also been found that sources in the water near the under-ice surface produce strong 7 A problem is that the coupling mechanism from SH SH waves in the ice plate. waves in the ice plate to energy in the water is unknown and ignoring the SH waves may effect the estimates of propagation loss used later. Solutions for the P and SV waves which satisfy the wave equations 2.1 can easily be shown to be of the form: qi = [A sinh(z) + B cosh(Ez)] exp[i(kx [C sinh(iz) + D cosh(ijz)j exp[i(kx c”2 = E exp(—z) exp[i(kx — wt)], — — wt)j, (2.4) where = 2 (1 k = 2 (1 k = v). (1—c 2 k / — /c), 2 c (2.5) The constants A, B, C, D and E can be found by substituting into the boundary conditions. The boundary conditions are the conservation of normal particle dis placement and of normal and shear stresses across the boundaries. For the vacuum interface, the particle displacements at the interface of the non-vacuum are uncon strained but the stresses must vanish; while for water, only the shear stress must 9 vanish. Thus, the boundary conditions reduce to: 1 (T) = 0 at z=—H 1 (T) = 0 at z=—H 1 ) 2 (T = 2 (T) at z 1 (T) = 0 at z—H at z = where the stress tensor T 13 is defined as T 3 stiffness constants and = = H = CijkiSki being the strain defined as Ski H , (2.6) with k1 = 8 Cijkl being the elastic (ôuk/8ai + üul/ xk) 8 Assuming the ice to be an isotropic solid, the stress tensor can be reduced to T, 2,us + AskkS, where reduces further to T 3 and A are Lame’s constants. For a fluid, the stress tensor t = = AskkS. Lame’s constants are related to the density p and the compressional and shear speeds as = , 1 (Ai-f-2i)/p = m/pi, 2 = V /p 2 A . Thus, the boundary conditions can be written as: A V q 2 xôz + Ui + 8x2 ,\ VqiH-2 ( = 0 at z ) = 0 at z ) = A V q 2 at z = H ) = 0 at z = H = —H —H — + + — 8& 8z Then by substituting q, j° 8 ’) 8b 1 ôx 842 8z at z=H (2.7) and q into the boundary conditions, we get 5 equations with the 5 unknowns A, B, C, D and E. A solution for all 5 unknowns exists when the determinant of the coefficients vanishes. 10 Press and Ewing 5 found a solution to these equations by using a Poisson’s ratio of 0.25 for the ice. This ratio is equivalent to using ) as o = ice (a = i’i since Poisson’s ratio is given \/2 + i’)• Measurements show that Poisson’s ratio is approximately 0.32 for = 3500 m/sec, 3 = 1800 m/sec) and thus, the solutions by Press and Ewing are not exact but may be used for determining the wavetypes which may exist in the 8 also solved the above equations numerically on a floating ice system described. Stein computer. The solutions for these equations will be discussed below but the reader is directed to the above papers for an in-depth study on the calculation of the solutions. First, examine the waves in a free plate with a vacuum above and below. The solutions for the F and SV waves in a free plate are called Lamb waves and break down into symmetric and antisymmetric modes where the particle displacements u and w are symmetric or antisymmetric about the midplane of the plate. The symmetric modes have u with the same sign about the midplane and w with opposite sign about the midplane while the antisymmetric modes have u with opposite sign and w with the same sign. These particle displacements cause the boundaries of the plate to periodically dilate and contract for symmetric modes or periodically flex for antisymmetric modes as shown in Fig. 2-1. Thus, the symmetric modes are also known as longitudinal or dilatational modes while the antisymmetric modes are also known as flexural modes. Although the symmetric modes are sometimes called longitudinal modes, it should be noted that both the longitudinal and flexural modes are produced from combinations of both longitudinal (F) and vertically polarized shear (SV) waves. Some of the characteristics of the symmetric and antisymmetric plate modes can be found by examining a dispersion curve for these waves as shown in Fig. 2-2 (see 11 Ref. 9). For a plate of thickness 2H, there are only two possible traveling waves in the plate when kH —* 0. These are called the zeroth order symmetric (s ) and 0 antisymmetric (a ) modes and correspond to the real roots of the governing equations. 0 There are also an infinite number of purely imaginary roots to the equations but these represent motions which grow or decay exponentially along the plate and are not traveling waves. For small kH, the lowest order symmetric (or longitudinal) mode has a phase speed equal to the plate longitudinal speed O.9a) and is (ci nondispersive. As kH increases, the mode becomes dispersive as the phase velocity decreases. As kH continues to increase, the mode becomes a surface Rayleigh wave propagating along the upper and lower surfaces with a phase velocity equal to that of the Rayleigh wave 0.9/3). For small kH, the lowest order antisymmetric (r (or fiexural) mode is highly dispersive with a phase velocity which starts at zero for an infinitely thin plate and increases with increasing kH. At very high kH, the antisymmetric mode also becomes a surface Rayleigh wave propagating along the upper and lower surfaces of the plate. As kH increases, new traveling waves appear corresponding to the first, second and higher order symmetric (Si, 2, , 3 s ...) and antisymmetric (ai, a , a 2 , 3 ...) modes. At the critical values of kH, when an even or odd number of longitudinal P or transverse SV half waves fit into the thickness of the plate, a new mode produced by an uncoupled purely longitudinal or transverse standing wave in z is formed. Just above the critical value of kH for a given mode, both P and SV waves couple together to form a standing wave in z. These P and SV waves travel along the plate as coupled waves by propagating at different angles to match phase speeds. As kH continues to increase, the P wave eventually travels in a direction parallel to the axis of the plate. 12 A further increase in kH transforms the P wave into inhomogeneous surface waves which decay exponentially from the boundaries. Thus, in the limit as kH —* oc, only an SV wave is left which propagates with a phase speed equal to that of the bulk transverse wave speed. When a floating plate is considered with a fluid halfspace below, the modes dis cussed above are no longer purely symmetric or antisymmetric due to the different boundary conditions on the upper and lower surfaces of the plate. For small kH, the lowest order symmetric or longitudinal mode travels with a phase speed of approx imately 90% of the bulk dilatational wave speed. This is greater than the speed of sound in water and thus, this wave radiates into the water at an angle of cosO . 1 v/c This mode is often referred to as the “leaky” plate wave due to this radiative loss into the water. For large kH, the symmetric mode becomes a Rayleigh wave propagat ing along the air/ice interface. For small kH, the lowest order antisymmetric mode is usually called the flexural mode and is highly dispersive as for a free plate. For large kH, the antisymmetric mode turns into a Scholte wave propagating along the ice/water interface with a phase speed slightly less than the speed of sound in water. Because of the low phase speed, the first antisymmetric mode does not radiate into the water but instead decays exponentially away from the interface. As for the free plate, the higher order symmetric and antisymmetric modes are introduced as kH increases but these modes are highly attenuated due to leakage into the water and do not propagate far beyond the source which generated these modes. To determine the arrival times of these modes, the group velocities must be known. 13 The group velocities are given by: ciw d(ck) Cg= Thus, at the limits as kH dc/dk = —* oo de =c+k. for all modes, or kH (2.8) —* 0 for s (for which 0), the group speeds of all modes are the same as the phase speeds. For intermediate values of kH, the group speed of the zeroth order symmetric mode stays near the Rayleigh wave speed (approximately 90% of the bulk transverse wave speed) while the group speed of the zeroth order antisymmetric mode rapidly increases to the Scholte wave speed (somewhat less than the sound speed in water). Higher order modes are introduced with group speeds near zero which quickly converge about the bulk transverse wave speed as kH increases. 2.2 Dilatational Point Source The above presentation examined plane waves in the ice and their radiation into the water. It gave an indication of the type of waves which travel to a hydrophone mainly along a path in the ice plate and radiate into the water near the hydrophone. 8 also examined the waves produced in the near field of an acoustic monopole Stein which travel to a hydrophone mainly along a path in the water. Stein started with the same model as Press and Ewing except that he added a purely dilatational point source in the ice. Introduction of a point source in the ice requires a change to cylindrical coordinates and the governing wave equations in the ice and water become: 14 V 2 4’ V2 1 82 = — 1 V2:2 2 V O2 8(r) s(t)—8(z — zn), =: — 2 ôt (2.9) where the right hand side of the first equation represents a forcing function at range r = 0 and depth z = . 0 z Again, the boundary conditions are the conservation of normal particle displace ment and of normal and shear stresses across the boundaries. Solutions to the forced wave equations with these boundary conditions contain all the solutions of the pre vious unforced system along with a wave radiated into the water in the near field of the source. Stein calls this solution the acoustic mode since it travels from source to receiver nearly entirely as an acoustic wave in the water. This mode is believed to be caused by unequal flexing of the ice plate in the vicinity of the source. The acoustic mode for a monopole source in the ice was shown by Stein to radiate into the water as: cc w sine, R 2 v (2.10) where R is the propagation path length from the source to the receiver and 6 is the declination angle of the ray from horizontal. Results shown in chapters three and six indicate that the energy observed in the water below the ice is dominated by the acoustic mode with only occasional small contributions from the plate waves. 15 2.3 Horizontal and Vertical Point Forces Stein’s model of a dilatational point source (monopole) in the ice correctly accounts for the large energy contained in the acoustic mode under the ice. However, a point source is a crude representation of an ice crack and may not reproduce the vertical directivity (energy radiated as a function of declination angle) of a crack correctly. Xie’° and Xie and Farmer’ 1 have examined the radiation patterns produced by a single vertical point force and a pair of horizontal point forces applied at the surface of the ice. Because the acoustic mode is assumed to be generated by flexing of the ice plate in the vicinity of the source, Xie and Farmer derived the radiation patterns of the vertical and horizontal point forces by starting with plate vibration theory instead of platewave propagation theory. They calculate the sound field under the ice as an integral form of the product of the impulse response of the ice and the forcing function of the crack. An outline of the derivation of these sound fields is given below while a complete derivation is available in 1 Xie and Xie and Farmer’ ° . 1 The impulse response of the ice is found by considering an incident plane wave of amplitude P 02 on the upper surface of the ice and determining the resulting reflected (For) and transmitted (F ) waves as: 2 = exp [ik 0 (x 0 sinO )J, 0 + z cos6 0 (x sin& 0 For = A exp [ik = — z cos ) 0 j, 2 (x sin B exp [ik 2 + (z 9 — H) 9 cos ) 2 j, (2.11) where o represents the air, 2 represents the water, H is the ice plate thickness and A 16 and B are the reflection and transmission coefficients of the ice plate. Then, by separating the motion of the plate into symmetric (s) and antisymmetric (a) modes, the symmetric oscillations of the plate can be represented as the sum of the pressures acting on the plate while the antisymmetric oscillations are caused by the differences. Thus, using Snell’s law of k 0 sin6 0 5 P = -‘oi + For z=O zO = + 2 sin k ‘2t , get: z=H xsin8 exp(ik ) , = (1+A+B) 2 Pa = 0 F = (1 + A + For z=O — z=O — t 2 P (2.12) Iz=H B) exp (ik x2 2 sin ) . (2.13) Then the vertical component of the plate vibration velocity is the sum of the velocities of the symmetric and antisymmetric modes at the upper surface of the ice and the difference of the velocities at the lower surface of the ice. Thus, V V z0 zH = /Z (P ) , (Pa/Za) + 8 (2.14) 8 / 5 (P ) Z , (2.15) (Fa/Za) — where Z 3 and Za are the impedances of the symmetric and antisymmetric modes in the plate. 17 But the vertical components of the plate vibration velocity can also be expressed as: 1 vz=o (8FO, I 0 ZWp = = Vz-H + ÔZ \ 0z z=O z=U 1—A ), 2 8 x sin 2 0 cos (ik ) exp (ik 0 iwpo 1 (8P2t Z 2 jj P (2.16) zH = —— 2 iwp (2.17) . sin ) 2 2 cosO (ik ) exp (ik 2 x 8 2 By combining the above equations, the transmission coefficient can be solved as: 2 — B — where Z0) 2 z 8 (Z Za) — (2 18) (Z+Z (Zs+Za) + 2 ZsZa+4ZZ ) = 0 /cosO c (p ) , 2 ( 0 z and . = ) /cosO c 2 (p The impedances can be found for a thin plate (H << )) by examining the sym metric and antisymmetric mode equations: 5 8U — 2 Cs ÜUS 2 = Ox H —- M’ + 1(o2 — 1) 3 H 1 E + 2 C 5 ‘\ (2.19) 2 Ox (2.20) = Pa, 8 is the where U is the vertical displacement of the plate, P is the applied pressure, c /p JE 5 = 1 longitudinal plate wave speed c , 1 are the M = p H and o and E 1 Poisson’s ratio and elastic modulus of the plate which are related to the Poisson’s ratio and elastic modulus of the ice as o = o/(1 — ) 1 = E/(1 and E — o2). 1 by assuming that U and P are harmonic of the form U = U° exp[i (kix sinG 1 and P = P° exp[i (kix sinG — Then — wt)j wt)j, the symmetric and antisymmetric impedances 18 can be found from Z = P/iwU as: 2iE [1 1 wH [1 — — Za = —iwiVi [1 with (c/c sin ) 2 j & 2 /c sin 5 (c ) 2 (2.21) ] 2 sin8 (2.22) — — 4 (cf/c2) /12M) 3 H 1 E 2 (4 = (w Now the sound field produced under the ice by a point force applied at the surface of the ice will be solved using the principle of reciprocity. In other words, place a point source at some location M(r ,z 2 ) under the ice (see Fig. 2-3) and find the 2 scattered field P 8 at the crack location. Then, the sound field at M caused by a crack in the ice can be expressed in terms of the scattered field P 8 and the forcing function f of the crack in an integral form. For a point source under the ice at location M(r ,z 2 ), and with strength 2 Q, the resulting radiation field measured below the ice is: Pg = — iwp Q 2 exp (ik R) 2 47rR where R is the distance from the point (?2, (2.23) z ) 2 . The scattered sound field P 8 measured at some location N(r, z) above the ice is then found by multiplying each path from ,z 2 M(r ) to N(r, z) by the transmission coefficient B 2 21 of the ice and integrating over all paths. Note that 2 B 1 is the transmission coefficient from the water to the air and is thus related to the transmission coefficient B already found by interchanging Zb0) and Zr). Following the above procedure, get: = wp Q k 2 ) 2 z, r , z 2 f H1) 2 (k — (6) 21 r sin&)B e2z2c5O_k00s00)sin8 d8 (2.24) 19 where ff) is the zero order Hankel function of the first kind and I’ denotes the path of integration. Then assuming the crack initially forms as a cylindrical cavity of radius a and height h at the upper surface of the ice, the radiation field measured at M(r ,z 2 ) 2 below the ice is given as: —1 Q 0 iwp where a cylindrical coordinate ,z,r 5 8P , 2 z s —8r jj system (r, z, q) is used, f(,z)addz (2.25) f(5, z) is the forcing function of the crack, and the integration is performed over the entire inner surface of the cylin drical cavity. Note that although a cylindrical cavity is assumed here, this method can be used to construct solutions for cracks of other shapes. For a pair of horizontal point forces, the forcing function is given as: (F/a) [S(ç) 6(z) + 6( — ir) S(z)] er f(q, z) ë,. = where r is a unit vector along the radial direction and F is the magnitude of the two point forces. The field at M(r ,z 2 ) is: 2 ,z 2 P(r ) k 2 iFp i B 2 sine ) e2R. (& Po cc sin9 (0 21 B ) 2 . (2.27) For a vertical point force, the forcing function is given as: (F/i’) 6(çb) 6(r) e where (2.26) f(q, r) ë,. = is a unit vector along the z direction and F is the magnitude of the vertical point force. The field at M(r ,z 2 ) 2 ,z 2 P(r ) is: c 1 i B 2 ) eik2R. (6 os ) 2 z( cos6 2 (& 2 B ) 1 . 20 (2.28) (2.29) The directivity patterns produced by both a pair of horizontal point forces and a vertical point force are shown in Figs. 2-4 and 2-5 respectively. Figs. 2-6 and 2-7 show the resulting directivity patterns for the horizontal or vertical point forces for either thinner or thicker ice. Comparisons of both measured and modeled directivity are shown in detail in chapter six. They show that for the frequencies examined and for grazing angles below the critical angle of the bottom, the acoustic monopole, the vertical point force and the pair of horizontal point forces all give a reasonable approx imation to the vertical directivity of real ice-cracking events. Based on these results, the acoustic monopole was chosen as a source model for an individual event due to its ease of implementation. This model can then be combined with the power spectrum of an individual event along with the spatial, temporal and strength distributions of events to reproduce the ambient noise. 2.4 Propagation Model Acoustic wave propagation deals with finding solutions to the wave equation. These solutions may be very complicated in nature due to the variability of the environment (changing sound speed, irregular bottom stratification, rough ice cover, etc.) and closed form solutions exist for simplified cases only. Thus, models of wave propagation in the Arctic vary from purely analytic to numeric methods. Analytic models use appropriate approximations to the boundary or initial conditions thus permitting algebraic solutions to a reduced wave equation. Numerical models allow accurate specification of boundary and initial conditions and give direct numerical solutions to the wave equation. 21 The most common types of propagation models are normal mode, parabolic equa tion, ray theory, finite element or finite differences, and full wavefield techniques. The normal mode model provides an exact solution to the wave equation for long range propagation by determining the modes of propagation in a bounded fluid. However, it is not appropriate for grazing angles greater than that of the bottom critical angle for which the field cannot be broken into discrete modes, and it usually ignores shear waves. The parabolic equation model is similar to the normal mode model in that it calculates modes of propagation in a fluid. It is also restricted to grazing angles less than critical and generally does not include shear waves. Ray theory works by tracing rays from the source to the receiver and coherently summing the pressure field of all rays at the receiver. Ray theory is appropriate mainly for close range and usually does not accurately model long range effects such as caustics or shadow zones. Finite element or finite differences models are purely numerical techniques which break up the differential wave equations into piecewise polynomial functions. These techniques are very general and can approximate the boundary and initial conditions to any desired accuracy. However, these techniques are extremely computationally intensive and difficult to implement. The propagation model left is the full wavefield technique, also known as a fast field technique or a Green’s function technique. This type of propagation model solves the wave equation for horizontally stratified media by applying a series of integral transforms to the wave equation. This procedure reduces the four dimensional partial differential equation (three space coordinates and one time) into a series of ordinary differential equations separated in depth only. These equations are then solved within each layer in terms of unknown amplitudes which are determined by matching the 22 boundary conditions between layers. For our purposes, the advantages of the full wavefield technique over previously mentioned techniques are that it is a fully elastic model capable of including shear waves and that it is applicable to both close and far range. The Kuperman-Schmidt full wavefield technique, SAFARI 3 (Seismo-Acoustic ” 12 Fast field Algorithm for Range Independent environments) was used for the propa gation model part of our noise model. This technique seeks solution to the partial differential wave equation in cylindrical coordinates: 2 (V — c2(r’z) ) (r,z,t) = (r,z,t) 8 F where F (r, z, t) is the forcing term and I1 refers to both the scalar 8 wave potentials with c(r, z) (2.30) 4 and vector & representing the bulk compressional or transverse wave speeds respectively. Note that the azimuthal dependence is removed by using an azimuthally independent source placed on the z axis. The first step to solving the partial differential wave equation is to remove the time dependence by using the Fourier transform: f(w) = 1 t dt, F(t)e” 27r-x, — to get where km(r, z) = J 2 + k(r,z)) Ti(r,z,w) (V = (r,z,w), 8 f (2.31) (2.32) w/c(r, z) is the wavenumber of the media. Note that capital [i is still used after the Fourier transform to avoid confusion with the vector wave potential b. Then, for a range independent environment with the source on the vertical axis, equation 2.32 becomes: 2 + k(z)) (r,z,w) = (V 23 (z,w) 8(r). 8 f (2.33) The next step is to remove the range dependence by using the Hankel transform: (k) = f g(r)J ( 0 kr) r dr, (- - (k to get - k(z))) (k,z,w) (2.34) = (2.35) where k is the horizontal wavenumber (related to the phase speed of the wave in the given layer). Thus, we have an ordinary differential equation in depth only. Solutions are then found for each angular frequency w as: ‘(k, z) = 1,(k, z) + A(k) 1P(k, z) + A(k) z) (2.36) where the argument w is dropped but implied, and (k, z) and k, z) are solutions to the homogeneous wave equation, ‘(k, z) is a particular solution to the inhomo geneous wave equation, and A(k) and A+(k) are arbitrary coefficients determined from the boundary conditions. The complete solution (r, z, t) to the partial differential wave equation is then found by performing the inverse Hankel and Fourier transforms, 1(r,z,w) (2.37) = (r,z,t) = f (r,z,w)edw. (2.38) The trick to the full wavefield technique is to restrict the depth dependent sound speed and the forcing term to cases where the solutions ‘I’(k,z), 4’ik,z), and +(k, z) are known analytically and the unknown coefficients A(k) and A+(k) can then be solved numerically by matching the boundary conditions. In practice, c(z) is usually restricted to be either a constant over a given depth interval or is allowed to change with depth according to a specified formula for which an analytic solution 24 to the wave equation is known. In SAFARI, elastic solid layers are restricted to having constant sound speeds over specified depth intervals. This restriction leads to solutions which are simple exponential functions of the form: where a (k) 2 = — ilJ+(k,z) = ‘1r(k,z) = (2.39) e° . Fluids however do not generally have constant sound 2 (w/c(z)) speeds with depth or changes in sound speed in large discrete steps (although this behavior is allowed in SAFARI). From the definition of the bulk compressional sound speed in a fluid, c allows )i (\ + 2p)/p, SAFARI assumes that p and p are constant but to vary inversly with depth so that, c = 1/(az + b). This assumption leads to solutions which are Airy functions of the form: Note that q(k, z) = 3 (k / 2 Ai{(pw2a) 2 qY(k,z) = 2 ) (k 213 a 2 Bi[(pw — — 2 (az + b))J, pw az + b))]. pw ( 2 (2.40) is used here instead of ‘1 because fluids do not support shear waves. In general, the boundary conditions between two elastic solids are the conserva tion of normal and tangential particle displacements and the conservation of normal and si-Lear stresses across the boundaries. For any interface not involving two elastic solids, slip may occur and the horizontal particle displacements no longer need to be conserved. For any interface involving a vacuum, the particle displacements at the interface of the non-vacuum are not constrained. For a solid/fluid interface, the shear stress must vanish while for a solid/vacuum interface, both the normal and shear stresses must vanish. Finally, for a fluid/fluid interface, only normal parti cle displacements and stresses are involved and these must be conserved across the 25 boundary while for a fluid/vacuum interface, only the normal stress is involved and it must vanish. Finally, for our particular problem, an acoustic monopole source in the ice is used as the forcing function (as described in the source model) and we start with the partial differential wave equations: 2 (V - 2 (V - c2(r’z) c(r,z) ) 2) (r,z,t) = s(t) (r,z,t) = 0. S(z - zn), (2.41) For this case, the solutions to the homogeneous depth separated problems are first determined as exponential or Airy functions depending on the layer type and how the sound speeds are defined within the layer. The particular solution to the nonhomo— geneous depth separated wave equation is then given as: (2.42) = The full solution to the depth separated wave equations is then determined by fitting to the boundary conditions. Finally, the range, depth and time dependent fields are determined by numerically integrating the inverse Hankel and Fourier transforms of the full solution from the depth separated wave equations. For further details on the mathematical implementation of this propagation model, the user is directed to the SAFARI user’s guide. 13 26 >—-H — t I > ( I / — — — —‘ r 1’ E— ( ‘ ———— >—--: I I > ‘ — — ‘ - I I Figure 2-1. Longitudinal (symmetric) and Flexural (antisymmetric) modes in a free plate. Arrows indicate particle displacements. 27 5 4 3 cci) a) ci C/) ci) C’) (‘3 1 0 2 4 6 8 10 kH Figure 2-2. Dispersion curves for first three symmetric and antisymmetri c modes in a free plate for a Poisson’s ratio of 0.34. Ct and k are the bulk transverse phase speed and wavenumber respectively. (Reproduced from ) 9 I.A.Viktorov 28 N( r, z 0 C F ) F r 2 13C z ) 2,2 M(r z Figure 2-3. Coordinate system used for a pair of horizontal point forces F applied at the inner surface of a cylindrical cavity with radius a and height h. (Reproduced from Y.Xie’°) 29 Hor i. zonta I Lfl ro -DI w L w w Ui LW U-I 50 ‘Do ‘so 0D C Figure 2-4. Vertical directivity predicted from a pair of horizontal point forces applied at the surface of 6 m thick ice for frequencies of 50. 100, 150 and 200 Hz. 30 Hor—izonta I LI) -DI \-J Qi L D U) U) Ui LW 0-I 50 100 ‘Sc Dc C Figure 2-5. Vertical directivity predicted from a vertical point force ap plied at the surface of 6 m thick ice for frequencies of 50, 100, 150 and 200 Hz. 31 Hor—zcnta 1 LO 0 \-, w L U) U) cii Lw u-I 60Hz 100 Hz 150 Hz aoo Hz 0 Figure 2-6. Vertical directivity predicted from both horizontal (solid) and vertical (dashed) point forces applied at the surface of 3 m thick ice for frequencies of 50, 100, 150 and 200 Hz. 32 Hor-izonta 1 QJ 0 \-I Ui L D U) U) Ui L U Figure 2-7. Vertical directivity predicted from both horizontal (solid) and vertical (dashed) point forces applied at the surface of 9 m thick ice for frequencies of 50, 100, 150 and 200 Hz. 33 Chapter 3 Data Collection 3.1 Environment and Instrumentation The data analyzed in this thesis were collected on the pack ice off the northern coast of Ellesmere Island over several days during April 1988. The ice cover remained relatively stable but was very rough, consisting of a mixture of both new and multiyear ice. The ice thickness varied from approximately 2 m on re-frozen leads to 7 m on floes and to larger values on ridges. An ice thickness of 7 m is much larger than the 2 m to 4 m thick ice commonly found in the central Arctic but is very common for the Lincoln Sea area north of Ellesmere Island.’ 4 Snow cover was as thick as 60 cm, although in the rough pack ice many areas remain exposed. Measurements of air temperature, solar radiation, barometric pressure, and wind speed and direction were obtained every 15 minutes throughout the duration of the experiment and are shown in Fig. 3-1. Air temperatures and winds were measured from the top of a 10 m tower while solar radiation was measured at 1 m height away from the shadow of any structures. Currents were measured at 25 m depth during each recording of ambient noise and are also shown in Fig. 3-1. The data were collected over an area of continental shelf in 420 meters of water with a sound speed profile shown in Fig. 3-2. A seismic survey showed the bottom to be acoustically flat to beyond 1000 Hz and depth measurements within a few kilometers around the array indicated a shallow slope of less than 34 10. To aid in modeling propagation ioss, measurements of the seabed and ice proper 15 and an acoustic seismic refraction ties were also obtained. A bottom grab sample 6 indicated that the bottom consisted of a layer of sand approximately 15 survey’ 3 and a compressional wave speed of approximately thick with a density of 1.8 g/cm 1800 rn/sec. Below the upper 15 rn thick layer was a second bottom layer with an 3 and a compressional wave speed of 2000 rn/sec. These estimated density of 1.9 g/cm bottom characteristics were supported by measurements of the bottom reflectivity us ing ice cracking noise as a source (described further in Appendix A). Realistic shear wave speeds of 300 rn/sec and 500 rn/sec were used for the first and second bottom layers respectively and compressional and shear wave absorptions of 0.5 dB/.) and 17 to complete the bottom properties required for later analy 0.25 dB/ were chosen sis. For the ice, compressional and shear wave speeds of 2800 m/sec and 1750 rn/sec along with compressional and shear wave absorptions of 2.0 dB/.\ and 3.0 dB/) re spectively were used based on previous measurements obtained from smoother and 18 Measurements of the plate wave speed at the experimental site were thinner ice. obtained by examining the energy radiated into the water and are consistent with the values of cornpressional and shear wave speeds used. A set of 69 two-minute samples of ambient noise were collected at the times indicated in Fig. 3-1. The data were collected on a vertical array of 24 hydrophones and a 7-hydrophone horizontal array as shown in Fig. 3-3. The vertical array was equispaceci with a hydrophone separation of 12 m and the top hydrophone was 18 rn below sea level. However, the second and third hydrophones (at 30-rn and 42-rn depth) were not working and hence could not be used in any of the analysis. The L-shaped horizontal array was at 102 m depth and used a low redundancy spacing 35 with a total separation of 12.5 m in one direction and 200 m in the other. A sampling rate of 516 Hz was used, and the data were filtered using a 150-Hz low-pass filter with a high-frequency roll-off of 45 dB per octave. After collecting the two-minute noise samples mentioned above, a pressure ridge built itself approximately 2 km from the experimental site. Continuous ambient noise measurements were recorded for several hours during the time of this ridge building event. 3.2 Source Detection and Description As stated in the introduction, the Arctic ambient noise is believed to be produced by the summation of individual transient noise sources produced by the ice. The detection of a transient signal in a noisy background is a common but difficult problem in signal processing, and the many techniques that are used depend on the source and background characteristics. Two simple techniques were used here. The first technique was to scan a suitable length (generally 2 minutes) of data from a single hydrophone to determine the average pressure peak height, and then rescan the same data while recording the position of all peaks greater than some user-supplied multiple of the average peak height. Although this technique is not very robust, it was useful for finding the transient sources that had a high signal-tonoise ratio. Fig. 3-4 shows the unprocessed output of the vertical array for an event at 480-rn range. This figure clearly shows multipath arrivals corresponding to a direct path, a bottom reflection, and a bottom and under-ice reflection. These arrivals are 36 all produced from the acoustic mode (i.e. energy entering the water in the vicinity of the source). Neither the longitudinal plate wave nor the flexural plate wave were detected for this event. The range of the source was determined using a ray tracing model which calculates the eigenrays (the acoustic rays joining a source to a target) for a range independent, vertically stratified fluid with a flat bottom and surface. The range independence and flat bottom hypothesis were confirmed by a seismic survey and depth measurements, as described previously. Close inspection of the transient in Fig. 3-4 shows that an ice-cracking event may contain several closely spaced high amplitude peaks. These may correspond to a single arrival path such as the direct arrival for the 480-rn range source shown, or to multipath arrivals overlapping in time for sources at longer range as shown in Fig. ° that 2 ’ 9 3-5. This observation led to the development of a second detection technique’ seeks sections of data where high amplitude peaks are clustered closely together. It is based on the probability of finding x values out of a subsample of length y within the top fraction N of the entire sample z and is given by a standard statistical formula as: y F(x,y,N) = i!(y— i)! NZ (1— N). (3.1) By scanning the full length of data for one channel, a distribution of peak heights can be obtained which is then used on a second scan of the data to find all subsections of data of length y with x peaks within the top fraction N of the peak heights. By adjusting x, i and N to detect all transients in a section of data which has been examined visually, these values can then be used to detect transient events in all the data. Over 900 ice-cracking events were detected using the above procedure. 37 Ice cracking events were sought only in the 69 two-minute samples of noise collected prior to the time when the pressure ridging event occurred. The number of events detected per minute for each data sample is shown in Fig. 3-6. The strong correla tion between the number of detected events per minute and a decreasing temperature (shown in Table 3-I) suggests that most of these events are likely to be thermal ice-cracking events. 22 This hypothesis is further supported by the observation that ’ 21 approximately 83% of the data files containing more than the median number of events detected per minute occurred from 7 PM to 4 AM local time while 91% of the data files with fewer events occurred from 4 AM to 4 PM. Although thermal ice cracking contains a broad peak in its power spectrum near 300 - 500 Hz (see Refs. 1,2,10,11,21-23), energy is still expected at the lower frequencies measured in this thesis. This is described in more detail in section 6.3. Several possible explanations are given for the events which occur when the air temperature is rising. The first possibility is that these events are still thermal icecracking events and that the snow cover creates a thermal delay between the air and ice temperatures. Thus, the ice temperature may still be decreasing as the air temperature starts to rise. A thicker snow cover would allow for a greater lag between air and ice temperatures and at the same time insulate the ice from the extreme air temperature changes. Thus, areas with snow cover would exhibit fewer thermal ice-cracking events than areas without snow cover but these events could occur during times when the air temperature may be increasing. Other possible explanations are that these are not thermal ice-cracking events but are caused by some other environmental condition such as wind, current or tides which builds up stress in the ice until the ice fractures. Dyer 24 suggests that wind or current shear 38 acting on the hummocks of old pressure ridge sites could twist the hummock causing fractures in the ice plate surrounding the ridge. A comparison of the characteristics of the events which occur during times of cooling with those of the events which occur during times of warming was not performed here. However, a difference in the power spectra between events occurring during warming and cooling periods was found by ° who speculate that different source mechanisms are involved for 2 Zakarauskas et.al. these conditions. Visual confirmation of each of the detected events showed that the false alarm rate for the above detection technique was less than 10%. Visual confirmation was performed using the entire vertical array, and a false alarm is defined as an event for which no distinct arrival paths can be seen across the array. Note that although a transient ice-cracking event usually exhibits multiple arrivals across the entire vertical array, oniy the direct path may be visible for an event which is close enough that the bottom grazing angle is larger than the bottom critical angle. Also, for very distant events, the direct path and possibly even low order reflections may disappear due to both the source directivity and the effects of the upward refracting sound speed profile. The probable cause of a false alarm is the fluctuations in the background noise level over the length of the two-minute sample. Visual examination of the entire length of three data files obtained during quiet, moderate and noisy background levels showed that over 90% of the total observed ice-cracking events were detected. Several of the events detected using the first detection technique were markedly different from that shown in Figs. 3-4 or 3-5. These events have no discernible independent arrivals such as direct path, bottom or under-ice reflections. They also extend over longer periods of time than the ice-cracking events previously discussed, 39 and have characteristics of modal propagation such as nulls and phase changes with changing depth as shown in Fig. 3-7. Although the exact range of these events could not be determined because of the lack of individual arrivals, their modal properties indicate that they were very distant events. These events were found to have a maximum power near 10 Hz with a bandwidth of approximately 20 Hz and are later shown to be likely caused by active pressure ridging. Because these events are very different from the other transient events detected, they were not included in the database of thermal ice-cracking events, and all the data were high-pass filtered at 30 Hz before the second detection method was used. Subsequent analysis used the original unfiltered data. Finally, an arrival due to leakage of the longitudinal plate wave in the ice was seen on approximately 20% of the transients with source ranges less than 1 km and on a very small number at greater ranges. This leaked plate wave appeared as a precursor to the acoustic mode, as shown in Fig. 3-8, and always contained only a small fraction of the total energy of the acoustic mode. The absence of this arrival for most sources appears, as will be shown later, to be due to absorption and scattering by discontinuities in the ice. For those events at greater range that exhibit a leaked plate wave, comparison of the arrival times of the plate wave and the acoustic mode show that the plate wave did not originate at the source but was instead produced by energy from the acoustic mode re-entering the ice. The flexural plate wave, which decays exponentially into the water was not seen on any of the data. Therefore, the total energy observed in the water was produced mainly by the acoustic mode (energy entering the water in the vicinity of the source) with occasional small contributions due to plate waves propagating in the ice. This result agrees with observations from 40 ors. °” other 8 25 auth ” A few days after the ambient noise data were collected, a pressure ridge built itself approximately 2 km from the experimental site. The location and time of this active pressure ridge are known because of some experimental equipment which was at the site during the building process. Continuous ambient noise measurements were recorded for several hours during the time of this ridge building event. Fig. 3-9 shows the unprocessed output of three hydrophones in the vertical array for two minutes of the ridge building event. This figure is representative of approximately thirty to sixty minutes of the ridge building event showing two or three large pulses every minute with each pulse lasting on the order of five to tens of seconds. This is quite different from one of the two-minute data samples shown in Fig. 3-10 which was collected several days prior to the ridge building event and shows typical thermal ice cracking events with short bursts of energy lasting a maximum of approximately one second (individual thermal ice-cracking events typically last 0.05-0.1 sec with multiple arrivals extending the observed signal to a maximum of approximately 1 sec as seen in Figs. 3-4 and 3-5). 41 Table 3-I. Cross correlation of the number of detected ice-cracking events per minute with environmental conditions. Temperature and solar radiation changes were mea sured over one hour prior to the ambient noise measurements. Environmental Parameter Current Speed Wind Speed Temperature Temperature Change Solar Radiation Solar Rad Change Barometric Pressure Correlation Coefficient 0.19 -0.12 -0.22 -0.59 -0.35 -0.33 -0.02 42 -10 -15 a) a) 4- a) H -30 -35 10 11 12 13 14 15 16 April Figure 3-la. Air temperature for several days during time of experi ment. Crosses indicate times when two-minute ambient noise samples were recorded. 43 400 300 E I 200 t3 1 ct5 0 C’) 100 0 10 11 13 12 14 15 16 April Figure 3-lb. Solar radiation for several days during time of experi ment. Crosses indicate times when two-minute ambient noise samples were recorded. 44 30.5 30.4 C) z C 30.3 30.2 E 0 Ct5 30.1 30.0 10 11 12 13 April 14 15 16 Figure 3-ic. Barometric pressure for several days during time of exper iment. Crosses indicate times when two-minute ambient noise samples were recorded. 45 12 10 0 (-I) 0 C’) 2 0 10 11 13 12 14 15 16 April Figure 3-id. Wind speed for several days during time of experiment. Crosses indicate times when two-minute ambient noise samples were recorded. 46 350 300 a) D -D 200 0 .4- 0 (2) . 150 C : 100 50 0 10 11 13 12 14 15 16 April Figure 3-le. Wind direction for several days during time of experi ment. Crosses indicate times when two-minute ambient noise samples were recorded. 47 10 I I I I I + 8 * + 0 ci + -H+ - + + • + • a- +÷+ + C,) + ++ -H ( + • • + 2 • 0 + I 10 I I 11 I i 12 13 April I I 14 15 16 Figure 3-if. Current speed for several days during time of experiment. Crosses indicate times when two-minute ambient noise samples were recorded. 48 0 100 200 300 400 500 1430 1435 1440 1445 1450 1455 1460 Velocity (m/sec) Figure 3-2. Measured sound speed profile along with the profile used for analysis such as range finding, propagation loss estimation and vertical source angle estimation. 49 Figure 3-3. Array configuration. A linear equispaced vertical array with a 12 m hydrophone spacing and the first hydrophone 18 m below sea level is used along with a low redundancy L shaped horizontal array with 7 hydrophones at 102 m depth. 50 E -C Qi (0 0 C 0 0.6 0.2 0.8 TImB (s6c) Figure 3-4. Time series of received acoustic pressure for an ice-cracking event at 480 m horizontal range. The output of all functioning hy drophones in the vertical array is shown and clearly indicates the di rect arrival (D), the bottom reflection (B), and the bottom and surface reflection (BS). 51 1 18 sq 78 102 C 126 I 150 17q 198 I [ BSBS BSB 0 0.2 0.6 8SBSB 0.8 1 Tima (sac) Figure 3-5. Time series of received acoustic pressure for an ice-cracking event at 3150 m horizontal range. The output of the hydrophones in the vertical array is shown and indicates the direct arrival (D), the bottom reflection (B), the bottom and surface reflection (BS) and subsequent reflections from the bottom and surface (BSB, BSBS, BSBSB). Note that • the reflections are compressed in time when compared to a closer range event as shown in Fig. 3-4. 52 30 25 j20 15 > LU 0 10 0 2 z 5 0 April Figure 3-6. Number of detected ice-cracking events per minute for each of the two-minute ambient noise recordings. 53 vJVVW-v -‘\fVV/WW 102 I-’ 126 160 JVWVWVWv ‘WVWV’JW’iW I 179 W 198 WVVJVVV%.JVVW ‘\rvv\AJVWvWw v 222 26 cn v— v v v ‘JV,’AJ’Af\jVVV’-’VV’ zzz= i “ 270 29q 2 1.5 2.8 3 3.6 Time (s6c) Figure 3-7. Time series of an event (or events) with distinct modal prop erties such as changing amplitude and phase with depth. An example can be seen at approximately 0.9 sec. It has a null at 186 m depth and a 1800 phase shift between the received signal above and below this depth. 54 L 8 D BS I-’ E -c 0 Ui (U U 0.6 0 0.6 1 TimB (s6c) Figure 3-8. Time series of an ice-cracking event at 400 m horizontal range which shows a leaked longitudinal plate wave arrival (L) preceding the direct arrival (D), followed by a bottom reflection (B) and a bottom and surface reflection (BS). 55 18 S \-, C 160 -p 0 Ui ID 10 U 0 (J ihiL I. m4w,U 0 20 °rO 1 60 1 Jih .LiJI,L. 80 100 120 Time (sec) Figure 3-9. Time series of the received acoustic pressure of three hy drophones in the vertical array for two minutes during a nearby (approx imately 2 km range) active ridge building event. 56 18 2 : iso -p w 10 0 a 3D Ti.ma (sec) Figure 3-10. Time series of the received acoustic pressure of three hy drophones in the vertical array for one minute during a time of active thermal ice cracking but several days prior to the ridge building event shown in Fig. 3-9. 57 Chapter 4 Arctic Ambient Noise Measurements The 69 two-minute samples of ambient noise recordings were separated into four distinct classes by examining their power spectra. These are shown in Figs. 4-la to 4-ld. Class one shows a peak with a level of approximately 86 / 2 t 1 dB// Hz Pa at /Hz at 200 Hz. Class two shows the same peak 2 8 Hz and a fall-off to 48 dB//Pa near 8 Hz but the fall-off at higher frequency has two stages with a rapid decrease in level out to 35 Hz and a slower decrease beyond 35 Hz to a level of 57 dB//Pa /Hz 2 at 200 Hz. Class three shows a weaker and broader peak at 4 Hz with a fall-off at higher frequency to 58 dB/fliPa /Hz at 200 Hz. Class four shows a continual but 2 slow decrease in noise level with increasing frequency from a level of 85 dB//Pa /Hz 2 at 2 Hz to 66 dB/fltPa /Hz at 200 Hz. The minimum number of data sets used in 2 any class was 14. The four classes of ambient noise spectra are compared to environmental condi tions and the number of detected ice cracking events occurring per minute in Table 4-I. The most striking feature of the comparison of ambient noise spectra with environ mental parameters is the increase in noise levels above 35 Hz as both the temperature change becomes more negative and the number of detected ice cracking events per minute increases. This observation is consistent with previous measurements of ther mal ice cracking and temperature change, although thermal ice cracking is usually 58 associated with higher frequencies from 300 - 500 Hz (see Refs. 1,2,10,11,21-23). It can also be seen that the noise levels above 35 Hz increase as the average solar ra diation decreases and the solar radiation change becomes more negative; however, the large variance in these measurements makes any correlations suspect. The other noticeable feature of the comparison of ambient noise spectra with environmental parameters is the high wind speeds and barometric pressures associated with the strong peak at 8 Hz as seen in Figs. 4-la and 4-lb. This result agrees with previous measurements made by Makris and Dyer. 26 The correlations between the ambient noise levels at 10 Hz and 200 Hz with the environmental conditions are shown in Table 4-IT. There are good correlations between the ambient noise level at 200 Hz and both the number of detected events and a negative temperature change. A moderate correlation is also shown between the ambient noise level at 10 Hz and the barometric pressure. Again, this result is consistent with the correlation study performed by Makris and 26 Dyer. Surprisingly, the correlation between the noise level at 10 Hz and the wind speed was very low. Our measurements and those of other authors indicate that the ambient noise at 200 Hz is dominated by thermal ice cracking. The source mechanism for the infrasonic peak however, is not yet positively identified. 27 showed that low frequency noise correlates well with wind stress and thus Buck might be due to ice movement or pressure ridging. He also examined the correlation of noise at 1200 Hz with that at various lower frequencies and found that correlation dropped as frequency decreased. Due to the large propagation loss at high frequencies, he suggested that the 1200-Hz noise must be local, and that the low frequency noise 59 is more dependent on distant ice movement. 28 showed that Although they did not study ambient noise, Thorndike and Colony approximately 50% of the long term (several months) average ice motion was due to the geostrophic wind with the rest due to ocean circulation. Over shorter time scales, they found that more than 70% of the variance of the ice motion could be explained by fluctuations in the geostrophic wind. They showed theoretically that ice motion should depend not only on wind and current shearing stresses acting on the ice, but also on the normal stresses of the sea surface tilt and on the Coriolis 26 later examined the cross-correlation of low frequency noise effect. Makris and Dyer with the above forces along with two composite stresses forming the horizontal load on a vertical section of the ice sheet and the stress moment acting about the central horizontal plane of the ice sheet. They found the highest cross-correlations were obtained using the stress moment which is dominated by opposing current and wind shearing stresses. The high cross-correlations shown for both low frequency ambient noise and ice motion with the wind and current shearing stresses applied to the ice has led to the general belief that low frequency ambient noise in the Arctic is caused by large scale ice motion and the resulting pressure ridging. Several models of pressure ridging have appeared in the literature, 29 each explaining some feature of pressure ridging or its 4 ’ 3 relation to ambient noise. Parmerter and Coon 29 developed a model of pressure ridge formation consisting of two ice sheets moving together to close a lead. As the ice sheets move together, the rubble from the lead thrusts over or under a sheet, bending the sheet until the stresses fracture the ice into large blocks which then continue to be over or under thrust. They were able to reproduce measured profiles of pressure 60 ridges and showed that wind forcing contained enough energy to produce ridging. However, they did not examine the spectral shape or level of noise that would be produced. Pritchard 3 developed a model which converted measurements of ice drift into pressure and shear ridging events. He showed that the modeled noise resulting from pressure ridging was more highly correlated with the measured noise than was the modeled noise produced by shear ridging. Using only pressure ridging as a noise source, he was able to simulate 46% of the variance of the noise at 10 Hz and 32 Hz measured over 120 days in the Beaufort Sea and up to 80% of the variance of the noise over shorter time periods of 20 days. Buck and Wilson 1 measured the source level per unit length of a pressure ridging event which occurred near their campsite and used it to predict the average ridge separation required to reproduce the background noise level. Although they had no direct measurements of the average active ridge separation to verify their work, they predicted an average separation of 37 km which compared favorably with pan sizes of 10 - 100 km measured by SEASAT SAR. Note however that Buck and Wilson obtained their measurements in April while the pan sizes were measured in October and also that they assumed the noise generated by all pressure ridges to be identical to that measured for this single ridge. ’ suggests that although pressure ridge building is indeed very noisy, the low 2 Dyer frequency noise may not be dominated by this type of ice fracturing event due to the low percentage of ice which is undergoing active ridge building. He also states that a plausible source mechanism must produce energy with the correct spectral shape (i.e. it must have a peak in the spectrum near 10 Hz), which has not yet been shown for pressure ridging events. Dyer proposes a possible source mechanism involving wind or current shear acting on old pressure ridge sites which need not be active. The 61 wind or current pushes the hummock of the old ridge thereby transferring stress to the thinner, weaker ice sheet. This stress results in both circumferential and radial cracks emanating from the ridge site. Further wind or current shear can then twist the ridge vertically, bending the ice sheet between several radial cracks. Finally, the cracks will slip allowing the ice sheet to vibrate back to its stable position. Dyer shows that there is enough energy input in the ice to produce such a fracture and that the resulting radiation will peak near 11 Hz. In chapter five, I show that a source mechanism with a broad spectral peak near 10 Hz is not required to reproduce the infrasonic peak in the ambient noise and present evidence that this peak is due to the effects of frequency-dependent propagation loss acting on the spectral shape of distant ridge building events. Chapter six will show the effects of thermal ice cracking on the ambient noise while chapter seven will indicate over which frequency band pressure ridging and thermal ice cracking dominate by combining each source type to reproduce the measured ambient noise spectra. 62 Table 4-I. Mean and variance of measured environmental conditions and the number of detected ice-cracking events per minute for the four classes of detected power spec tra shown in Figs. 4-ia to 4-id. Temperature, barometric pressure and solar radiation changes were measured over one hour prior to the ambient noise measurements. Environmental Parameter Current Speed ( cm/sec) Wind Speed (m/sec) Temperature (°C) Temp Change (°C/hour) Solar Radiation ) 2 (W/m Solar Rad Change hour) 2 (W/m Barometric Pressure (in-Hg) Bar Pres Change (in-Hg/hour) Detected Events ( events/mm) Class 1 Fig 4-ia 3.0 + 1.9 Class 2 Fig 4-lb 4.6 + i.8 Class 3 Fig 4-ic 4.5 ± 0.6 Class 4 Fig 4-id 4.4 ± 1.3 7.8 + 1.5 7.2 + 2.0 3.3 + 2.0 4.6 + 1.1 -21.3 + i.4 -21.8 + 2.3 -18.3 + 2.i -21.6 + 2.3 0.35 + 0.i6 -0.26 + 0.16 -0.i8 ± 0.i5 -0.45 + 0.30 154 + 70 123 + 82 i03 + 73 65 + 23 24 + 34 -2 + 30 5 + 25 -i8 + 14 30.40 +0.07 30.35 + 0.12 30.15 ±0.ii 30.22 ±0.11 0.00 ± 0.01 0.00 ± 0.01 0.01 + 0.03 -0.02 ± 0.01 1.0 + 1.0 7.2 ± 5.6 3.3 + 1.3 22.2 + 5.2 63 Table 4-IT. Cross correlation between the measured ambient noise levels at 10 Hz and 200 Hz with the measured environmental conditions and the number of detected ice-cracking events per minute. Temperature, barometric pressure and solar radiation changes were measured over one hour prior to the ambient noise measurements. Environmental Parameter Current Speed Wind Speed Temperature Temp Change Solar Radiation Solar Rad Change Barometric Pressure Bar Pres Change Detected Events Correlation 10 Hz -0.06 0.18 -0.01 0.20 0.28 0.20 0.52 -0.19 -0.18 Coefficient 200 Hz 0.14 -0.11 0.01 -0.72 -0.23 -0.33 -0.07 -0.05 0.76 64 100 90 N z c’i I 80 70 60 50 40 10 Frequency (Hz) 100 Figure 4-la. Average ambient noise spectra (solid) and standard devi ation (dashed) for Class 1 type ambient noise spectra indicating strong infrasonic peak at 8 Hz with little or no thermal ice cracking. 65 100 I I I I I I II I I I III 90 N I c’J / — 80 / / -o \ \ 0 / 70 ci) > ci) -J ci) C,) 60 0 z jI 50 40 I I I I I I 10 Frequency (Hz) I III 100 Figure 4-lb. Average ambient noise spectra (solid) and standard devi ation (dashed) for Class 2 type ambient noise spectra indicating strong infrasonic peak at 8 Hz with some thermal ice cracking. 66 100 90 N z c’J 80 0 -4- -D 70 a) > a) 1 a) (1) 60 0 z 50 40 10 Frequency (Hz) 100 Figure 4-ic. Average ambient noise spectra (solid) and standard devia tion (dashed) for Class 3 type ambient noise spectra indicating weaker and broader infrasonic peak at 4 Hz with some thermal ice cracking. 67 100 I I I I I III I I I III 90 N z c’J — 80 0 / \. -D 70 > ci) _1 ci) Cl) ‘‘\ — V J 60 0 z 50 40 I 1 I liii 10 Frequency (Hz) - I I II 100 Figure 4-id. Average ambient noise spectra (solid) and standard devi ation (dashed) for Class 4 type ambient noise spectra indicating very intense thermal ice cracking with no noticeable infrasonic peak. 68 Chapter 5 Pressure Ridging Active pressure ridges occur when two ice sheets are pushed together, usually by wind or current, forcing one sheet over the other. This bends the sheets until the resulting stresses fracture the ice into large blocks which pile up forming long rows with a triangular shaped vertical cross section. The full effects of active pressure ridging on the ambient noise spectra from 2 - 200 Hz will be examined here. It will be shown how the source spectral level of an active pressure ridge, when corrected for the propagation loss of a distant event at 40 km or more, produces the infrasonic peak found in the Arctic ambient noise spectra. A simple method of determining the role of active pressure ridges on the ambient noise would be to sum the received energy from all occurring active ridges at a given time. This approach requires knowledge of the spatial, temporal and source level distributions of active pressure ridges, about which very little is known. It will be shown that the measured ambient noise below 40 Hz can be accurately reproduced by a single active pressure ridge at a range of tens of kilometers. 5.1 Spatial Distribution Sonar measurements of the under surface of the ice performed by the TJSS 30 give an average of 6 keels/km across the entire Arctic basin. Laser altime Nautilus 69 try measurements of the upper surface of the ice show reasonable agreement with an average ridge separation of approximately 100 m (see Ref 31). However, these mea surements show the sum of both active and old, inactive ridges. Members of Defence Research Establishment Pacific have been conducting experiments in the Arctic pack ice over spans of one or more months each year since 1986. The occurrence of an ac tive pressure ridge at or near an experimental site is very rare suggesting that active pressure ridges are only a small fraction of the ridges observed using sonar or laser altimetry. Buck and Wilson 4 estimate an average active pressure ridge separation of 37 km to account for the ambient noise levels and compare this separation to pan sizes of 10 - 100 km measured by SEASAT SAR. Pans are defined as groups of ice floes which move together. Because of the large spatial separation of active pressure ridges, the component of ambient noise caused by pressure ridging may be dominated by a single or few events occurring at some large distance from the array. Thus, examining a single pressure ridging event as a function of range may provide insight into the role of pressure ridging on the ambient noise. This is what is done here. It requires only knowledge of the source spectral level and the propagation loss. 5.2 Source Spectrum The received spectrum of each 5 - 10 sec pulse within the ridge building event of Fig. 3-9 had a spectral shape and overall levels within 5 dB of that shown in Fig. 5-1. The source spectral level estimated from these received levels is found to be monotonously decreasing and agrees with the source level per unit length of an active pressure ridging event measured by Buck and Wilson. 4 The spectral shape we observed 70 persisted for at least 1.5 hours with a continuous rise in level of approximately 15 dB over the first thirty minutes followed by a relatively consistent ambient noise level over the next sixty minutes with the exception of two or three large pulses occurring every minute with durations of five to tens of seconds (as shown in Fig. 3-9) and levels 10 - 15 dB above the ambient level. The absolute levels shown in Fig. 5-1 correspond to one of the pulses observed after the initial thirty minute rise. Details on the entire duration of the active pressure ridge are not available but the event recorded by Buck and Wilson lasted approximately two days. 4 An obvious feature of the received spectral shape of the ridge building event is the increase in level with decreasing frequency. This observation is in contrast with the spectral shape of the ambient noise which exhibits a broad peak near 10 - 20 Hz. Thus, either a different source mechanism is dominant over this frequency band or the propagation loss must increase dramatically below 20 Hz. 5.3 Propagation Loss Propagation loss in ice covered Arctic water behaves as a band-pass filter with the minimum propagation loss occurring in the octave 15 - 30 Hz (see Ref. 32). For high frequencies, the upward refracting sound speed profile traps energy in the surface channel as shown in Fig. 5-2. This trapping results in propagation loss that is dependent on spreading and ice interaction and thus increases with increasing fre quency. At low frequency, modal leakage from the surface channel results in bottom interaction (as shown in Fig. 5-3) which increases with decreasing frequency and greatly increases the propagation loss. The increase in propagation loss at low fre 71 quencies was shown by Mime 33 who found that the received energy in 2500-rn water in the Arctic over the frequency band 12 - 24 Hz decreased faster with increasing range than over the band 24 48 Hz. This minimum in the propagation loss has been - measured by several authors for the open ocean also. 3436 Modeling propagation loss in the Arctic is a very difficult problem because of the rough ice cover. To date, no complete model is available which allows both a fully elastic ice layer and incorporates a realistic approximation of the under-ice roughness. Development of such a model would be a thesis in itself and will not be performed in this work. Instead, results from two different propagation models will be given. The first propagation loss model used was the wave model SAFARI which includes refraction effects from the sound speed profile (Fig. 3-2) and the effects of absorption and shear waves in both the ice and bottom (ice and bottom characteristics are outlined in Table 5-I). SAFARI implements absorption by allowing km in Eq. 2.32 to be complex of the form = km(1 — iS). This results in plane harmonic waves having the form: F(r,t) A exp[i(wt — km)] = A exp(—Skmr) exp[i(wt which is a wave decaying exponentially in range. — km)] (5.1) The parameter 5 is defined by specifying the attenuation coefficient ‘y in dB per wavelength. For linearly frequency dependent attenuation, the attenuation coefficient is given as: = —20 log[F(r + )i,t)/F(r,t)] = —20 log [exp(—Skm))j = 4O7rSlog e. 72 (5.2) The result of the propagation loss determined by SAFARI, shown in Fig. 5-4, does indeed indicate that at longer ranges the propagation loss has a minimum at approximately 50 Hz and greatly increases below 10 Hz. Combining this pattern with the spectrum of ridge building could easily result in a peak near 10 Hz as found in the ambient noise. Although this model allows a fully elastic ice layer, it does not model the under-ice roughness correctly. It instead uses the Kirchholf approximation which assumes that at any point, the surface can be treated as being locally flat. This allows the reflected field at any point to be determined using: UrRUi 8n 8n (5.3) (54) where U and U are the incident and reflected fields, n is the normal to the surface at the scattering point in question, and R is the reflection coefficient obtained by assuming infinite plane waves and an infinite plane interface. The Kirchhoff scattering requires small roughness with small slope and a radius of curvature of the rough surface much less than the incident wavelength. Both measurements ’ and modeling 3 29 show that ridge keels form in a roughly elliptical shape with keel depths as large as 10 times the ice thickness and ridge widths often as small as 3 times the keel depth. Thus, the Kirchhoff approximation is a very poor estimate of the under-ice roughness, especially at the shallow grazing angles involved with long range propagation, and will lead to an underestimation of the propagation loss. The second propagation loss model used was the normal modes model KRAKENC. This model also includes refraction effects from the sound speed profile and allows 73 fully elastic bottom layers. The implementation of this model as used for this work did not incorporate an elastic ice layer though and instead used a scattering model developed by Burke and Twersky 37 to estimate the under-ice reflection coefficient as a function of frequency and grazing angle. This scattering model determines reflectivity from a uniform distribution of protuberances on a perfectly reflecting boundary. The model considers plane waves incident on a one dimensional distribution of semiel liptic, infinitely long cylinders. A reflection coefficient for the rough surface is then constructed by combining the effects of the scattering for each individual protuber ance. Reflection coefficients are then estimated for a given average keel depth, keel width and number of keels per kilometer. The propagation loss estimated from this model also indicates a minimum near 50 Hz and a large increase below 10 Hz as shown in Fig 5-5. Combining this pattern with the spectrum of ridge building could also easily result in a peak near 10 Hz as found in the ambient noise. Estimates of the average keel depth, keel width and number of keels per kilometer were obtained from ’ This model provides an accurate estimate of the under-ice propagation loss 3 Diachok. when both the source and receiver are in the water but does not include the effects of having the source in the ice. A more detailed comparison of the two propagation loss models and the effects of changing various environmental parameters will be given in the next section. Evidence of the band-pass filtering effect of propagation at our experimental site is obtained by examining the spectral levels of the thermal ice cracking events as a function of source range. When the spectral levels of these events are calculated using all the bottom and under-ice reflections, a relatively flat spectrum results for close range events but a broad peak appears in the spectrum which narrows slightly 74 and shifts towards lower frequency as the source range increases. This behavior is shown in Fig. 5-6 which indicates that the events are being band-pass filtered with the very low frequencies (below 20 Hz) being attenuated at a faster rate than the higher frequencies (above 40 Hz) in agreement with the predictions shown in Figs. 5-4 and 5-5. 5.4 Modeled Pressure Ridge Noise When the received spectral level of the pressure ridging event at 2 km range is corrected for propagation ioss to larger ranges using the SAFARI wave model, the resulting spectra exhibit broad peaks at 10 - 30 Hz as shown in Fig. 5-7. This figure assumes a source depth of 5.5 m while the true source depth is unknown. Fig. 5-8 shows that the modeled peak at 10 30 Hz persists for varying source depths in the ice. - Buck and Wilson 1 found the acoustic source of an active pressure ridge they examined to be in the keel of the ridge at a depth below the thickness of the surrounding ice plates. To keep the modeled source within the ice, a source near the bottom of the ice at 5.5 m depth is used for all further modeling. Although the source depth has little effect on the frequency at which the infrasonic peak occurs, Fig. 5-8 does show that it affects the spectral levels by as much as 6 dB with the lowest source levels occurring for a source at mid depth. These observations agree with results found by 8 Stein. The modeled peaks at 10 30 Hz shown in Figs. 5-7 and 5-8 resemble the infrasonic - peak found in many real data ambient noise spectra with the exception that the modeled ambient noise level remains relatively flat until 30 75 - 60 Hz while the real ambient noise level often begins decreasing at 10 - 20 Hz (Figs. 4-la and 4-ib). The modeled results also show that the peak narrows as the range of the event increases and suggest that the infrasonic peak could be explained if active pressure ridges were separated by several hundred kilometers. This idea disagrees with measurements of pan sizes and an alternative explanation for the narrow peak is examined in the propagation loss model. As mentioned in the previous section, the wave model SAFARI uses the Kirchhoff approximation of small roughness with small slope to estimate the interface roughness. This is a poor approximation to the under-ice roughness and leads to an underesti mation of the propagation loss. Livingston and Diachok 38 estimated the under-ice reflectivity at approximately 18 Hz and 24 Hz along several tracks using matched field processing and found the scattering loss to be approximately 10 times as large as the Kirchhoff’ predictions. In an effort to more accurately reproduce the propagation loss caused by under-ice scattering when using the SAFARI wave model, the absorption loss in the ice was allowed to increase. Although this is an entirely different loss mechanism, it has the desired characteristics of increasing the loss with increasing frequency and with each interaction with the ice. The resulting spectrum of a ridging event at 90 km away for varying ice absorptions is shown in Fig. 5-9. This figure clearly shows that as the ice absorption increases, the modeled infrasonic peak narrows and becomes a better approximation of the peak observed in real data in Figs. 4-la and 4-lb. Because of the uncertainty in bottom shear characteristics, the effects of small changes in the shear wave speed and absorptions in the bottom layers were examined. 76 These effects are shown in Figs. 5-l0a and 5-lob. Fig. 5-lOa shows that as the bottom shear wave speed increases, the infrasonic peak in the ambient noise spectrum becomes more pronounced and shifts slightly towards higher frequency. Fig. 5-lob shows that the infrasonic peak also becomes more pronounced as the shear wave absorption increases. The received spectral level of the pressure ridging event at 2 km range corrected for propagation ioss to larger ranges using the KRAKENC normal modes model with Burke-Twersky ice scattering is shown in Fig. 5-11. This figure shows a broad peak between 8 - 20 Hz depending on source range. This result agrees well with the in frasonic peak found in the ambient noise spectra. This model appears to accurately reproduce the shape of the ambient noise spectra without the need to artificially in crease the absorption levels in the ice as required by the SAFARI model with Kirch hoff scattering. However, this model simply estimates reflection coefficients from the under-ice scattering caused by ridge keels and does not include an actual ice layer. Thus, it does not include the effects of having the source in the ice. Because the active pressure ridges examined here and the thermal ice cracks examined in the next chapter all occur in the ice, this model will not be used further. All the modeling up to this point has assumed a water depth of 420 m as found at the experimental site. It is interesting to examine the propagation loss as a function of bottom depth as shown in Fig. 5-12. This figure shows that at very far range, the propagation loss minimum is near 30 Hz for water 500 m deep and increases to approximately 50 lIz for water 3000 m deep. It also shows that the increased loss at frequencies above and below the frequency of minimum propagation loss is much higher for shallow water than deep water. This last effect becomes more pronounced 77 as the source range increases. Because of the deficiencies of the propagation loss models available for the Arctic, some caution should be used when drawing conclusions from their usage. Estimating the range of an active pressure ridge strictly by using the ambient noise spectrum is likely to be inaccurate because of the uncertainty in the propagation loss and possible differences in the spectral shape of active pressure ridges. It is shown though that for our data, both the spectral shape and level of the ambient noise below 40 Hz can be accurately modeled by active pressure ridges at ranges of tens of kilometers. Table 5-I. Parameters of ice and bottom layers used for propagation loss modeling in Safari. C,, and C 5 are the sound speeds for the compressional and shear waves while K,, and K 5 and the compressional and shear wave attenuations. Thickness (m) ) 3 Density (g/cm C,, (m/sec) 5 (m/sec) C K,, (dB/)) 5 (dB/)i) K RMS roughness (m) upper lower Ice 6 0.9 2800 1750 2.0 3.0 1.0 4.0 Bottom 15 1.8 1800 300 0.5 0.25 Sub-Bottom - - - - - 1.9 2000 500 0.5 0.25 78 120 115 N I 0 zL ci) > 110 105 ci -J a) > 100 ci C-) ci) 95 90 1 10 Frequency (Hz) 100 Figure 54. Received spectral level of a typical pulse within the ridge building event. 79 0 100 200 300 400 500 600 Figure 5-2. First 3 modes at 100 Hz in water 420-rn deep with a sound speed profile as shown in Fig. 3-2. Note that the modes are trapped near the surface resulting in propagation loss that is dependent on spreading and ice interaction. 80 0 100 200 400 500 600 Figure 5-3. First 3 modes at 20 Hz in water 420-rn deep with a sound speed profile as shown in Fig. 3-2. For this low a frequency, the modes are no longer trapped near the surface (as in Fig. 5-2) resulting in bottom interaction which in turn increases the propagation loss. 81 100 N > C.) C ci) 1 0 ci) U- 0 10 20 30 40 50 60 Range (km) Figure 5-4. Propagation loss in dB determined using the wave model SA FARI for a source at 0.2-rn depth in 7-rn thick ice for water 420-rn deep and depth averaged over all hvdrophones in the vertical array. 82 100 N > C-) C a) 10 0 a) U- 1 0 20 40 60 80 100 Range (km) Figure 5-5. Propagation loss in dB determined using the normal modes model KRAKENC with Burke-Twersky scattering for water 420-rn deep and depth averaged over all hydrophones in the vertical array. An average of 11.5 keels per kilometer with keel depths of 5.3 m and keel half widths of 11.9 m is used. 83 90 I I • I 26Cm 330Cm 1100Cm —— • -- 60 —. • - \“ \.. - > 0 ci) / cl:i:zn / / 40 ••• I I I I 100 10 Frequency (Hz) Figure 5-6. Received spectra of 3 ice-cracking events at different ranges when all multiple arrivals including direct path, bottom reflection, under ice reflection, etc. are used. Approximately 20 ice-cracking events at each range were examined. Although absolute levels varied between individual events, spectral shapes were consistent for any given range. 84 100 90 \ c’ a — \ N S..—” S.-— /N/ \ 80 % — — -S \ •/.\ ••‘ I /,••/• \/ / ,/ \ . \ \\. 13 a) > a) -J -D a) a) 70 \ \. \ \ \ I. \ 60 .1•1• \ \ 30km 60km 90km 120 km 150 km / 0 50 \ \ \ \ ‘ .‘. \ 40 1 10 Frequency (Hz) 100 Figure 5-7. Resulting ambient noise spectra produced by distant ridge building events using the environmental conditions given in Table 5-I to determine propagation loss. 85 100 90 N c’J cE5 U 80 cr -o 70 > -J ci) 60 0 0 50 40 1 10 Frequency (Hz) 100 Figure 5-8. Resulting ambient noise spectra produced by a ridge building event at 90 km range for sources at varying depths in the ice. 86 100 90 N z cJ 0 80 -o 70 > -J 60 0 50 40 1 10 Frequency (Hz) 100 Figure 5-9. Resulting ambient noise spectra produced by a ridge building event at 90 km range for different levels of ice absorption. Levels of ab sorption for the compressional wave in the ice are given in dB/A with shear wave absorption 1.5 times the compressional wave absorption. 87 100 250, 400 300, 450 350, 500 400, 550 03, 04 (rn/see) 90 N C” Ct5 0 80 I \‘ /., / / -D ci) > ci) -J -D ci) ci) / / / \J 70 / / / 60 / 0 50 40 1 10 Frequency (Hz) 100 Figure 5-lOa. Resulting ambient noise spectra produced by a ridge building event at 90 km range for different bottom shear wave speeds. Speeds are ) layers respectively. 4 ) and sub-bottom (C 3 given in m/sec for bottom (C ice of 10 and 15 dB/.\ the in Compressional and shear wave absorptions are used respectively. 88 100 90 N cN 80 - 70 > a) -J -c 60 a) -c 0 50 40 1 10 Frequency (Hz) 100 Figure 5-lOb. Resulting ambient noise spectra produced by a ridge building event at 90 km range for different shear wave absorptions in the bottom. Both bottom layers use the same level of absorption given in dB/). Corn pressional and shear wave absorptions in the ice of 10 and 15 dB/A are used respectively. 89 100 90 N c’.J a 80 ,— — , \ G) > 70 ,• / \ ‘7 ,,/ -J / 60 \ \ 50 \ \. 30km 60km 90km 120 km 150 km \ 0 .-. / N \ \‘. \.‘ 40 1 10 100 Frequency (Hz) Figure 5-11. Resulting ambient noise spectra produced by distant ridge building events using the normal modes model KRAKENC with Burke Twersky scattering. A source depth of 5 m is used along with an average of 11.5 keels per kilometer with keel depths of 5.3 m and keel half widths of 11.9 m. 90 1 N > C.) ci) ci) U- 500 1000 1500 2000 2500 3000 Bottom Depth (m) Figure 5-12. Propagation loss in dB as a function of frequency and total water depth for a source at 200 km range. 91 Chapter 6 Thermal Ice Cracking Thermal ice cracks are small ice fracturing events which occur near the surface of the ice as it contracts during times of atmospheric cooling. By using the spatial, temporal and source level distributions of thermal ice cracking, the average energy per unit area entering the water due to thermal ice cracking can be determined. This level in turn is used to determine the average energy received at a hydrophone suspended below the ice by summing the energy input over all locations about the hydrophone and subtracting the associated propagation loss for each location. In order to develop the thermal ice cracking component of the ambient noise model, the spatial, temporal and source level distributions along with the source spectrum and directivity of thermal ice cracking must be known. I derive the temporal and source level distributions of thermal ice cracking from the received levels and ranges of individual events along with the propagation loss and probability of detecting an event at a given range and source level. The spatial distribution of events is measured and compared to results by other authors. The directivity of individual events is measured and compared to the source models introduced in chapter two. 92 6.1 Spatial Distribution In determining the spatial distribution, the range of an individual source is found using a vertically stratified ray tracing model with the sound speed profile shown in Fig. 3-2. This model calculates the eigenrays for all propagation paths (direct arrival, bottom reflection and multiple reflections) to all hydrophones on the vertical array. Ranges were determined to the nearest 10 rn out to 2 km and to the nearest 50 m beyond 2 km. The bearing of a source was determined using only the direct arrival path on the horizontal array and assuming straight ray propagation. Tests at several angles showed a maximum error of approximately 100 between straight ray and refracted ray propagation for a source at 100-rn range. The error was reduced to less than 10 for a source at 500-rn range. The bearing of each event was determined to the nearest increment of 5°. A scatter plot of all the detected events, shown in Fig. 6-1, reveals that most detected events are within 5 km of the vertical array. This grouping occurs because the increased propagation loss associated with increasing range makes an event of a given source level harder to detect with increasing range. When propagation loss is considered, the lack of preferred source locations or directions supports the idea of a large scale spatially isotropic noise field and agrees with previous results for areas of Arctic pack ice. 39 This isotropy gives some justification for the proposed method of determining an average input energy per unit area. Note that two forms of short term fluctuations of the average input energy can occur. The first is a strength fluctuation in the overall input level applied to all locations as the rate of ice cracking changes. The second is a random statistical fluctuation in the spatial distribution which may 93 cause local areas of weak or intense ice cracking. These random statistical fluctuations have more effect on the ambient noise when occurring at close range due to the smaller number of events and lower propagation loss associated with close range. Thus, statistical fluctuations will be applied only within 1 km of the hydrophone. These two types of fluctuations could account for some of the differences between classes of real ambient noise spectra measured in chapter four and are included in the model. 6.2 Source Directivity An important characteristic in modeling the ambient noise produced by in dividual events is the vertical directivity of these events, which is a measure of the relative power radiated from a source as a function of vertical angle. Due to the high propagation loss associated with near vertical rays, long range propagation is restricted to angles near horizontal. Therefore, the source directivity at these shallow angles is critical in modeling the ambient noise. In the open ocean, a major source of noise is entrapped bubbles from rain or breaking waves. A spherical bubble which expands and contracts in the water is a monopole source radiating equal energy in all directions. When the bubble depth is small compared to the wavelength of the energy radiated, interference of the bubble with its image source above the surface results in dipole radiation. Acoustic sources in the ice are more complicated, with the measured radiation pattern depending on the shape of the source, the elastic properties of the ice and the complicated inter actions with the rough ice surface and ice bottom. Therefore, there is no obvious radiation pattern for a source in the ice, and several theoretical models have been 94 ”°” The models of Stein 8 proposed. 4042 , Xie’° and Xie and Farmer’ 8 1 have been shown in chapter two. Stein 8 predicts a dipole radiation by using a point source in the ice. Xie ° and Xie and Farmer 1 ’ predict an angularly dispersive directivity by 1 using plate vibration theory to describe the motion of the ice plate and the resulting waves produced from either a vertical point force or a pair of horizontal point forces at the surface of the ice. Langley’° predicts a higher order multipole radiation pattern by using an extended source in the ice. Kim ’ uses a combined mathematical and 4 numerical model to find the radiation pattern of typical sources used in geophysical studies such as strike-slip, dip-slip and tensile cracks. Dyer 42 states that the ice frac turing process of a crack is important above 200 Hz while the deformation unloading or plate vibration of the crack is important below 200 Hz. He also states that the low frequency plate vibration should have a dipolar radiation while the higher frequency fracture process will have an octopolar radiation. 1 the ’ 3 Observation of the number of detectable ice-cracking events with range,’ ratio of energy in the direct arrival versus bottom reflection, 23 and the ratio of energy 4 have shown that ice cracking in a lead pressure ridge to that of a floe pressure ridge events often radiate more energy vertically than horizontally. These papers all assume a dipole directivity to determine other characteristics of the source or propagation parameters. However, the theoretical models mentioned above do not all agree that a dipole directivity is the appropriate form to use. Also, the only published data show ing direct measurements of the vertical directivity (at more than two angles) known to the author are those given by Stein. 25 Stein shows the directivity of two events ’ 8 as measured on a 24-element horizontal array with a 1-km aperture. The low signal to-noise ratio along with the limited span of vertical source angles available from a 95 horizontal array resulted in an inconclusive measurement which neither supported nor contradicted a dipole directivity model. This section presents direct measurements of the vertical directivity of 160 icecracking events and compares them to results obtained from the wave model SAFARI and to the directivity predicted by the source models of Stein, Xie and Farmer. Using the 22-element vertical array, the received signals spanned source angles from 10 to 80° below horizontal. Only those events within 2 km of the array and with a minimum signal-to-noise ratio of 3 dB were used. The vertical directivity of an individual ice-cracking event was obtained in the following manner. An event is first identified and isolated as described in chapter three. The received pressure level in the direct arrival is then measured for each hydrophone. Pressure levels are averaged over one octave bands centered at 48, 96 and 145 Hz. These levels must then be corrected for background noise, spherical spreading loss and the focusing of rays due to changes in the refractive index. The noise is removed by subtracting the pressure level contained in an equal length of data immediately preceding the direct arrival. Measurements of ambient noise pres sure levels showed a maximum change of only 0.5 dB across the vertical array for the frequencies examined. Because of this small change, the noise level was sampled at only one hydrophone and assumed constant along the array. The effects of spherical spreading and ray focusing are determined by using SAFARI to calculate the prop agation loss from a source at the surface to the receivers in the vertical array using the sound speed profile shown in Fig. 3-2. Reflections from the surface, bottom and under-ice are eliminated from the propagation loss by removing the ice and using infinite half spaces of isovelocity water above the source and below 420-rn depth with 96 sound speeds equal to those of the surface and bottom water respectively. Absorption in the water can be ignored as it is insignificant (approximately 10 dB/km at 100 Hz) for these short ranges and low frequencies. 45 A ray tracing model can then be used to give the vertical source angle to each hydrophone for a given range, and thus, measurements of radiated pressure level as a function of angle are obtained. For a given ice-cracking event, the measured sound pressure level Pd(O) in the direct arrival at each hydrophone (corrected for spreading loss, focusing and back ground noise) is used to calculate the vertical directivity pattern of the source. We chose to parametrize the directivity of the source by a model of the form: 47 ’ 46 P(8) = 0 sin P 8 m (6.1) where P 0 is the source pressure level (in dB// iPa/Hz at lm) and P(8) is the modeled 1 radiated pressure level in the direct arrival at source angle 8, normalized back to 1 m. However, it was found to provide a useful parametrization of the directivity at shallow angles which controls long range propagation. The continuous parameters m and P 0 may be determined by minimizing the squared difference (Pd — . 2 P) Figs. 6-2 and 6-3 show the best fit of the above model to the horizontal and vertical point forces used as a source model by Xie’° and Xie and Farmer ’ for angles 1 less than 45°. They show very close agreement for frequencies of 150 Hz or less. Although the fit is not accurate at 200 Hz, it is still reasonable for angles less than 30°. It is shown in Appendix A that the bottom critical angle is approximately 40° and thus, our model of 8 m 5111 provides a reasonable estimate to nearly all the energy predicted from distant horizontal or vertical point forces. Fig. 6-4 shows the measured directivity of an ice-cracking event as a function 97 of source angle along with the best fit directivity pattern calculated using the above model. This figure shows that the model fits these data very well. Of the 160 ice-cracking events examined, 95 (approximately 60%) were found to fit the model with an average deviation of less than 0.75 dB per hydrophone. A further 42 events (approximately 26%) were found to fit the model with an average deviation of 0.75 - 1.5 dB. The deviations in the first case tended to be random while those in the second case generally followed some small fluctuating pattern as shown in Fig. 6-5. The 95% confidence limits (assuming a time scale of approximately 0.15 sec for the direct arrival) in the pressure levels are 1.2 dB at 150 Hz, 1.5 dB at 100 Hz and 2.2 dB at 50 Hz. Thus, these deviations from the fit could be caused by the estimation error in determining the pressure levels from the short time samples. Although our simple model does not account for these fluctuations, it provides a useful first estimate of the directivity of these events and therefore was used to model all the above events. The remaining 23 events (approximately 14%) were found to have complex directivity patterns often exhibiting a peak in the directivity at source angles ranging from to 350 100 as shown by the example in Fig. 6-6. The directivity of these events could not be approximated by our model and they were not used in any further processing. A comparison of the directivity of these events with horizontal or vertical point forces (Fig. 2-7) shows that this type of directivity pattern may result from a source in thicker ice. It will also be shown, while examining the directivity of modeled events using SAFARI, that it is still possible to reproduce such a directivity pattern using a monopole source. Although the model of the form sin tm 8 provided an acceptable fit to the directivity of approximately 86% of the 160 transient events analyzed, the directivity index m 98 of the model was found to vary between individual events. The distribution of m for all 137 ice-cracking events which fit the model is shown in Fig. 6-7. This distribution has a mean of 0.87, a variance of 0.20 and a positive skew. This distribution also shows two peaks for values of m of approximately 0.6 and 1.0. If the distribution of m is examined for different horizontal source ranges as shown in Fig. 6-8, it is seen that the lower values of m occur mainly for sources at ranges of less than approximately 40 wavelengths (1300 m at 48 Hz, 650 m at 96 Hz and 430 m at 145 Hz) while for further range events, the values of m are narrowly distributed about 1.0. Values of the mean, variance and skewness of these distributions are shown in Table 6-I. The distribution of m was examined for different sets of horizontal source range but the clearest separation between events with m narrowly distributed about 1.0 and those with m broadly distributed about a smaller value occurred at 40 wavelengths. The lower values of m for sources at shorter range may be caused by nearfield effects which are not included in the transmission loss. Therefore it appears that the vertical directivity of an ice-cracking event at long range may be approximated as a dipole and thus the source may be approximated as a monopole. Note that the models of Langley, ° Kim, 4 ’ and 4 Xie and Xie and Farmer” may also all approximate a dipole directivity pattern when observed at long range and low frequency. It was also found that not only did the order m of the model depend on range, but also the goodness of fit of this model to the measured source directivity. For the 96 Hz band, of the 65 events with an average deviation above 0.75 dB, only 2 were at a range of 60 wavelengths or greater. Also, all of the 23 events with complex directivity patterns were at ranges of 20 - 40 wavelengths. Therefore, the model sin6 appears 99 to be a good fit to the directivity of an ice crack at long range while deviations from this model are concentrated at shorter ranges. These results will also be compared to modeled directivity produced by SAFARI. Although a dipole directivity pattern (monopole source) was found to accurately represent most of the detected events, an attempt was made to positively identify one of the source models. One method was to examine the directivity for different frequencies simultaneously. Stein’s model of a monopole source gives purely dipole directivity for all frequencies while Xie and Farmer’s model of horizontal or vertical point forces predicts a directivity pattern dependent on frequency. Most events were found to either radiate equal energy at all frequencies or have no noticeable patterns distinguishing different frequencies as shown in Fig. 6-9. This result is consistent with a monopole source in the ice but may also be produced by horizontal or vertical point forces occurring in thinner ice as shown in Fig. 2-6. Approximately 15% of the events within 400 m range were found to have distinctly different radiation patterns for 50 and 100 Hz than for 150 and 200 Hz as shown in Fig. 6-10. At the lower frequencies, these events were found to fit our directivity model with values of m between 0.6 to 0.8. The higher frequencies did not fit our model but were instead found to peak at 15° to 300. This peak in the directivity at 15° to 30° is consistent with the radiation predicted by horizontal or vertical point forces for events occurring in thicker ice as shown in Fig. 2-7. Also, approximately 10% of the events beyond 1000 m range were found to have different radiation patterns for different frequencies as shown in Fig. 6-11. These events were all found to contain more energy at 100 and 150 Hz than at 50 or 200 Hz. The second method used to try to distinguish the source model was to exam 100 me events occurring at close enough range that several hydrophones received energy at source angles greater than 700 below horizontal. The pair of horizontal point forces predicts a sharp decrease in energy for these large source angles while both the monopole source and vertical point force do not. Only seven events satisfied the above condition with four events showing a decrease in energy above 70° while the remaining three events did not. This inconsistency in the level of energy above 70° could be explained by cracks occurring on vertical faces of upthrust ice but may also be a result of near field effects not considered in any of the source models. Unfor tunately, a definite source mechanism could not be identified from the data but the plate vibration theory used by Xie’° and Xie and Farmer 11 appears to be able to account for all observed effects if areas of different ice thicknesses are present. Finally, although the sin 8 model was an accurate fit to the directivity of 86% m of the events identified, an excess in the sound pressure levels of 1 - 3 dB above the fit was found centered about a 60° 65° source angle as shown in Fig. 6-12. This increase - was found on 9 out of 13 or 70% of the events that had source angles this high, while in total, fluctuations of a few dB were found on only 30% of the 137 events used. Better statistics on this increase in energy may be obtained by examining the bottom reflected arrivals for which more events occur with a 60° source angle. These arrivals showed an increase in pressure level of 3 dB above the model fit (after correction for bottom reflectivity) with an approximately Gaussian distribution centered at 60° with a 5° standard deviation as shown in Appendix A. This appendix also shows how thermal ice-cracking events can be used to measure the bottom reflectivity function. The increase in pressure levels of both the direct arrival and the bottom reflection at 60° may be explained as the leaked plate wave which coincides with the acoustic 101 wave at this angle and therefore cannot be separated in time from the acoustic wave as it could for the event in Fig. 3-8. Using plate vibration theory, Xie’° and Xie and Farmer” also predict an increase in energy in the water at this angle for a thin plate as the plate vibration impedance vanishes. This increase is clearly shown in Figs. 2-4 to 2-7. Thus, this increase should be included in the directivity of the source and a proposed model of the vertical directivity is: P(8) = 0 [sinm8 + C exp P L) 2 j] (6.2) 0 is where P(8) is the modeled pressure level in the direct arrival at source angle 8, P the pressure level of the source, m is the directivity index, C is a constant giving the relative contributions of the acoustic mode and the leaked longitudinal plate wave, and L 8 and w are the critical angle and beamwidth of the leaked longitudinal plate wave respectively. For our data, C 1.0, 8, 60° and w 5°, while m 1.0 for horizontal source ranges greater than 40 wavelengths but decreases to approximately 0.7 for shorter range events. Note that the contribution to the directivity due to the leaked longitudinal plate wave will have little effect on the long range propagation if the bottom critical angle is less than 60° above horizontal. Also, although the leaked plate wave contributes to the acoustic mode, it was noted earlier that as the range increases the leaked plate wave itself is rarely observed. The modeling discussed next suggests that the absence of this wave could be due to scattering and absorption in the ice. Finally, it should be remembered that this proposed model of source directivity comes from a statistical average over m, where the distribution about m at long range is fairly narrow but broadens for shorter ranges. To compare the source model with measurements of vertical directivity, a simple three-layer horizontally stratified model which approximated the experimental site 102 was used as the environmental input for SAFARI. It consisted of a vacuum halfspace above, followed by a layer of ice and a water halfspace below. Ice thicknesses of both 3 m and 6 m were used with compressional and shear speeds of 2700 rn/sec and 1750 rn/sec respectively. Although an average ice thickness of 3 rn for the central Arctic has been measured in August, ° our measurements of ice thickness obtained during 3 late spring at multiple locations and over several years have usually shown thicknesses of 6 m or more for level undeformed ice and agrees with other measurements made in the Lincoln Sea area. 14 The change in ice thickness had little effect on the modeled source directivity and only the results for 6 rn thick ice are shown. An isovelocity water layer with a sound speed of 1450 rn/sec was chosen to minimize the number of layers used, thereby reducing artifacts introduced at boundaries. Also, since only the direct path from source to receivers was used for measuring the directivity, an infinite half space of water was chosen to prevent interference between the direct path and bottom reflections. Although the water layer in the model does not resemble that at the site, the differences will alter only the spreading losses and source angles of the received signal, both of which can be determined and corrected easily. The ice crack itself was modeled as a monopole pulse source at varying depths in the ice. The pulse form used was: f(t) where sin(2 f t) — sin(4 f t) 0 <t <fr’ (6.3) f is the center frequency or peak frequency of the signal (100 Hz for our data). This pulse form was chosen as it approximates the frequency response seen by our system. Fig. 6-13 shows the modeled response for a source in the ice at a range of 500 m, a depth in the ice of 5.5 m and for a value of absorption in the ice 18 Although thermal ice cracking is expected to occur which approximates smooth ice. 103 near the ice surface where thermally applied stress is greatest, a deep source is used here for illustrative purposes and the effects of source depth will be examined. Note that both the leaked plate wave and direct path acoustic mode are clearly visible across the entire array while the fiexural wave is visible on the shallowest receiver only. The direct path acoustic mode also shows interference from multiple arrivals (indicated by the separation of a single pulse near the surface into two pulses for deeper receivers). These multiple arrivals could be caused by the unequal fiexural 8 and result in highly vibrations of the ice plate near the source as described by Stein non-dipolar simulated radiation patterns as shown in Fig. 6-14. This figure is to be compared with the measured directivity shown in Fig. 6-6. The directivity pattern of the acoustic mode of a source in the ice as modeled by SAFARI was found to depend on source depth, source range and the level of absorption in the ice. As the source range or level of absorption in the ice increased, interference from the multiple arrivals decreased and the directivity pattern shifted from the non-dipolar pattern shown in Fig. 6-14 to a more dipolar radiation pattern. Dependence on depth was more complex with the directivity pattern most closely approximating a dipole for a source near mid-depth in the ice but becoming more complicated as the source approached the ice surface and even further complicated as the source approached the ice bottom. Fig. 6-15 shows the resulting directivity when a shallow source depth of only 0.25 m is used. Fig. 6-16 shows the directivity for a shallow source when the level of absorption in the ice is increased to approximate rough ice 18 while Fig. 6-17 shows the directivity when the source range is increased to 2000 m. In general, the modeled directivity always approximated a dipole for distant events while for shorter ranges, it approximated a dipole for events near mid-depth 104 in the ice with high levels of ice absorption but became significantly non-dipolar as the depth changed or the level of ice absorption decreased. This behavior compares favorably with measured results which also always approximated a dipole at long range but sometimes had complex directivity patterns at short range. The mixture of dipolar and non-dipolar source directivity measurements at short range can easily be caused by differences in source depth or by local areas of low or high absorption in the ice. Finally, high absorption in the ice also eliminates the leaked plate wave in the simulation, which could explain why this arrival is not always observed. 6.3 Source Spectrum Although ambient noise caused by thermal ice cracking is shown to contain a broad peak in its spectrum near 300 - 500 Hz (see Refs. 1,2,10,11,21-23), very little ’ show the 1 has been published on the spectrum of individual events. Xie and Farmer received spectra of individual ice-cracking events for frequencies above 100 Hz and find a peak near 300 - 600 Hz with a rapid decrease in energy at higher frequencies but a slow decay with an almost flat spectrum for the lower frequencies. Zakarauskas ° have also published spectra of individual events, including that of a thermal 2 et.al. ice crack. That spectrum was fairly flat from 25 - 400 Hz, with a negative slope above 42 shows a frequency-time analysis of an ice cracking event from 30 to 590 400 Hz. Dyer Hz and shows that individual components or peaks within the event have band widths and time lengths of approximately 100 Hz and 10 msec respectively. He also shows that individual components tend to progress in time from higher to lower frequency. This progression from high to low frequency can be seen in the direct arrival for the 105 bottom hydrophones of Fig. 3-4. When the spectra of individual pulses from a single ice-cracking event are averaged together, Dyer’s results would also indicate a fairly flat spectrum from 30 - 400 Hz. Unfortunately, the sampling rate used to collect data for this thesis does not allow as fine a frequency-time resolution as that used by Dyer and the spectra of individual pulses within a single crack are averaged together. A frequency-time analysis of the hydrophone at 150 m depth for Fig. 3-8 is shown in Fig. 6-18. This figure shows that the leaked plate wave arrives at approximately 0.26 seconds with energy concentrated below 120 Hz. It is followed by the direct arrival at 0.35 seconds, the bottom reflection at 0.60 seconds and the bottom, under-ice reflection at 0.80 seconds. For the data used in this thesis, the received spectra are averaged over the entire length of the direct arrival. It was then found that nearly all the ice-cracking events had a relatively flat spectrum over the frequency band 2 - 200 Hz, as shown in Fig. 6-19. Although averaging the spectra of individual pulses from a single ice-cracking event does not allow identification of the mechanism involved for each pulse, the emphasis of this thesis is to determine if the ambient noise can be modeled by the individual events and not to determine all the mechanisms involved in a single ice crack. 6.4 Source Level Distribution In measuring the source level distribution of underwater noise in the Arctic, 2 6 8 2t correlates; 2 ’ several papers have related the ambient noise level to environmental 1 however, only one report known to the author contains information on the number ’ Unfor 1 of individual events detected or the distribution of strengths of these events. 106 tunately, that thesis reports only on those events which were detected and does not attempt to correct the measurements to derive the number of events which actually occurred. Thus, the measurements are dependent on both site and array character istics such as propagation loss and the detection threshold. The measurements in this thesis have been corrected to produce distributions of all the events which ac tually occur, not just those which are detected, and thus should be site and system independent. Two techniques were used to determine the source intensity level of individual events. The first technique was used only for events within 2 km of the vertical array and for which the direct arrival could be isolated from other arrival paths. For each hydrophone in the vertical array, the measured sound pressure level Fd() in the direct arrival is first averaged over a one-octave band centered at 96 Hz and corrected for spreading loss and ambient noise. Spreading loss includes both spherical spreading along the ray path and focusing of rays due to changes in the refractive index with depth. This loss is determined using SAFARI with the sound speed profile shown in Fig. 3-2. Ambient noise is determined by measuring the pressure level in an equal length of data immediately preceding the direct arrival. The true source pressure level can then be determined by correcting for the source directivity. As shown in the section on source directivity, it can be estimated by using a model of the form F(O) = 0 P sinme where P 0 is the true source pressure level, P(6) is the modeled source pressure level in the direct arrival at source angle 0, and m is the directivity index (m = 1 corresponds to a dipole). The source angle S at each hydrophone is given by the ray tracing model used to determine range. The continuous parameters m and P 0 may be determined by minimizing the squared difference (Pd(S) 107 — . 2 P(S)) 0 is then squared to give the source intensity level. These strength measurements P can be used to fine tune or verify the second source level estimation technique. The second method of determining the source level of an individual event can be used for events at any range and requires only a single hydrophone, although less variability in the results was obtained by averaging over all hydrophones in the vertical array. The received intensity level from all arrivals including the direct path, bottom reflection and any multiple reflections is summed, averaged over a one octave band centered at 96 Hz, and corrected for ambient noise. The true source level can then be obtained by correcting for the propagation loss from the source to the hydrophone. Propagation loss was estimated using the wave model SAFARI with the sound speed profile shown in Fig. 3-2 and the ice and bottom characteristics outlined in Table 5-I. In an attempt to correct for the underestimation of loss caused by the Kirchhoff approximation of the under-ice surface roughness, the shear and compressional wave absorptions in the ice were allowed to vary as outlined in chapter five. The source levels calculated by this technique were then compared to the levels determined by the first method to estimate the correct levels of absorption to use. It was found that a compressional wave absorption of between 1.0 and 10.0 dB/) with a shear wave absorption 1.5 times as large generally gave source levels within 1 - 2 dB of the levels determined using the first method. A wide range of values of absorption fit the model due to the small ice interaction involved for short range events. A more accurate estimate of absorption is obtained later when events at further range are used for which the propagation loss depends more strongly on ice interaction. Due to the increased signal to noise ratio which results from using all arrival paths, and the ability to determine source levels for events at any range, the sec 108 ond estimation technique was used to determine the source level of all the detected events. Although the exact absorption rates required to model both the absorption and scattering in the ice are not known, they can be estimated more accurately by examining the distributions of the number of detected events and their source levels as a function of range. The next paragraphs will explain the determination of the true source level distribution. The observed distribution of source levels differs from the true distribution because the further away an event occurs, the louder it must be to be detected. Hence, the observed distribution of source levels is biased toward stronger events. This bias can be avoided by using only the events which occur very close to the array. This precedure however would demand the analysis of very long records to accumulate the desired statistics. The method I have chosen is to use all events which are detected and correct them for the increasing source level required to detect an event as the source range increases. Consider first only the events which are detected over the small range interval r — Sr to r + Sr. Then for a spatially uniform distribution of events, the number of events which will be detected over this range interval as a function of source level SL is given by: Dr(SL) = 2irr8r n E(SL) T(SL — FLr) (6.4) where E(SL) is the true source level distribution of all occurring events which has been normalized so that E(SL) = 1 where SLmin and SLmar are the minimum and maximum detected source levels; n is the number of events/area/time occurring over the entire interval of observed source levels; PLr is the propagation 109 loss at range r and T(SL — PLr) is a detection threshold function representing the probability of detecting an event with a received level RL = SL — PLr. Although this method is sufficient to estimate the true source level distribution, better statistics are obtained by summing over all ranges at which events are detected. Thus, the observed distribution of source levels for all detected events is given as: rmax D(SL) .(SL) 7 D = rmax = 27r8r Ii E(SL) r T(SL — PLr). (6.5) Then by measuring the total number of events detected at each source level D(SL) over some time interval, the number of events occurring per unit area per time interval at each source level is given as: - E(SL) = 28r D(SL) max r T(SL — FLr) (6.6) The remaining tasks are to estimate the detection threshold function T(RL), and to check the accuracy of the ice absorption terms used in the propagation loss. The detection threshold function should allow detection of all events with a received level (source level minus propagation loss) greater than 2 - 3 dB above the ambient noise level, while events below this level have some finite but decreasing probability of being detected, as shown schematically in Fig. 6-20. By examining the distribution of re ceived levels of all events, as shown in Fig. 6-2 1, one could assume that all events with Pa are detected while there is an exponentially de 2 t 1 dB// Hz received levels above 75 / creasing probability of detecting an event below this level which falls to approximately 110 /Hz may 2 Pa However, because this fall-off below 75 dB//pPa 2 i 1 dB// Hz. 10% at 60 / be due in part or even wholly to the true strength distribution, both the level at which the detection probability begins to fall and the rate of exponential fall are left as variables which must be determined by some other means. Two methods are available for ensuring the consistency of the model and input variables. The first technique is to use the true source level distribution calculated from Eq. 6.6 to predict the observed source level distribution of detected events over a finite but large interval of ranges Lr — r2 — ri and compare the result to the measured distribution. Because the measured source levels depend on the propagation loss used, it is easier to compare the distribution of levels measured at the receiver. This distribution can be determined by a variation of Eq. 6.5 as: (6.7) r E(RL + PLr). Dr(RL) = 28r n T(RL) r =r 1 This test was performed over the range intervals of 0 7 - - 1 km, 1 - 3 km, 3 - ‘7 km and 15 km. The second technique for ensuring the consistency of the model is to use the true source level distribution calculated from Eq. 6.6 to predict the range distribution of detected events D(r), and compare to the measured range distribution. This distribution can be determined by summing Eq. 6.4 from the minimum to maximum detected source levels in the following manner: SLmax E(SL) T(SL D(r) = 27rr6r m SL=SLmin 111 — PLr). (6.8) Thus, by using a given level of ice absorption to determine propagation loss, the number of events detected at each source level D(SL) over some time period is first measured. This number is then combined with a given detection threshold function T(RL) to estimate the true source level distribution n E(SL) using Eq. 6.6. The true source level distribution is then used to estimate the observed source level distribution of detected events over a given range interval using Eq. 6.7 and the observed range distribution of detected events using Eq. 6.8. Finally, by varying the ice absorptions and the detection threshold function, the error between the measured and calculated distributions of Eqs. 6.7 and 6.8 can be minimized resulting in the best-fit true source level distribution. The absolute level of nE(SL) can be further confirmed by summing Eq. 6.5 over all detected source levels or by summing Eq. 6.8 over all ranges and comparing the results to the total number of events detected. The median number of events detected over the survey for all source levels was 3.1 events per minute. This number converts to a median source level distribution as shown in Fig. 6-22. This figure shows that a median of four events occur per square /Hz 2 kilometer per minute over a 1 dB band of source levels centered at 110 dB//Pa at 1 m. It also shows that more events occur at the low power end of the distribution and the number of events decreases with increasing source level. The decrease in occurring events with increasing source level is proportional to /Hz at 1 m and a 2 for source levels below 160 dB//iPa SL with a 0.08 0.12 for source levels above. The mean and maximum number of events detected per minute are 6.6 and 31.0 respectively. Thus, the mean and maximum source level distributions can be obtained by multiplying the number of events shown in Fig. 6-22 by approximately 2.1 and 10.0 respectively. 112 The shape of the source level distribution curve of Fig. 6-22 (a linearly decreasing function on a log-dB scale of the number of events versus source level with a change to a more steeply decreasing slope at higher source levels) agrees with the mea 49 sured distribution of earthquake magnitudes reported by Gutenberg and Richter. This relation is often an indication of a self similarity feature of the quantity being ° The general idea is that large earthquakes are composed of many smaller 5 measured. earthquakes which in turn are composed of even smaller earthquakes and that the smallest “building block” earthquakes and the resulting large earthquakes have many ’ proposed that the magnitude dis 5 similar characteristics (are scale invariant). Aki tribution curve of earthquakes may be related to their self similar (or fractal) nature 52 The self similarity structure and this relation was later shown to be so by Rundle. 5 distributions. temporal 5 ’ 53 and 54 of earthquakes was also shown in their spatial 5658 have developed simple slip-stick mechanical models which Several authors are capable of reproducing the spatial, temporal and strength distributions of earth quakes. These models are usually a system of blocks hung by springs from a stationary platform. The blocks are then coupled together by other springs and rest on a fric tional moving surface. Consider first a single block hung by a spring from a stationary platform and resting on a moving surface. The block sticks to the moving surface and moves with it until the spring force exceeds the frictional coefficient between the block and the surface. At this point, the block slips along the surface back towards its origin beneath the spring. Now consider many blocks hung from the stationary platform in a two dimensional grid and connected by horizontal springs. If the horizontal spring constant is much smaller than the vertical spring constant, when one block slips, it does not effect the neighboring blocks. This situation corresponds to that in which 113 small earthquakes occur frequently when the crust is sufficiently fractured. When the horizontal spring constant is greater than the vertical spring constant, the slip of one block propagates to many surrounding blocks corresponding to the situation of a large earthquake. A slip-stick mechanism has also been shown to be important in 9 and this mechanism may explain why the cracks 5 ’ the propagation of thermal ice 23 magnitude distributions of earthquakes and thermal ice cracks are similar. Although the distribution of source levels for thermal ice cracks was obtained by examining source levels at 96 Hz only, the relatively flat power spectrum of ice cracking shown in Fig. 6-19 suggests that this relation is valid for the entire frequency range of 2 - 200 Hz. Also, it should be noted that no attempt was made to distinguish between times of high and low ambient noise levels, so the distribution of Fig. 6-22 represents an averaged distribution for the entire observation period. The self-consistency of the model is shown by the comparisons of the measured and calculated distributions for Eqs. 6.7 and 6.8 shown in Figs. respectively. Only the range interval of 0 range intervals of 1 - 3 km, 3 - - 6-23 and 6-24 1 km is shown in Fig. 6-23; the remaining 7 km and 7 - 15 km have similar accuracies. The best-fit ice absorptions determined by the model were 8.0 dB/) for the compressional wave and 12.0 dB/.) for the shear wave. These absorption rates are high compared to 18 but may be realistic for this the ice absorptions previously measured for smooth ice fairly rough ice, especially when including the effects of under-ice scattering. Also, these values of absorption agree favorably with those required in the pressure ridge model and the resulting source levels agree within 1 levels determined using the direct arrival only. 114 - Hz of the source dB//iPa / 2 2 6.5 Modeled Thermal Ice Cracking Noise Using the temporal and source level distributions given in Fig. 6-22 along with the fact that the events are spatially uniform, the mean energy input into the ice per square kilometer as a function of source power can be determined as: P2(P) = St N(P) P (6.9) where N(P) is the mean number of events occurring at source power P per square kilometer per minute, and St is the mean time duration in minutes of an event. From our data, St was found to be approximately 0.1 seconds. The total average energy entering the ice per square kilometer is then obtained by summing over all source powers as: Pmax P2= St > N(P) P. (6.10) P=Prnin When summing over only the observed source powers (Pmin = 0.1 Pa , Pmax 2 = 106 //pPa at 1 m. When extended 50 dB/km ), the average energy input is 116.6 2 2 Pa dB above and below the observed powers (from 106 (SL = - 1011 ) using the 2 Pa SL fit 10 Log P with P given in iiPa ), the average energy input increased by only 2 1.1 dB. Because the true minimum and maximum source powers are unknown, the average energy input of 116.6 2 / dB/km i 1 Pa / at 1 m is used and the small increase obtained by extending the range of source powers will be ignored. Using the average energy input per square kilometer calculated above, the average 115 energy received at a hydrophone from a given source location is simply the average input minus the propagation loss associated with that location. The average received energy is then summed over all possible source locations to determine the ambient noise produced by thermal ice cracking. Our model steps out in range increments of 100 m to a total range of 200 km and determines the input energy for each range increment based on the area of the annulus ir(rmax+rmjn)(rmax—rm;n). Propagation loss is then averaged from the midrange of the annulus to 21 equispaced receivers from 100 - 300 m depth using the Kuperman-Schmidt propagation model SAFARI. An arbitrary maximum range of 200 km was chosen based on the propagation model used but later results will show that much shorter maximum ranges could have been used. Finally, the short term fluctuations in the strength distribution and the random statistical fluctuations in the spatial distribution of thermal ice cracking must be modeled. The strength distribution of Fig. 6-22 represents an average distribution over the entire observation period. Insufficient data exist to produce separate distri butions for intense or quiet times of ice cracking and these times are assumed to result in a strength distribution curve which is simply shifted up or down respectively. This shift can be estimated for real data by comparing the number of events detected per minute for a data sample with the average number of events detected per minute for all the data used to produce the strength distribution curve. For all 69 data files used in the strength distribution curve, the average number of detected events per minute was 6.6. Thus, for Fig. 4-id, with an average of 22.2 events detected per minute, the strength distribution curve is assumed to be shifted up by a factor of 3.4. This shift in turn results in an increase in the average input energy per square kilometer by a 116 factor of 10 Log(3.4) = 5.3dB. The random statistical fluctuations in the spatial distribution have a large effect on the ambient noise levels when occurring at small range. These effects are included by varying the average input noise level within 1 km of the hydrophone. Ignoring short term strength fluctuations, the modeled ambient noise due to thermal ice cracking is shown in Fig. 6-25 for the input noise level within 1 km of the array varying from -20 to +20 dB above the average input noise level. When short term strength fluctuations are included, the curves in Fig. 6-25 are simply shifted up or down by the appropriate factor. Thus, to model the real data in Fig. 4-id, the curves of Fig. 6-25 are shifted up by 5.3 dB as determined in the previous paragraph. Ice and bottom characteristics used to produce Fig. 6-25 are given in Table 5-I with the exception that compressional and shear wave absorptions in the ice were five times higher in an attempt to better compensate for the effects of under-ice roughness. For frequencies above 40 Hz, Fig. 6-25 shows the general characteristics of the real data shown in Figs. 4-la to 4-id. A comparison between real and modeled data above 40 Hz shows the validity of allowing the close range input noise to vary. Fig. 4-la, which is approximated by a lower close range than average modeled input noise level, represents data files with very few detected thermal ice cracking events. Of those events detected, only two events were within 1 km of the array and the received level of both these events was less than the ambient noise level at the time (events with a SNR < 0 can still be detected because of the array gain of the vertical array). At the other extreme, Fig. 4-id, which is approximated by a higher close range input noise level, represents data files with many detected thermal ice cracking events. These data files were each found 117 to contain several events within 1 km of the array with received levels at least 15 dB higher than the background ambient noise level. No other data files contained such events. Finally, the thermal ice cracking model outlined above is capable of determining the relative contribution of close versus far range events in producing the ambient noise. Fig. 6-26 shows the required range to model 80% (within 1 dB) of the total noise energy produced from all thermal ice cracking events out to a range of 200 km. This result is independent of the short term strength fluctuations but does depend on the short term spatial fluctuations. For frequencies near 10 Hz, if the local thermal ice cracking level is low (within 1 km), events beyond 100 km must be considered to model the thermal ice cracking noise. However at this frequency, unless local thermal ice cracking levels are very high, the ambient noise is dominated by pressure ridging and thermal ice cracking need not be considered. For frequencies above 40 Hz, events within 30 km range suffice to model within 1 dB of the total ambient noise. Fig. 6-27 shows that for frequencies above 40 Hz, only the events within 6 km range are required to model 50% (within 3 dB) of the total ambient noise. 118 Table 6-I. Mean, variance and skewness of the distribution of the value of m in the sinm6 model of source directivity as a function of range and frequency. Range (m) 0-2000 1300-2000 650-2000 430-2000 0-1300 0-650 0-430 Frequency (Hz) 96.7 48.4 96.7 145.1 48.4 96.7 145.1 Mean 0.87 0.95 1.04 1.05 0.68 0.68 0.70 Variance 0.21 0.14 0.15 0.18 0.24 0.23 0.44 119 Skew 0.68 -0.10 0.54 0.47 0.88 1.58 1.73 15 I I 10 I I I I I I I I I • • 1.• I • • • I • I I • • • • • I • • . • • •• • •• I. I • • • •i •• .1 I I I. — • c I • • • •• 5 Q I I • • ci) I • — • • c3) I I II • • I II II. I •I I I • I I •••• I • -5 I • •I I I I • •I I I II I I I •.I I • I • 10 -15 -15 I I I I I -10 I • I I I. • • I I I I I I I I -5 t I i i I I 0 5 Range (km) I I I I i i 10 Figure 6-1. Spatial distribution of all detected events about the vertical array which is centered at (0,0) km range. The number of events detected decreases with increasing range due to propagation loss but the lack of preferred locations or directions suggests a spatially uniform distribution of occurring events. 120 15 Hor-izor,ta 1 -DI \-, w L D U) U] Ui LW Q-I 0 Figure 6-2. Comparison of the vertical directivity of a pair of horizontal point forces with the sin 8 model for angles less than 45°. The solid line m shows the directivity of the horizontal point forces while the dashed line shows the best fit of the sin 8 model with the values of m = 0.89, 0.90, m 1.05 and 1.54 for 50, 100, 150 and 200 Hz respectively. 121 Hor-izcrta 1 U) Ui L D LI) (1) UI L u-I 50Hz 100 Hz 150 Hz 200 Hz 0 Figure 6-3. Comparison of the vertical directivity of a vertical point force with the sin 6 model for angles less than 450 The solid line shows the m directivity of the vertical point force while the dashed line shows the best fit of the sin 8 model with the values of m = 1.00, 1.00, 1.14 and 1.62 tm for 50, 100, 150 and 200 Hz respectively. 122 w rc -UI w C 3 U) U) w LL1) U-I 0 Figure 6-4. Vertical directivity of an ice-cracking event at 450 m range. The output is shown on a polar scale with each cross representing the measured pressure level in the direct arrival (after correction for propa gation loss) for a different hydrophone, or source angle. The dashed line corresponds to the best fit to a model of the form sin O with the value tm of m = 0.76. 123 Hor-izonta 1 m 13 Qi C D U) U) QJ L 0 Figure 6-5. Vertical directivity of an ice-cracking event at 300 m range which shows a small fluctuating pattern about the best fit to the model sinO. The value of m = 1.00. 124 Horizontal I-’ -U Qi C D 1J3 w w C 0 Figure 6-6. Vertical directivity of an ice-cracking event at 500 m range O model. The best fit with a value of m tm which does not fit the sin 0.58 is shown. 125 0.200 0.150 C 0 -Q (1) 0.100 > C’) C a) 0.050 0.000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 m Figure 6-7. Normalized distribution of the directivity index m (binwidth = 0.1) for all events within 2000 m range and with at least a 3 dB signal to noise ratio. Pressure levels were determined by averaging over a one octave band centered at 96 Hz. 126 0.200 0.150 C 0 -4- D -Q -4- (I) 0.100 > -4- C’) C ci) 0.050 0.000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 m Figure 6-8a. Normalized distribution of the directivity index m (binwidth = 0.1) for one octave frequency bands centered at 48 Hz, 96 Hz and 145 Hz. Distributions of m are given for all events less than approximately 40 wavelengths. 127 0.200 0.150 C 0 •1 D -o -e u) a 0.100 >% 4- C,) C a) a 0.050 0.000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 m Figure 6-8b. = 0.1) and 145 Hz. wavelengths Normalized distribution of the directivity index i-n (binwidth for one octave frequency bands centered at 48 Hz, 96 Hz Distributions of m are given for all events greater than 40 but less than 2000 m. 128 LI) -a’ \-, Qi L U) (I) Qi LU) 0 SD 100 ‘SD 200 0 Figure 6-9. Vertical directivity of an ice-cracking event at 300 m range showing little or no dependence on frequency. 129 m -D cv L D U) U) cv L U Figure 6-10. Vertical directivity of an ice—cracking event at 450 m range showing strong dependence on frequency. 130 Hor—jzor,ta Lfl .1 -U, w L D U) In Iii LW Q_I 60Hz 100 Hz 160 Hz 200 Hz 0 Figure 6-11. Vertical directivity of an ice-cracking event at 1150 m range showing some dependence on frequency. 131 Horizonta I Lfl I-” Q -Ut Qi C (I) (1) Qi Lu, u-I C Figure 6-12. Vertical directivity of an ice-cracking event at 140 m range showing an excess in pressure level of 1 dB 2 dB above the sinm8 model at a source angle of 600 65°. The value of m = 0.56. - - 132 D L P 30 sq 79 11’ 1)’ 102 2126 1S0 198 222 _____________________ 270 0.2 0. 1 0.3 0.6 0.q 0.6 Tima (sec) Figure 6-13. Synthetically generated time series for an ice-cracking event at 500 m range and 5.5 m depth in 6 m thick ice. Both the leaked longitu dinal plate wave (L) and direct arrival acoustic mode (D) are clearly seen across the entire array (at all depths) while the low frequency flexural wave (F) is seen following the direct arrival (at the 18 m depth. 133 0.35 - 0.6 sec) only for Hor-izorita 1 m -o Ui C D U) U) Ui C 0 Figure 6-14. Vertical directivity of a synthetically produced ice crack at 500 m range and 5.5 a depth in 6 m thick ice. The ice crack is modelled as a monopole source and the compressional absorption in the ice is 0.2 8 model has a value of m = tm dB/wavelength. The best fit to the sin 0.71. 134 -U Qi L 3 U) U) w L 0 Figure 6-15. Vertical directivity of a synthetically produced ice crack at 500 m range and 0.25 m depth in 6 m thick ice. The compressional 0.88. absorption in the ice is 0.2 dB/wavelength and the value of m 135 Hor i. zonta I U) ‘-4 ‘‘0 -UI w L U) U) QJ L ci’ C Figure 6-16. Vertical directivity of a synthetically produced ice crack at 500 m range and 0.25 m depth in 6 m thick ice. The compressional absorption in the ice is 2.0 dB/wavelength and the value of m = 0.99. 136 Hor—izorta I LI) ‘-4 r\o 1 -a w L D w (n w L U-I C Figure 6-17. Vertical directivity of a synthetically produced ice crack at 2000 m range and 0.25 m depth in 6 m thick ice. The compressional absorption in the ice is 2.0 dB/wavelength and the value of m = 1.10. The receivers were at a depth 4 times larger than in figures 6-13 to 6-16 so the same source angles would be used as for those figures. 137 210— N > 0 C ci) 110 U 10 0.0 — -- 1 1 0.2 ABOVE 110 105-110 100-105 95-100 90- 95 85- 90 80- 85 75- 80 70- 75 70 65 60- 65 BELOW 60 0.4 0.6 0.8 1.0 Time (sec) Figure 6-18. Received power spectrum of the hydrophone at 150 m depth as a function of time for the event shown in figure 3-8. 138 140 I 130 120 > -J G) C.) 110 0 C/) 100 I I I liii I I 10 liii 100 Frequency (Hz) Figure 6-19. Source spectral level of a typical ice-cracking event. 139 >.‘ _4Q 1 -a’nj -Q 0 C C 0 -I U w Ui U NL+SNR Race i ved Level Figure 6-20. Detection threshold function indicating the probability of detecting an event of a given received level. An event with a received level of approximately 2 dB 3 dB (SNR) above the noise level (NL) should always be detected, with a decreasing probability of detection for events with received power below this level. The rate of decrease is determined by the model for calculating the source level distribution. - 140 5 ci) 4 cDci) 4-•’cI) C> 0)•— > () III 3 0 .4- C 2 1 0 40 100 60 80 Received Level (dB//iPa /Hz) 2 120 Figure 6-2 1. Distribution of received levels of all detected events. Received level is the source level minus the propagation loss from the source to receiver. 141 I I I f I I I I I I ( I I I I I I I I 1 > CQ) 10-1 c—J 10-2 -4- >N WI io Ct5 lo z’ a- io I 100 I I I I 180 160 120 140 /Hz at 1 m) 2 Source Level (dB//tPa 200 Figure 6-22. Median number of events per square kilometer per minute Pa at 1 m source level interval versus source level. tHz 1 dB// / per 1 2 142 6 5 0 4.) C> > 0 III .4- C 1 0 40 120 100 60 80 a Hz) (dB//iP / Received Level 2 Figure 6-23. The measured and modeled normalized distributions of re ceived levels for all detected events over the range interval 0 1 km. The modeled distribution is calculated from Eq. 6.7 using the source level dis tribution determined previously and shown in Fig. 6-22. - 143 3.0 2.5 (l)W •1 C C > 2.0 0— CC C 0•’ cDa) - 1.5 1.0 - Qa 0.5 0.0 0 2 4 10 6 8 Range (km) 12 14 Figure 6-24. The measured and modeled normalized distributions of source ranges for all detected events. The modeled distribution is calculated from Eq. 6.8 using the source level distribution determined previously and shown in Fig. 6-22. 144 100 90 N z c’J a. 80 7j0 60 0 50 40 1 10 Frequency (Hz) 100 Figure 6-25. Modeled thermal ice cracking noise. The close range input noise (within 1 km of the array) is allowed to vary from -20 dB (lower curve) to +20 dB (upper curve) above the average input noise level with a 5 dB interval between individual curves. Compressional and shear wave absorptions in the ice of 10.0 and 15.0 dB/A respectively were used. 145 140 120 100 80 c,) C 60 40 20 0 1 10 100 Frequency (Hz) Figure 6-26. Required range to model 80% (within 1 dB) of the total noise produced from all thermal ice cracking events out to a range of 200 km. Compressional and shear wave absorptions in the ice of 10.0 and 15.0 dB/) respectively were used with the close range input noise (within 1 km) varying from -20 dB (upper curve) to +20 dB (lower curve) above the average input noise level with a 5 dB interval between individual curves. 146 60 50 40 -‘ ‘30 c,) 20 10 0 1 10 Frequency (Hz) 100 Figure 6-27. Required range to model 50% (within 3 dB) of the total noise produced from all thermal ice cracking events out to a range of 200 km. Compressional and shear wave absorptions in the ice of 10.0 and 15.0 dB/A respectively were used with the close range input noise (within 1 km) varying from -20 dB (upper curve) to +20 dB (lower curve) above the average input noise level with a 5 dB interval between individual curves. 147 Chapter 7 Modeled Ambient Noise A comparison of the two component noise model with the four classes of measured real ambient noise spectra is shown in Figs. 7-la to 7-ld. The sound speed profile shown in Fig. 3-2 along with the measured and estimated bottom and ice parameters from Table 5-I were used to determine propagation loss for the model with the exception that the compressional and shear wave absorptions used in the ice were five times higher (10.0 and 15.0 dB/\ respectively) in an effort to better compensate for the effects of under-ice roughness (as outlined in chapters 5.4 and 6.4). These figures show that the measured ambient noise spectra can be reproduced by a single active pressure ridging event, along with a distribution of thermal ice cracking events. For frequencies below 40 Hz, the ambient noise spectrum may be determined by the range and level of the strongest received active pressure ridge. For frequencies above 40 Hz, the ambient noise spectrum is determined by thermal ice cracking, with overall levels and spectral shape dependent on the intensity of ice cracking and the relative strength of local to average events. For purposes of our model, local events are considered to be within 1 km of the hydrophone. It was also noted that all of the data files used in classes 1 and 2 for real data occurred during a 66 hour span within the middle of the experiment while all except one of the data files used in classes 3 and 4 occurred before or after this time. This separation suggests that active pressure ridging was occurring at approximately 40 km range during the entire 100 hours of ambient noise measurements and that for a 148 66 hour span of time in the middle of the experiment, a much stronger active pressure ridge built itself at a range of approximately 70 km. Although the stronger and more distant active pressure ridge appears to be associated with times of weaker thermal ice cracking, no correlation is assumed due to the short time sample and the fact that the two source mechanisms are controlled by different environmental conditions. Also, although the frequency of the infrasonic peak in the ambient noise spectrum is related to the range of the strongest received active pressure ridge, estimating its range is likely to be inaccurate because of possible differences in active pressure ridge spectra and the inadequacies of current propagation loss modeling for the Arctic. All the events as shown in Fig. 3-7 also occurred only during the middle 66 hours at which time a strong active pressure ridge occurred at a range of approximately 70 km. For frequencies below 40 Hz, the spectra of these events were found to have similar shapes with higher overall levels as the ambient noise spectra at these times. This observation suggests that these events originate from the active pressure ridge at 70 km range and may correspond to the several second long bursts of intense energy (see Fig. 3-9) found in active pressure ridges. Finally, it can be noticed from Figs. 7-la to 7-ic that the modeled ambient noise spectra have negative slope below 3 Hz while the measured spectra have a positive slope. The reason for this discrepancy is unknown but may be due to the assumed spectral shape of active pressure ridging which was based on measurements from a single event using equipment which was not very reliable below 4 Hz. 149 100 90 N C\i ct5 0 :± -o > -J Cl) 60 0 z 50 40 1 10 Frequency (Hz) 100 Figure 7-la. Comparison of two component noise model (solid) to aver age ambient noise (dash) and standard deviation (dash-dot) of real noise. Modeled ridge levels are relative to that shown in Fig. 5-1. Thermal ice cracking levels are relative to the average input energy determined from Fig. 6-22 with local levels applied above this but only for ranges within I km of the hydrophone. Modeled noise for ridge of level +3 dB at 70 km range with thermal ice cracking at -8.2 dB and local ice cracking at -3 dB; versus class 1 real data from Fig. 4-la. 150 100 90 N c”J 0 a) > a) -J G) U) 60 0 z 50 40 1 10 Frequency (Hz) 100 Figure 7-lb. Comparison of two component noise model (solid) to aver age ambient noise (dash) and standard deviation (dash-dot) of real noise. Modeled ridge levels are relative to that shown in Fig. 5-1. Thermal ice cracking levels are relative to the average input energy determined from Fig. 6-22 with local levels applied above this but only for ranges within 1 km of the hydrophone. Modeled noise for ridge of level +3 dB at 70 km range with thermal ice cracking at +0.4 dB and local ice cracking at +0 dB; versus class 2 real data from Fig. 4-lb. 151 100 90 N c’.j C” 0 cJ) > -J Cl) 60 0 z 50 40 1 10 Frequency (Hz) 100 Figure 7-ic. Comparison of two component noise model (solid) to aver age ambient noise (dash) and standard deviation (dash-dot) of real noise. Modeled ridge levels are relative to that shown in Fig. 5-i. Thermal ice cracking levels are relative to the average input energy determined from Fig. 6-22 with local levels applied above this but only for ranges within 1 km of the hydrophone. Modeled noise for ridge of level -5 dB at 40 km range with thermal ice cracking at -3.0 dB and local ice cracking at +0 dB; versus class 3 real data from Fig. 4-ic. 152 100 90 N cJ U Q) > -J Cl) 60 0 z 50 40i 10 Frequency (Hz) 100 Figure 7-id. Comparison of two component noise model (solid) to aver age ambient noise (dash) and standard deviation (dash-dot) of real noise. Modeled ridge levels are relative to that shown in Fig. 5-1. Thermal ice cracking levels are relative to the average input energy determined from Fig. 6-22 with local levels applied above this but only for ranges within 1 km of the hydrophone. Modeled noise for ridge of level -5 dB at 40 km range with thermal ice cracking at +5.3 dB and local ice cracking at +4 dB; versus class 4 real data from Fig. 4-id. 153 Chapter 8 Summary This thesis has shown that the spring-time Arctic ambient noise spectra mea sured in the pack-ice over the frequency band 2 - 200 Hz can be modeled by a com bination of active pressure ridging and thermal ice cracking. A single or few active pressure ridges at ranges of tens of kilometers produces the low frequency end of the ambient noise spectra up to approximately 40 Hz while a distribution of thermal icecracking events produces the higher frequency end. Over 50% of the ambient noise produced by thermal ice cracking is generated by events occurring within 6 km of the hydrophone while over 80% is generated by events occurring within 30 km of the hydrophone. In developing the two-component noise model of low frequency ambient noise, several characteristics of both thermal ice cracking and active pressure ridging were determined. These are outlined in the following paragraphs. It was found that the energy measured in the water from events occurring in the ice was dominated by the acoustic source with contributions from leaked plate waves falling off rapidly away from the source due to scattering and absorption in the ice. It was also found that the measured vertical source pressure directivity of individual ice cracking events approximated a dipole radiation pattern for events at ranges beyond 40 wavelengths. For shorter ranges, the radiation pattern often became either less directional or more complex. The directivity is also expected to become more complex 154 at higher frequencies. These results could be reproduced using a simple monopole source in the ice but are also consistent with either a pair of horizontal point forces or a vertical point force in the ice. Superimposed on this radiation pattern is a 3 dB increase in pressure level near 600. Using plate wave theory, this increase in pressure level may be explained as the leaked longitudinal plate wave coinciding with the acoustic mode at these source angles. Using plate vibration theory for a thin plate, this increase in pressure level may be explained by the plate vibration impedance vanishing at this angle. The spatial distribution of thermal ice-cracking events measured in the rough Arctic pack ice was found to be consistent with a large-scale spatially isotropic dis tribution of noise sources. The distribution of source intensity levels measured from /Hz at 1 m decreases with increasing source level as 10 2 110 to 180 dB//Pa with a Pa at 1 m and a 2 i 1 dB// Hz 0.08 for source levels below 160 / 0.12 for source levels above. The shape of this source level distribution curve agrees with the measured distribution of earthquake magnitudes and this result is believed to be due to the self similarity nature of the slip-stick process involved in both earthquake and ice crack propagation. A median of four events per square kilometer per minute have /Hz at 1 m. The mean 2 source levels within a 1 dB band centered at 110 dB//Pa and maximum number of events occurring at any source level are approximately 2.1 and 10.0 times the median. Evidence was also presented in this thesis that the infrasonic peak found in the Arctic ambient noise is due to the band-pass filtering effect of the propagation loss on the noise generated by ridge building. A ridge building event was shown to have a power spectrum which increases with decreasing frequency. However, the propagation 155 loss was shown to have a minimum near 30 Hz and increase dramatically below 20 Hz due to leakage of energy out of the near surface sound speed channel. Combining the source spectrum and propagation loss produces a spectrum at longer ranges (beyond 40 km) which has a peak near 10 Hz. This explanation is supported by the observed power spectra of ice cracking events as a function of range and by the occurrence of several distant events in the data which have time scales and power spectra consistent with both ridge building and ambient noise. Finally, it was shown that it is possible to use local thermal ice-cracking events to measure the reflectivity of the seabed as a function of reflection angle. This method circumvents the difficulties and expense of introducing artificial sound sources through the thick Arctic pack ice. 156 References 1. A.R.Milne and J.H.Ganton, “Ambient noise under Arctic sea ice,” J.Acoust. Soc.Am., 36, 855-863 (1964). 2. A.R.Milne, “Thermal tension cracking in sea ice: A source of underice noise,” J.Geophys.Res., 77, 2177-2192 (1972). 3. R.S.Pritchard, “Arctic Ocean background noise caused by ridging of sea ice,” J.Acoust.Soc.Am., 75, 419-427 (1984). 4. B.M.Buck and J.H.Wilson, “Nearfield noise measurements from an Arctic pres sure ridge,” J.Acoust.Soc.Am., 80, 256-264 (1986). 5. F.Press and M.Ewing, “Propagation of elastic waves in a floating ice sheet,” Trans.Am.Geophy.Union., 32, 673-678, (1951). 6. Y.Xie and D.M.Farmer, “The sound of ice break-up and floe interaction,” J.Acoust.Soc.Am., 91, 1423-1428, (1992). 7. B.E.Miller and H.Schmidt, “Observation and inversion of seismo-acoustic waves in a complex arctic ice environment,” J.Acoust.Soc.Am., 89, 1668-1679, (1991). 8. P.J.Stein, “Acoustic monopole in a floating ice plate,” Doctoral thesis, De partment of Ocean Engineering, MIT., Cambridge, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, (1986). 9. I.A.Viktorov, Rayleigh and Lamb Waves, Plenum Press, New York, 1967. 10. Y.Xie, “An acoustic study of the properties and behavior of sea ice,” Doctoral 157 thesis, Department of Oceanography, University of British Columbia, Vancou ver, British Columbia, Canada, (1991). 11. Y.Xie and D.M.Farmer, “Acoustical radiation from thermally stressed sea ice,” J.Acoust.Soc.Am., 89, 2215-2231, (1991). 12. W.A.Kuperman and H.Schmidt, “Rough surface elastic wave scattering in a horizontally stratified ocean,” J.Acoust.Soc.Am., 79, 1767-1777, (1986). 13. H.Schmidt, “SAFARI, Seismo-Acoustic Fast field Algorithm for Range Indepen dent environments, User’s guide,” Rep. SR-113, SACLANT Undersea Research Center, San Bartolomeo, Italy, 1988. 14. R.H.Bourke and A.S.Mcbaren, “Contour mapping of Arctic Basin ice draft and roughness parameters,” J.Geophys.Res., 97, 17,715-17,728, (1992). 15. L.A.Mayer and J.Marsters, “Measurements of geophysical properties of Arctic sediment cores,” DREP Contractors Report 89-19, Defence Research Establish ment Pacific, Victoria, B.C., Canada, (1989). 16. J.P.Todoeschuck, J.M.Ozard and J.M.Thorleifson, “Refraction and reflection experiments with a vertical array of hydrophones in the Lincoln Sea,” EOS, 69, 1320 (1988). 17. D.M.F.Chapman, “Surface-generated noise in shallow water: a model,” Proc. I.O.A., 9 (4), 1-11, (1987). 18. G.H.Brooke and J.M.Ozard, “In-situ measurement of elastic properties of sea ice,” in Underwater Acoustic Data Processing, Kluwer Academic Publishers, 113-118, 1989. 158 19. P.Zakarauskas, C.J.Parfitt and J.M.Thorleifson, “Statistiques de bruits am biants transitoires dans 1’Arctique,” in Proceedings of the First French Confer ence on Acoustics, Lyon, France, April 1990, Edited by P.Filippi and M.Zakharia, (Les editions de Physique, Les Ulis Cedex, France), 33-736. 7 pp. 20. P.Zakarauskas, C.J.Parfitt and J.M.Thorleifson, “Automatic extraction of spring time Arctic ambient noise transients,” J.Acoust.Soc.Am., 90, 470-474 (1991). 21. J.H.Ganton and A.R.Milne, “Temperature-and wind-dependent ambient noise under midwinter pack ice,” J.Acoust.Soc.Am., 38, 406-411 (1965). 22. A.R.Milne, J.H.Ganton and D.J.McMillin, “Ambient noise under sea ice and further measurements of wind and temperature dependence,” J.Acoust.Soc. Am., 41, 525-528 (1967). 23. D.M.Farmer and Y.Xie, “The sound generated by propagating cracks in sea ice,” J.Acoust.Soc.Am., 85, 1489-1500 (1989). 24. I.Dyer, “Speculations of the origin of low frequency Arctic Ocean noise,” in Sea Surface Sound, ed: B.R.Kerman, Kluwer Academic Publishers, 1988. 25. P.J.Stein, “Interpretation of a few ice event transients,” J.Acoust.Soc.Am., 83, 617-622 (1988). 26. N.C.Makris and I.Dyer, “Environmental correlates of pack ice noise,” J.Acoust.Soc.Am., 79, 1434-1440 (1986). 27. B.M.Buck, “Arctic acoustic transmission loss and ambient noise,” in Arctic Drifting Stations, ed: J.E.Sater, The Arctic Institute of North America, 1968. 159 28. A.S.Thorndike and R.Colony, “Sea ice motion in response to geostrophic winds,” J.Geophys.Res., 87, 5845-5852 (1982). 29. R.R.Parmerter and M.D.Coon, “Model of pressure ridge formation in sea ice,” J.Geophys.Res., 77, 6565-6575, (1972). 30. A.S.Mcbaren, “Analysis of the under-ice topography in the Arctic Basin as recorded by the USS Nautilus during August 1958,” J. Arctic Institute of North America, 41, 117-126, (1988). 31. O.I.Diachok, “Effects of sea-ice ridges on sound propagation in the Arctic Ocean,” J.Acoust.Soc.Am., 59, 1110-1120, (1976). 32. R.J.Tjrick, Principles of Underwater Sound, McGraw-Hill Book Company, New York, 1983. 33. A.R.Milne, “Sound propagation and ambient noise under sea ice,” in Underwa ter Acoustics, Vol 2, ed: V.M.Albers, Plenum Press, New York, 1967. 34. M.J.Sheehy and R.Halley, “Measurement of the attenuation of low-frequency underwater sound,” J.Acoust.Soc.Am., 29, 464-469 (1957). 35. R.J.Urick, “Low-frequency sound attenuation in the deep ocean,” J.Acoust. Soc.Am., 35, 1413-1422 (1963). 36. A.C.Kibblewhite and R.N.Denham, “Long-range sound propagation in the South Tasman Sea,” J.Acoust.Soc.Am., 41, 401-411 (1966). 37. J.E.Burke and V.Twersky, “Scattering and reflection by elliptically striated sur faces,” J.Acoust.Soc.Am., 40, 883-895, (1966). 160 38. E.Livingston and O.Diachok, “Estimation of average under-ice reflection ampli tudes and phases using matched-field processing,” J.Acoust.Soc.Am., 86, 19091919, (1989). 39. R.J.Nielsen et.al., “TRISTEN/FRAM IV Arctic ambient noise measurements”, NTJSC Technical Document 7133, Naval Underwater Systems Center, New Lon don, Connecticut, 1984. 40. A.J.Langley, “Acoustic emission from the Arctic ice sheet,” J.Acoust.Soc.Am., 85, 692-701 (1989). 41. J.S.Kim, “Radiation from directional seismic sources in laterally stratified media with application to Arctic ice cracking noise,” Doctoral thesis, Department of Ocean Engineering, MIT., Cambridge, Massachusetts, 1989. 42. I.Dyer, “Source mechanisms for Arctic Ocean ambient noise,” in Sea Surface Sound (2), Natural Physical Sources of Underwater Sound, ed: B.R.Kerman, Kluwer Academic Publishers, 1993. 43. A.R.Milne, “Statistical description of noise under shore-fast sea ice in winter,” J.Acoust.Soc.Am., 39, 1174-1182 (1966). 44. M.Townsend-Manning, “Analysis of central Arctic noise events,” Master’s The sis, Department of Ocean Engineering, MIT., Cambridge, Massachusetts, 1987. 45. L.M.Brekhovskikh and Y.Lysanov, Fundamentals of Ocean Acoustics, Springer series in electrophysics, New York, 1982. 46. R.M.Hamson, “The theoretical responses of vertical and horizontal line arrays to wind-induced noise in shallow water,” J.Acoust.Soc.Am., 78, 1702-1712, (1985). 161 47. P.Zakarauskas and J.M.Thorleifson, “Directionality of ice cracking events,” J.Acoust.Soc.Am., 89, 722-734, (1991). 48. C.R.Greene and B.M.Buck, “The influence of atmospheric pressure gradient on under-ice ambient noise,” J.Underwater Acoust., 28, 529-538, (1978). 49. B.Gutenberg and C.F.Richter, Seismicity of the earth arid associated phenom ena, Princeton University Press, Princeton, New Jersey, 1954. 50. B.B.Mandelbrot, The Fractal Geometry of Nature, W.H.Freeman, New York, 1982. 51. K.Aki, “A probabilistic synthesis of precursory phenomena,” in Earthquake Pre diction: An International Review, eds: D.W.Simpson and P.G.Richards, Amer ican Geophysical Union, Washington, D.C., 1981. 52. J.B.Rundle, “Derivation of the complete Gutenburg-Richter magnitude- frequency relations using the principle of scale-invariance,” J.Geophys.Res., 94, 12,337-12,342 (1989). 53. Y.Y.Kagan and L.Knopoff, “The spatial distribution of earthquakes: The twopoint correlation function,” Geophys.J.R.Astron.Soc., 62, 303-320 (1980). 54. Y.Y.Kagan and L.Knopoff, “Stochastic synthesis of earthquake catalogs,” J.Geophys.Res., 86, 2853-2862 (1981). 55. Y.Ogata, “Statistical models for earthquake occurrences and residual analysis for point process,” J.Am.Stat.Assoc., 83, 9-27 (1988). 56. J.M.Carlson and J.S.Langer, “Mechanical model of an earthquake fault,” Phys.Rev.A, 40, 6470-6484 (1989). 162 57. S.R.Brown, C.H.Scholz and J.B.Rundle, “A simplified spring-block model of earthquakes,” Geophys.Res.Lett., 18, 215-218 (1991). 58. M.Matsuzaki and H.Takayasu, “Fractal features of the earthquake phenomenon and a simple mechanical model,” J.Geophys.Res., 96, 19,925-19,931 (1991). 59. Y.P.Doronin and D.E.Kheisin, Sea Ice, Amerind Publishing Co., New Delhi, India, 1977. 60. M.J.Buckingham and S.A.S.Jones, “A new shallow-ocean technique for deter mining the critical angle of the seabed from the vertical directionality of the ambient noise in the water column,” J.Acoust.Soc.Am., 81, 938-946 (1987). 163 Appendix A Seabed Reflectivity Function Detailed knowledge of the seabed properties is often needed in order to pre dict propagation characteristics in the ocean. Amongst the most useful parameters are the compressional and shear sound speeds. These two parameters are sufficient to characterize the reflection as a function of angle if the bottom is flat and no layering is present. Layering or roughness of the bottom may modify the reflection function in a frequency-dependent manner. The techniques traditionally used to extract the seabed properties are: laboratory measurement of physical parameters of coring or grab samples, and in-situ acoustic reflection or refraction experiments. Analysis of samples provides unambiguous and precise values of physical properties of the sub strata. Reflection and refraction measurements provide information about the acous tic effects of layering and roughness. Sources for reflection experiments are explosive charges, although Buckingham and Jones ° have developed a technique in which the 6 inter-sensor coherence of the ambient noise in shallow water is used to determine the critical angle of the seabed. Unfortunately, the environmental model Buckingham and Jones used does not include shear, and the difference in loss between the regions below and above critical angle must be large for the technique to be used successfully. The concept of making use of the ambient noise as an acoustic source is appealing, as it eliminates the time-consuming task of deploying sources. This is a problem especially in the Arctic environment, where one must cut through the thick (3 - 7 m) Arctic pack ice in order to drop the charges. The harsh weather conditions in 164 the Arctic often makes it difficult to operate driffing equipment. Thus, a technique which requires only one hole in the ice for deployment of the receiving array may help increase the possible number of sites surveyed. In this Appendix, a technique is described for measuring the reflection coefficient of the Arctic seabed as a function of angle with a single vertical array of hydrophones. Noise from naturally occurring jce cracking was used as the acoustic source. A com plication arises compared to the use of charges as sources, since ice cracking noise has some directivity. We parametrize the source directivity for every crack. The relia bility of the method depends on the goodness of fit of the parametrization employed to the reflectivity function. That parametrization was found in chapter six to be adequate. The range of the source is first determined by comparing the difference in arrival times across the array with those predicted by a ray-based model using both the direct arrival and the multiple reflections from the seabed and under-ice surface. Then the source directivity is determined using the direct path arrival only. The expected pres sure level at angles corresponding to the bottom path is extrapolated using the source directivity index thus calculated. It is then straightforward to compute the bottom reflection coefficient as a function of grazing angle by using various combinations of source locations and hydrophones from different depths. For a given ice-cracking event, the vertical directivity of the pressure level of the event is first parametrized as: P(&) = p jn 9 m (A.l) as shown in chapter five. P 0 is the source pressure level (in dB// iPa/Hz at im) and 1 165 P(8) is the modeled radiated pressure level in the direct arrival at source angle 8, normalized back to 1 m. The continuous parameters m and P 0 are found for each event by minimizing the squared difference (Pd — 2 where Pd is the measured pressure P) level received in the direct arrival. Over 80% of the 160 transients used to determine source directivity were found to closely fit the above parametrization. Those events that were found to fit the model are used to extract the reflectivity function from the seabed. The reflectivity function is found by comparing the pressure levels Pr measured in the bottom-reflected arrivals at each hydrophone with those predicted by extrapolating from Eq. A.i using the parameters m and P 0 extracted from the direct arrivals (Fig. A-i). The difference between the two is assumed to be the loss due to reflection at the seabed. The arrival at each hydrophone corresponds to a different bottom scattering angle which is calculated using the ray propagation model mentioned above. Thus, the reflectivity can be plotted against the bottom grazing angle as shown in Fig. A-2. The validity of the extrapolation of the directivity measured at low angles to higher angles was tested using direct arrivals from events close enough to span both low and high angles at the array. The test was performed the following way. All events that met the following conditions were selected from the database: 1 of 3 dB S/N; 2 - Having at least five points arriving below one point arriving above 430• - 300; Having a minimum 3 - Having at least Thirty events were found to fit these criteria. Only the points arriving at angles below 30° were used for the fitting of the parameters m and . The pressure level at the other hydrophones was estimated by extrapolation of 0 P Eq. A.1. The difference between the measured and the extrapolated pressure levels is shown in Fig. A-3. The difference is seen to cluster around 0 dB, except for a few 166 individual events. This result is in contrast with the ratio of Fig. A-2 for reflected arrivals, which exhibits a definite fall off above 400. Fig. A-3 tells us that results from individual events are not reliable, but if a large number of events are used, with much overlap in their angle coverage, noise and errors in fit are averaged out. The bottom reflectivity function measured for all events, using the method de scribed, is shown in Fig. A-2 as a scatter diagram. Despite the large scatter in the reflectivity measurement, one can discern that the critical angle, defined as the an gle at which the reflectivity begins to drop, occurs somewhere between 35° and 40° grazing angle. In order to make the extracted directivity function more explicit, the measured values are averaged using a window 1.5° wide from 30° to 45° and 3° wide elsewhere. The reflectivity function thus averaged is displayed in Fig. A-4 along with the reflectivity calculated using a single bottom layer with three different compres sional sound speeds. The critical angle is now seen to occur near 350 and corresponds to a bottom compressional sound speed of approximately 1800 m/sec with minimum and maximum compressional speeds of approximately 1750 m/sec and 1900 m/sec respectively. A bottom shear speed of 300 m/sec with compressional and shear wave absorptions of 0.5 dB/.\ and 0.25 dB/) were used. Increasing the absorption in the bottom produces a smoother and less abrupt drop in the reflectivity as the critical angle is approached. The large uncertainty in the measurements however makes es timating the bottom absorptions very difficult and levels up to six times larger than those specified above were found to fit within the uncertainty. Increasing the shear speed results in a quicker drop in reflectivity past critical angle and a very large range of shear speeds was found to fit within the uncertainty. The reasons for the 167 large uncertainty in the measurements are discussed later. The estimated compressional sound speed in the bottom of 1800 m/sec with a minimum of 1750 m/sec and maximum of 1900 m/sec can be compared with the ye locity measurements of 1794 and 1683 rn/sec obtained from two bottom grab samples and a measurement of 1980 + 18 rn/sec obtained from a seismic refraction survey. The value extracted in the present study compares rather well with those obtained from the bottom grab samples. These grab samples were collected directly below the midpoint of the horizontal array. It does not agree very well with that obtained from the seismic refraction survey. The reason for this is likely due to the lower frequency used in the refraction survey. The seismic refraction survey used a 60 lb charge det onated at 341 m depth resulting in a peak bubble pulse frequency of approximately 21 Hz. The arrival times of the head wave from a shot at a range of 2686 m was then measured at 8 of the hydrophones in the vertical array using a sampling rate of 2064 samples per second. The lower frequency of the seismic refraction survey results in a deeper propagation path, and higher sound speeds, than those measured using the ice-cracking events as sources. A rise in the reflectivity function around 60° is also very noticeable. This rise is not actually due to an increased reflectivity at this angle, but is an artifact due to the use of an incomplete source directivity function (Eq. A.1) which does not include the leaky plate wave radiating around 60° from the ice at the site. This increase in level was also seen in the directivity measurements of thermal ice cracking obtained in chapter six. If the source’s pressure levels at high angles are higher than those predicted by the model source function of Eq. A.1, the difference between the measured and predicted sound pressure levels will be greater than it should, and will 168 show up in the reflectivity function. The extra radiated pressure level due to the plate wave may now be quantified. It corresponds to a pressure level of approximately 3 dB above the sin tm 6 model with an approximately Gaussian distribution centered on 600 and a standard deviation of approximately 50 The radiation angle L 6 of a leaky plate wave into the water below corresponds to the critical angle between the two media. A grazing angle of 60° at the water-seabed interface corresponds to a source angle of 60.5°. The leaky ice plate wave speed is thus found to be 2914 m/sec. The value for the leaky plate wave speed can be compared to a direct measurement made at the site using a hammer and geophones. The speed thus obtained was 3050 + 100 rn/sec. The error interval for the value obtained from the present study overlaps with that obtained directly using the hammer and geophones. Several factors contribute to errors in both the grazing angle and the reflectivity value. Since the duration of each arrival is of finite length, it happens in some cases that the direct and bottom-bounce partially overlap. A boundary is nonetheless placed between the two arrivals, and therefore some of the direct arrival’s pressure levels will be assigned to the bottom-bounce arrival. The pressure levels for the direct arrival are underestimated, and that for the bottom-bounce overestimated. This error tends to happen for only a few channels toward the bottom of the array for distant events, where the inter-arrival delay is at a minimum. The main source of scatter in Fig. A-2 is due to misfit of the value of the directivity index m. A slight misfit im the value of m at the low angles corresponding to direct arrivals leads to a rather large difference in the extrapolated pressure levels at the larger angles corresponding to bottom-bounce arrivals. This error in extrapolation 169 of the expected bottom-bounce pressure levels leads to a systematic error in the reflectivity function for one given event. To make this result evident, the reflectivity function for a few events for the arrival at each hydrophone is plotted in Fig. A-5, where the arrivals corresponding to one single event are joined together by a solid line. One may now notice that although there can be a large difference in the reflectivity value corresponding to different events arriving at the same angle, the scatter around the mean for a single event is much smaller. The scatter from the multiple events results in a large uncertainty in the reflectivity at a given angle making the estimation of bottom properties other than the compressional sound speed very difficult. The residual scatter within a single event is thought to correspond to the irre ducible error in measurement due to the relatively low signal-to-noise ratio, of be tween 3 and 10 dB and the short time length of the direct or bottom reflected arrival. This scatter becomes larger beyond the bottom critical angle for which signal to noise ratios are even lower. Moreover, since the same estimate of the noise level is used for all channels, small fluctuations of the ambient noise level with depth or inequali ties in absolute calibration of each channel would lead to further random inequalities between channels. The estimate of arrival angles depends entirely on estimating time delays between different channels for a given arrival. If the time delays can be measured to an accuracy of one sampling point for a given channel, then the accumulated error across the array leads to an error in angle measurements of the order of 2.3° corresponding to an error in the bottom compressional sound speed of 45 rn/sec. The study of source directivity through the measurement of the pressure levels 170 in the direct arrivals yielded very little data on the relative strength and width of the leaky plate wave contribution. This lack of data is because very few events occur close enough to the array for the direct arrival to occur at 600 or more. Better statistics are available through the present study, since it corresponds to a much larger number of arrivals: because bottom-bounce events with a source angle of around 60° arriving at the array lay on a much larger circle around the array, there is a greater surface area providing suitable cracking events. In this study, the leaky plate wave contribution shows up as an artifact in the reflectivity function, which would not happen if its contribution was included in the source model instead. Inclusion of the plate wave would be desirable, since one wants the reflectivity function derived through this method to represent the true reflectivity function of the seabed. A new source directivity model, as proposed in chapter six is the sum of the sinmO model contribution and the leaky plate wave contribution represented by a Normal function, P(8) = 0 [sinmO + P c exp [(6 ]J 2 6L) (A.2) where C is a constant giving the relative contributions of the acoustic mode and the leaked longitudinal plate wave, and O. and w are the critical angle and beamwidth of the leaked longitudinal plate wave respectively. For our data, C and w 1.0, 60°, 5°. It is not known whether the radiated pressure level and radiating angle of the plate wave will be the same in other ice cover conditions. On the encouraging side, Brooke and Ozard 18 reported that the leaky plate wave speed was almost the same ( 2950 m/sec) in 2.5 m thick new ice, as it was at the present much thicker ice. It has been shown in this Appendix that it is possible to use local ice cracking events and a vertical array of hydrophones to measure the reflectivity of the seabed as 171 a function of reflection angle. Although a large uncertainty exists in the reflectivity at a given angle, the critical angle at the seabed interface is easily extracted from the reflectivity function, and can be used to determine the sediment sound speed. The steps involved in using this method are: detect and isolate ice cracking events, determine the range of each event using a ray tracing model, separate the direct arrival and the bottom-bounce arrival from each other and higher order arrivals, subtract the noise contained in an interval of time before the events, fit the pressure level in the direct arrival at each hydrophone to the source directivity model in order to extract the parameter m, and thus extrapolate the pressure level to that expected at angles corresponding to bottom-bounce paths. The difference between the expected and the measured bottom-bounce pressure level is assumed to be due to reflection loss at the seabed. The method is fairly time-consuming, and it may take several days for a trained operator to extract the full directivity function at one site. The amount of recording needed depends entirely on the frequency of suitable ice cracking events at the time of recording. During some periods, no ice cracking is taking place at all, and the ambient noise is totally stationary. At some other times, one event occurs every few seconds, and a few minutes of data may be all that is needed to make the reflectivity measurements. 172 Horazonta 1 -o Qi L J U) U) w L 0 Figure A-i. Polar plot of the pressure level for a single event arriving at the array along two paths for the octave band centered at 96 Hz, corrected for spherical spreading loss. The diamonds indicate the pres sure level measured at each hydrophone from the direct arrivals, and the crosses that of the bottom-reflected arrivals. The drop in pressure level for grazing angles greater than about 400 corresponds to the passage through the critical angle. 173 qs ) 9 1 (da 3 Rn Figure A-2. Scatter plot of the pressure level ratio between the bottomreflected arrivals and that extrapolated from the direct arrival, using a sinmO function corrected for spherical spreading losses, as a function of grazing angle at the bottom. Each cross indicates the pressure level ratio at one hydrophone for one event. 174 3D 36 qs SO 66 60 ) 9 a (da An l 9 Figure A-3. Sound pressure ratio between the measured direct arrivals 6 m 5111 di above 300 and that extrapolated from angles below 30°, using a rectivity function corrected for the spherical spreading losses, as a function of source angle, for all 30 events that fit the criteria of pg. 166. The sound pressure ratios as calculated for a given event for different hydrophones are linked up with a solid line. 175 2 0 . -2 > -8 -10 0 20 60 40 Angle (deg) 80 Figure A-4. Averaged plus and minus one-standard-deviation (solid lines) pressure level ratios between the bottom-reflected arrivals, and that extrap olated from the direct arrival, using a sin 8 directivity function corrected tm for the spherical spreading losses, as a function of grazing angle at the bot tom. Dashed lines show the bottom reflectivity calculated using bottom compressional sound speeds of 1750 m/sec (lower), 1800 rn/sec (middle) and 1900 rn/sec (upper). 176 -a >‘ > Ii 0) 0) ) 9 An l 9 a (da Figure A-5. Sound pressure ratio between the bottom-reflected arrivals and that extrapolated from the direct arrival, using a sin O directivity tm function corrected for the spherical spreading losses, as a function of grazing angle at the bottom, for a few individual events. The sound pressure ratios as calculated for a given event for different hydrophones are linked up with a solid line. 177
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A two-component Arctic ambient noise model Greening, Michael Victor 1994
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Title | A two-component Arctic ambient noise model |
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Greening, Michael Victor |
Date Issued | 1994 |
Description | Short term Arctic ambient noise spectra over the frequency band 2 - 200 Hz are presented along with a two component noise model capable of reproducing these spectra. The model is based on the measured source spectrum and the spatial, temporal and source level distributions of both active pressure ridging and thermal ice cracking. Modeled ambient noise levels are determined by summing the input energy of the distributions of ice cracking and pressure ridging events and removing the propagation loss. Measurements were obtained on a 22-element vertical array along with a 7-element horizontal array deployed beneath the Arctic pack ice in 420 meters of water. Over 900 thermal ice-cracking events were detected in approximately 2 hours of data col lected over several days during April 1988. The source directivity for events beyond 40 wavelengths range was found to be accurately represented by a dipole with an approximate 3 dB increase above the dipole directivity pattern near 60° - 65° caused by the leaked longitudinal plate wave. A technique for measuring the bottom reflectivity function by correcting the bottom reflection of a thermal ice crack for the measured directivity is presented. The spatial distribution of thermal ice-cracking events is consistent with a uniform distribution. Source levels were measured from 110 to 180 dB //μPa²/ Hz at 1 m with the distribution of all events approximating a linearly decreasing function on a log-dB scale of the number of events versus source level. Near the end of the data collection period, measurements from a nearby active pressure ridge were obtained. Evidence is presented that the infrasonic peak observed near 10 Hz in Arctic ambient noise spectra may result from a frequency dependent propagation loss acting on the source spectrum of pressure ridging. Both modeled and measured ambient noise spectra show that ice cracking may dominate the spring-time ambient noise to frequencies as low 40 Hz. Below 40 Hz, the ambient noise is dominated by a single or few active pressure ridges at ranges of tens of kilometers. Above 40 Hz, the ambient noise is dominated by a large distribution of thermal ice-cracking events with over 50% of the total noise level produced by events within 6 km range and over 80% produced by events within 30 km range. |
Extent | 2553620 bytes |
Genre |
Thesis/Dissertation |
Type |
Text |
File Format | application/pdf |
Language | eng |
Date Available | 2009-04-08 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0053203 |
URI | http://hdl.handle.net/2429/6916 |
Degree |
Doctor of Philosophy - PhD |
Program |
Oceanography |
Affiliation |
Science, Faculty of Earth, Ocean and Atmospheric Sciences, Department of |
Degree Grantor | University of British Columbia |
Graduation Date | 1994-05 |
Campus |
UBCV |
Scholarly Level | Graduate |
Aggregated Source Repository | DSpace |
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