ENHANCING ACTIVE AND PASSIVE REMOTE SENSING IN THE OCEAN USING BROADBAND ACOUSTIC TRANSMISSIONS AND COHERENT HYDROPHONE ARRAYS

Transcription

1 ENHANCING ACTIVE AND PASSIVE REMOTE SENSING IN THE OCEAN USING BROADBAND ACOUSTIC TRANSMISSIONS AND COHERENT HYDROPHONE ARRAYS A Dissertation Presented By Duong Duy Tran to The Department of Electrical and Computer Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the field of Electrical Engineering Northeastern University Boston, Massachusetts May 2015

2 Enhancing active and passive remote sensing in the ocean using broadband acoustic transmissions and coherent hydrophone arrays by Duong Duy Tran Submitted to the Department of Electrical and Computer Engineering on May 1, 2015, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract The statistics of broadband acoustic signal transmissions in a random continental shelf waveguide are characterized for the fully saturated regime. The probability distribution of broadband signal energies after saturated multi-path propagation is derived using coherence theory. The frequency components obtained from Fourier decomposition of a broadband signal are each assumed to be fully saturated, where the energy spectral density obeys the exponential distribution with 5.6 db standard deviation and unity scintillation index. When the signal bandwidth and measurement time are respectively larger than the correlation bandwidth and correlation time of its energy spectral density components, the broadband signal energy obtained by integrating the energy spectral density across the signal bandwidth then follows the Gamma distribution with standard deviation smaller than 5.6 db and scintillation index less than unity. The theory is verified with broadband transmissions in the Gulf of Maine shallow water waveguide in the Hz frequency range. The standard deviations of received broadband signal energies range from 2.7 to 4.6 db for effective bandwidths up to 42 Hz, while the standard deviations of individual energy spectral density components are roughly 5.6 db. The energy spectral density correlation bandwidths of the received broadband signals are found to be larger for signals with higher center frequencies and are roughly 10% of each center frequency. Sperm whales in the New England continental shelf and slope were passively localized, in both range and bearing using a single low-frequency (< 2500 Hz), densely sampled, towed horizontal coherent hydrophone array system. Whale bearings were estimated using time-domain beamforming that provided high coherent array gain in sperm whale click signal-to-noise ratio. Whale ranges from the receiver array center 1

3 were estimated using the moving array triangulation technique from a sequence of whale bearing measurements. The dive profile was estimated for a sperm whale in the shallow waters of the Gulf of Maine with 160 m water-column depth, located close to the array s near-field where depth estimation was feasible by employing time difference of arrival of the direct and multiply reflected click signals received on the array. The dependence of broadband energy on bandwidth and measurement time was verified employing recorded sperm whale clicks in the Gulf of Maine. Thesis Supervisor: Purnima Ratilal Title: Associate Professor 2

4 Acknowledgments First and foremost, I would like to express my most sincere gratitude to my advisor, Purnima Ratilal, for her incredible guidance, encouragement and support through the years I spent at Northeastern. Her passion, vision, patience, and kindness, which were certainly unmatched, played a definite role in my training to become a scientist. I would like to thank my committee members, Dr. Aaron Thode, Prof. Hanoch Lev- Ari, and Dr. Peter Worcester for their helpful feedback and insights on my submitted manuscripts as well as my dissertation revisions. I would like to thank my fellow students and colleagues, together with whom I enjoyed and endured many days in the lab, in conferences, and out in the ocean. I am grateful to my housemates, or adopted family members Minh and Khanh for our unique brotherhood and the home away from home we have built. A grand thank you goes out to all my friends in Boston and abroad, I am truly blessed that neither time nor distance could ever make our friendship dwindle. Last but not least, I am forever indebted to my family for their neverending unconditional love. I dedicate this thesis to my parents, Tran Duy Thanh and Duong Thi Bich Ngoc. 3

5 Contents 1 Motivation and approach 14 2 Probability distribution for energy of saturated broadband ocean acoustic transmission: Results from Gulf of Maine 2006 Experiment Probability distribution for saturated broadband signal energy as a function of signal bandwidth, measurement time, frequency correlation and temporal correlation Probability distribution for the energy of a broadband signal with measurement time smaller than energy spectral density correlation time Probability distribution of broadband signal energy with measurement time larger than the energy spectral density correlation time Broadband transmission scintillation statistics from 2006 Gulf of Maine experiment Experimental data collection and processing Probability distribution of log-transformed bandwidth-averaged energy spectral densities Mean and standard deviation of energy spectral density across signal bandwidth

6 2.2.4 Dependence of signal energy standard deviation and scintillation index on bandwidth and center frequency Energy spectral density correlation bandwidth from measured broadband data Temporal averaging and broadband spectrum reconstruction in a random multi-modal range-dependent ocean waveguide Discussion and comparison to other shallow water measurements 48 3 Using a coherent hydrophone array for observing sperm whalerange and shallow-water dive profiles Methods Experimental data collection and analysis Determining click arrival time and azimuthal bearing Range estimation for sperm whales in the near- or far-field of the towed horizontal coherent receiver array Simultaneous depth and range estimation for a sperm whale in shallow water Results: Tracking a sperm whale in shallow waters of the Gulf of Maine Analysis of vocalizations Tracking range and depth of a sperm whale close to array nearfield Sperm whale detection range in shallow water Conclusion Localizing sperm whales using the array invariant technique and statistical characteristics of sperm whale clicks Localizing sperm whales using the array invariant technique Statistical characteristics of sperm whale click received broadband energy Conclusion

7 5 Conclusion 80 Appendix A Mean and standard deviation of bandwidth-averaged energy spectral density 83 Appendix B Mean and standard deviation of log-transformed bandwidthaveraged energy spectral density 86 Appendix C Simultaneous range-depth localization using multiple-reflection time difference of arrival (MR-TDA) 90 C.1 Depth-localization when range information is available

8 List of Figures 2-1 Hypothetical scenario for the energy spectral density correlation coeffient of a broadband signal. Here when the frequency shift is 0, the correlation coefficient ρ(ξ,τ = 0) is 1. ρ(ξ,τ = 0) decreases linearly to become 0 when the frequency shift ξ reaches 100 Hz (A) Locations of source and receiver during GOME 06 [1, 2]. Isobath contours have the unit of m. The sound speed profiles shown in Fig. 2-3(A) were collected roughly at the begining, middle, and end of each receiver track and at the source locations. (B) Normalized histogram of the number of transmissions as a function of source and receiver separation or range. Figure adapted from [3] (A) Sound speed profiles and (B) buoyancy frequency profiles obtained from XBT and CTD measurements at the experimental site. A total of 185 sound speed profiles and 35 buoyancy frequency profiles are shown. Figure adapted from [3] Example of source waveform and received broadband signal at arange of 7.6 km for the Tukey-windowed linear frequency modulated pulse centered at f m =415Hz.(A)Sourcewaveform,(B)sourcespectrum, (C) received signal waveform, and (D) received signal spectrum. The results are normalized for a 0 db re 1 µpa at 1 m source level. Figure adapted from [3]

9 2-5 Modeled transmission loss for 50-Hz bandwidth Tukey-windowed broadband signals centered at (A) f m =415Hzand(B)f m =1125Hz, calculated using the range-dependent parabolic equation model [4]. Transmission losses are obtained by averaging over 20 independent Monte Carlo realizations of the broadband signal in the Gulf of Maine environment randomized by internal waves. Figure adapted from [3] Histograms showing distribution of measured log-transformed bandwidthaveraged energy spectral densities L J received in the 7 to 9 km range for two center frequencies f m =415 Hz (left) and f m = 1125 Hz (right) with (A) and (B) 0.5 Hz bandwidth (nearly monochromatic components), and (C) and (D) 50 Hz bandwidth Tukey windowed signals with effective bandwidth of 42 Hz. The histograms are overlain with the theoretical exponential-gamma distribution modeled using Eq. (2.9) (black curve), with the number of frequency correlation cells µ F determined from the data s mean and standard deviation. The exponential- Gamma distribution corresponding to assumed µ F = 1 is also shown for comparison. Figure adapted from [3] Mean and standard deviation of the log-transformed energy spectral density L E as a function of frequency for broadband signals received between 7 to 9 km range, centered at (A) f m =415Hzand(B)f m = 1125 Hz. Figure adapted from [3]

10 2-8 (A) Empirically measured standard deviations of the log-transformed bandwidth-averaged energy spectral densities L J obtained from broadband transmissions in the Gulf of Maine shown as points. (B) The number of frequency correlation cells µ F are obtained from the measured signal standard deviations via Eq. (2.11). The dotted curves in (A) and (B) are obtained from the minimum mean-squared error fit to the data points using the equation and coefficients in Table 2.2. The errorbar shown applies to all data points. Figure adapted from [3] Measured scintillation indices in the Gulf of Maine for all 4 center frequencies as a function of relative bandwidth. The errorbar shown applies to all data points. Figure adapted from [3] Average energy spectral density correlation coefficient ρ(ξ,τ =0 f m ) calculated from received broadband signals at the four center frequencies shown as a function of frequency shift within the signal bandwidth. Figure adapted from [3] Time-averaged energy spectral density S(f) calculated from received broadband signals in the 7 to 9 km range for the waveforms centered at (A) f m =415Hzand(B)f m = 1125 Hz. Figure adapted from [3] Locations of the two test sites where the densely-sampled, towed horizontal coherent receiver array was deployed to collect ambient noise data in May Site A is in the Gulf of Maine shallow water environment and site B is in the deeper continental slope environment. Figure adapted from [5] Measured sound speed profiles at the two test sites shown in Fig Figure adapted from [5]

11 3-3 (A) Spectrogram of a series of sperm whale echolocation clicks recorded at frequencies up to 2.5 khz in the Gulf of Maine on May 14, starting at 17:19:07 EDT. The spectrogram was calculated using a short-time Fourier transform with window size 256 and 75% overlap. (B) Beamformed pressure time series of the clicks, bandpass filtered between Hz. (C) Beamformed pressure time series plotted in decibel (db) scale. The solid curve with errorbars shows the mean and standard deviation of beamformed background ambient noise level in the Hz band, estimated from regions outside of clicks. Figure adapted from [5] (A) Spectrogram of 3 consecutive slow clicks followed by a train of echolocation clicks recorded at frequencies up to 2.5 khz in the Gulf of Maine on May 14, starting at 17:16:15 EDT. (B) Beamformed pressure time series of the clicks, bandpass filtered between Hz. (C) Beamformed pressure time series plotted in decibel (db) scale. The solid curve with errorbars shows the mean and standard deviation of beamformed background ambient noise level in the Hz band, estimated from regions outside of clicks. (D) Corresponding signal received on a single hydrophone, bandpassed filtered between Hz. Figure adapted from [5] Array beamformer output as a function of steering angle from array broadside 0 shown for two distinct time instances. Sperm whale clicks with relative bearing 3.7 near array broadside and 73.7 near array endfire. The corresponding 1-dB beamwidths are approximately 1.7 near broadside and 8.0 near endfire. Rectangular window was applied across the array aperture. Figure adapted from [5]

12 3-6 Measured bearings of sperm whale echolocation and slow clicks detected in the Gulf of Maine on May 14 over a 1-hour period from 16:35 to 17:35 EDT. Figure adapted from [5] (A) Single sperm whale in Gulf of Maine localization result using the two methods, MAT and MR-TDA for the period between 17:15:20 and 17:32:40 EDT. The ellipses represent contours of localization uncertainty at each time instance with MAT (solid curve) and with MR- TDA (dashed curve). The origin of the coordinate system is located at ( N, W). (B) Range estimates using MAT and MR- TDA between 17:18:00 and 17:32:40 EDT. The errorbars show the standard deviation of the range estimates in a 4-minute time window. (C) Depth estimates for the same time period. Figure adapted from [5] Multiple reflection arrival pattern of the sperm whale clicks detected on May 14 in the Gulf of Maine. The order of arrival is: direct path; pairs of bottom and surface reflected, bottom-surface-bottom and surfacebottom-surface reflected etc. Between 17:26:00 and 17:32:30 EDT, reflections from up to 7 interface bounces are detected. Figure adapted from [5] Average broadband transmission loss in the frequency range of khz obtained using the RAM model at distances up to 80 km for the Gulf of Maine environment. Figure adapted from [5] Bearing-time migration of beamformed received intensity of a sperm whale click at 17:16:15 EDT on May 14. The click was highpass filtered using a cut off frequency of 800 Hz to focus on the dominant spectrum as well as eliminate high noise level at low frequencies. At each time instance, a spatial peak detector is used to determine the arrival angle s = sin θ. The array invariant estimate is ˆχ h = ds 1 (t) dt (Eq. (9) of [6]) 75 11

13 4-2 Average energy spectral density of the received sperm whale clicks shown for frequencies from 1750 to 2500 Hz Standard deviation of the broadband energy plotted as a function of relative bandwidth for the received sperm whale clicks. The center frequency is f c = 2150 Hz. Measurements were performed at shallow water site A (Fig Decorrelation of the energy spectral density as a function of frequency shift ξ, with respect to the central frequency component C-1 Calculated time delays from direct arrival for the bottom-bounce t b (upper left), surface-bounce t s (upper right), bottom-surface bounces t bs (lower left), and surface-bottom bounces t sb (lower right) as a function of whale range and depth. The receiver depth is set at 65 m and the water depth is 160 m. Figure adapted from [5]

14 List of Tables 2.1 Two-sided chi-squared test results to verify the distributions of the logtransformed bandwidth-averaged energy spectral density L J for the 4 scenarios shown in Fig A significance level of α=0.05 gives χ 2 within the range from lower-tail to upper-tail critical values for both the Gamma and exponential distributions Empirically determined number of frequency correlation cells µ F is related to relative bandwidth B/f m by the inverted exponential decay relationship µ F = A (A 1)exp( kb/f m ), with coefficients A and k determined by curve fitting as shown in Fig The case (B=0, µ F = 1) corresponds to one unique independent fluctuation. When B becomes very large, µ F tends to A, its upper saturation value for each center frequency, which is 3 for the lowest frequency f m =415Hzand 1.6 for the highest frequency f m =1125Hz

15 Chapter 1 Motivation and approach When an acoustic field propagates through a temporally random and spatially inhomogeneous ocean waveguide, its intensity or energy fluctuates in both time and space. In both deep ocean and shallow water continental shelf environments, a major source of acoustic field scintillation is internal waves [7 9]. Early efforts to describe signal scintillation statistics in the ocean were based on multipath theory, with the resultant field being the sum of multiple random phase components [10 12]. The instantaneous received signal therefore has an exponential distribution for intensity or a Rayleigh distribution for amplitude [10 12] and a 5.6 db intensity standard deviation [11]. The formulations in [10 12] assume a uniform distribution for instantaneous phase at saturation due to multipath effects. In a later study [13], statistics of acoustic signals were characterized as a function of measurement time T and intensity correlation time τ c, where a time-averaged measurement of signal intensity was shown to be equivalent to a measurement of instantaneous intensity contributions from µ T independent and identically distributed fluctuating sources or correlation cells. The time-averaged signal intensity therefore has a Gamma distribution [13 16] and a standard deviation less than 5.6 db. In Chapter 2 we derive the distributions for the energy of a broadband signal by applying coherence theory, which characterizes the coherence or correlation properties of a wave field through second or higher-order correlation 14

16 functions [13, 14, 17, 18]. Both the bandwidth-integrated energy and time-averaged energy of the broadband signal where studied. The derivation here generalizes and extends the statistical theory of [13] since it includes the frequency correlation of broadband signals not considered therein. We show that the total number of independent statistical fluctuations or correlation cells [13, 14] µ can be increased for a broadband signal by extending either or both the signal bandwidth and measurement time. The statistical theory is verified with data from the Gulf of Maine 2006Ex- periment (GOME 06) [1, 2], where broadband acoustic transmissions in the 300 Hz to 1200 Hz frequency range and effective bandwidths up to 42 Hz were measured at source-receiver separations of up to 20 km. The energy at a single frequency of the received broadband signals in the Gulf of Maine were found to have standard deviations of approximately 5.6 db and scintillation indices (SI) that approach 1, which are characteristics of a saturated field. The energy spectral density components of the measured data fit well with the exponential distribution based on a two-sided chi-squared test. The broadband signal energies, obtained by integrating the energy spectral densities over the signal bandwidth, were found to have smaller standard deviations ranging from 2.7 to 4.6 db and scintillation indices significantly smaller than 1 when the signal s effective bandwidth ranges up to 42 Hz. The broadband signal energies were found to follow the Gamma distribution and depart significantly from the exponential distribution when the total number of frequency correlation cells of the broadband signal, which is a measure of the number of independent fluctuations that contribute to the overall field, exceeded 2. Smaller standard deviations and SI were associated with larger bandwidth and smaller center frequency signals. The measured broadband signal contains saturated frequency components, but decorrelation across its bandwidth after forward propagation and scattering in a random ocean waveguide leads to one or more independent frequency fluctuations or frequency correlation cells, thereby reducing the broadband signal s 15

17 energy standard deviation. The energy spectral density correlation bandwidth of the measured broadband signals were found be roughly 10% of the center frequency. Measurements of broadband signal energy standard deviations in other shallow water waveguides are consistent with the statistical theory presented here [19, 20] as discussed in Sec Previous experimental and theoretical studies of ocean acoustic transmission scintillation in shallow and deep ocean environments have examined a variety of quantities including intensity and arrival time of individual rays or modes, pulse time spreads, phase and energy distributions [7, 19, 21, 22]. Several of these experiments employed vertical receiving arrays at fixed locations from a source to analyze the statistics of individual ray or modal arrivals from the depth-dependent received fields [19, 22, 23]. Many deep ocean acoustic transmission experiments found the acoustic field to be partially saturated with a significant mean field contributing to the total intensity or energy [24, 25]. The acoustic transmission data from shallow water, on the other hand, were often found to be saturated with negligible mean field at sufficiently large ranges from the source [19, 20]. The theory developed here is applicable for analyzing broadband acoustic propagation at ranges beyond roughly 3 km in typical continental shelf environments, where the received field is expected to be saturated [19, 20]. In Chapter 2, we focus our analysis on the statistics of the energy spectral density and total energy of broadband acoustic transmissions in the Gulf of Maine shallow water waveguide with measurements made on a single hydrophone. The received field on the hydrophone is a sum of multi-modal contributions that involve significant bottom interaction along the propagation path, as will be shown in Sec. 2.2A, which leads to a received field that is saturated. The energy of a broadband signal is an important quantity often used to infer parameters such as target strength or scattering strength of objects in active sensing [1, 2, 26 28], digital logic levels of transmitted messages in 16

18 underwater acoustic communication systems [29, 30], and level of underwater broadband sources, such as vocalizing marine mammals [31 33] and underwater vehicles. An understanding of the statistics of broadband signal energy and its dependence on signal bandwidth, center frequency and measurement time is necessary to efficiently design experiments, and to quantify the accuracies with which the related parameters can be determined. The materials in Chapter 2 have been published in [3]. Conventional surveys of marine mammals are often carried out using intensive visual sightings, based on inputs from observers on platforms of opportunity such as whale watching boats or research aircrafts [34 36]. The aggregation of data from several sources at different time instances requires significant effort to consolidate, and is subject to spatio-temporal aliasing if localization results are required. Acoustic monitoring techniques are therefore often employed to address this issue. The active approach to tracking whales has been performed with small areal coverage, at ranges within a few hundred meters [37, 38], and could only give information on target sizes. Passive monitoring methods [39 42] often employ a single hydrophone, or a network of sparsely located hydrophones to acoustically detect vocalizing marine mammals. Localization of these requires deploying a sufficient number of widelyspaced receivers [43], in order to employ time difference of arrival (TDOA) methods [44,45]. The challenge to this method lies in being able to associate the different vocalizations to different individuals in a large area, especially for species whose individuals have near identical sound patterns. Some studies have made use of digital acoustic recording tag to monitor marine mammals, however approaching the whales at close range is needed for tagging [46, 47]. Recording time is constrained by the tag s memory and power capacity, making this approach more suitable for individual movement monitoring than for wide area surveys. In Chapter 3 we demonstrate the instantaneous passive acoustic detection, local- 17

19 ization and tracking of marine mammals in a shallow water waveguide using a single high-resolution coherent linear hydrophone array system. We focus our analysis on the sperm whale (Physeter macrocephalus), employing only the low frequency components (up to 2500 Hz) of their vocalizations. Sperm whales (Physeter macrocephalus) in the Northwest Atlantic during spring and summer are concentrated along continental slope regions from the Mid-Atlantic Bight to south of Georges Bank [48] and the Scotian shelf edge. While foraging, sperm whales perform deep dives lasting from several minutes to more than an hour [49] while emitting short-duration broadband clicks with frequencies ranging from several hundred Hz to more than 30 khz [50, 51]. Each click exhibits a multi-pulse structure [52 54] arising from reflections of the acoustic signal generated by the phonic lips off the frontal and distal air-sacs bounding the spermaceti organ of a sperm whale. The inter-pulse interval (IPI) provides a measure of the length of the spermaceti organ which has been shown to be strongly correlated with the size of a sperm whale individual [55 61]. Here, we show that it is possible to distinguish and classify multiple vocalizing sperm whale individuals located in the far-field of a single, densely-sampled, towed horizontal coherent hydrophone array system using the instantaneous sperm whale position estimates in both range and bearing, and the inter-pulse intervals of the vocalized click signals. Most studies of the vocalization behavior and dive profile of sperm whales have been confined to deep continental slope environments bounding the Pacific and Atlantic ocean [49,51,62,63]. In Chapter 3, we provide estimates of the 3-dimensional (3D) dive profile of a sperm whale individual whose vocalizations were opportunistically recorded in the shallow water environment of the Gulf of Maine with roughly 160 m water-column depth during a sea test of a newly-developed, densely sampled, towed horizontal coherent receiver array system in May Localization of an acoustic source, such as a vocalizing sperm whale, in the far-field 18

20 of a single, densely sampled, towed horizontal coherent hydrophone array system is often a two-stage process. First, the bearing or horizontal direction of arrival of the acoustic signal is determined by time-delay analysis or beamforming of the signals received on the individual hydrophone elements of the array. Second, the range or horizontal distance of the acoustic source from the receiver array center is determined by tracking changes in the bearing of a series of acoustic emissions over time [64 67]. Short-aperture, towed horizontal coherent hydrophone array systems have been previously used to record vocalizations from sperm whales. However, the coherent receiver array data have only been applied to determine the bearing of a sperm whale. No subsequent range estimates have been made based solely on the coherent receiver array measurements. Consequently, coherent array gain of densely-sampled hydrophone array systems have not been previously exploited for range localization of sperm whales. In [68], a 128-element horizontal coherent hydrophone array system of the NATO Undersea Research Center (NURC) with an array aperture length of 11.6 m was employed to determine sperm whale vocalization bearings and to separate whale clicks from different azimuthal directions, but no range estimates or range analysis were provided. In [52], click data from a single sperm whale acquired using the same NURC receiver array was used to determine the bearings of the whale individual. The sperm whale was primarily tracked using a digital tag (DTAG) attached to its body consisting of a hydrophone used to record sounds directly from the whale [52]. The sperm whale range to the receiver array center was determined from click travel time difference between the DTAG hydrophone and the towed array hydrophones [52]. In Chapter 3 we localize multiple sperm whales in the far-field of a single lowfrequency (< 2.5 khz), densely-sampled, towed horizontal coherent hydrophone array system, providing estimates of both range and bearing for each sperm whale. Since no other acoustic sensors were available to us apart from the towed horizontal receiver array system, the whale ranges were estimated from their bearing-time trajectories. 19

21 A review of methods that can be applied to passively estimate the range of an acoustic source from a single, densely-sampled, towed horizontal coherent receiver array is provided in Sec. I of [65]. Here we employ the moving array triangulation technique developed in [65] to estimate sperm whale ranges from the measured click bearings. This technique combines bearing measurements from spatially separated apertures of the towed horizontal coherent receiver array and employs the conventional triangulation ranging algorithm for localizing a source that may be in the near- or far-field of the array. Since data from only a single towed horizontal coherent receiver array is used here to remotely and passively localize both the range and bearing of sperm whales and to classify them, the methods and results developed here are highly relevant and can be directly applied to address the feasibility of monitoring sperm whales with other towed horizontal coherent receiver array systems, such as those employed in naval and geophysical applications, where it may be important and necessary to remotely sense marine mammal activity from long ranges. An advantage of bearings-only range-localization with a densely-sampled, towed horizontal coherent receiver array system is that no additional information about the environment, such as bathymetry or sound speed profile, is needed in order to estimate source range in the far-field of the array. Other approaches for localizing sperm whales include (i) hyperbolic ranging with a small network of single hydrophones [69 71], and (ii) time-delay measurement of click reflections from ocean boundaries acquired with a single hydrophone or a sparse array of hydrophones [63, 72 77]. In Chapter 3, we utilize time-difference-of-arrivals of the sperm whale direct and multiple bottom and surface reflected click (MR-TDA) signals after beamforming to estimate the depth and hence the dive profile of a sperm whale in shallow waters of the Gulf of Maine with 160 m water-column depth. This sperm whale individual s horizontal range r = 1 km was very close to the array s nearfield distance r N (r N L 2 /λ 750 m, where L is the array aperture length and 20

22 λ is the wavelength) making it possible to estimate its depth. Depth estimation for acoustic sources at long ranges, in the farfield (r >>L 2 /λ) of a single, horizontal coherent receiver array system is challenging because the acoustic wavefield received by the array is multi-modal in nature having undergone many surface andbottom bounces in a random ocean waveguide making the received field less sensitive to the source s depth location, except in the endfire direction of the horizontal array. The materials in Chapter 3 have been published in [5]. In chapter 4 we investigate the ability to localize sperm whales in shallow water using the array invariant method [6], and show that the multimodal impulsive broadband clicks arriving at a hydrophone array can be employed to estimate sperm whale location at short ranges (< 1.5 km). We then analyze the statistics of broadband sperm whale clicks as a function of bandwidth and frequency, and verify the results presented in Chapter 2 for a center frequency over 2 khz and bandwidths up to 500 Hz. 21

23 Chapter 2 Probability distribution for energy of saturated broadband ocean acoustic transmission: Results from Gulf of Maine 2006 Experiment The probability density functions for the energy spectral density [14] and total energy of a broadband signal transmitted through an ocean-acoustic waveguide are derived using fourth-order coherence theory [13, 14, 17, 18]. The probability distributions are formulated in terms of the signal bandwidth, measurement time, frequencyand temporal correlation of the broadband signal s energy spectral density components. The theory presented here generalizes the derivation of Makris [13], by also considering the correlation across the frequency componets of a broadband signals. The statistical theory is verified with data from the Gulf of Maine 2006 Experiment (GOME 06) [1, 2], where saturated broadband acoustic transmissions in the 300Hzto1200Hz frequency range and effective bandwidths up to 42 Hz were measured at source- 22

24 receiver separations of up to 20 km. chapter have been presented in [3]. The material and figures presented in this 2.1 Probability distribution for saturated broadband signal energy as a function of signal bandwidth, measurement time, frequency correlation and temporal correlation Probability distribution for the energy of a broadband signal with measurement time smaller than energy spectral density correlation time Here we derive the probability density function for the energy of a broadband signal in terms of its physical bandwidth B and the frequency correlation width B c of its energy spectral density components. This derivation parallels that given in [14] and [13] where the probability distribution of time-averaged intensity is formulated in terms of a signal s measurement time T and the correlation time τ c of its instantaneous intensity measurements. The correlation time [13,14] refers to the characteristic time period of fluctuation of the random acoustic field. It can be derived by considering the fourth-order temporal coherence [14] of the underlying complex field (see Eqs. (A.8) and (2.32)). Here, we first consider the scenario where the measurement time is smaller than the energy spectral density correlation time (T < τ c ), so that the broadband signal has only one temporal correlation cell µ T =1. Let the received broadband signal in time with bandwidth B and center frequency f m be denoted by Ψ(t). We assume that the broadband signal duration T D is much smaller than its correlation time (T D τ c ). This is a reasonable assumption since 23

25 the broadband signals transmitted in the ocean typically have durations on the order of seconds [2, 26], while the correlation time scale of signal fluctuation is much larger, on the order of several to tens of minutes [22,78,79]. We also assume the observation or measurement time T satisfies T > T D and T < τ c, such that the signal is fully observed. The complex spectral amplitude Φ(f t k ) of the signal can be obtained by Fourier analysis, Φ(f t k )= tk +T D t k Ψ(t)e j2πft dt, (2.1) where t k is the time instance when the signal first arrives at the receiver. For asaturated broadband signal, its baseband components Φ(f t k )e j2πft each have an envelope Φ(f t k ) that can be modelled as a circular complex Gaussian random (CCGR) variable. At saturation, the real and imaginary parts of Φ(f t k ) are independent Gaussian random variables with zero mean and the same variance [11, 13]. Since T D τ c, the Fourier complex amplitude Φ(f t k ) can be approximated as instantaneous in time. This means that for a broadband signal arriving at the receiver at t k, the complex spectral amplitude Φ(f t k )ateachfrequencyf cannot be decomposed into multiple independent fluctuations. The arrival time t k is factored in to account for variation in the propagation medium for different t k. The energy spectral density E(f t k ) obtained from magnitude-squared amplitude of a Fourier component E(f t k )= Φ(f t k ) 2, (2.2) obeys the exponential distribution, 1 p(e) = E exp [ E/E ], for E 0, 0, elsewhere, (2.3) 24

26 with mean and standard deviation both equal to E. ThephaseofΦ(f t k ) is uniformly distributed over 2π radians for a saturated signal. The bandwidth-averaged energy spectral density J (f m t k,b) is J (f m t k,b)= 1 B = 1 B fm+b/2 f m B/2 tk +T D t k E(f t k )df (2.4) Ψ(t) 2 dt where the last equality is obtained by application of Parseval s theorem (since the signal only exists within [t k,t k + D] in time, and within [f m B/2,f m + B/2] in frequency). The mean and variance of J (f m t k,b) are derived in Appendix A and given by Eqs. (A.1) and (A.14) respectively. A measure of the number of independent spectral fluctuations or frequency correlation cells µ F averaged over bandwidth B is given by the squared-mean-to-variance ratio or signal-to-noise ratio [13, 14] of the measurement J, J (f m t k,b) 2 µ F (f m )= (2.5) J 2 (f m t k,b) J(f m t k,b) 2 [ 1 ( ) 1 ξ = B f B ρ(ξ,τ =0 f m )dξ], (2.6) where ρ(ξ,τ f m ) is the joint temporal-spectral correlation coefficient of the energy spectral density components of the broadband signal defined in Eq. (A.11), and the triangular function ( ξ B ) is defined in Eq. (A.10) of Appendix A. The energy spectral density undergoes fluctuations over a characteristic bandwidth B c that is referred to as its frequency correlation width. A useful measure of the correlation bandwidth of the energy spectral density of the broadband signal centered at frequencyf m is then given by B c (f m )= ρ(ξ,τ =0 f m )dξ. (2.7) 25

27 Another measure of the correlation bandwidth B c (f m ) is twice the e-folding frequency shift ξ e satisfying ρ(ξ e,τ =0 f m )=1/e. An illustration of the correlation coefficient ρ(ξ,τ =0 f m ) for different frequency shift of ξ is shown in Fig Here the correlation bandwidth, calculated using Eq. (2.7) is B c =100Hz. Thee-folding frequency shift is 63 Hz, yielding a comparable correlation bandwidth of 126 Hz. Figure 2-1: Hypothetical scenario for the energy spectral density correlation coeffient of a broadband signal. Here when the frequency shift is 0, the correlation coefficient ρ(ξ,τ = 0) is 1. ρ(ξ,τ = 0) decreases linearly to become 0 when the frequency shift ξ reaches 100 Hz. The physical meaning of the number of frequency correlation cells µ F can be understood by considering its limiting values. For a small bandwidth signal B B c, the energy spectral density across the signal s physical bandwidth B can be considered perfectly correlated, so that ρ(ξ,τ =0 f m ) 1for B/2 ξ B/2. Equation [ 1 (2.5) can then be approximated as µ F = ( ) ] 1 ξ B B dξ = 1. This result may be interpreted as that when the bandwidth shrinks, the number of frequency correlation intervals influencing the experimental measure asymptotically approaches unity. 26

28 Values of µ F less than unity are not possible because the results are always influenced by the state of the field in at least one correlation cell [14]. For a large bandwidth signal, B B c, since the width of the triangular function is 2B and the width of the frequency correlation coefficient is roughly B c, Eq. (2.5) can be approximated [ ] 1 as µ F = ρ(ξ,τ =0 f m)dξ = B/Bc. The number of frequency correlation 1 B intervals contained within the physical bandwidth B in this case can be obtained by dividing B by the correlation bandwidth B c. These values for the number of frequency correlation cells µ F are obtained in direct analogy to Eqs and of [14] which are expressed for the number of temporal correlation cells. This implies that more accurate experimental estimates of the correlation bandwidth can only be obtained from received broadband signals with large physical bandwidths. Since the bandwidth-averaged energy spectral density J (f m t k,b)ofthebroadband signal can be decomposed into the sum of µ F independent random variables, each exponentially distributed with the same mean and variance, its probability density function is then described by the Gamma distribution [13, 14] with shape parameter µ F and scale parameter E/µ F, ( 1 µf ) µf Γ(µ p(j )= F J (µ F 1) exp ( ) J µ ) E F E, for J 0 0, elsewhere. (2.8) The above equation is readily obtained from the inverse Fourier transform of the characteristic function [14, 15] or moment generating function of the exponential distribution raised to the power µ F. To obtain Eq. (2.8), we have assumed that the mean of the energy spectral density E is approximately constant for the frequency components across the signal bandwidth B. We will show in Sec. 2.2C that this is a valid assumption for the signals considered here. Compared to the exponentially distributed energy spectral density of a monochromatic component E(f t k ), the expected value of the Gamma distributed bandwidth-averaged energy spectral density 27

29 J (f m t k ) is still E but the variance is modified to E 2 /µ F (see Appendix A). When µ F > 1 the bandwidth-averaged energy spectral density has a smaller variance than a corresponding monochromatic component, so its scintillation index, definedasthe ratio of variance to squared-mean-intensity will be smaller than the unity value of the monochromatic component at saturation. When µ F =1,orwhenB B c, Eq. (2.8) reduces to the exponential distribution described in Eq. (2.3). The log-transformed bandwidth-averaged energy spectral density is defined as L J = 10log 10 [J /J ref ], where the choice of reference level J ref only adds a bias term to L J. The probability distribution of L J = 10log 10 J then is described by p(l J )=p(j =10 L J /10 ) dj dl J ( ) µf ) 1 µf = 10 µ F L J /10 10 exp ( µ L J /10 F, for <L J <, (10log 10 e)γ(µ F ) E E (2.9) which is an exponential-gamma distribution [13]. The mean and standard deviation of L J are derived in Appendix B and given by [13] L J = 10log 10 (E/µ F ) + (10log 10 e) Γ (µ F ) Γ(µ F ) (2.10) σ LJ = (10log 10 e) ζ(2,µ F ) 4.34 ζ(2,µ F ), (2.11) respectively, where ζ(ν, µ F ) is the generalized Riemann zeta function ζ(ν, µ F )= k=0 1 (k + µ F ) ν (2.12) which converges to π 2 /6whenµ F =1andν = 2, so that the standard deviation σ LJ = 5.6 db [11]. Equations (2.11) and (2.12) show that a standard deviation smaller than 5.6 db is obtained when µ F is larger than 1. For a given data set, the 28

30 number of frequency correlation cells µ F can be found from the empirically determined standard deviation by solving Eq. (2.11). As shown in Ref. [13], when the number of correlation cells is large, µ F 1, the standard deviation of L J in Eq. (2.11) can be simplified to σ LJ /µ F. When the broadband signal energy E(f m t k,b) obtained by integrating the energy spectral density over the signal bandwidth is considered, E(f m t k,b)=bj (f m t k,b)= tk +T D t k Ψ(t) 2 dt, (2.13) its probability density functions in both linear and log-transformed (L E = 10log 10 E) quantities can be readily obtained, ( 1 µf ) µf Γ(µ p(e) = F E (µ F 1) exp ( ) E µ ) BE F BE, for E 0 0, elsewhere (2.14) and p(l E )= ( ) µf ( 1 µf 10 µ F L E /10 10 L E ) /10 exp µ F, <L E <, (10log 10 e)γ(µ F ) BE BE (2.15) respectively. The mean and standard deviation of the broadband signal energy in linear and log-transformed domain are then given by E = BE (2.16) σ E = E / µ F, (2.17) and L E = 10log 10 ( E µ F ) + (10log 10 e) Γ (µ F ) Γ(µ F ) (2.18) σ LE = (10log 10 e) ζ(2,µ F ), (2.19) 29

31 respectively. Note that the log-transformed broadband signal energy L E has a standard deviation identical to the log-transformed bandwidth-averaged energy spectral density L J, while their means differ by 10log 10 B. It should be noted that even though the measurement time is smaller than the signal correlation time (T <τ c )sothatµ T = 1, the total number of correlation cells µ of the broadband signal obtained as the product µ = µ T µ F can still be larger than 1 when the signal bandwidth is larger than its correlation bandwidth, since then µ F > 1. This result then generalizes the derivation of Ref. [13] by also considering the correlation across the frequency components of a broadband waveform not addressed in [13]. Here the broadband signal has gamma distributed energy (see Eq. (2.14)) which reduces to the exponential distribution only when the signal bandwidth is smaller than its correlation bandwidth so that µ F = 1 as well for measurement times that satisfy T<τ c Probability distribution of broadband signal energy with measurement time larger than the energy spectral density correlation time We now consider the case when the measurement time T is larger than the correlation time τ c of a broadband signal s energy spectral density components. We assume that the time separation between the arrival of any two broadband pulses t i t j is larger than the correlation time τ c and that the broadband signal is statistically stationary over the measurement time T. Under these conditions, the measurements of the energy spectral densities of the broadband signal E(f t k ) over time t k for k = 1, 2, 3,... are independent fluctuations each having an exponential distribution with identical mean and standard deviation both equal to E. 30

32 The time-averaged energy spectral density S(f) is, S(f) = 1 N N E(f t k ), (2.20) k=1 where N is the number of temporally independent broadband signals received over measurement time T. In this case, the number of temporal correlation cells is µ T = N. The probability density function for the time-averaged energy spectral density S(f) then has a characteristic function that can be obtained from the product of µ T identical characteristic functions of the exponential distribution. This again leads to Gamma distribution for S(f) given by ( 1 µt ) µt Γ(µ p(s) = T S (µ T 1) exp ( ) S µ ) E T E, for S 0 0, elsewhere. (2.21) The time-averaged energy spectral density has mean E and variance E 2 /µ T. time-averaged energy spectral density is equivalent to the time-averaged intensity W This in [13], which has a probability distribution given by Eq. (9) of Ref. [13] and the number of correlation cells specified in that equation is µ T. The distribution of the log-transformed time-averaged energy spectral density L S = 10 log 10 S(f) is p(l S )= ( 1 µt (10log 10 e)γ(µ T ) E ) µt 10 µ T L S /10 exp ( µ T 10 L S/10 E ), for <L S <, (2.22) 31

33 which is an exponential-gamma distribution [13] with mean and standard deviation given by L S = 10log 10 (E/µ T ) + (10log 10 e) Γ (µ T ) Γ(µ T ) (2.23) σ LS = (10log 10 e) ζ(2,µ T ). (2.24) The time-averaged broadband signal energy with center frequency f m and bandwidth B, averaged over measurement time T, is E T (f m B) = 1 N N E(f m t k,b). (2.25) k=1 where we assume as before that there are exactly µ T = N statistically independent broadband signal receptions over the measurement time interval. distribution for the time-averaged broadband signal energy is ( 1 µ ) µ E (µ 1) Γ(µ) EB T exp ( ) µ E T BE, ET 0 p(e T )= 0, elsewhere, The probability (2.26) where µ = µ F µ T is the total number of independent statistical fluctuations or correlation cells of the broadband signal averaged over the measurement time period and is expressed as the product of the number of correlation cells in frequency µ F and the number of correlation cells in time µ T. The mean and standard deviation of the time-averaged broadband signal energy are E T = BE (2.27) σ ET = E T / µ F µ T, (2.28) The log transformed time-averaged broadband signal energy L ET = 10log 10 E T then 32

34 has probability distribution, mean and standard deviation given by p(l ET )= where µ = µ F µ T and ( 1 µ (10log 10 e)γ(µ) BE ) µ 10 µl ET /10 exp ( µ 10L E T /10 BE ), <L ET < (2.29) ( ) ET L ET = 10log 10 + (10log µ F µ 10 e) Γ (µ F µ T ) T Γ(µ F µ T ), (2.30) σ LET = (10log 10 e) ζ(2,µ F µ T ), (2.31) respectively. Finally, in analogy to the correlation bandwidth defined in Eq. (2.7), we define the correlation time of the broadband signal s energy spectral density component as, τ c (f m )= ρ(ξ =0,τ f m )dτ. (2.32) 2.2 Broadband transmission scintillation statistics from 2006 Gulf of Maine experiment Experimental data collection and processing The Gulf of Maine Experiment [1, 2] (GOME 06) conducted from Sep. 19 tooct. 6, 2006 near the northern flank of Georges Bank (Fig. 2-2(A)) was sponsored by the Sloan Foundation and the Office of Naval Research. A vertical source array was used to transmit broadband Tukey-windowed linear frequency modulated pulses each of 1 s duration and 50 Hz bandwidth with azimuthal symmetry at four distinct center frequencies; 415, 735, 950 and 1125 Hz. The pulse repetition interval was 150 s at each center frequency. The signals were received on a towed horizontal line array [1, 2, 80] of which one hydrophone was desensitized with a lower gain setting, 33

35 giving it a larger dynamic range for recording the one-way propagated waveforms. The tow tracks of the receiver array are shown in Fig. 2-2(A) with mean tow speed of 2 m/s. The source-receiver separations varied between 1 and 20 km, with over 80% of the transmissions occurring in the 4 to 12 km range (Fig. 2-2(B)). The source array was centered at a depth of between 60 to 70 m while the receiver array was centered at 105 m depth with typical depth variation of up to 10 m. The water depth at the location where the data was acquired was fairly level with an average of roughly 200 m. The water-column temperature and salinity were measured using expendable bathyther- Figure 2-2: (A) Locations of source and receiver during GOME 06 [1, 2]. Isobath contours have the unit of m. The sound speed profiles shown in Fig. 2-3(A) were collected roughly at the begining, middle, and end of each receiver track and at the source locations. (B) Normalized histogram of the number of transmissions as a function of source and receiver separation or range. Figure adapted from [3]. mographs (XBTs) and conductivity-temperature-depth (CTD) sensors. The derived water-column sound speed and buoyancy frequency profiles are shown in Fig. 2-3 and contain 185 samples for the sound speed profiles and 35 samples for the buoyancy frequency profiles. Other details about the measurement geometry and oceanographic 34

36 properties of the environment are provided in Sec. II of Ref. [1]. An example of the source waveform and the propagated signal received on the 0 20 (A) (B) Depth (m) Sound speed (m/s) Buoyancy frequency (cph) Figure 2-3: (A) Sound speed profiles and (B) buoyancy frequency profiles obtained from XBT and CTD measurements at the experimental site. A total of 185 sound speed profiles and 35 buoyancy frequency profiles are shown. Figure adapted from [3]. desensitized hydrophone at a source-receiver separation of 7.6 km are shown in Fig Fluctuations of the received signal can be observed over both its time duration and bandwidth. 35

37 The received broadband signals were processed following the approach outlined Normalized pressure (µpa) Normalized spectrum (db re µpa) Transmitted signal Time (seconds) (A) (B) x 10 4 Received signal at 7.6 km range Time (seconds) Frequency (Hz) Frequency (Hz) Figure 2-4: Example of source waveform and received broadband signal at a range of 7.6 km for the Tukey-windowed linear frequency modulated pulse centered at f m = 415 Hz. (A) Source waveform, (B) source spectrum, (C) received signal waveform, and (D) received signal spectrum. The results are normalized for a 0 db re 1 µpa at 1 m source level. Figure adapted from [3] (C) (D) in Sec. IIB of [20] to determine the signal energies. Let Ψ(r r 0,t) be the received pressure in time t at receiver location r from a source located at r 0. The complex spectral amplitude Φ(r r 0,f) is obtained by Fourier transform analysis: Φ(r r 0,f)= Ψ(r r 0,t)e j2πft dt, (2.33) T where T is the time window used to isolate the direct arrival from reverberation and other noise sources. The time window was 2 s long, including 0.5 s before the initial 36

38 arrival and 0.5 s after the 1 s signal duration to sufficiently capture the signal and its later arrivals. The energy spectral density is next calculated via, E(r r 0,f)= Φ(r r 0,f) 2. (2.34) The bandwidth-averaged energy spectral density J (r r 0,f m,b) is then calculated as a function of bandwidth B and center frequency f m for each received waveform, J (r r 0,f m,b)= 1 B fm+b/2 f m B/2 E(r r 0,f)df. (2.35) The log-transformed bandwidth-averaged energy spectral density level, L J = 10log 10 [J (r r 0,f m,b)/j ref ], was then calculated for each center frequency f m and bandwidth B. The broadband signal energy E(r r 0,f m,b) is calculated using E(r r 0,f m,b)=bj (r r 0,f m,b)= fm+b/2 f m B/2 and its log-transform is L E = 10log 10 [E(r r 0,f m,b)/e ref ]. E(r r 0,f)df. (2.36) Standard deviations σ LJ were first calculated for transmissions within a running range window of 2 km length in each track and then averaged across tracks. The 50 Hz bandwidth Tukey-windowed signals had 5 Hz tapered on either side of the spectrum so that their effective bandwidth was only 42 Hz. It should be noted that the 1 s time duration of the transmitted signals is much shorter than their energy spectral density correlation time scale of fluctuation which is expected to be on the order of several minutes [81, 82]. We model the broadband transmission losses for the 50 Hz bandwidth Tukey-windowed linear frequency modulated signals centered at f m =415 Hz and f m =1125 Hz transmitted from a vertical source array for one example of the source-receiver geometry 37

39 identical to the experiment in Fig The transmission losses are calculated using a range-dependent parabolic equation model [4]. The bottom is assumed to be sandy with sound speed of cb = 1700 m/s, density ρb = 1.9 g/cm2 and attenuation coefficient of 0.8 db/λ [1]. The results are plotted after averaging over 20 independent Monte Carlo realizations of the broadband signal energy in a waveguide randomized by internal waves [1, 20]. The acoustic field has negligible surface interaction, but significant bottom interaction due to the downward refracting sound speed profile for the source depth of 65 m. This significant bottom interaction will cause the acoustic field to be become fully randomized and saturated at source-receiver ranges roughly ten times the water depth. & (A) f m =415 Hz, B =42 Hz 0/ (B) f m =1125 Hz, B =42 Hz +%,-.&')* 34 1//!7/ 10/!6/!5/ 2// 20/ / & 0 1/!"#$%&'()* 10 2/ / 0 1/!"#$%&'()* 10 2/ Figure 2-5: Modeled transmission loss for 50-Hz bandwidth Tukey-windowed broadband signals centered at (A) fm = 415 Hz and (B) fm = 1125 Hz, calculated using the range-dependent parabolic equation model [4]. Transmission losses are obtained by averaging over 20 independent Monte Carlo realizations of the broadband signal in the Gulf of Maine environment randomized by internal waves. Figure adapted from [3] Probability distribution of log-transformed bandwidthaveraged energy spectral densities Histograms of the log-transformed bandwidth-averaged energy spectral densities LJ (r r0, fm, B) for the approximately monochromatic components with B = 0.5 Hz bandwidth and 38

40 for the B = 42 Hz effective bandwidth Tukey windowed signals centered at f m =415 Hz and f m =1125 Hz are plotted in Fig. 2-6 for transmission data having source-receiver separations between 7 and 9 km. The histogram is created from roughly 400 broadband signal receptions at each center frequency. The measured number of frequency correlation cells µ F indicated in Fig. 2-6 are obtained using Eq. (2.11) after standard deviations σ LJ were calculated in each case. The theoretical exponential-gamma distribution described by Eq. (2.9) with measured mean intensity E and number of frequency correlation cells µ F as parameters are plotted for each case in Fig The exponential-gamma distribution of Eq. (2.9) with assumed µ F = 1 is also shown for comparison. It should be noted that these distributions would correspond to the exponential distribution when µ F = 1 and the Gamma distribution when µ F > 1 if the linear quantities were plotted instead. 39

41 Measured µ F = , Gamma Assumed µ F = 1, exponential (A) Measured µ F = , Gamma Assumed µ F = 1, exponential (B) 0.15 f m =415 Hz, B=0.5 Hz f m =1125 Hz, B=0.5 Hz 0.1 Normalized number of occurences Measured µ F = , Gamma Assumed µ F = 1, exponential f m =415 Hz, B=42 Hz (C) Measured µ F = , Gamma Assumed µ F = 1, exponential f m =1125 Hz, B=42 Hz (D) Normalized received pressure level (db) Figure 2-6: Histograms showing distribution of measured log-transformed bandwidthaveraged energy spectral densities L J received in the 7 to 9 km range for two center frequencies f m =415 Hz (left) and f m = 1125 Hz (right) with (A) and (B) 0.5 Hz bandwidth (nearly monochromatic components), and (C) and (D) 50 Hz bandwidth Tukey windowed signals with effective bandwidth of 42 Hz. The histograms are overlain with the theoretical exponential-gamma distribution modeled using Eq. (2.9) (black curve), with the number of frequency correlation cells µ F determined from the data s mean and standard deviation. The exponential-gamma distribution corresponding to assumed µ F = 1 is also shown for comparison. Figure adapted from [3]. 40

42 For the signals with center frequency f m =415Hz,thenumberoffrequencycorrelation cells µ F increased from 1.48 to 2.29 as bandwidth increased from 0.5 Hz to 42 Hz, since there was a corresponding reduction in the standard deviation, as will be shown in the next section. For the higher frequency signals centered at f m =1125 Hz, the number of frequency correlation cells µ F increased only slightly from 1.15 to 1.38 when the bandwidth increased. We perform a two-sided chi-squared test [15] with significance level α = 0.05 to quantify the goodness of fit of the bandwidth-averaged energy spectral density levels L J with the exponential-gamma distributions parameterized by either assumed µ F = 1 (corresponding to exponential distribution for linear quantity) or the value of µ F > 1 experimentally obtained from the measured standard deviations (corresponding to Gamma distribution for the linear quantity). The results are tabulated in Table 2.1. For the approximately monochromatic components (B=0.5 Hz) with experimentally determined µ F close to 1, the χ 2 values are within the critical bounds of the corresponding degree of freedom so that both the exponential and Gamma distributions are considered acceptable for the linear quantity. It should be noted that this is expected since the Gamma distribution converges to the exponential distribution when µ F =1. For the 42 Hz effective bandwidth signals centered at f m = 415 Hz with experimentally determined µ F =2.29, the exponential distribution for the linear quantity is rejected because χ 2 is much larger than the upper critical value. For this case, the Gamma distribution is accepted by the chi-squared test and provides a better match to the data for the linear quantity. For the 42 Hz effective bandwidth signals centered at f m = 1125 Hz, both distributions are acceptable based on the chi-squared test since the experimentally determined µ F is still close to 1. 41

43 2.2.3 Mean and standard deviation of energy spectral density across signal bandwidth A basic assumption of the statistical theory presented in Sec. 2.1 is that the frequency components of a broadband signal are each saturated, so that the energy spectral density components E(r r 0,f) follow the exponential distribution with 5.6 db standard deviation and a mean that is approximately constant across the signal bandwidth. In Sec , we showed the energy spectral density of the center frequencycomponent of the received broadband signals in the Gulf of Maine are well matched to the exponential distribution. A similar result is obtained when we consider the energy spectral density distribution of other frequency components of the signals. In Fig. 2-7, we plot the mean and standard deviation of the log-transformed energy Transmission loss (db re 1 m) (A) Frequency (Hz) (B) Frequency (Hz) Figure 2-7: Mean and standard deviation of the log-transformed energy spectral density L E as a function of frequency for broadband signals received between 7to 9kmrange,centeredat(A)f m =415Hzand(B)f m = 1125 Hz. Figure adapted from [3]. spectral densities L E = 10log 10 [E(r r 0,f)/E ref ] of the received broadband signals in the 7-9 km range centered at f m = 415 and 1125 Hz, as a function of frequency 42

44 after source level correction. Roughly 400 received broadband signals were used in the calculation. The mean level stays relatively constant across the signal bandwidth for both waveforms, and standard deviations are close to the saturation value of 5.6 db for all frequencies across the signal bandwidth. This validates our assumption of saturated frequency components with equal means for the received broadband signals Dependence of signal energy standard deviation and scintillation index on bandwidth and center frequency The measured standard deviations of the log-transformed bandwidth-averaged energy spectral densities L J averaged over all tracks and source-receiver ranges are plotted as functions of center frequency f m and relative bandwidth B/f m in Fig. 2-8(A). The standard deviations approach 5.6 db only for the approximately monochromatic components, but decrease gradually with increasing bandwidth for the broadband signals. For signals with equivalent relative bandwidths, B/f m =constant, the signal with the lower center frequency has a smaller standard deviation. The error in the mean standard deviation estimates shown in the plot is small, approximately 0.02 db, and the same for all 4 center frequencies and bandwidths shown since roughly 1800 distinct broadband transmissions at each center frequency were used in the analysis. The number of frequency correlation cells µ F calculated from the standard deviations by solving Eq. (2.11) are plotted as a function of center frequency and relative bandwidth in Fig. 2-8(B). When the signal bandwidth approaches zeroorwhen the signal becomes monochromatic, µ F converges to one at all four center frequencies, which corresponds to the case of unity time-bandwidth signals described in [11] and [13]. For the broadband signals with larger bandwidths, the number of frequency correlation cells µ F is larger than 1. Curve fitting with an inverted exponential decay function shows that the number of frequency correlation cells are higher for signals 43

45 6 3 Standard deviation σ (A) f m =415Hz f m =735Hz f m =950Hz f m =1125Hz Number of correlation cells µ F (B) f m =415Hz f m =735Hz f m =950Hz f m =1125Hz Relative bandwidth B/f m Relative bandwidth B/f m Figure 2-8: (A) Empirically measured standard deviations of the log-transformed bandwidth-averaged energy spectral densities L J obtained from broadband transmissions in the Gulf of Maine shown as points. (B) The number of frequency correlation cells µ F are obtained from the measured signal standard deviations via Eq. (2.11). The dotted curves in (A) and (B) are obtained from the minimum mean-squared error fit to the data points using the equation and coefficients in Table 2.2. The errorbar shown applies to all data points. Figure adapted from [3]. with lower center frequencies. This relationship is tabulated in Table 2.2. While the experimental data have a maximum effective bandwidth of 42 Hz, it is expected that µ F will continue to increase with bandwidth, further reducing the standard deviation. Note that since the log-transformed broadband signal energies L E have identical standard deviations to the log-transformed bandwidth-averaged energy spectral densities L J (compare Eqs. (2.11) and (2.19)), the results obtained here regarding the measured standard deviations and their dependencies also apply to the signal energies L E. The scintillation indices (SI) for the bandwidth-averaged energy spectral densities J (r r 0,f) at the four center frequencies f m are plotted as a function of relative bandwidth B/f m in Fig Consistent with the theory developed in Sec. 2.1, the scintillation indices are smaller than 1 for all broadband signals, and decrease with 44

46 1 Scintillation index (SI) f m =415 Hz f m =735 Hz f m =950 Hz f m =1125 Hz Relative bandwidth B/f m Figure 2-9: Measured scintillation indices in the Gulf of Maine for all 4 center frequencies as a function of relative bandwidth. The errorbar shown applies to all data points. Figure adapted from [3]. increasing bandwidth. The scintillation indices approach 1 only when the signal bandwidths are small enough to be nearly monochromatic. For the signals with identical relative bandwidths, B/f m = constant, a smaller scintillation index is obtained at the lower center frequency f m. Since the broadband signal energies E can be obtained from the bandwidth-averaged energy spectral densities J by multiplication with the signal bandwidth (see Eq. (2.13) and (2.36)), they have identical measured scintillation indices and the results obtained here also apply to the broadband signal energies. The results in Fig. 2-9 are consistent with the assumption made in the theory of Sec. 2.1 that the energy spectral density components of the broadband signal have unity scintillation indices because they are saturated. It should be noted the results presented here do not provide any information on the approach to saturation discussed in [83] and [19]. This is because the present data set were acquired at largely 4 to 12 45

47 km range where the signals were already fully saturated. To determine the approach to saturation, measurements at much shorter ranges < 3 km would be needed [20] where they are expected to transition from the unsaturated to the partially saturated [12] then fully saturated regimes Energy spectral density correlation bandwidth from measured broadband data The energy spectral density frequency correlation coefficients ρ(ξ,τ =0 f m ) are calculated for the broadband signals at each of the four center frequencies using Eq. (A.11) and plotted in Fig Broadband received signals with higher center frequencies have larger energy spectral density correlation bandwidths since their correlation coefficients decay much slower with frequency shift ξ from the center frequency f m. From Fig. 2-10, the correlation coefficient for the broadband signal with center frequency f m =415 Hz has an e-folding bandwidth of approximately 35 Hz, implying that there are two frequency correlation cells within its 50 Hz physical bandwidth. This result is consistent with the inferred value of µ F from the measured standard deviation shown in Fig. 2-8(B) for center frequency f m = 415 Hz. The broadband signal with center frequency f m =1125 Hz, on the other hand is highly correlated across its physical bandwidth, having correlation coefficient values ρ(ξ,τ = ) > 0.6. This implies that the number of frequency correlation cells µ F is close to 1 for the received signals with center frequency f m = 1125 Hz, consistent with the results obtained by considering the standard deviations in Fig. 2-8(B). An exponential decay fit for ρ(ξ,τ =0 f m ) gives the energy spectral density relative correlation bandwidth B c /f m of roughly 8.5% ± 2% for all four center frequencies. When the signal bandwidth B is sufficiently large, the number of frequency correlation cells µ F can also be approximated [13] from the linear relationship, µ F B/B c. This is equivalent to dµ F /d(b/f m ) f m /B c, which enables an estimate of the correlation 46

48 1 Correlation coefficient ρ(ξ) f m =415 Hz f m =735 Hz 0.3 f m =950 Hz 0.2 f m =1125 Hz Frequency shift ξ (Hz) Figure 2-10: Average energy spectral density correlation coefficient ρ(ξ,τ =0 f m ) calculated from received broadband signals at the four center frequencies shown as a function of frequency shift within the signal bandwidth. Figure adapted from [3]. bandwidth B c to be obtained from the gradient of the plot of µ F versus relative bandwidth B/f m in Fig. 2-8(B). By applying a linear curve fit to the last four data points for each center frequency f m where the trend of µ F is relatively linear, we obtain relative correlation bandwidths B c /f m of 9.5% ± 2% at the four center frequencies. This is a rough estimate, however, since B is not significantly larger than B c for all four broadband waveforms. Signals with much larger physical bandwidths are required in order to more accurately quantify the correlation bandwidth as a function of center frequency. The approximately 10% energy spectral density correlation bandwidth of the received ocean-acoustic broadband signals correspond to roughly a whole tone in the chromatic scale of music. This implies that given a short-duration broadband signal with arbitrary bandwidth B, the number of energy spectral density frequency correlation 47

49 cells after forward propagation through the random ocean waveguide can be easily approximated by subdividing the physical bandwidth into the number of whole tones Temporal averaging and broadband spectrum reconstruction in a random multi-modal range-dependent ocean waveguide When averaging the received broadband signal energy spectral densities over a measurement time larger than the correlation time, the theory in Sec suggests that the total number of correlation cells µ = µ T µ F will be increased, leading to smaller standard deviations across all the frequency components. Figure 2-11 shows the timeaveraged energy spectral density S(f) plotted as a function of frequency estimated from all broadband transmissions within the 7-9 km range for waveforms with center frequencies f m =415Hzandf m = 1125 Hz. The error in the time-averaged energy spectral density estimates are significantly reduced from 5.6 db for a single sample to less than 0.6 db. The time-averaged energy spectral density of the received broadband signals in Fig provide an excellent reconstruction of the original Tukey-windowed spectrum (compare Fig. 2-11(A) with Fig. 2-4(B)). In contrast, the spectrum obtained from an individual received signal (see Fig. 2-4(D)) is highly distorted with as large as 6 db variation across the signal bandwidth from multi-modal interference Discussion and comparison to other shallow water measurements Previous measurements [19, 20] of broadband signal energy standard deviations in other shallow water waveguides are consistent with the statistical theory and experimental results presented here. For instance, in the continental shelf environment off Long Island-New York, broadband acoustic signals with bandwidths up to

50 10 (A) Source waveform Time averaged received data (B) Normalized spectrum (db) Frequency (Hz) Frequency (Hz) Figure 2-11: Time-averaged energy spectral density S(f) calculated from received broadband signals in the 7 to 9 km range for the waveforms centered at(a)f m = 415 Hz and (B) f m = 1125 Hz. Figure adapted from [3]. Hz at various center frequencies from 300 to 1500 Hz propagated between 2 and 10 km range from a source array in 80 m water depth were measured with standard deviations between 2.9 and 4 db [20] for the signal energies. The broadband signal energies were also found to follow the Gamma distribution. In [20], it was shown through the center frequency component of the broadband signal that the energy spectral density of the Fourier components were statistically saturated with roughly 5.6 db standard deviation and a distribution that matched the exponential. In [19], broadband signals with 100 Hz bandwidth centered at 400 Hz propagated through the New England continental shelf environment approximately 200 m deep were measured with standard deviations of approximately 2 db at 40 to 50 km range. This is smaller than the characteristic 5.6 db standard deviation of a monochromatic signal. Furthermore, it was shown in [19] that the distribution of the point intensity closely followed an exponential distribution, approximating an instantaneous measurement of a statistically saturated acoustic field. The broadband signals in [19] and [20] both 49

51 had durations smaller than their correlation time. 50

52 Table 2.1: Two-sided chi-squared test results to verify the distributions of the log-transformed bandwidth-averaged energy spectral density LJ for the 4 scenarios shown in Fig A significance level of α=0.05 gives χ 2 within the range from lower-tail to upper-tail critical values for both the Gamma and exponential distributions. fm(hz) B(Hz) Number of bins (N) µf χ 2 χ 2 χ 2 critical,lower χ 2 critical,upper (Gamma) (Exponential) (α =0.05) (α =0.05)

53 Table 2.2: Empirically determined number of frequency correlation cells µ F is related to relative bandwidth B/f m by the inverted exponential decay relationship µ F = A (A 1)exp( kb/f m ), with coefficients A and k determined by curve fitting as shown in Fig The case (B=0, µ F = 1) corresponds to one unique independent fluctuation. When B becomes very large, µ F tends to A, its upper saturation value for each center frequency, which is 3 for the lowest frequency f m = 415 Hz and 1.6 for the highest frequency f m =1125Hz. f m (Hz) A k

54 Chapter 3 Using a coherent hydrophone array for observing sperm whale range and shallow-water dive profiles In this chapter, we show the effectiveness of range localization as well as dive profiling of sperm whales in a shallow water environment using a single horizontal coherent hydrophone array. We show that it is possible to estimate sperm whale direction without spatial aliasing, by taking advantage of the impulsive nature of their clicks. Range estimation was performed using 2 techniques: moving array triangulation (MAT) [64 67] and array invariant [6]. The materials in Sections have been published in [5]. We investigate the statistics of broadband energy level, using clicks emitted by the sperm whale localized and tracked in the Gulf of Maine, and extend the results of Chapter 2 to a center frequency over 2000 Hz and a bandwidth up to 500Hz. 53

55 3.1 Methods Experimental data collection and analysis A newly developed, densely-sampled, towed horizontal linear hydrophone array system funded by the National Science Foundation and the Office of Naval Research was deployed and tested in the continental slope region south of Cape Cod between 500 m to 2000 m water depth on May 13 (site B in Fig. 3-1) and in the Gulf of Maine in 150 to 180 m water depth on May 14 and 15 of 2013 (site A in Fig. 3-1). Passive acoustic data were collected on a sub-aperture of the array with N = 32 elements having an inter-element spacing of 0.75 m. The hydrophone elements, each having -188 db re µpa/v sensitivity were sampled at 5 khz with 24-bit digital resolution. The array was towed by the research vessel Endeavor at various speeds between 1 and 4 knots. The water-column sound speed at the experiment sites were monitored using a conductivity-temperature-depth (CTD) sensor and expendable bathythermographs (XBT). The measured sound speed profiles are shown in Fig. 3-2 for the two test sites. The array depth was maintained between 60 to 80 m near the thermocline in the Gulf of Maine, and varied between 10 and 50 m at the continental slope region. 54

56 Figure 3-1: Locations of the two test sites where the densely-sampled, towed horizontal coherent receiver array was deployed to collect ambient noise data in May Site A is in the Gulf of Maine shallow water environment and site B is in the deeper continental slope environment. Figure adapted from [5]. 55

57 Site A: Gulf of Maine Depth (m) Site B: Continental slope Sound speed (m/s) Figure 3-2: Measured sound speed profiles at the two test sites shown in Fig Figure adapted from [5]. To investigate the presence of sperm whale clicks, time-frequency spectrograms of the received signal on each hydrophone were first calculated, and the spectrogram incoherently averaged across several hydrophones were obtained. Sperm whale clicks were consistently present in all 75 minutes of passive acoustic recordings on May 13 at the continental slope region and one hour of passive acoustic recordings in the Gulf of Maine shallow waters. No active acoustic sound sources were used in the towed receiver array sea test. The maximum frequency of the acoustic data recorded by the receiver array system here is 2.5 khz. Our analysis of sperm whale clicks is therefore limited to the 56

58 low frequency component of the click signals in the several hundred Hz to a couple of khz range that is more omnidirectional [52, 73, 74] and suffer less transmission loss. In contrast, the sampling frequencies of acoustic systems in previous sperm whale studies were significantly higher, by at least a factor of three [73, 74]) to over ten times that used in this study to provide a more complete coverage of the bandwidth of the sperm whale click that can extend to 30 khz [49, 52, 63, 68, 72, 84] Determining click arrival time and azimuthal bearing The relative horizontal azimuthal direction or relative bearing ˆβ of each sperm whale click, measured from array broadside, was next estimated using time-domain delayand-sum beamforming [85]. The pressure-time series data from each hydrophone of the array were first high-pass filtered with 300 Hz cut-off frequency. Each twodimensional (2D) matrix of high-pass filtered pressure-time series data from the 32- elements of the array within roughly 13 s duration was next converted to 2D beamtime data by steering the array in 400 azimuthal directions equally spaced from -1 to 1 in sin β,whereβ is the azimuthal angle measured from array broadside. An angle of sin β = 1 corresponds to the back endfire direction and sin β =1 corresponds to the forward endfire direction. The relative azimuthal direction and time of arrival of each sperm whale click were determined from the local peak energy levels of the 2D beam-time data. In general, the sperm whale clicks after high-pass filtering and beamforming stood between 10 and 35 db above the background. A detection threshold of 10 db above the background was applied in the local peak detection to reduce the false alarm rate. 57

59 Frequency (Hz) 2500 (A) Pressure (µpa) 5 x 10 Normalized level (db) (B) 0 Pressure level (db re 1 µpa) 5 Beamformed filtered signal Average in band noise level Detection threshold 100 (C) Time (seconds) Figure 3-3: (A) Spectrogram of a series of sperm whale echolocation clicks recorded at frequencies up to 2.5 khz in the Gulf of Maine on May 14, starting at 17:19:07 EDT. The spectrogram was calculated using a short-time Fourier transform with window size 256 and 75% overlap. (B) Beamformed pressure time series of the clicks, bandpass filtered between Hz. (C) Beamformed pressure time series plotted in decibel (db) scale. The solid curve with errorbars shows the mean and standard deviation of beamformed background ambient noise level in the Hz band, estimated from regions outside of clicks. Figure adapted from [5]. Spectrogram and time-series examples of the beamformed received click trains are shown in Figs. 3-3 and 3-4. Since each sperm whale click contains multiple sharp pulses highly localized in time with a width of less than 1 ms per pulse (see Fig. 3-8), the click signal resembles the output of a matched filter. This enables high resolution beamforming in the time domain, since coherent addition of the pulses across all hydrophones decorrelates within a small time lag of roughly 1/8 ms, corresponding to 58

60 bearing estimation accuracies of approximately 1.7 at array broadside and 8 near array endfire. In contrast, the array angular resolution is much broader, roughly λ/(l cos β )=3.7 at broadside and λ/L =22.7 at endfire from planewave beamforming of a time-harmonic signal, where λ, L, and β are respectively the wavelength, array aperture and azimuthal direction from array broadside [85] for the given array aperture L=23.25 m at a frequency of 2 khz. Examples of the beam pattern obtained from beamforming two distinct sperm whale clicks, one located near array broadside and the other near array endfire are shown in Fig The direction of arrival is clearly distinguishable since the main lobe stands more than 8dBabove the grating lobe in both cases, mitigating any potential effect of spatial aliasing. 59

61 Frequency (Hz) 2500 (A) Normalized level (db) 5 Pressure (µpa) 2 x 10 (B) 0 Pressure level (db re µpa) 110 (C) Pressure level (db re µpa) (D) Beamformed filtered signal Average in band noise level Detection threshold single hydrophone, filtered Time (seconds) Figure 3-4: (A) Spectrogram of 3 consecutive slow clicks followed by a train of echolocation clicks recorded at frequencies up to 2.5 khz in the Gulf of Maine on May 14, starting at 17:16:15 EDT. (B) Beamformed pressure time series of the clicks, bandpass filtered between Hz. (C) Beamformed pressure time series plotted in decibel (db) scale. The solid curve with errorbars shows the mean and standard deviation of beamformed background ambient noise level in the Hz band, estimated from regions outside of clicks. (D) Corresponding signal received on a single hydrophone, bandpassed filtered between Hz. Figure adapted from [5]. 60

62 0 5 Endfire steering Broadside steering Beamformer output (db) Steered direction (sin θ) Figure 3-5: Array beamformer output as a function of steering angle from array broadside 0 shown for two distinct time instances. Sperm whale clicks with relative bearing 3.7 near array broadside and 73.7 near array endfire. The corresponding 1-dB beamwidths are approximately 1.7 near broadside and 8.0 near endfire. Rectangular window was applied across the array aperture. Figure adapted from [5]. 61

63 The estimated relative bearings ˆβ measured with respect to array broadside were then converted to absolute bearings ˆβ, measured from the array center with respect to true North by correcting for the corresponding array heading measurement α. To resolve the left-right ambiguity inherent in linear receiver array measurement of a source bearing, the left and right absolute bearing sequences were statistically correlated to the measured array headings. The true bearing sequence was selected to be the one with the smaller correlation coefficient, since the ambiguous bearing sequence closely follows the array heading changes as shown in Fig. 2 of [65]. When thearray is steered in the azimuth of sperm whale clicks, the array gain [28,86] obtained from coherent addition of the click signals measured across all N = 32hydrophonescan enhance the signal-to-noise ratio by approximately 10 log 10 N 15 db over that of a single hydrophone (compare beamformed click signals in Fig. 3-4(C) with single hydrophone measured click signals in Fig. 3-4(D)). This significantly improves sperm whale click detectability and ranging capability. Note that an incoherent array of hydrophones also has no array gain over noise, regardless of the number of hydrophones, since coherence between sensors is necessary to accumulate array gain. Subsequent analyses on the temporal and spectral characteristics of the clicks were performed on the noise-suppressed beamformed clicks Range estimation for sperm whales in the near- or farfield of the towed horizontal coherent receiver array Each sperm whale individual was localized and tracked from its corresponding sequence of click bearing measurements using the moving array triangulation (MAT) technique [65, 87], which combines bearing measurements from spatially separated apertures of a towed horizontal receiver array and employs the conventional triangulation ranging algorithm to localize a source in either the near- or far-field of the array. The whale range from the receiver array center was calculated using Eqs.(1)through (3) of [65] given a pair of whale bearing measurements. The synthetic aperture length 62

64 A s created by the array movement between pairs of whale bearing measurements in the MAT technique has to satisfy the near field condition, A 2 s /λ r w,wherer w is the whale range from the receiver center and λ is the wavelength of the click signal. To localize and track sperm whales at ranges less than 5 km from the array, with λ set to be 0.75 m, the synthetic aperture length should be at least 60 m. The array can be towed over this distance in half a minute, so that near real-time tracking of sperm whales is feasible with this method. To track sperm whales at longer ranges with the MAT technique, longer observation times would be necessary. The sperm whale inter-click interval is approximately 1 second or less in a click train and the receiver array heading was updated at roughly 12 s intervals. The MAT technique was applied to pairs of click bearing measurements that were at least 12 seconds apart to estimate each whale range. The whale range estimates obtained here are expected to have smaller fractional errors than the MAT localization fractional errors reported in [65]. This is because, by the law of large numbers [14,88], there are roughly six times more numerous range estimates derived from bearing measurements embedded in noise which can be regarded as statistically uncorrelated across time for the sperm whale problem compared to [65] where only one range estimate was available at every 75 seconds interval for the source localization problem discussed there. We also demonstrate here the feasiblility of employing the array invariant [6] to localize the sperm whale in range using only one single broadband click arrival. Previous localization results have shown that the method was efficient for medium [6, 65] and long ranges, using measurements from a man-made broadband chirp or explosions. Here we show that the broadband nature of the sperm whale clicks, which results in multi-modal arrival structures, can enable localization at short ranges on the order of a few hundred meters. The ranging result is then compared to those obtained using the moving array triangulation technique. 63

65 3.1.4 Simultaneous depth and range estimation for a sperm whale in shallow water The range and depth of a sperm whale located approximately 1 km from the receiver array in the Gulf of Maine were simultaneously estimated using multiple-reflection based time difference of arrival (MR-TDA) of beamformed direct and singly or multiply reflected click signals from sea bottom and surface. The concept for whale range and depth inference is similar to that presented in [89]. However, since thearray depth was accurately known from depth sensor measurement sampled every 10 ms, there was one fewer unknown. As a result, only three arrivals: direct path, bottom bounce, and surface bounce were required to solve for whale range anddepthasde- rived and discussed in Appendix A. When more than three arrivals were present, the localization result could be obtained with higher accuracy by employing all available information (see Appendix A). The whale range estimates obtained using MR-TDA will be compared to those obtained with bearings-only MAT method in Sec

66 3.2 Results: Tracking a sperm whale in shallow waters of the Gulf of Maine Analysis of vocalizations Vocalizations from a sperm whale individual at site A in the shallow-waters of the Gulf of Maine were recorded using the towed receiver array for over anhourfrom 16:35:00 to 17:40:00 EDT on May 14. An example of the beamformed time series and spectrogram of an echolocation click train is shown in Fig These measurements were made in water-column depths of roughly 160 m where the receiver array was located at roughly 65 m depth. The average inter-click interval was approximately 0.7 s, which implied that these clicks could be categorized as usual clicks [90]. Spectrogram analysis indicates that the clicks contain significant energy at low frequencies in the 1.5 khz to 2.5 khz range. This enabled the beamformed, high-pass filtered, timeseries data of the clicks to stand between 15 db to 30 db above the mean background ambient noise level (Fig. 3-4C). Click rates were found to vary within an echolocation click train, as shown in Fig. 3-3, where the inter-click intervals and click amplitudes decrease slowly over a time interval of about 20 seconds. This implied that the sperm whale vocalizations could be transitioning from clicks to creaks, which are a sequence of low energy clicks closely spaced in time emitted when homing in on a prey [51,91]. Besides these usual echolocation clicks, we also recorded intense broadband clicks with dominant energy contained in the 0.5 khz to 2 khz frequency range. These loud clicks were separated by intervals of 5 seconds or longer (see Fig. 3-4) and can be categorized as slow clicks [62, 92 94]. The spectra of both the echolocation and slow clicks recorded here closely match those of DTAG-recorded sperm whale click vocalizations shown in Fig. 1 of [92]. The occurrences of the recorded vocalizations are shown against time in Fig

67 with click types indicated. Each echolocation click train lasted roughly 2 minutes with periods of silence varying between 20 seconds and several minutes. Longer periods of silence lasting between 5 to 10 minutes observed here may be associated with the sperm whale s ascent in the water-column [52] and resting near the surface. 120 Bearing from true North (degrees) Array heading Echolocation clicks Slow clicks 16:40 16:50 17:00 17:10 17:20 17:30 17:40 Time (EDT) Figure 3-6: Measured bearings of sperm whale echolocation and slow clicks detected in the Gulf of Maine on May 14 over a 1-hour period from 16:35 to 17:35 EDT. Figure adapted from [5]. By analyzing each received click in the time interval from 17:18:00 to 17:33:00 EDT, we estimated the mean inter-pulse interval (IPI) for this sperm whale individual to be 3.0 ms with a standard deviation of 0.3 ms. This corresponds to a sperm whale length of approximately 9.3 m, according to [57]. 66

68 3.2.2 Tracking range and depth of a sperm whale close to array near-field The estimated bearings of the vocalizations obtained via time-domain beamforming are plotted in Fig The instantaneous sperm whale ranges were estimated from the measured whale bearings using the bearings-only MAT technique for the time interval from 17:08:00 to 17:33:00 EDT and plotted in Fig. 3-7A. 1 (A) 17:32:40 Receiver track MAT MR TDA Range (m) (B) Northings (km) :18:30 17:15:20 Depth (m) 0 17:15 17:20 17:25 17:30 17: (C) Eastings (km) :15 17:20 17:25 Time (EDT) 17:30 17:35 Figure 3-7: (A) Single sperm whale in Gulf of Maine localization result using the two methods, MAT and MR-TDA for the period between 17:15:20 and 17:32:40 EDT. The ellipses represent contours of localization uncertainty at each time instance with MAT (solid curve) and with MR-TDA (dashed curve). The origin of the coordinate system is located at ( N, W). (B) Range estimates using MAT and MR- TDA between 17:18:00 and 17:32:40 EDT. The errorbars show the standard deviation of the range estimates in a 4-minute time window. (C) Depth estimates for the same time period. Figure adapted from [5]. In the shallow water Gulf of Maine environment, clicks arriving at the receiver array from the sperm whale in close range to the array nearfield distance display clear patterns of multiple reflection between the sea bottom and surface. The evolution of multipath arrival times is shown for all the clicks recorded between 17:18:00 67

69 and 17:33:00 EDT in Fig The direct arrival time of each click was first determined and aligned in time before the stacked sequence of clicks was created. Between 17:18:00 and 17:23:00 EDT, the first-order bottom and surface reflected arrivals are distinguishable in time, crossing each other due to vertical displacement of the whale. At other time instances, the bottom and surface reflections are not clearly distinguishable. The higher-order reflected arrivals are more prominent with shorter time separation for the later clicks in the time period analyzed. Multiple reflections in the shallow water waveguide extends the received sperm whale click time duration from ms of the direct arrival [53] to more than 250 ms. 18 Time (minutes from 17:00 EDT) Relative travel time (ms) Figure 3-8: Multiple reflection arrival pattern of the sperm whale clicks detected on May 14 in the Gulf of Maine. The order of arrival is: direct path; pairs of bottom and surface reflected, bottom-surface-bottom and surface-bottom-surface reflected etc. Between 17:26:00 and 17:32:30 EDT, reflections from up to 7 interface bounces are detected. Figure adapted from [5]. The sperm whale range and depth were also simultaneously estimated by applying the multiple reflection time difference of arrival (MR-TDA) technique described in Appendix A for the time interval from 17:18:00 EDT to 17:33:00 EDT. All esti- 68