Shallow Water Acoustics

Broadband Geoacoustic Inversion using Single Hydrophone Data

R. Chapmana, A. Agarwala, J. Deserta, X. Demoulinb and Y. Stephanb

aSchool of Earth and Ocean Sciences, University of Victoria, PO Box 3055, Victoria, B.C. Canada V8W 3P6 bCMO-SHOM, B.P. 426, 29275 Brest, France

Inversion methods based on spatial coherence of multi-tone CW data have been applied extensively in underwater acoustics to estimate geoacoustic profiles. This paper presents results for a different approach based on broadband waveform inversion at a single hydrophone. The inversion is formulated as an optimization problem to determine the geoacoustic model that provides the best fit between calculated and measured waveforms. A hybrid simulated annealing algorithm is used to search the multi-dimensional model parameter space. The method is applied to data from the INTIMATE98 shallow water experiment to estimate the sound speed and density at the sea floor.

INTRODUCTION and uncertain knowledge of the experimental geometry precluded conventional matched field processing. The Matched field inversion methods that take advantage broadband chirp signals (bandwidth of 300 – 1000 Hz) of the spatial coherence of acoustic field information at were time-compressed using a template signal an array of hydrophones have been used successfully recorded near the source, and averaged over one to invert geoacoustic profiles in shallow water[1,2]. minute. The processed replica correlogram About 10 years ago, Frazer and Pecholcs introduced an approximated the impulse response of the waveguide, alternative approach to narrow band/wide aperture and was used as the data for the inversion. matched field methods and showed formally that similar inversion performance could be expected for broadband data and small aperture geometries[3]. More recently, this approach was applied in work INVERSION METHOD reported by Hermand[4] and Michalopolou[5]. This paper uses a time domain approach and presents The inversion method is based on waveform modeling results for geoacoustic inversion using broadband data in the time domain. The inverse problem is formulated measured at a single hydrophone. as an optimization problem to determine the geoacoustic model that provides the best match between the measured and modeled impulse responses of the shallow water waveguide. We assume that the INTIMATE’98 EXPERIMENT processed replica correlogram of the chirp signal is an adequate representation of the impulse response. In The method was applied to data from the this work, the modeled impulse response is calculated INTIMATE98 experiment that was carried out at three using the ORCA normal mode propagation model to sites on the continental shelf in the Bay of Biscay[6]. compute pressure fields at specific frequencies within The data considered in this paper were obtained on a the signal band[7]. The time series is generated by very short 8-element, 6-m vertical line array that was inverse Fourier transforming the spectral components. deployed at one of the sites at a depth of about 80 m. The cost function, E(m), for comparing the waveforms The array recorded 2-s and 4-s chirp signals that were is given as the cross-correlation function calculated transmitted every 12 s from a projector at a depth of over lags : about 90 m as the source ship closed range on the array to about 600 m. At this close range, the ocean N waveguide approximated a range-independent sand max p (t )r(t) i1 i sediment environment. The water sound speed was E(m) 1 (1) N N sampled by XBTs and CTD casts at regular intervals 2 2 pi (t) ri (t) during the experiment. The very small array aperture i1 i1 where P(t) is the measured impulse response, r(t) is the The estimated values for the experimental modeled impulse response and is the time delay that geometry agree closely with the experimental maximizes the cross-correlation between the two time measurements for range and source depth. Array series. For the perfect match, E = 0, otherwise the depth (for the topmost hydrophone) was known only value of E will lie between -1 and 1. A hybrid search within about 5 m during the experiment. Water depth algorithm that combines simulated annealing with a was known to be around 150 m from available local downhill simplex algorithm is used to search the bathymetric data, and the estimated values of sea floor multi-dimensional geoacoustic model parameter sound speed and density are consistent with the values space[8]. The simplex method has proved to be an expected for the medium-grain sandy sediment at the efficient search process for navigating parameter site. Although not shown in the table, the estimates for spaces in which parameters are correlated. water depth and source depth were strongly correlated. As might be expected, the estimates for source depth and receiver depth are negatively correlated. The correlations between the measured and the modeled INTIMATE98 DATA INVERSION impulse responses that were calculated using the values estimated from the inversions for each The inversion estimated the parameters of a simple individual hydrophone were around 90%. three-layer geoacoustic model consisting of a water layer with known sound speed profile over a thin The results presented in this paper demonstrate that sediment layer and a half space. The most sensitive broadband, single-hydrophone information is effective geoacoustic parameters were the water depth and the for matched field inversion, especially in this sediment sound speed at the sea floor. Since the experiment where the conventional approach was not experimental geometry was not well known, the source viable due to the very small array aperture and the depth and range, and the array depth were also uncertain experimental geometry. The inversion has included in the search process. A total of twelve achieved an overall low level of mismatch in the geoacoustic and geometric parameters were estimated. acoustic data, internal consistency among the estimates However, as might be expected for the high frequency from the array hydrophones, and close agreement with chirp signal, the sensitivity of all but the sea floor known a priori or ground truth information. geoacoustic parameters was very low.

The inversion was applied to data from the end of one of the approaching source tracks where the ship REFERENCES held position at a range of about 650 m. For this range, the impulse response consisted of three strong 1. N. R. Chapman and C. E. Lindsay, IEEE J. Oceanic multipath signals followed by much weaker secondary Eng., 21, 347-354, (1996). arrivals. The dominant multipath signal corresponded 2. J-P. Hermand and P. Gerstoft, IEEE J. Oceanic Eng., 21, to the direct path, single bottom reflection and single 324-346, (1996). surface reflection paths, and the bottom and surface reflected paths. Arrivals comprised of multiple 3. L. N. Frazer and P. I. Pecholcs, J. Acoust. Soc. Am., 88, bottom/surface reflections followed the dominant 995-1002, (1990). group and were about ten times weaker. 4. J-P. Hermand, IEEE J. Oceanic Eng., 24, 41-66, (1999). The inversion was applied separately to the same signal received on each of the array hydrophones. The 5. Z-H. Michalopulou, J. Acoust. Soc. Am., 108, 2082-2090, results are shown in Table 1 where the mean over the (2001). eight hydrophones and the ranges of the estimates are 6. Y. Stephan, T. Folegot, J. Leculier, X. Demoulin and J. shown. Small, Report 48/EPSHOM/CMO/OCA/NP (1999)

Table 1. Parameter estimates 7. E. K. Westwood, C. T. Tindle and N. R. Chapman, J. Parameter Mean Estimated value Acoust. Soc. Am., 100, 3631-3645, (1996). Water depth (m) 149 ± 3 Sediment sound speed (m/s) 1660 ± 5 8. M. R. Fallat and S. E. Dosso, J. Acoust. Soc. Am., 105, 3 Sediment density (g/cm ) 1.8 ± 0.2 3219-3230, (1999). Range (m) 651 ± 5 Source depth (m) 90.5 ± 2 Array depth (m) 79 ± 1 Coral reef and tropical shallow water soundscapes John R. Potter(a) and Eric Delory(b) (a) Acoustic Research Laboratory, Tropical Marine Science Institute, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260. [email protected] http://www.arl.nus.edu.sg (a) Unidad de Investigacion para la Conservacion de los Mamiferos Marinos, Departamento de Morfologia, Facultad de Veterinaria, Universidad de Las Palmas de Gran Canaria, Trasmontaña, 35416 Arucas, Gran Canaria, Islas Canarias, España. [email protected] Much is known about deep ocean ambient noise, rather less about the more highly structured and variable noise in temperate coastal waters, and rather little about the tropical shallow waters that include coral reefs and the biological diversity these ecosystems support. Interest in shallow water acoustics has been growing over the last decade, and more recently specific interest has bloomed in tropical shallow water and the features particular to these areas. As sonar systems and operations become more complex, moving towards the use of ambient noise and the need for communicating via networked acoustic modems in noisy environments, the soundscape of shallow waters has become more important. This paper presents some of the challenges and advantages of tropical shallow water acoustic environments, and makes some geographic comparisons. While some aspects of tropical ambient noise make life more difficult, such as the non-Gaussian energy distribution of snapping shrimp noise, other aspects are seen to be quite robust, such as the very similar pulse signatures of snapping shrimp over widely- separated regions. The development of signal processing tools based on wavelet and other compact transforms to deal with the detection, separation, and classification of overlapping tropical shallow water noise sources is discussed. commonly usable bandwidth (from a few kHz INTRODUCTION to over 350 kHz) We present a simplified characterisation of ambient noise conditions in shallow tropical SOME CHARACTERISTICS OF waters, excluding wind-driven noise from the SNAPPING SHRIMP SOUNDS sea surface. Wind and resulting wave noise has been more extensively studied and much The characteristics of snapping shrimp more is known about these sources than noise are remarkably consistent across the biological sources in warm shallow water. globe. This may perhaps be explained by the Surf noise can also be very important, but recent discovery that it is not the mechanical obviously only when near a surf line. This impact of the animals jaw parts that creates the paper concerns itself with ambient sources in sound, but the cavitation bubble formed by the somewhat deeper water, in the region of 5-50 rapidly ejected water jet [1]. Thus, while the m. exact physiological characteristics of the jaws may differ between slightly different species, WARM SHALLOW WATER cavitation bubble physics remains much the same. Differences in amplitude and some NOISE SOURCES changes in bandwidth may be expected from In the absence of wind and surface wave larger or smaller shrimp. A typical time series sources (or, if present, in addition to them), acoustic record (normalised to ±1) in warm this paper argues that the plethora of ambient shallow water is shown in the upper panel of noise sources in shallow water can be usefully Fig. 1. The lower panel shows the time- divided into four main classes, so separated frequency plane result for the same data. A because of their very different structures in the measure of the degree of non-Gaussian time-frequency plane. These classes may be behaviour can be made by calculating the described as: scintillation index, SI (normalised variance of intensity) given by · Near transients (such as snapping shrimp) 2 2 · Near tonals (such as shipping machinery SI = I 2 - I I Equation 1 noises) · Coloured background (smoothly varying where I is the acoustic intensity and <> in the frequency domain) indicates the ensemble average [2]. The value · Time-Frequency transients (biologic or of SI increases as extreme values of acoustic man-made). pressure become more common. For a zero- The Near-transients are of particular mean Normally distributed random variable, SI interest to us, since they often consist of = 2 irrespective of the mean power. We have snapping shrimp (at least in warm waters, analysed shallow-water acoustic records from above 11 degrees C) and dominate 99% of the several widely spread countries and calculated FIGURE 1. Time series and spectrogram of snapping shrimp from San Diego (courtesy of SIO, UCSD) the SI. In each case, the record was dominated must be relied upon for ANI. by snapping shrimp sounds, although with varying degrees of other noise sources also audible. The results are given in Table I. WAVELET SEPARATION OF SHALLOW WATER SIGNALS The results indicate that the records are all We have developed a shift-invariant highly non-Gaussian and also highly non- stationary (the standard deviation of the method for separating near-transients based on scintillation index is often comparable to the a first-level wavelet decomposition and index value itself). Nevertheless, the pseudo-entropy test [3]. If the information cost of representing the data at the first level consistency of bubble pulse transient across decomposition exceeds the zeroth level, then wide geographical areas is striking, and may significant near-transients are present and a be of fundamental importance to reef health and shallow water ecosystems; it has been cross-correlation between the two first-level suggested that fish fry navigate to and from decomposition coefficients identifies the common features. These can then be removed reefs to find food and avoid predators by and the signal reconstituted. A similar homing on the sound of snapping shrimp [Eric method, using Cosine Packet Transforms, can Wolanski, personal communication]. be used to remove near-tonal signals. Smooth- Fig. 1 also shows that there is generally a spectrum coloured noise is then removed by considerable interval between snaps compared soft thresholding a conventional biorthogonal to snap length (typically 30 ms). A Poisson wavelet packet decomposition, leaving only model applied to data from several locations the time-frequency transients. An acoustic indicates that there are 0.01-0.25 snaps per signal can thus be neatly split into these four square m of seabed per second (depending on classes, with each class separately terrain), and that typically some 30 ms lapses reconstituted for further analysis. For between snaps that are 20 dB or more above example, near-transients may be used for ANI, the mean power level. This temporal structure and time-frequency transients for the passive permits deterministic ambient noise imaging detection of whales or submarines. (ANI) to be performed for ranges up to 50 m or so. At larger ranges, statistical techniques ACKNOWLEDGEMENTS Table I. Scintillation Index values for several We thank the many helpful colleagues who shallow-water sites around the world. have provided acoustic time series records from around the globe in support of this work. Location Scintillation Sigma of SI Index, SI estimates REFERENCES 1. Versluis, M. Schmitz,B, Von der Heydt, A Domenican 427 132 Republic and Lohse, D. Science 289 2020-2021, (2001). Eilat, Israel 88 83 2. Uscinski, B.J. “The elements of wave Johore, Malaysia 48 15 propagation in random media”, McGraw Hill, London, p 62, (1977). San Diego, USA 223 114 3. Delory, E. and Potter, J.R. DSO/NUS joint Singapore 33 10 seminar series, 1999. Parabolic equation techniques for scattering in a waveguide J. F. Lingevitcha, M. D. Collinsa and M. J. Millsb aU. S. Naval Research Laboratory, Washington, DC 20375 bMitre Corporation, McLean, VA 22102-3481

Parabolic equations are an efficient technique for solving wave propagation problems in range-dependent media. The method is based upon a factorization of the wave equation into incoming and outgoing waves. Wide propagations angles are handled by implementing higher order rational approximations of the factored operator. In gradually varying range-dependent media, the outgoing energy dominates the backscattered component and the outgoing wave satisfies a parabolic equation which can be solved accurately and efficiently with a range marching algorithm. Accuracy of the outgoing wave is maintained by conserving energy flux across vertical interfaces. In cases where backscattered energy is significant, the single scattering approximation is used to derive the two-way parabolic equation. This method has been applied to diffraction gratings and the Sommerfeld diffraction problem. Multiple scattering can also be incorporated into the parabolic equation method by implementing an iterative sweeping method whereby incoming and outgoing energy is coupled. We demonstrate these methods and compare with analytic results and benchmark solutions generated by a coupled normal mode model.

PARABOLIC EQUATION METHOD In a slowly varying range-dependent environment where the backscattered energy is negligible, an accurate The linearized wave equation for the pressure p in a solution is obtained with the parabolic equation by con- ﬂuid can be expressed as an elliptic equation of the form: serving energy ﬂux across vertical interfaces. A linear

condition for conserving energy ﬂux across vertical inter- ∂2

2 faces is given by

¦ §

k 1 X £¥¤ p 0 (1)

¢ ¡

∂x2 ¡ 0

1 2 1 4

¦ §

ρ 1 X £ p 0 (6) ¢ where k0 is a reference horizontal wavenumber. The ¡

depth operator X is given by, where denotes the jump across a vertical interface [7]. ∂ 1 ∂ The narrow angle approximation of Eq. (6),

2 ρ 2 © 2 ¨ ¤ §

X ¦ k k k (2) 0 ∂ ρ ∂ ¡ 0

z z p ρ ¦ 0 (7)

1 c

ρ ¦ ω where is the ambient density, k c ¨ is the medium ω wavenumber, c is sound speed and is circular fre- is sufﬁcient for many applications in ocean acoustics. quency. In a range-independent environment the operator

in Eq. (1) factors,

∂ ∂ TWO-WAY PARABOLIC EQUATION

1 2 1 2

¤ £ ¤ ¦ §

ik 1 X £ ik 1 X p 0 ¢

0 ¢ 0

¡ ¡ ∂x ¡ ∂x (3) For problems involving strong backscatter, the two- into incoming and outgoing waves. In this case the out- way parabolic equation has been developed to enforce going wave satisﬁes a ﬁrst order equation in range continuity of pressure and displacement at a vertical interface in the single scattering approximation [8], ∂p

1 2

£ § ¦ ik 1 X p (4)

0 ¢ ¡ ∂ pi pr ¦ pt (8)

x ¡

∂ ∂

pi pr pt § with a solution [1] that can be marched outward in range ∂x ¦ ∂x (9)

according to, § where the subscripts i § t r refer to the incident, transmit-

1 2 ted and reﬂected ﬁelds respectively. The interface condi-

∆ £ £ £

p x ∆x £ ¦ exp ik x 1 X p x (5)

¢ ¢ ¢

¢ 0 ¡ ¡ tions are implemented by replacing the range derivatives The operators in Eqs. (4,5) are approximated by ratio- with depth operators derived from the outgoing and in- nal functions [2, 3, 4]. Operator approximations of the coming factors of Eq. (3), square root operator based on rotations of the branch cut

pi pr ¦ pt (10)

are useful in stabilizing the iteration formulas to be dis- ¡

−2 In problems where multiple scattering is important, the

−1 two-way parabolic equation can be generalized to an iterative sweeping algorithm over the computational domain. 0 y (m) Consider a problem involving N range-independent re- 1 gions, where the vertical interface between regions j and 2

j 1 is located at x ¦ x j and the source is located in the ¡

3 ﬁrst region at x ¦ 0. To avoid stability problems associ-

¤ © 4 ated with the evanescent modes, we define p j to be the −2 −1 0 1 2 3 4 5 6 © x (m) outgoing field at the beginning of region j and ¥ p j to be the incoming field at the end of region j. The vertical FIGURE 1. Parabolic equation solution for the Sommerfeld

knife edge problem with Dirichlet conditions on the knife edge. interface conditions become,

¤ ¤

The incident ﬁeld is a plane wave. ©

¥ ¥ E p p ¦ p E p (13)

j j 1

j j j 1 j 1 ¡ ¡

¤ ¢ ¢ ¤

1.2

¦ ¥ ¥ £

D E p p £ D p E p (14)

j j j 1 j 1 j j j 1 j 1

1 1 2

ρ ¨ £ D ¦ ik 1 X (15) j 0 ¢ j

j ¡

0.9

¢ ©

1 2

¦ £ £

E exp ik x x 1 X £ (16) ¢

j 0 ¢ j j 1 j

¡ ¨

0.6

Amplitude

¦ ¥ The unknowns include p for 2 ¦ j N and p for

¤ j j

¦ ¦ 0.3 1 j N 1; p 1 and p N are speciﬁed by source and radiation conditions respectively. Iteration formulas for the

0.0 outgoing and incoming ﬁelds can be solved efﬁciently by -4 -3 -2 -1 0 1 2 3 4 y (m) repeatedly iterating out and back in range.

FIGURE 2. Quantitative comparison of amplitudes of the parabolic equation solution (solid) and exact solution (dashed) at x 5 m for the Sommerfeld diffraction problem shown in ACKNOWLEDGMENTS Figure 1.

Work supported by ONR. ¡

1 2 §

where L 1 X £ and the subscripts A B refer to the ¢

¡ REFERENCES incident and transmitted medium respectively. An iteration formula for the transmitted field follows from elimi- 1. M. D. Collins, J. Acoust. Soc. Am. 93, 1736-1742 (1993). nating the reflected field in Eqs. (10,11), 2. J. F. Claerbout, Fundamentals of Geophysical Data Pro- cessing McGraw-Hill, New York, 1976 pp. 206-207.

1 ¢

¦ ¨ pt pi 1 L LB £ pt (12) 3. A. Bamberger, B. Engquist, L. Halpern and P. Joly, SIAM

¡ A 2 J. Appl. Math. 48, 129-154 (1988). In the limit of gradual range dependence, the two-way 4. M. D. Collins, J. Acoust. Soc. Am. 86, 1097-1102 (1989). parabolic equation yields solutions consistent with the en- 5. F. A. Millinazzo, C. A. Zala and G. H. Brooke, J. Acoust. ergy conserving solution [6]. Soc. Am. 101, 760-766 (1997). A similar method has been developed for solving scat- 6. J. F. Lingevitch and M. D. Collins, J. Acoust. Soc. Am. 104, tering problems with Neumann or Dirichlet conditions 783-790 (1998). on the scatterer [9]. In this case the incident and scat- 7. M. D. Collins and E. K. Westwood, J. Acoust. Soc. Am. 89, tered ﬁelds may be of comparable amplitude. For a scat- 1068-1075 (1991). terer that is a delta function in range, the single scattering method should yield the exact solution. The parabolic 8. M. D. Collins and R. B. Evans, J. Acoust. Soc. Am. 91, 1357-1368 (1992). equation solution for scattering of an incident plane wave from a knife edge (the Sommerfeld diffraction problem) 9. M. J. Mills, M. D. Collins and J. F. Lingevitch, Wave Mo- is shown in Figure 1. Figure 2 shows that the amplitude of tion 31, 173-180 (2000). the parabolic equation solution is in excellent agreement

with the exact solution at x ¦ 5 m [9]. Acoustical signal ﬂuctuations in time–varying shallow–water environments P. L. Nielsen and M. Siderius SACLANT Undersea Research Centre, Viale S. Bartolomeo 400, 19138 La Spezia, Italy

Oceanographic and acoustic data collected in two benign shallow-water areas in the Mediterranean Sea are presented. These data are processed to assess the extent of time variability in received acoustic signals transmitted over ﬁxed propagation path over a period of several hours. The variability in received energy levels and de-correlation time of the acoustic signals is clearly affected by this weakly time-varying ocean environment.

SOUND-SPEED STRUCTURE INTRODUCTION The sound-speed structure along the acoustic propagation track was obtained by a towed Conductivity- Sound propagation in shallow-water is strongly Temperature-Depth (CTD) chain. The left panel in Fig. dependent on the actual underwater environment, e.g. 1 shows the CTD-chain data for the PROSIM’97 exper- seabed properties, water-column sound speed, sea iment (total of 4 tows over a 36 h period) and the right surface state etc. Recently the effect of a time-varying panel for the ADVENT’99 experiment (total of 18 tows ocean on sound propagation in shallow-water has been over a 18 h period). assessed experimentally [1, 2]. A strong filtering effect ( 20 dB) in received energy levels at around 600 Hz was PROSIM’97 (m/s) ADVENT’99 (m/s) 1514 seen in the Yellow Sea (China) [1], and a de-correlation 0 1522 time of received acoustic signals down to a few minutes 20 1519 1513 at a frequency of 224 Hz over a 40-km propagation path 40 1516 1512 was observed in the SWARM experiment off the coast of 1511 60 1513 New Jersey (USA) [2]. These fluctuations in the acoustic Depth (m) 1510 1510 80 signals are most likely due to strong time-dependent 1507 1509 internal waves altering the sound-speed structure along 0 5 10 0 5 10 Range (km) Range (km) the acoustic propagation path. This strong internal wave activity in the two experimental areas was known a priori FIGURE 1. Sound-speed structures measured by a towed CTD- to the acoustic measurements. The time variability of the chain along the acoustic propagation track for the PROSIM’97 water-column sound speed is often neglected in sound (left panel) and ADVENT’99 (right panel) experiments. propagation prediction although these oceanographic The PROSIM’97 CTD-data clearly shows a warm fluctuations can have significant impact on stability of (high sound speed) surface layer with a thermocline ex- arrival time and received energy levels. Also, the uncer- tending down to a depth of 30 m. Hereafter the sound tainty in inferred bottom properties from Matched-Field speed is almost constant with depth. The depth of the geo-acoustic inversion increases with the presence of thermocline varies along the track and with time, and a water-column sound-speed fluctuations [3]. front-like feature is seen at a range between 5 and 10 km. The ADVENT’99 CTD-chain data shows an almost isovelocity water column with only 5 m/s variation in sound SACLANTCEN conducted the PROSIM’97 (May speed from sea surface to the bottom. However, the 1997) and ADVENT’99 (April/May 1999) experiments acoustic track is divided into a low and high sound-speed in the Mediterranean Sea in order to assess acoustic signal region. The position of the boundary between these 2 re- fluctuations in benign shallow-water areas. Broadband gions and the shape of the high sound-speed part along acoustic signals (200-850 Hz) were transmitted over fixed the track (> 5 km) change with time. propagation paths: PROSIM’97 for 36 h over a 15-km path, ADVENT’99 for 18 h along a propagation path of ACOUSTIC DATA 10 km. The acoustic signals were received on a bottom- moored vertical array, and extensive oceanographic mea- The acoustic data were processed to obtain time- surements were performed during the acoustic experi- averaged transmission loss (TL) and standard deviation as ments in order to correlate the changes in the environment a function of depth at 15 and 10 km for the PROSIM’97 with changes in the received acoustic signals. and ADVENT’99 experiments, respectively. In addi- R=15km, F=350Hz R=15km, F=700Hz PROSIM’97 ADVENT’99 0 0 1 30 50 50 20 0.5 100 100 Depth (m) 10 Geo−time (h) 0 0 R=10km, F=350Hz R=10km, F=700Hz 400 600 800 400 600 800 0 Frequency (Hz) Frequency (Hz)

20 FIGURE 3. Normalized Bartlett power of received acoustic 40 signals as a function of frequency and transmission time for PROSIM’97 (left panel) and ADVENT’99 (right panel).

Depth (m) 60 cantly to within less than 1 h of transmission for both 80 80 70 60 80 70 60 experiments. Notice the significant decrease in correla- Loss (dB) Loss (dB) tion around a particular frequency over the entire trans- FIGURE 2. Time-averaged TL (black signature) and standard mission period. This decrease in correlation appears at deviation (gray shading) over depth at ranges of 15 km for a frequency around 500 Hz for PROSIM’97 and around PROSIM’97 (upper panels) and 10 km for ADVENT’99 (lower 650 Hz for ADVENT’99. The behavior of the Bartlett panels). The TL is shown for centre frequencies of 350 and correlator can be explained by the time-varying sound- 700 Hz averaged over a 10 Hz band. speed structure. Numerical modelling of sound propagation for ADVENT’99 including all 18 measured sound- speed structures shows similar behavior as observed in tion, the normalized Bartlett correlator was applied co- the data. herently over hydrophone depth for individual frequencies representing the coherence of the acoustic signals SUMMARY over time. The TL (low level) and Bartlett correlator The two fixed acoustic propagation path experiments (high level) represent two levels of processing to assess PROSIM’97 (15-km track) and ADVENT’99 (10-km the fluctuations of the received acoustic signals over time. track) show weakly range- and time-varying sound-speed The TL over depth at 350 and 700 Hz (10 Hz band aver- structures along the propagation path. This fluctuating aged) from PROSIM’97 (upper panels) and ADVENT’99 water column causes a maximum variation in the re- (lower panels) is shown in Fig. 2. In general the standard

ceived energy levels of ¢ 5 dB at higher frequencies. The deviation of the TL increases with frequency for both ex- correlation time between received signals varies from periments as higher acoustic frequency is more sensitive several hours at low frequency but decreases to < 1 h to changes in the environment. The deviation is high-

¡ at higher frequencies. The data show a clear transi- est for the PROSIM’97 experiment ( 5 dB) which may tion at a particular frequency where the correlation time be caused by: (1) longer propagation range, (2) trans- changes significantly. This behavior is attributed to the mission over 36 h compared to 18 h or (3) that the envi- changing environment. The results from the experiments ronmental fluctuations have more impact on the acoustic clearly demonstrate the complexity of sound propagation signals in the PROSIM’97 experiment. The correlation in shallow-water regions. (normalized Bartlett power) of the received acoustic signals across the array is shown in Fig. 3 for PROSIM’97 REFERENCES (left panel) and ADVENT’99 (right panel), respectively. 1. J. Zhou, X. Zhang, and P.H. Rogers, “Resonant interaction One signal received early in the transmissions is denoted of sound wave with internal solitons in the coastal zone”, as the reference signal, and all subsequently received sig- J. Acoust. Soc. Am., 90, 2042-2054 (1991). nals over time are correlated with this reference signal. 2. J.R. Apel et al, “An overview of the 1995 SWARM The correlation has a value of 0 for totally uncorrelated shallow-water internal wave acoustic scattering experi- signals and 1 for completely correlated signals. In gen- ment”, IEEE Journal of Oceanic Engineering 22, pp. 465- eral a high correlation is obtained for several hours at 500 (1997). frequencies below 500 Hz. However, after around 10 h 3. M. Siderius, P.L. Nielsen, J. Sellschopp, M. Snellen and D. the low frequency signals from the PROSIM’97 experi- Simons, “Experimental study of geo-acoustic inversion un- ment start to de-correlate while the correlation from the certainty due to ocean sound speed fluctuations”, Accepted ADVENT’99 seems stable over the 18 h of transmission. for publication in the Journal of the Acoustical Society of At higher frequencies the correlation decreases signifi- America (2001). A Method for Rapid Bathymetric Assessment Using Reverberation from a Time Reversed Mirror B. Edward McDonalda, Charles Hollandb,c aNaval Research Laboratory, Washington DC 20375, USA bSaclant Undersea Research Centre, La Spezia, Italy cPenn State University, State College PA 16804, USA

Analysis of a recent experiment (FAF99 near Elba) suggests a method for wide area rapid assessment of gently varying bathymetry. Transmissions from a vertical source/ receive array (SRA) were brought to focus at a range of several km using a time reversed signal from a 3.5kHz probe source. Adiabatic mode theory and propagation models indicate that if the focal range were set along a given gently varying shallow water path, then transmission into a slightly more upslope (downslope) environment would tend to reduce (increase) the focal range. In FAF99 we initiated probe source signals 1m from the ocean bottom, so that the time reversed SRA signal resulted in a bottom- interacting focal annulus near the probe source range. Enhanced reverberation from the focal annulus was measured at the SRA location. As illustrated in simulation studies, the gentle bathymetic variation appropriate to FAF99 implies azimuth- dependent focal shifts of order 200m for a 3km focus. A properly placed azimuth- resolving array should then be able to reveal azimuthal variation in reverberation from the focal annulus. Variations in reverberation travel time then yield bathymetric trends as a function of azimuth.

REVERBERATION AS A PROBE studies conducted for FAF99 [3, 4] indicate that the near- bottom focus is shifted away from the SRA on azimuths Boundary reverberation in the ocean is considered a around the focal annulus where the ocean is deeper than problem to sonar performance. When the properties of at the probe source, and shifted toward the SRA where the the boundary ensoniﬁcation can be controlled, however, ocean is shallower. A theoretical explanation of this effect reverberation may help to probe boundary properties. is easily derivable from adiabatic mode theory and the One method by which boundary interaction may be partly WKB approximation applied to waveguide invariants [5]. limited to a desired region is the use of a time reversed mirror [1, 2]. A probe source operating around 3500Hz was placed near the ocean bottom in some of the work Theory conducted by Saclantcen and the Scripps Oceanographic Institution in the Focused Acoustic Fields (FAF) experi- We express the acoustic ﬁeld far from a source in shal- ments north of Elba in July, 1999. The probe signal was low water as a sum of modal responses:

recorded on a vertical send - receive array (SRA) at var-

i ¥ 0 kndx

¢¤£ ¢ ¡ ious ranges between 3 and 11km from the probe source. p r¡ z ∑Anψn z e (1) The retransmitted time reversed signal resulted in a nearly n circular focal annulus centered on the SRA and passing where A and ψ are only weakly dependant on r. The through the probe source (FVLA in Figure 1). Modeling n n

acoustic intensity is then expressed as

¦ ¦ ¦

¦ r

§ ¨ ¥

2 2 i k k dx

0 n m

ψ ψ ψ p ∑ An n 2Re ∑ AnAm n me (2)

n n © m For nearly horizontally propagating modes in shallow water of constant depth D, we can derive simple parameter estimates using pressure release surface and bottom boundary conditions. The modal wavenumbers are then

ω2 nπ 2 k2 § (3)

n 2

c D

¨ ¢

If we perturb the depth D £ D δD r we ﬁnd

FIGURE 1. Bathymetry for FAF99. For the SRA at F4, the

δD r ¢ nπ § focal shift from the dashed circle is schematically illustrated. δkn r ¢ (4)

knD D Table 1. Simulation vs. theory for bathymetric focal shift. the RAM code were rounded off in bins of length 8m, and the theory leading to equation (5) has introduced several Propagation Depth (m) Shift (m) Shift (m) approximations. The higher difference for site F4 is con- Path at Focus RAM Theory sistent with the sampling of more variable bathymetry. F2 - FVLA (3.0km) 112.0 0 0 F2 - SW 111.0 -24 -24 F2 - W 117.0 144 136 SUMMARY F2 - NW 116.7 144 129 F2 - N 114.1 64 56 We find from the data in Table 1 that modeled bathy- F2 - NE 112.2 16 6 metric changes in round trip propagation paths to the fo- F2 - E 111.2 -24 -22 cus have an rms value of 158m for site F2, and 1709m F2 - SE 109.8 -56 -56 for site F4. The corresponding rms travel time changes are 0.10 sec and 1.14 sec. respectively. If the reverber- F4 - FVLA (7.4km) 112.0 0 0 ant return from the focal annulus could be resolved in F4 - SW 111.0 792 538 azimuth, it is quite reasonable that the F4 results could F4 - W 117.0 1552 1662 be related to the bathymetry by equation (5) in a statis- F4 - NW 116.7 1376 978 tically meaningful way. One possible payoff the method F4 - N 114.1 864 636 suggested here is rapid bathymetric assessment of many F4 - NE 112.2 288 293 square km of an unknown shallow water body. In fact a F4 - E 111.2 -200 -196 probe source moving away from a fixed SRA could be F4 - SE 109.8 -200 -196 used to map out concentric circles from which the two dimensional bathymetry could be obtained by differenti- ation in radius. Future refinements of the method could assist in locating shoals endangering near shore craft. The shift in focal range is derived from requiring that

the phase integral in equation (2) be stationary for each

modal pair n ¡ m . The result is ACKNOWLEDGMENT

δk δk ¢ dx

§ n m δr 0 Work supported by Saclantcen and the US Ofﬁce of kn km Naval Research.

¢¡

∂δkn ∂kn

¢¤£ ¢ £ dx (5) 0 ∂n ∂n

r ¡

¥ 2 δDdx REFERENCES D 0 1. H. C. Song, W. A. Kuperman, and W. S. Hodgkiss, A time- The last expression in equation (5) is independant of reversal mirror with variable range focusing, J. Acoust. mode number, so it expresses the shift of the total acous- Soc. Am. 103, 3234-3240 (1998) tic field intensity due to small bathymetric variation. 2. W. S. Hodgkiss, H. C. Song, W. A. Kuperman, T. Akal, A long-range and variable focus phase-conjugation experiment in shallow water, J. Acoust. Soc. Am. 105, 1597 Comparison with Numerical Results (1999) 3. Charles Holland and B. E. McDonald, Shallow Water Re- Two way propagation along the eight principal com- verberation from a Time Reversed Mirror, Saclantcen Re- pass directions from SRA sites F2 and F4 of Figure 1 was port SR-326 (December, 2000) calculated with the RAM code [6]. The complex acoustic field near the ocean bottom was decomposed into upgoing 4. B. E. McDonald and Charles Holland, Shallow Water Re- verberation from a Time Reversed Mirror: Data- Model and downgoing waves. The intensity of the downgoing Comparison, J. Acoust. Soc. Am. 109, 2495 (2001) wave from RAM was examined for maxima near the focal range. The range shift of the focal maximum relative to 5. G. A. Grachev, Theory of acoustic field invariants in lay- the probe source range is tabulated along with the predic- ered waveguides, Acoust. Phys. 39, 33-35 (Akust. Zh. 39, 67-71), (1993) tion of equation (5) in Table 1. One finds that focal shifts for the SRA at site F2 have a root mean square difference 6. M. D. Collins, Generalization of the Split-Step Pade Solu- of 9.5%, and for F4 an rms difference of 22%. This is ad- tion, J. Acoust. Soc. Am. 96, 382-385 (1994) equate agreement considering that the focal ranges from Matched field detection and localization by a ‘’ shape array GONG XianYi, GE Huiliang, LI Ranwei

State Key Lab. Of Oceanic Acoustics, Hangzhou Applied Acoustics Research Institute, P.O.Box 1249,Hangzhou, China

A ‘’ shape array, which is consisted of respectively 60-element vertical and horizontal arrays, is used for matched field detection and localization in a shallow-water experiment carried out in East China Sea in June early, 2001. This paper presents a preliminary matched-field analysis and puts emphasis on the weak-signal detection and its performance compared with that by use of just the vertical array or the horizontal array in terms of threshold SNR normalized on number of elements.

angle estimations, and signals received by HLA/VLA and INTRODUCTION monitored/measured are simultaneously acquired into the multichannel recording system. Matched Field Processing has been extensively studied The projecting array with the different depths deployed since last two decades and mostly concentrated on vertical from transmitting vessel, which moves to the positions line arrays(VLA) or horizontal line arrays(HLA)[1]. The being 5, 10, 20 and 40km away from the receiving vessel, range and depth of the source can be estimated by use of radiates signals with different forms, for example, CW, VLA, but the its bearing can not be obtained except the PCW, LFM, and PRN. In the paper only signals of 630Hz environment of acoustic propagation is of significant CW and at range 40km are matched-field-analyzed for azimuthal variation and modeled. On the other hand, the source detection and localization. source’s bearing can be given using HLA, but its range and depth are often difficult to be estimated accurately except MATCHED FIELD ANALYSIS for endfire direction. Besides, VLA or HLA themselves have no or poor horizontal or vertical resolutions, The matched field analysis used in this paper is linear respectively, resulting in detection performance Bartlett estimator: [2] degradation. Booth et.al. describe the detectability of low B(r, z, ) p* (r, z, )Rp(r, z, ) (1) o level signals using a tilted line array (45 ) and demonstrate where R is cross-spectral matrix of the sound data sampled the performance improvement compared with that of the by the ‘’ shape array, p(r, z, ) is the modeled pressure VLA with same length and number of elements. vector which is calculated with Porter’s model KRAKEN. This paper presents the preliminary detection and For comparison, the matched field result of VLA is localization (bearing, range and depth) results using ‘’ also calculated by: array which is consisted of a VLA and HLA in a shallow- * water experiment carried out in ECS in June early, 2001. B(r, z) p (r, z)Rp(r, z) (2) The following Sec. II describes the ECS acoustical The range/depth, range/bearing, depth/bearing experiment data used for matched field analysis of ‘’ ambiguity surfaces for the matched field results of the ‘’ array, Sec. III contributes to the data analysis and the final shape array is given in Fig. 1, 2 and 3, respectively. The section (Sec. IV) concludes the paper. maximum of the ambiguity surface is located at r=41.6km , z=39m and 28 . The result is very near to the true ECS ACOUSTICAL EXPERIMENT DATA source location which is at range 40km and depth 40m. The ambiguity surface for the matched field results of Matched field analysis using ‘’ shape array is performed the VLA is given in Fig. 4. One of the maximum of the with data from ECS acoustical experiment which was ambiguity surface is located at r=37km , z=37m. It is conducted from June 2 to 7, 2001 in the site centered at E shown that the accuracy of localization (r,z) using VLA is degraded from that using ‘’ array and there is no 126 49.02> and N 29 40.52> . The ‘’ array deployed from azimuthal resolution in VLA. Moreover, due to many the receiving vessel is consisted of a drift 60-element, sidelobes in the ambiguity surface, detectability of VLA is 147.5m long HLA and a suspended 60-element, 56m long also poor than that of ‘’ array, and its is expected that the VLA. The deployed depth of HLA is 10m and the array threshold SNR normalized on number of elements of just shape is monitored by base-line method. The depth of the first element of VLA is about 3.4m and the array’s tilt angle VLA or HLA is higher than that of ‘ ’ array. is measured by the depth/tilt sensors for array shape and tilt (b) FIGURE 3. (a) Depth/bearing ambiguity surface for ‘’ shape array (b) A slice of the ambiguity surface at z=39m

FIGURE 1. Range/depth ambiguity surface for ‘’ shape array.

FIGURE 4. The ambiguity surface for VLA

IV SUMMARY

The matched-field analysis of ‘’ array for source detection and localization presented in the paper is preliminary. The future works are directed to effects of geoacoustic features and range-dependent environment and (a) coherent broadband processing.

REFERENCES

1. Gong, X.Y., Matched-field processing for source detection and localization, Lecture(in Chinese), 1997 2. N. O. Booth, A.T. Abawi, et.al. IEEE J. Oceanic Eng. 25,296-313 (2000) (b) FIGURE 2. (a) Range/bearing ambiguity surface for ‘’ shape array (b) A slice of the ambiguity surface at r=41.6km

(a) Modal Travel Time Methods for Shallow Water Geoacoustic Inversions

M. I. Taroudakis

Department of Mathematics, University of Crete, 71409 Heraklion, Crete, Greece and Institute of Applied and Computational Mathematics, FORTH, P.O.Box 1527, 711 10 Heraklion, Crete, Greece

The paper presents briefly the procedures developed at FORTH for treating the problem of geoacoustic inversions using the information on the modal structure of the acoustic field due to a known source. The configuration considered is that of a single source-receiver pair and the emitted signal is modelled as a gaussian pulse. Its arrival pattern is used for the inversions. A two- stage algorithm is proposed. First stage involves the characterization of the peaks of the signal as modal arrivals based on the information at the central frequency of some "candidate" environment defined through a systematic search over the search space. Second stage involves an analysis of the identified modal peaks based on the individual candidate environments, which under an optimization procedure leads to an environment closer to the actual one. An iterative linear inversion scheme based on a perturbation analysis over the observed modal peaks could eventually fine tune the recovered environment towards the actual one.

INTRODUCTION For the definition of the inverse problem, we assume that a single source receiver pair is available Modal travel time inversions have been applied by and that the sound source is broad-band. several researchers over the last ten years for Measurements of the acoustic field in the time domain underwater acoustic identification problems with good will be the input data. The characteristic feature of the results, under the assumption that there is good a-priori signal is that its magnitude contains peaks, some of knowledge of the parameters to be recovered which are characterized as "modal peaks" or "modal (reference environment) which leads to the application arrivals" corresponding to energy propagating at the of linear inversion techniques. individual modes

In our approach a relatively wide search space is The core of the inversion procedure has two stages: considered. The inversion procedure adopted is hybrid Modal peak identification and inversion. The modal in the sense that an optimization procedure for the identification is performed on the basis of associating estimation of the most probable reference environment predicted modal travel times with arrival times of the is combined with a linear inversion method to estimate signal arrival pattern peaks. The prediction of the the unknown parameters. Both stages are supported by modal arrivals is done using standard group velocity an identification process to assign modal arrivals at the theory and a reference environment chosen peaks of the measured signal while each one can stand systematically among the environments defined within alone as an inverse scheme for the problem in hand. the search space. If a multidimensional search space is to be examined, an appropriate search algorithm should be used to accelerate the procedure which THE INVERSION PROCEDURES otherwise is time demanding. The predicted modal arrivals are compared with the peaks of the signal and Our study is referred to the problem of a peak of the signal is considered “identified” if the simultaneous inversion for the sound velocity in the difference between its arrival time and the predicted water column and the compressional velocity in the modal travel time is minimum. The whole procedure is sediment layer. This is a special case of tomographic described in [1]. Among the various candidate problems, which in underwater acoustics are normally environments used for modal identification, we keep related to the recovery of the sound speed in the water the ones leading to the maximum number of identified column only. In shallow water, these problems modal peaks. normally include the simultaneous recovery of the A statistical analysis performed over the set of bottom parameters, as the seabed influence on the environments thus defined leads to the “most acoustic field is of profound importance. probable” environment corresponding to the given set of measurements. This environment could be Table 1. The acoustic parameters of the test waveguide. alternatively defined as the one giving minimum value Actual values and search bounds values. With bold italics we to a norm defined on the basis of the travel time indicate the recoverable parameters differences between predicted modal travel times and actual travel times of the identified peaks. Sometimes Actual Search it is adequate to stop the inversion procedure at this bounds point. In some other cases it is desirable to fine-tune Sound speed at the sea 1490 1460-1500 the results using an appropriate local search. This is surface (m/sec) C1(0) accomplished using an already developed method for Sound speed at the 1500 1490-1520 linear modal travel time inversions, using the most water/bottom interface probable environment defined above as the reference C1(h) environment for performing the inversions [2]. Sound speed at the upper 1680 1600-1750 part of the sediment layer C2(h) AN EXAMPLE OF APPLICATION Sound speed at the lower 1700 1680-1800 part of the sediment An inversion toolbox consisting of the layer C2(h+d) identification process and the two-stage inversion Water depth (m) 100 scheme has been developed at FORTH. The input of Sediment thickness 40 the toolbox is the tomographic signal measured in the Sediment density (kg/m3) 1500 time domain. Normally it is the average of several Substrate sound speed 1800 receptions recorded at the receiver. The procedure has Substrate density 1700 been validated so far using synthetic data. For the case presented here, linear variation of the sound speed in Table 2. Inversion results the water and the sediment layers has been considered Actual Most Estimated and thus the unknowns at these layers are the sound probable after local speed values at the top and the bottom of the search corresponding layers. Further we assume for simplicity C1(0) 1490 1480.52 1489.94 that the substrate parameters are known. The density in C1(h) 1500 1497.15 1500.14 the sediment and its thickness is also considered C2(h) 1680 1690.42 1682 known. This is a realistic assumption taking into C2(h+d) 1700 1700 1700 account that the thickness is normally derived using alternative inversion methods.

The acoustic source is considered gaussian with central frequency 150 Hz and bandwidth 50 Hz. Source and receiver depths are the same 50 m. The receiver has been placed at the distance of 10 Km. Table 1 presents the environmental parameters for the actual environment along with the search bounds for the unknown parameters. The inversion results, using the linear inversion approach based on the reference environment defined as the most probable one defined after a suitable analysis of the candidate environments as the one ensuring the fastest convergence of the linear scheme is presented in Table II. The performance of the method is remarkably good. REFERENCES

1. M.I.Taroudakis J. Comput.Acoustics, 8, 307-324 (2000). FIGURE 1. Arrival pattern of the actual and the “most probable”environment. 2. E.C. Shang, J.Acoust.Soc.Am., 85, 1531-1537 (1989). Observed Internal Solitons on a Shelf and their Effects on Sound Propagation

A. N. Serebryanya and A. I. Belovb

aN. N. Andreyev Acoustics Institute, Shvernik Str. 4, Moscow 117036, Russia bWave Research Center, General Physics Institute, RAS, Vavilov Str. 38, Moscow 117942, Russia

Up-to-date review on intense internal waves in sallow water based on long-term field observations on shelves of the former Soviet Union are presented. These waves frequently referred to as “solitons” are often not stationary waves with equilibrium between dissipation and nonlinearity, but are strongly nonlinear in nature. A variety of important nonlinear effects in observed internal waves, including vertical and horizontal asymmetry of wave profile, change of internal wave polarities, and others, are considered. Some observed properties of waves identified with soliton features are demonstrated. The impact of the internal soliton packets on acoustic propagation on a shelf for different hydrological conditions (strong and weak thermocline) is analysed on the basis of field observations and numeric modelling.

SPECTRUM OF INTERNAL WAVES our own results which were obtained on the basis of ON A SHELF almost 20-year investigation in the field. During this time we carried out 15 experiments on internal wave study on shelves of the former Soviet Union Study of shallow water internal waves and acoustic (observations were made in the Caspian, Black and effects produced by them is a popular topic during last Barents Sea, the Sea of Japan, and on Pacific coast of decade (see, for example [1,2]). In the frame of this Kamchatka) [3,4]. Fig.1 shows typical frequency paper we have no possibility to make overview of all spectrum of internal waves on a shelf. There are clear last achievements in this topic. Our task is to present seen two main peaks (semidiurnal tidal and short- period waves, shown by arrows) on averaged spectrum of vertical displacement of thermocline. During an approach of intense short-period internal waves the spectral levels in high frequency band became significantly higher while peaks became more prominent. Our observation showed that the peak of short -period waves is formed by non-linear internal waves. NONLINEAR FEATURES OF OBSERVED INTERNAL WAVES

We will summarise main features of intense internal waves, which were revealed in our long-term observations on a shelf as follows: 1. An arrangement of experimental points (parameters of observed waves) above the first mode dispersion curve of the linear internal waves, a typical feature for waves consisted in trains, is connected with non-linearity of the waves; 2. Next non-linear effects are widespread phenomena on a shelf: - the effect of vertical asymmetry of internal . waves (wave depressions take place in the case of FIGURE 1. Frequency spectrum of internal waves thermocline close to the sea surface, while wave obtained from measurements on shelf of the Sea of elevations – in the case of thermocline close to the Japan. Averaged spectrum (solid line); spectra bottom, see Fig.2); - the effect of change of internal calculated for trains of intense waves (1-3) and G-M wave polarity, which takes place for internal waves spectrum (broken line). propagating in the shoreward direction from deep to FIGURE 2. Vertical asymmetry of internal waves: trains with opposite polarities (consist of wave elevations and depressions) propagated to the shore. Observation was made on shelf of the Sea of Japan on August 1982 [5,6]. shallow water and passing through “turning point”; - the effect of horizontal asymmetry (asymmetry owing to difference in the slope of the leading and following ACKNOWLEDGMENTS edges) is widespread both for depression and elevation waves; 3- it was observed in some cases a good The research work described in this publication was agreement with KdV soliton theory (manifestation of made possible in part by Award N RP2-2255 of the soliton properties were revealed, in particularly, the U.S. Civilian Research & Development Foundation for evidences of the dependency of internal wave speed on the Independent States of the Former Soviet Union amplitude were obtained); 4 - internal wave– (CRDF). predecessor, small-amplitude wave ahead of a train of intense waves (behaviour of wave which is in a disagreement with theory of KdV equation) can be explain by including into consideration an effect of REFERENCES horizontal turbulent viscosity and a shoaling effect. 1. J. Zhou, X. Zhang and P.H.Rogers,J. Acoust.Soc.Amer., SOME EFFECTS OF INTERNAL 90, 2042-2054 (1991). WAVES ON SOUND PROPAGATION 2. J.R. Apel et al, IEEE J.Oceanic Eng., 22, 465-500 (1997). Effect of internal waves on sound propagation on shelf we studied both by carrying out field experiments and 3. A.N. Serebryany, Short-period internal waves on a shelf.(In Russian). Candidate Sc. Dissertation (PhD), by numeric modelling, utilising data of our observation Moscow: N. N. Andreyev Acoustics Institute, 1987, on internal waves [7]. The important result we 220 p. obtained is that in the case of weak thermocline and normal crossing of the acoustic track by a short 4. A.N. Serebryany, Nonlinear internal waves on a shelf internal wave train, the amplitude and phase variations and near bottom rises in the ocean.(In Russian). Dr. Sc. of sound pressure (low-frequency CW signal) are Dissertation, Moscow: N.N. Andreyev Acoustics similar to the form of internal wave train. In the case Institute, 2000, 263 p. of sharp thermocline, the amplitude and phase variations of sound pressure exhibit arising of higher 5. A.N. Serebryany, Oceanology., 25, 744 -751 (1985). frequency oscillations, which can be explained by 6. A.N. Serebryany, Izv. AN SSSR. Atmos. Ocean. Phys., mode coupling. In the paper some new results of 26, 285-293 (1990). numeric simulations of acoustics effects connected with crossing of a track by internal wave depressions 7. A.I. Belov, A.N. Serebryany and V.A. Zhuravlev, and internal wave elevations will be present. “Observations of internal wave effects on acoustic signals in a shallow sea with a weak thermocline”, in Shallow water acoustics, edited by R. Zhang and J.-X. Zhou, Beijing: China Ocean Press, 1997, pp. 283-288. A Unified Model for Reverberation and Scattering from both Stationary and Moving Objects in a Stratified Ocean Waveguide Nicholas C. Makris, Purnima Ratilal and Yi-San Lai Massachusetts Institute of Technology. 77 Massachusetts Avenue Room 5-222 Cambridge, MA 02139 Phone: 617-258-6104 Fax: 617-253-2350 email: [email protected] A unified model for reverberation and submerged object scattering in a stratified medium is developed from full-field wave theory. The unified approach enables the first consistent predictions to be made of target-echo-to-reverberation ratio. The model is applied to determine whether submerged targets can be detected above seafloor reverberation for a variety of watercolumn and sediment types, measurement geometries and target shapes and sizes. The model is also applied to deterimine conditions necessary for discrete geomorphological features of the seafloor and sub-seafloor to be detected above diffuse seafloor reverberation. A spectral formulation for the 3-D field scattered by an object moving in a stratified medium is also derived using full-field wave theory. The derivation stems directly from Green’s theorem and accounts for Doppler effects induced by target motion as well as source and receiver motion. A normal mode formulation that is more computationally efficient but less general is also derived from first principles. The Doppler effects are illustrated through a number of examples in a Pekeris waveguide.

THE UNIFIED MODEL analytic expressions for the three-dimensional 3-D field scattered bistatically by both stochastic and deterministic A common problem in the active detection and local- objects from a source with arbitrary time function, as well ization of a radar or sonar target arises when scattered as the associated spatial and temporal covariances. This returns from the target become indistinguishable from re- enables realistic modeling of the moments of the raw returns from randomly rough boundaries, volume inhomo- verberant field received over extended spatial and tempo- geneities, or deterministic features of the environment. ral apertures as well as the output after subsequent pro- The goal of the present article is to investigate the extent cessing with standard beamforming and broadband sig- to which environmental reverberation limits the ability to nal processing techniques. In the present article, applica- detect and localize a target submerged in an ocean waveg- tions of the theory are restricted to systems which employ uide, where methods developed for the radar half-space the beamforming and temporally incoherent processing problem are inapplicable due to the added complications widely used in narrow-band signal reception. Analytic of multi-modal propagation and dispersion. expressions for the statistical moments of the scattered To this end, a unified model for 3-D reverberation field are obtained directly, but can also be obtained by and submerged target scattering in a stratified medium is sample averaging over realizations by Monte Carlo sim- devel- oped from wave theory. The model is fully bistatic ulations, as for example is done for rough surface scat- and stems directly from Green’s theorem, since it gener- tering in Ref. 7. The relative merit of either approach alizes Ingenito’s approach [1, 2] for harmonic scattering depends on the relative difficulty in evaluating the analyt- in a stratified medium by incorporating stochastic scat- ically obtained moments or performing the Monte Carlo terers and time-dependent sources. While it is consis- simulations for the given problem. The analytic approach tent with certain narrow-band results of previous “heuris- has proven to be more advantageous and insightful for the tic” [3] derivations [3-6] for shallow water reverberation illustrative examples of the present article. measured with an omni-directional receiver that are based In this paper, the single scatter theory is generalized on the work of Bucker and Morris [4], it offers more in- to include the effects of source, receiver and target mo- sight and generality since it is developed from first prin- tion. Analytical expressions are obtained for the field ciples with explicitly stated assumptions. For example, scattered to a moving receiver from a moving target in it clearly obeys reciprocity for source-receiver locations a stratified ocean waveguide by a moving source. The within a layered media, which is important in properly formulations are fully bistatic, and all the motions are as- modeling the absolute level of returns from targets or sur- sumed to be horizontal with constant velocities. Both the faces within the seafloor, and it allows absolute compar- expressions for a simple harmonic source and a source ison between reverberation and deterministic target re- with arbitrary time dependence are derived in this paper. turns. Such comparison led to inconsistencies in previ- Spectral and modal representations of the scattered field ous formulations as noted in Ref. 3. It also provides are derived from first principles using the time-domain formulation of Green’s theorem. The spectral representa- ergy returned from the target or scattering patch. This tion makes fewer assumptions and is more accurate than approach is used in the illustrative examples. A viewer- the normal mode representation at closer ranges, but the oriented reference frame is then adopted, translating from normal mode formulation provides a compelling physical the traditional target-oriented frame of waveguide scat- interpretation and can be used at longer ranges without ter theory, to incorporate the continuous distribution of significant loss of accuracy. The single scatter theory of scatterers encountered in waveguide boundary and vol- Ref. 1 and 2 then becomes a special case of the present ume reverberation. This enables analytic expressions to more general theory when the source, receiver and target be developed for the reverberant field returned bistatically are at rest. from seafloor within the resolution footprint of a typical active sonar system after narrow-band beamforming with a horizontal array. Analytical expressions for the 3-D field scattered by CONCLUSION a moving target from a moving source at a moving receiver in a general stratified ocean waveguide are derived One of the greatest challenges to active sonar opera- from first principles using the time-domain formulation tions in shallow water arises when echo returns from the of Green’s theorem. Spectral and modal representations intended target become indistinguishable from reverber- of the Doppler-shifted scattered field for a simple har- ation returned by the waveguide boundaries and volume. monic source and a source with arbitrary time depen- To determine conditions in which a typical low-frequency dence are also obtained. The modal representation has active sonar system may operate effectively in a shal- a compelling physical interpretation exhibited by the fact low water waveguide, a unified model for submerged ob- that a simple harmonic source that excites N modes in ject scattering and reverberation is developed. The ap- the waveguide, for example, will excite roughly N2 dis- proach is to use a waveguide scattering model that follows tinct harmonic components in the scattered field due to directly from Green’s theorem but that takes advantage coupling between the incident modes and the scattered of simplifying single-scatter and far-field approximations modes. The spectral representation, however, is more that apply to a wide variety of problems where the source general and can be used at closer ranges to the target. and receiver are distant from the target. To treat rever- Simulations show that Doppler shifts induced in the beration from randomly rough boundaries and stochastic scattered field by target motion are highly dependent on volume inheterogeneties, the waveguide scattering model the waveguide environment, target shape and measure- is generalized to include stochastic targets. Analytic ex- ment geometry. For a highly dispersive waveguide that pressions for the spatial covariance of the field scattered supports many trapped modes, the frequency spectrum of from a stochastic target are then obtained in terms of the the field scattered by a moving target typically exhibits waveguide Green’s function and the covariance of the tar- significant distortion compared to that of a stationary target’s plane wave scatter function. This makes the for- get or the same target moving in free space. mulation amenable to a wide variety of approaches for computing a stochastic target’s scatter function. For diffuse seafloor reverberation, two approaches are adopted, REFERENCES an empirical one of Lambert and Mackenzie and a fundamental one based on first-order perturbation theory. It is 1. Ingenito, F., J. Acoust. Soc. Am. 82, 2051-2059 (1987). most convenient to describe the diffuse component of dis- 2. Makris, N. C., Ingenito, F., and Kuperman, W. A., J. tant seafloor reverberation with a modal formulation since Acoust. Soc. Am. 96, 1703-1724 (1994). the modes comprise the statistical entities of the field that the scattering surface may decorrelate. 3. Ellis, D. D., J. Acoust. Soc. Am. 97, 2804-2814 (1995). Since reverberation is measured in time but the waveg- 4. Bucker, H. P. and Morris, H. E., J. Acoust. Soc. Am. 44, uide scattering formulation is for harmonic field compo- 827-828 (1968). nents, the time dependence of the field scattered by a dis- 5. Zhang, R. H., and Jin, G. L., J. Sound. Vib. 119, 215-223 tant object from a source of arbitrary time dependence is (1987). derived analytically using the saddle point method. The 6. Lepage, K., J. Acoust. Soc. Am. 106, 3240-3254 (1999). resulting expression is given in terms of modal group ve- 7. Schmidt, H. and Lee, J., J. Acoust. Soc. Am. 105, 1605- locities, the frequencies of which vary as a function of 1617 (1999). time and source, receiver, and target position. A sim- 8. Mackenzie, K. V., J. Acoust. Soc. Am. 33, 1498-1504 pler analytic approach involving Parseval’s theorem can (1961). be applied when the integration time of the measurement system is sufficiently long to include the dominant en-

The Relationship Between Low-Frequency Phase Rate and Source-Receiver Motion in Shallow Water: Theory and Experiment

George V. Frisk

Department of Applied Ocean Physics & Engineering, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543 U.S.A. [email protected]

A theory is presented that relates the phase rate of low-frequency cw signals to the range rate between source and receiver in shallow water. The radiation condition and the paraxial approximation are incorporated into the method of normal modes to obtain a general result applicable to propagation in both range-independent and range-dependent waveguides. Specifically, it is shown that the leading-order behavior of the time rate-of-change of the phase is equal to the product of a typical wavenumber in the water column and the source-receiver speed. This result remains robust even for situations where the acoustic field magnitude displays a complex multimodal interference pattern. The theory accurately predicts the relative source-receiver speed from phase measurements obtained in several Modal Mapping Experiments. The experimental configurations consisted of a source transmitting several pure tones in the band 20-475 Hz to a field of freely drifting buoys, each equipped with a hydrophone, GPS navigation, and radio telemetry. Data were obtained in 50-150 m water depths for source-receiver speeds up to 2 m/s and ranges of 20 km in experiments off New Jersey and in the Gulf of Mexico. The applicability of the theory to long- range, deep-water scenarios is also discussed.

INTRODUCTION N iknr ikr N () = iφ = e ≈ e i kn −k r P Ae ∑ An ∑ An e . (1) Low-frequency sound propagation in shallow water n=1 k n r kr n=1 is characterized by multiple interactions with the surface and bottom in a waveguide whose properties Here A is the magnitude and φ is the phase of the field vary in depth, range, and azimuth. The complexities of which remain after shifting the measured signal to base the resulting propagation process are typically band. In Eq. (1), we have decomposed the field P into described, modeled, and measured in terms of their a sum of N radially propagating normal modes with effects on the acoustic field magnitude (or equivalently, eigenvalues kn and amplitudes An, where we have transmission loss). Far less attention is paid to the assumed that the source and receiver are separated by behavior of the phase, which we shall demonstrate has range r and remain at fixed depths during the course of simple and robust properties, even for situations where the experiment. In addition, we have explicitly the field magnitude displays a complex multimodal imposed the Sommerfeld radiation condition [1] interference pattern. Specifically, we will show both by factoring out the radiating cylindrical wave theoretically and experimentally, that for a source eikr kr associated with a typical wavenumber k=ω/c and/or receiver moving through a shallow-water and sound speed c in the water column (e.g., c=1490 waveguide, the leading-order behavior of the low- m/s). Finally, in Eq. (1), we apply the paraxial frequency phase rate is simply equal to the product of approximation [2], a typical wavenumber in the water column and the source-receiver speed. = − ε ≈ ()− ε ε << kn k 1 n k 1 n 2 for n 1 , (2)

THEORY which states that, although the source injects acoustic energy into the waveguide over a broad range of In the range-independent (horizontally stratified) angles, only a relatively narrow band of angles (less case, the measured pressure due to a time-harmonic than about 30° with respect to the horizontal) point source transmitting the frequency ω is given by -iω t dominates the radiated field, even in shallow water. Pe , where Equation (1) then becomes

ε eikr N −ik n r ≈ 2 P ∑ An e , (3) kr n=1 from which we can show that

dφ ≈ k + O()ε . (4) dr n

If the source and/or receiver are moving, so that r = r(t), we can use the chain rule and Eq. (4) to show that

dr 1 dφ ≈ , (5) dt k dt FIGURE 1. Comparison of GPS-derived range rate (solid line) with phase model results (dashed line) obtained using that is, we can determine the range rate dr dt between MOMAX I – 50 Hz data. the source and receiver from measurements of the phase rate dφ dt . Remarkably, the result in Eq. (5) CONCLUSIONS can be shown to hold true in long-range, range- We have presented a theory that relates the phase dependent, deep-water scenarios as well, simply by rate of low-frequency cw signals to the range rate using the radiation condition and the paraxial between source and receiver in shallow water. The approximation. radiation condition and the paraxial approximation were incorporated into the method of normal modes to EXPERIMENTAL RESULTS AND obtain a general result applicable to propagation in COMPARISONS WITH THEORY both range-independent and range-dependent waveguides. Specifically, it was shown that the During the past several years, three Modal leading-order behavior of the time rate-of-change of the Mapping Experiments (MOMAX) were conducted in phase is equal to the product of a typical wavenumber 50-150 m water depths off New Jersey and in the Gulf in the water column and the source-receiver speed. The theory accurately predicts the relative source-receiver of Mexico [3]. The experimental configurations speed from phase measurements obtained in several consisted of a source transmitting several pure tones in Modal Mapping Experiments. the band 20-475 Hz to a field of freely drifting buoys, each equipped with a hydrophone, GPS navigation, ACKNOWLEDGMENTS and radio telemetry. A key component of the method is the establishment of a local differential GPS system The support of the Office of Naval Research is between the source ship and each buoy, thereby gratefully acknowledged. The author greatly enabling the determination of the positions of the appreciates the contributions of his colleagues: Kyle buoys relative to the source with submeter accuracy. Becker, Laurence Connor, Barry Doust, James Doutt, During these experiments, data were obtained for Calvert Eck, Neil McPhee, Cynthia Sellers, Luiz source-receiver speeds up to 2 m/s and ranges up to 20 Souza, and Keith von der Heydt. km. An example of 50 Hz data obtained on one of the REFERENCES buoys (Shemp) during MOMAX I in 75 m of water off the New Jersey coast is shown in Fig. 1. Here the 1. G.V. Frisk, Ocean and Seabed Acoustics: A Theory of Wave Propagation, Prentice-Hall, Englewood Cliffs, NJ, range rate obtained directly from GPS measurements 1994. of the source and buoy positions is compared with the 2. F.D. Tappert, in Wave Propagation and Underwater range rate predicted from Eq. (5) using the 50 Hz Acoustics, J.B. Keller and J.S. Papadakis, eds., Springer- phase data. The agreement between theory and Verlag, Berlin, 1977, pp. 224-287. experiment is excellent. 3. G.V. Frisk, K.M. Becker, and J.A. Doutt, Proceedings of the Oceans 2000 MTS/IEEE Conference and Exhibition, Providence, RI, September 2000, Vol. I, pp. 185-188.

Internal Wave Fields in Shallow Water: Some Implications for Processing Acoustic Signals

S. Finettea, R. Obaa, M. Orra, B. Pasewarka, C. Stamoulisa, A. Turguta, S.Wolfa, J. Lynchb

aAcoustics Division, Naval Research Laboratory, Washington DC 20375 USA bWoods Hole Oceanographic Institution, Woods Hole, Massachusetts USA

An analysis of acoustic field data acquired in a shallow water region that exhibited significant internal wave activity illustrates inconsistencies between acoustic field properties in this environment and some basic assumptions concerning signal structure implied by phase sensitive signal processing schemes. Variability in the sound speed field induced by internal gravity waves is considered and some implications for acoustic signal processing are discussed in the context of an ocean medium that is both time-varying and horizontally anisotropic.

PROPAGATION IN A DYNAMIC crossed the propagation path at speeds of about .8 SHALLOW WATER ENVIRONMENT m/sec and often propagated through each other. Both the wave packet amplitudes and the number of packet oscillations changed as a function of range from their Sonar signal processing schemes are based on physical generation sites on the shelf break. While both assumptions concerning the spatial and temporal components contributed to the total sound speed structure of the acoustic field. Space-time perturbation as a function of space and time, data perturbations of the sound speed distribution within analysis indicated that the solitary wave contribution shallow ocean environments can alter the field played a more significant role in altering the structure structure, compromising the effectiveness of acoustic of the acoustic field. Instabilities and mixing signal processors by introducing inconsistencies associated with the internal wave packets randomized between these assumptions and the true signal the sound speed field at wave number scales larger structure of the experimental field data. than those associated with the internal wave spatial As an illustration, we refer to experimental and wave numbers. As a result, the sound speed field is numerical simulation results obtained from the neither stationary nor homogeneous in space or time, SWARM95 experiment, which was designed to address issues related to acoustic propagation through but intermittent and inhomogeneous. a random shallow water channel[1-7]. The experimental site was located on the continental shelf off the New Jersey coast in mildly sloping shallow SIGNAL PROCESSING ISSUES water. Oscillations of the strong density gradient resulted in significant depth-dependent sound speed Hydrophone arrays are used in conjunction with phase- variability, induced by internal gravity waves. Two coherent signal processing schemes to detect and fixed sources (center frequencies < 500 Hz) were localize acoustic sources in the presence of ambient deployed in 55 m of water. They were located 42 km noise. These techniques rely on a mathematical or shoreward from an NRL vertical line array spanning conceptual model of the signal and its differences from 21-85 m in water of depth 88 m. The internal wave interfering noise. Standard signal assumptions include field between the sources and receiving array consisted signal stationarity and signal coherence. Signal of two components. One component was a spatially stationarity was violated over integration times of diffuse random background field that was distributed minutes to several hours. Both short (5-30 min) and throughout the propagation region. The second long (semi-diurnal) time scales were significant in component consisted of high frequency solitary wave producing amplitude and phase variability in the signal packets that extended over some 10 km in range and structure. Amplitude variability resulted in signal-to- up to 30-35 km in cross-range. Several families of noise fluctuations of 20-30 dB, which can have these horizontally anisotropic, dispersive packets adverse effects for energy (i.e. signal) detection algorithms. Numerical simulations showed that mode components and their incoherence with the adiabatic coupling between the acoustic field and moving wave (uncoupled) term. Since the coupled-mode packets controlled the magnitudes and time scales of components have amplitudes which are of about the the fluctuations. In addition, adiabatic propagation same magnitude as the uncoupled terms, the success of along solitary wave crests is a significant cause of non- matched-field processing in such an environment will stationary changes in the intensity and phase of the require the prediction (or the suppression) of these wave front. This latter result is related to the horizontal stochastic components. Bartlett processing, minimum anisotropy of the internal wavefield. If the signal is constraint and minimum variance approaches were coherent (i.e. has a predictable spatial dependence of found to be ineffective, yielding errors in localization amplitude and phase) and that dependence is different of the order of the source range, even for short from the noise, then gain can be achieved through a ranges(< 2 km). Matched-mode processing yielded spatial matched filter such as a beamformer. For a improved localization. The horizontal wave fronts of normal mode representation of the field, the signal is coherently propagating acoustic signals may also be treated as a sum of perfectly coherent (in depth and perturbed by an internal wave field, affecting both cross range) modal components that propagate cross-range coherence and bearing estimation. The independently with individual phase and group speeds perturbation arises because local variations of the (which are functions of frequency, water depth, and sound speed profile create local perturbations of the other environmental parameters). In principle, the phase speed of an adiabatically propagating mode. coherence of such a signal can be exploited to achieve These (mode-order-dependent) phase speed variations gain against interference by processing on arbitrarily can, in turn, cause signal refraction--particularly if the large arrays. In addition, the signal can be resolved environmental perturbations are laterally anisotropic, into its modal components by vertical arrays and the as is the case with internal tides and solitary wave modal differences in phase speed (or group speed for packets. In some circumstances, particularly when the broadband signals) can be exploited to achieve range original signal is propagating in a direction nearly localization (e.g. by a matched field processor) as well parallel to wavefronts of these structures, model as further gains against noise that is spread in time. For calculations predict total internal reflection of the a given source and receiver position, the modal acoustic wave will be observed in the horizontal plane. structure in depth and delay (or phase) remains Phase speed changes accompanying mode coupling by constant in time, so processors can in principle correct extended internal wave fronts are also predicted to for this structure by using computed or data-adaptive induce lateral refraction and a loss of coherence. filters. Results of the SWARM95 data analyses demonstrate that the simple model described above is ACKNOWLEDGMENT strongly compromised if the acoustic signals propagate through an internal wave field. First, although the Work sponsored by the Office of Naval Research. depth dependence of the field's individual modal components is only slightly altered by the internal waves, the independence of propagation of these REFERENCES components is removed by mode coupling. The immediate consequence of the mode coupling is that 1. J. Apel et al., IEEE J. of Oceanic Engineering, 22, 465- the temporal structure of an individual mode of 500 (1997). propagation changes from a single pulse to a broadened pulse or a pulse train, which will overlap 2. J. Preisig and T. Duda, IEEE J. Ocean Engineering, 22, and coherently interfere with the pulses of other modal 256-269 (1997). components. This enriched time domain structure of 3. T. Duda and J. Preisig, IEEE J. Ocean Engineering, 24, the individual modal pulses is itself dynamic. The time 16-32 (1999). dependence has been shown by modeling the acoustic/internal wave interaction to be a consequence 4. R.H. Headrick.et al, J. Acoust. Soc. Am., 107, 201-236 of the motion of the internal waves that induce the (2000). modal coupling. Typical coherence times of the resulting complex structures in the complete signal 5 S. Finette et al., J. Acoust. Soc. Am., 108, 957-972 field are found to be of order a few minutes. In fact, (2000). the temporal coherence of pulse trains of single mode 6. A. Turgut, S. Wolf and D. Rouseff, in Oceans’99 fields was found to decay significantly over an interval MTS/IEEE, Vol. 2, 1052-1057 (1999). of a minute or so. The reduction of the single-mode pulse correlation has been shown numerically to be a 7. S. Finette and R. Oba, in Proc. of the Institute of consequence of the stochastic nature of coupled-mode Acoustics, 23, edited by T.G. Leighton, 321-326 (2001). Quantifying the Effects of Shallow Water Internal Waves on the Waveguide Invariant

D. Rouseff

Applied Physics Laboratory, University of Washington,1013 NE 40th Street, Seattle, WA 98105 U.S.A.

In the second edition of Fundamentals of Ocean Acoustics, Brekhovskikh and Lysanov introduced the concept of a waveguide invariant to a larger audience. They showed how plots of acoustic intensity, mapped in range and frequency, often exhibit striations, contours of constant intensity. They defined a parameter ÒbetaÓ as a simple function of range, frequency and the slope of the striations. For certain special cases, beta is an invariant quantity. While beta is no longer literally an invariant for more general shallow water waveguides, the concept remains useful. In the present work, the waveguide invariant is formulated as a distribution. The effect of shallow water internal waves on this waveguide distribution is quantified.

INTRODUCTION In the present paper, the effects of realistic shallow water internal waves on the waveguide invariant are When plotted versus range and frequency, the examined by numerical simulation. First, a method for interference pattern that is observed far from an estimating the Òbeta contentÓ of measured intensity acoustic source often exhibits striations. Chuprov [1] data is developed. The waveguide invariant is related the slope of these striations, ddrω , to the modeled as a distribution rather than a scalar. An range r from the source and the frequency ω via the internal wave model is then outlined based on oceanographic and acoustic data taken in a recent scalar parameter β: shallow water experiment. Both background internal waves and ÒsoliboresÓ are considered. Finally, an rdω β ≡ . (1) overview of the numerical simulations is given. ω dr

Beta is often called the Òwaveguide invariant.Ó For an ideal shallow water waveguide with perfectly IMAGE PROCESSING ALGORITHM reflecting boundaries, one can show β = 1. For more realistic shallow water scenarios, the numerical value Assume the acoustic intensity I is measured in β of beta may change; Hodgkiss et al. [2] found = 1.4 range r over some finite aperture and in frequency ω for a case where both the acoustic source and receiver over some finite bandwith. The resulting windowed were located below the thermocline. Ir(,ω ) has the two-dimensional Fourier transform Brekhovskikh and Lysanov [3] caution that (1) Ä κτ applies only Òfor a group of modes.Ó As the range and I (,). By ParsevalÕs theorem, frequency change, Òthe sound field will be determined ∞ ∞ ∞ ∞ 2 by another group of modesÉresult[ing] in a change of ≡=ωω2 ()1 2 Ä κτκτ EIrdrdIdd∫∫∫ (, ) 2π ∫ (,) . β.Ó Similarly, range-dependence in the environment −∞ −∞ −∞ −∞ can cause the sound field to be determined by another ()2 group of modes even for an observer at a fixed range and frequency. Internal waves, for example, disturb In the polar coordinates κφ= K cos and τφ= K sin , the thermocline and introduce range-dependence in the environment. This range-dependence could be π 2 sufficiently strong as to cause the modes to couple and EEd= ∫ φ φ, (3) thereby change the value for β. As the internal wave −π 2 β. field changes in time, so could the value for where B 2 and a model for the strong, tidally-driven internal = πφφ−2 Ä EIKKKdKφ ()2 ∫ ( cos , sin ) . (4) wave packets (ÒsoliboresÓ) that were observed. −B Because the background thermocline had a The integral has been truncated at some maximum significant gradient below the mixed layer, the lower spatial frequency of interest B. The ramp filter K order acoustic modes had upper turning depths inside arises naturally from the change of variables. Note the water column. Typically, the value of β for Ä φφ that IK( cos , K sin ) is the transform evaluated interaction between these modes was greater than for along a line in Fourier space passing through the origin the higher order, sea-surface interacting modes. The at angle φ . With some manipulation, this angle can be mode coupling induced by the internal waves cause related to β. In this approach, beta is treated not as a energy to be interchanged between these different single number but rather as a distribution. The output types of modes. The background internal waves produce moderate mode coupling. The details of the of the processing is the waveguide distribution Eφ waveguide distribution vary in time, but the β value at plotted versus β. This distribution might be sharply which it peaks remains relatively unchanged. The β peaked around a single value of in which case the solibores produce strong mode coupling. The traditional notion of a scalar invariant would be observed Ir(,ω ), and consequently Eφ , changes reasonable. Other cases producing different sorts of rapidly in time rendering the concept of a waveguide distributions can also be studied. invariant problematic. Numerical calculations illustrating these results will be given in the accompanying oral presentation. EFFECT OF INTERNAL WAVES

In Rouseff and Spindel [4], the proposed image ACKNOWLEDGMENTS processing method was more fully developed. A formula was derived expressing the waveguide This work was supported by the United States Office distribution in terms of the acoustic modes for a range- of Naval Research. independent environment. For a range-dependent environment, the simple formula does not apply. In the present study, the effects of range dependence introduced by shallow water internal waves are studied. Realizations of a three-dimensional, time- REFERENCES evolving internal wave field are generated using an ocean simulation model. Acoustic propagation 1. S. D. Chuprov, ÒInterference structure of a sound field in a layered ocean,Ó in Ocean Acoustics. Current State, through vertical slices of the realization is simulated edited by L. M. Brekhovskikh and I. B. Andreevoi, using the parabolic equation method. The acoustic Moscow: Nauka, 1982, pp. 71-91. simulation is repeated at multiple frequencies to synthesize broadband output. The result is a map of 2. W. S. Hodgkiss, H. C. Song, W. A. Kuperman, T. Akal, acoustic intensity plotted versus range and frequency, C. Ferla, and D. R. Jackson, J. Acoust. Soc. Am. 105, Ir(,ω ). These images are processed using a discrete 1597-1604 (1999). version of the algorithm outline in the previous 3. L. M. Brekhovskikh, and Y. P. Lysanov, Fundamentals section. This gives a plot of the waveguide of Ocean Acoustics, 2nd ed. New York: Springer-Verlag, distribution Eφ plotted versus β at an instant in time. 1991, pp. 140-145. The internal wave field is allowed to evolve and the waveguide distribution tracked in time. 4. D. Rouseff and R. C. Spindel, ÒModeling the waveguide invariant as a distribution,Ó to appear in Ocean Acoustic The internal wave model used in this study was Interference Phenomena and Signal Processing, edited by W. A. Kuperman and G. L. D'Spain, New York: AIP based on measurements taken during the 1996 Coastal Press, 2002. Mixing and Optics Experiment [5]. The water was nominally 70 m deep and the averaged sound speed 5. T. D. Dickey and A. J. Williams, J. Geophys. Res. 106, profile showed the effect of the thermocline, typical of 9427-9434 (2001). conditions during the summer. The model has two primary components: a background internal wave representation valid for relatively quiescent periods, Interference Patterns in Shallow Water Acoustic Fields G. L. D’Spain, P. Lepper, J. A. Smith, E. Terrill, L. Berger, and W. A. Kuperman Marine Physical Laboratory, Scripps Institution of Oceanography, La Jolla, CA, 92093-0704 U.S.A.

When a source transmits a continuous, broadband signal in a waveguide, the received field displays patterns due to the construc- tive/destructive interference between multipath components. Many aspects of these patterns are predictable using simple techniques and provide useful information on the properties of the waveguide and the source. Results from several shallow water experiments off the west coast of the U.S. illustrate the impact on these patterns of range-dependent bathymetry and environmental fluctuations. The analysis also indicates the effects of multipath arrivals on the temporal and spatial coherence of the field. In addition, since ocean acoustic measurements in upcoming experiments will be made using an AUV, numerical modeling of the broadband, multiple scattering from the AUV body is performed to understand the effects on these interference patterns of the AUV itself. These additional effects also contain useful information, analogous to the use of interference patterns in human hearing.

INTRODUCTION 0

Broadband interference patterns, formed by the inter- 4 action of correlated multipath components, often appear in acoustic ﬁeld data recorded both by omni-directional 8 hydrophones and directional elements (such as pressure- sensing array beams) deployed in waveguides. Associ- 12

ated with these patterns is an energy ﬂow, speciﬁcally Time (hrs)

the reactive component of vector acoustic intensity, that 16 maintains the spatial structure of these patterns. Several examples of such patterns measured during recent exper- 20 iments off the Southern California coast will be discussed in the conference presentation. The focus in this paper is 24 on one data set collected in a "ﬁxed/ﬁxed" experimental 200 225 250 275 300 325 350 375 400 Frequency (Hz) geometry in Fall, 2000. The experiment location was 50 km west of San Diego 73 83 93 Spectral Density (dB re 1 uPa^2/Hz) on a northwest/southeast-trending shallow water ridge called the Fortymile Bank. A 16-element hydrophone ar- FIGURE 1. Pressure spectrum over a 24-hr period starting at ray with equal 32-m interelement spacing was deployed 14:32 GMT, JD 313 recorded by element 14. on the ocean bottom in 180-m water and cabled back to R/P FLIP where the data were recorded continuously. An acoustic source was suspended at a depth of 43 m ual striations gradually increases with increasing center from a ship anchored a distance slightly more than 2 km frequency from about 12 Hz to 15 Hz over the 200-400 to the southeast. Signals transmitted by the source in- Hz band. cluded pseudo-random-noise (PRN) sequences and linear frequency modulated (LFM) sweeps over the 200-400 Hz The analysis of these patterns starts with the expression for the acoustic pressure spectrum, S , in terms of band. p normal modes. If a point source at depth zs has a frequency dependent source spectrum P(ω), then the pressure spectrum at range r and depth z is BROADBAND INTERFERENCE r

ω ω 2 Φ The received acoustic pressure spectrum recorded by Sp(r, ,zr,zs) = P( ) ∑Bn + 2 ∑ BnBm cos( ) (1) a single bottom array element at a nominal distance of n n,m ! 2.1 km from the source is shown in Figure 1. The Φ ∆κ ω η η peaks and troughs of the interference pattern display a The phase term is = mn( , j)r where j signiﬁes a beautiful undulating nature. Individual striations can be property of the waveguide itself, e.g., sound speed. The tracked for the most part throughout the full 24-hour pe- received amplitude of the n-th mode is Bn. Almost all of riod. The average spacing in frequency between individ- the spatial variability in range in Eq. (1) is determined by the cosine term. Applying a stationary phase condition1 by 34 m in the direction transverse to the source direction is shown in Figure 2. The undulating nature of the ∂∆κmn ∆κmn δω δr ∂∆κmn ∆κmn δη j ∂ω / ω ω = +∑ ∂η / η η 0 − ! r j j j ! j (2) 4 The ﬁrst term in brackets is equal to the standard waveguide invariant 1/β, a single scalar quantity that sum- marizes the dispersive propagation characteristics in a 8 waveguide[1]. The second set of terms in brackets are the environmental invariants[2]. The term associated with 12

sound speed fluctuations in complex media can be ob- Time (hrs) tained from a perturbation analysis and the assumption of 16 adiabaticity, i.e., Z Z Z 20 ω2 Ψ2(z) δκ (r)dr = n δc(r,z)dr dz (3) n κ 3 − n c (z) 24 ! 200 225 250 275 300 325 350 375 400 Frequency (Hz) Eq. (3) provides a basis for tomographic inversions using 0.13 0.38 0.63 0.88 the time-varying nature of interference patterns[3]. Coherence Squared Application of Eq. (2) keeping the waveguide proper- FIGURE 2. Spatial coherence over the same 24-hour period as ties fixed shows that the overall undulating character of in Figure 1 between elements 12 and 14, separated by 34 m and the interference pattern in Figure 1 is mostly due to the equidistant from the source. motion of the source ship in its watch circle. Likewise, the rapid oscillations in the 18-21 hour period, having a spatial coherence with time is identical to that in the 30-min period, are caused by source motion from cur- single element pressure spectrum. This figure clearly rents of an internal wave packet. These oscillations result illustrates the difficulty of fitting curves of the form m in a non-monotonic dependence of the narrowband tem- exp( (y/LT ) ),m = 1,1.5,2, to narrowband data to de- − poral and spatial coherence with time (re below). How- termine the transverse spatial coherence length LT [4, 5]. ever, other aspects of Figure 1 cannot be explained by source motion. For example, at certain times such as in the 14-18 hour interval over the 280-310 Hz band, a given ACKNOWLEDGMENTS striation suddenly splits into two or three striations having significantly smaller spacing in frequency and then Dave Ensberg, Jeff Skinner, Dick Harriss, and Pam coalesces later to reform the original pattern. The spac- Scott of the Marine Physical Lab, and Lee Culver, Rox- ing in frequency at fixed range equals the inverse of the anne Rishel, and Joe Keranen of the Applied Research largest travel time difference between those modes con- Lab, Penn State assisted in collecting the data presented tributing significantly to the field. Therefore, changes in here. The support of the Office of Naval Research for this spacing indicate changes in the spatial bandwidth of the work is greatly appreciated. ocean waveguide, e.g., by addition/elimination of a group of highest order modes. Arrays deployed on the ocean bottom are particularly sensitive to changes in the contri- REFERENCES bution from highest order mode groups. 1. S. D. Chuprov, in Ocean Acoustics, Current State, ed. L. M. Brekhovskikh, I. B. Andreevoi: Nauka, Moscow, 71-91 COHERENCE (1982). 2. G. A. Grachev, Acoust. Phys. 39(1), 67-71 (1993). The spatial coherence between the element whose data 3. V. G. Petnikov and V. M. Kuz’kin, in Ocean Acoustic In- are shown in Figure 1 and a second element separated terference Phenomena and Signal Processing, ed. W. A. Kuperman and G. L. D’Spain, AIP Press, 11 pgs. (2001). 4. W. M. Carey, IEEE J. Ocean. Engin. 16(3), 285-301 (1991). 1 This approach is analogous to the stationary phase technique that leads 5. V. A. Zakharov, V. A. Lazerev, A. A. Saltykov, A. D. to the concept of group velocity. However, whereas group velocity is Sokolov, L. I. Tatarinov, and G. A. Sharonov, Sov. Phys. Φ associated with the active component of intensity, the term in Eq. (1) Acoust. 38(2), 191-193 (1992). is associated with the reactive component. Correlation-Tracking with the Hydra Array

M. Portera, P. Hurskya, C. Tiemanna, M. Stevensonb

aScience Applications International Corp.,Ocean Sciences Division, La Jolla, USA bSPAWAR Systems Center, San Diego, USA

Hydrophone arrays are widely used for tracking sources in and on the ocean such as whales, autonomous vehicles, and ships. The most common approach uses planewave beamforming in which the individual channels are combined with the appropriate delay for a presumed bearing angle. Sweeping through different bearing angles then provides a measure of the sound level in each listening direction and therefore the bearing of sound source(s). As acoustic models have become much more rapid and reliable it has become increasingly obvious that more sophisticated features of the received energy can be exploited to provide the source location in 3-space rather than just in bearing space. Here we describe the application of a correlation-based approach for a sparse, 6-phone, horizontal line array.

INTRODUCTION

The limitations of conventional planewave beamforming are obvious if one considers the extreme case of an array consisting of just a single phone. Planewaves from all points in space look the same to that single phone so there is no resolution in depth, range, or bearing. Nevertheless, it is possible to localize a source in this configuration. The phone receives a different echo pattern for each source position. Modern ocean acoustic models can easily and reliably predict that echo pattern; a comparison of measured and modeled echo patterns then reveals the source position.

The process we are describing is a model-based one that exploits more subtle features than just the arrival FIGURE 1. Bathymetry for the Hydra Sea Test angle. Within this large class of model-based schemes (depths in m). one may include, 1) matched-field processing, 2) back- propagation/time-reversal methods, and 3) correlation During the experiment, both tonals and linear processing. Interestingly all of these methods can be frequency modulated (LFM) chirps were transmitted in traced back a couple decades and despite their the 30-230 Hz band. The resulting waveform thus apparently distinct nature are identical under simple simulates the spectrum of a surface ship. In addition, conditions. Space does not permit a complete correlating the waveform on a single channel with that discussion of these issues, so we confine ourselves transmitted yields the impulse response of the channel here to an experimental demonstration of the process. as shown in Fig. 2. During this period the acoustic projector was towed from east to west over the array EXPERIMENTAL DEMONSTRATION and then back again from west to east. The varying echo pattern is the signature of the source location that The Hydra array consists of 6 phones over a total is exploited for ranging purposes. length of about 650 m. The received data is processed autonomously relaying track information to the surface As a pre-cursor to localization, one would like to have via an acoustic link. However, in these tests the data is confidence that the acoustic model gives an accurate simply stored and processed later. The array was simulation. This is confirmed in Fig. 3 showing deployed off the coast of California near San Diego as simulated impulse responses as computed by a simple shown in Fig. 1. beam-tracing code (BELLHOP). FIGURE 3. Modeled impulse response as the source FIGURE 2. Measured impulse response as the source passed twice over the array. passed twice over the array.

FIGURE 4. Range-time track derived by correlation FIGURE 5. Range/cross-range localization derived processing. by correlation processing. To do the source tracking we use the acoustic model to (not shown) also show reliable tracking in depth. predict the echo pattern for a set of possible source Future work will demonstrate autonomous, real-time ranges. Then the measured echo pattern is compared to processing in the Hydra array. the ensemble of modeled echo patterns. Each candidate range generates a unique impulse response so that when the best match between model and data is found, the source range has been identified. ACKNOWLEDGMENTS

This work was sponsored by ONR 321SS. Additional We measure the similarity of measured and modeled support was provided by ONR 321OA. We thank also data by correlating the logs of the envelopes. The V. McDonald, M. Klausen, and J. Olson at SPAWAR argument for this is developed more thoroughly in for development work on the Hydra array. [1,2]. Figure 4 shows the correlation (similarity between model and data) as a function of the candidate range and using just a single phone in the array. The REFERENCES process is repeated over the 2-hour period of the experiment to reveal the source track. Note that time- 1. M. Porter, S. Jesus, Y. Stéphan and X. Démoulin, E. held is over 90%. Comparisons to GPS data verify that Coelho, “Exploiting reliable features of the ocean the range is accurate to a few percent. channel response”, Shallow-water Acoustics, eds. R.H. Zhang and J.X. Zhou, China Ocean Press (1997). Using additional phones (and then comparing modeled and measured cross-correlations) we achieve both 2. M Porter, S. Jesus, Y. Stéphan, X. Démoulin, E. Coelho, azimuthal resolution and increased gain. Figure 5 “Tidal effects on source inversion”, Experimental shows localization in the latititude-longitude plane Acoustic Inversion Methods, Eds. A. Caiti, S. Jesus, J-P. Hermand, M.B. Porter, pp. 107-124, Kluwer (2000). using the full array. This is a snapshot taken at a time when the source is at about 1.5 km range. Other results Simulations of Rough Boundary Effects on Shallow Water Propagation

E. I. Thorsos, K. L. Williams, F. S. Henyey, S. A. Reynolds, W. T. Elam, R. I. Odom, D. Tang, C. D. Jones and D. Rouseff

Applied Physics Laboratory, University of Washington, 1013 NE 40th St., Seattle, WA 98105, USA

Results of numerical simulations are described for propagation in a shallow water waveguide. Pressure fields are simulated in two space dimensions with a wide-angle parabolic equation (PE) method that accounts for a rough sea surface, while the bottom is taken as flat. A key goal in this work is to examine the limitations inherent in the common practice of ignoring rough boundary effects in shallow water propagation simulations. Results are presented for both mid-frequency (3 kHz) and low- frequency (100 Hz) propagation. At low frequency, a normal mode representation is also considered for representing the shallow water field. Results of PE simulations using single mode initial fields and sinusoidal surfaces are used to illustrate the effects of surface scattering on mode propagation and on mode coupling. A mode coupling model has been developed based on perturbation theory, and the mode-based propagation results are shown to be in excellent agreement with PE simulation results.

INTRODUCTION Moskowitz form [4]. At a frequency of 3 kHz and wind speed of 7.5 m/s, the behavior of the forward Traditional methods for modeling sound scattered field is found to depend dramatically on the propagation in shallow water waveguides generally do incident grazing angle. A narrow incident beam at a not treat scattering from roughness at the sea surface 10° grazing angle is completely broken up, with or bottom in detail [1]. When such scattering is treated energy scattered widely in angle. At a 1° angle, little within the framework of a ray-based propagation energy is scattered out of the beam. model, a common approach is to introduce a reflection With a broad incident beam in an isovelocity, loss at the boundary in an attempt to approximately shallow water waveguide (50 m depth to a sand account for the main effects of scattering. The errors bottom), sound energy fills the waveguide relatively associated with this simplification, or of ignoring quickly as the field propagates downrange, whether the forward scattering entirely in wave-based propagation surface is modeled as flat or rough. The effect of models, have not been well quantified. surface scattering, however, plays a role in the We have begun an investigation of shallow water attenuation of sound intensity downrange. When the propagation using a wide-angle PE method developed sea surface is modeled as flat, sound propagating at by Rosenberg [2] that accurately accounts in two space angles above the critical angle at the bottom is rapidly dimensions for forward scattering from a rough sea lost to the bottom at short range; at longer ranges the surface. The Rosenberg propagation model is an only energy that survives propagates below the critical extension to a wide-angle PE propagation model angle, and the losses are much reduced. When the sea developed by Collins [3] for a flat sea surface, and surface is modeled as rough, scattering continually should be extendable to the rough bottom case as well. repopulates the portion of sound energy propagating At present, however, the sea bottom is taken as flat. above the critical angle, increasing losses at Our initial investigations have focused on the intermediate ranges. Eventually, a range is reached at accuracy of a surface reflection loss formulation of which the remaining sound energy propagates at quite surface scattering for mid-frequency propagation, and low grazing angles, the angular redistribution due to on the development of a mode coupling formulation of surface scattering becomes ineffective, and losses surface scattering for low frequency propagation. become small. Simulation results will be presented illustrating these trends. The results have implications MID-FREQUENCY SIMULATIONS on the use of surface reflection loss models with ray models (or with full wave methods using flat surfaces) Rough surface realizations were generated to simulate mid-frequency propagation in shallow consistent with a one-dimensional cut through a two- water. dimensional isotropic spectrum of a Pierson- LOW-FREQUENCY SIMULATIONS

Simulations have also been carried out at 100 Hz for propagation in a waveguide of 50 m depth with a rough sea surface and flat sand bottom. For these conditions, it is useful to decompose the fields into normal modes, and seek to understand mode coupling due to surface roughness. To this end, we have found it instructive to also examine a simplified problem with a Dirichlet bottom boundary at a depth of 58.25 m. (The Dirichlet bottom yields discrete modes only, and this choice of depth matches well the mode coupling found with a sand bottom at 50 m depth.) It is also instructive to begin the PE propagation simulation with a pure mode starting field, and to take the rough surface as a single sine wave. FIGURE 1. PE simulation at 100 Hz with surface sine wave Figure 1 shows the result of using a mode 2 starting roughness. The gray scale has a 15 dB dynamic range; dark field with the surface wavelength (342 m) chosen to indicating high intensity. give strong coupling to mode 3; the surface wave amplitude is 1 m. This resonant case shows repeated 1.2 oscillation between modes 2 and 3 with nearly complete conversion to mode 3 at a range of about 4 1 Mode 2 Mode 3 km. Note that the scale of the smaller structure is about the same as the surface wavelength. When the surface 0.8 wavelength is chosen off resonance, the initial mode persists, but modified by small scale structure similar 0.6 to that in Figure 1. The mode amplitudes projected from the PE solution are shown in Figure 2. 0.4 We have also developed a propagation code based on coupling of unperturbed modes using perturbation 0.2 theory. This turns out to be nontrivial, since the Mode 4 Mode 1 perturbation condition on the field y is 0 0 1 2 3 4 5 6 7 8 9 10 ¶y Range (km) y + h(x) = 0, (1) z=0 ¶z FIGURE 2. Mode amplitudes corresponding to Figure 1. z=0 where h(x) is the surface profile, and the unperturbed modes all vanish at the mean surface (z = 0). Thus, in ACKNOWLEDGMENTS addition to a set of finite modes, one must also represent the remainder of the field in order to satisfy Work supported by the US Office of Naval Research. the boundary condition. The mode propagation code yields results that are essentially identical to Figures 1 and 2, but the REFERENCES computer run time is reduced about a factor of 800 (to about 2 s using 6 modes on a Macintosh G4). 1. Jensen, F.B., Kuperman, W.A., Porter, M.B. and Schmidt, H., The derivation of the mode coupling equations will Computational Ocean Acoustics, AIP Press, New York, 1994. 2. Rosenberg, A.D., J. Acoust. Soc. Am., 105, 144-153 (1999). be outlined, and examples shown comparing PE and 3. Collins, M.D., J. Acoust. Soc. Am., 93, 1736-1742 (1993). mode solutions. 4. Thorsos, E.I., J. Acoust. Soc. Am., 88, 335-349 (1990). Mode Filtering From Propagation And Reverberation Data Renhe Zhang, Fenghua Li, Zhenglin Li

National Laboratory of Acoustics, Chinese Academy of Sciences, P.O.Box 2712, Beijing, 100080, China

Mode propagation and scattering is one of the most interesting problems in ocean acoustics. In this paper, a mode filtering method for a vertical line array is used to the measured propagation data from a recent shallow water acoustic experiment. Good mode filtering results are obtained at different frequencies. The bottom attenuations are inverted from the normal mode amplitudes. The numerical calculations of the transmission loss from the inverted bottom parameters are in good agreement with the experiment data. The mode filtering method is also used to analyze the received reverberation data in the same experiment. Some theoretical derivations are presented. The mode attenuations and the bottom scattering index are estimated from the mode filtering of the reverberation. The mode attenuations inverted from reverberation are consistent with that from propagation data.

INTRODUCTION model, one has: ∆ RLmod e2−mod e1 =10log ()I −10log ()I Mode filtering is an important approach for the 10 rev−mod e2 10 rev−mod e1 2 2 research of mode propagation and scattering in shallow     =10log sinϕ ()z p(z) −10log sinϕ ()z p(z) water. Some papers about mode filtering from sound 10  ∑ 2 r  10 ∑ 1 r   zr   zr  propagation have been published in the last few     =10log σ ()α ,α −10log σ ()α ,α − 20[]log (e) ()β − β r decades. However, few results about the mode filtering 10 2 2 10 1 1 10 2 1 from reverberation have been presented. In this paper, a = A + Br mode filtering method from reverberation was 3 introduced to estimate the normal mode attenuation and where σ ()θ θ = ℘ ()θ θ 2 .ItisshowninEq.(3)that l , l l , l bottom scattering index at small grazing angles. The results show that the bottom attenuations obtained from A is a function of bottom scattering model, and B is a measured reverberation data and propagation data are function of mode attenuation. in good agreement with each other. In an isovelocity shallow water, it can be assumed that: θ ≈ θ , ()θ ≈ θ , 2h (4) 2 2 1 lnV Q S ≈ THEORY l ()θ tan l where θ is the grazing angle of lth normal mode, 1. MODE-FILTERING FROM REVERBERATION l V In a range-independent shallow water, the is the bottom reflection coefficient. [1] [2] reverberation time series R()z,t is : From BDRM theory, the mode attenuation can be expressed as: 8π µ q ()z q (z ) − β + µ = m m m b ϕ () m r i m r R(z,t) sin m zs e ln V ()θ ∑∑ r S (1) β = l (5) mn m l Sl 8π µ q ()z q (z ) − β + µ × n n n b ϕ () n r i n r℘ sin n zr e m,n Substitute Eqs. (4-5) into Eq. (3), r Sn β = − B (6) where ℘ is the bottom scattering coefficient, S is 1 () m,n n 60log10 e the cycle distance, µ is eigenvalue, β is mode If the bottom scattering model can be written as the m m following expressing, attenuation, t = 2r / c . The definition of q is discussed σ ()θ ,θ = µ sin n / 2 θ sin n / 2 θ (7) in Ref. [1]. 1 2 1 2 The mode filtering from reverberation can be where n is the bottom scattering index. Substitute Eq. written as: (7) into Eq. (3), µ () ( ) A (8) 8π m qm z qm zb −β + µ n = sinϕ ()z p(z) = sinϕ ()z e mr i mr () ∑ l r ∑ m s 5log10 2 zr m r Sm µ () ( ) 8π l ql z ql zb −β + µ × l r i l r 2 ϕ ()℘ 2. MODE-FILTERING FROM PROPAGATION e ∑sin l zr m,l r Sl zr 2 Mode filtering from propagation can be expressed On the basis of the separable bottom scattering as: π µ () ( ) 8 l ql z ql zb − β r +iµ r 2 (9) Table 2. It is shown in Table 2 that the results from the sinϕ ()z p(z) = e l l sin ϕ ()z ∑ l r ∑ l r reverberation and proapgation are in good agreement. zr r Sl zr

EXPERIMENTAL RESULTS

In this section, the mode filtering method was used to the measured reverberation and propagation data. The data were collected in an isovelocity shallow water by a 16-elment vertical line array, which spans the whole water column. The water depth is 40m.

1. MODE-FILTERING FROM REVERBERATION In Fig. 1 was shown ∆ defined in Eq. (3) RLmod e2−mod e1 vs. reverberation time at frequency of 400Hz. The line in the figure is the linear fitting of the experimental results. A and B are shown in table 1. The mode FIGURE 2 The waveform normal mode 1 and 2 by attenuation and bottom scattering index derived from using the mode filtering technology from pulse Eqs. (6) and (8) were also shown in table 1. waveform propagation.

Figure 3 The amplitude of the normal mode 1 in unit ∆ of dB vs. propagation range. FIGURE 1 RLmod e2−mod e1 defined in Equation s. reverberation time at the frequency of 400Hz. Table 2. Comparison of the bottom attenuation from reverberation and propagation Frequency(Hz) β (dB/km) β (dB/km) Table 1. Results from reverberation mode-filtering 1 1 Frequency(Hz) A B(dB/km) β (dB/km) n 1 400 0.010 0.012 400 2.172 -0.26 0.010 1.44 500 0.013 0.011 500 2.775 -0.34 0.013 1.84 CONCLUSIONS 2. MODE-FILTERING FROM PROPAGATION A mode-filtering method from reverberation to In Fig. 2 was shown the waveform of normal mode estimate the mode attenuation and bottom scattering 1 and 2 by using mode filtering method from pulse index was presented in this paper. Results show that the waveform propagation. The central frequency is 400Hz, mode attenuation obtained by using mode filtering and the range is 19km. In Fig. 3 was shown the from reverberation are in good agreement with that amplitude of the mode 1 in unit of dB vs. propagation from sound propagation. range. EFERENCE 3. COMPARISON 1. Zhang, R., and Jin, G., Journal of Sound and Viberation, 119, 215-223 (1987) The comparison of the mode attenaution obtained 2. Zhang, R. and Li, F., Science in China (Series A) (in Chinese), 31(2), 165-172 (1998) from reverberation and proapagtion was shown in Reverberation-Derived Bottom Scattering Strength in the Yellow Sea

J. X. Zhou a,b, X. Z. Zhang a,b, J. S. Martina, and P. H. Rogers a,

a School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405 b Institute of Acoustics, the Chinese Academy of Sciences, Beijing 100080 China

Reverberation data collected on a vertical hydrophone array in the Yellow Sea during the summer of 1996 was analyzed to determine the bottom scattering from the measured reverberation. Two published empirical relationships were compared with the data. These were the Lommel-Seeliger law and the Lambert-Mackenzie law. Below 700 Hz, both were found to fit well over short ranges however there were obvious differences between their long-range predictions and the Lommel-Seeliger law was found to better describe conditions at the experimental site. (Work supported by ONR and CAS)

1.9 BACKGROUND Values of Cb=1590 m/s and ab=0.28f dB/mkHz were In shallow water, reverberation can often be the obtained by this method [1]. limiting factor on the operation of active sonar systems. REVERBERATION-DERIVED In spite of this, long-range reverberation models have not been as well developed as propagation loss models. BOTTOM SCATTERING STRENGTH One of the reasons that the development of these Seabottom scattering at small grazing angles is models has lagged is the dearth of experimental data normally derived by inversion from long-range for low frequencies and shallow grazing angles. Since reverberation data. This procedure was followed for the shallow water problem is dominated by bottom the Yellow Sea 96 data. interactions when the sound speed gradient is negative, Normal-mode theory [2] was used to calculate the accurate reverberation modeling requires a reliable average reverberation level. Inputs to the model were model for bottom scattering. Due to normal mode the sound speed profile, sediment sound speed, and stripping, the effective grazing angle for sound seabottom attenuation derived for the test site. The propagation interacting with bottom in shallow water model was then used to fit the coefficients for two decreases with increasing sound propagation distance. commonly used seabottom scattering laws. These are Grazing angles of primary importance to shallow water the Lommel-Seeliger (L-S) law [3] and the Lambert- application range from about 20L to near 0L with the Mackenzie (L-M) law [4]. Both are semi-empirical smaller angles being more important. Direct seabottom scattering laws, which are as follows: measurement for bottom scattering strength at small (a) L-S law: grazing angles and low frequencies in shallow water is BS1 = 1sin nearly impossible. Therefore, the bottom scattering (b) L-M law: 2 strength at small grazing angles is generally derived BS2 = 2sin . from long-range reverberation measurements. In the Yellow Sea 96 experiment, reverberation Figure 1 shows the results of the fits for both of the data was collected on a 32 element vertical array of scattering laws at 200 Hz, 500 Hz, and 800 Hz. It is hydrophones. Explosive sources were used and the data clear from this figure that the seabottom scattering at exhibit high reverberation to noise ratios which are the Yellow Sea test site is equally well described by required for the testing of long range reverberation both laws for short and mid ranges. The L-S law models. The seabed at the experimental site was flat however, better fits the long-range data. This result, i.e. and composed primarily of silt. Water depth was the seabottom scattering strength decreases as the sine approximately 75m and there was a steep seasonal of the grazing angle to the first power, implies that the thermocline between 15 and 30 m at the time of the seabottom scattering at low angles and low frequencies experiment (August 1996). Near the surface the sound is mainly caused by inhomogeneities in the sediments speed was measured to be 1535 m/S this was constant at the test site [5,6]. This is consistent with the to a depth of about 15 m. Below the thermocline the observation that the bottom was flat but contradicts the sound speed was constant at 1480 m/S from 35 m to 75 observed homogeneity. The L-S coefficients from this m deep. The sound speed and attenuation in the bottom fit ( 1) are shown in Figure 2. The applicability of the sediment at the experiment site were determined, by L-S law for the Yellow Sea 96 site is dependent on the inversion, from sound propagation measurements. ground truth of the measured bottom attenuation. If the leading coefficient of the attenuation expression were waves. Figure. 3 shows that strong resonant volume reduced by 50%, the L-M law would match the data scattering can be observed in the reverberation at 1500 equally well. Hz. Thus, water column effects must be accounted for F=200( Hz ) if bottom scattering is to be determined from high -60 frequency reverberation data.

-70 From Yellow Sea 96 Reverberation data -25

-80

-90

RL(dB) -30

-100

-110 -35

-120 5 10 15 20 25 30 35 40

Time(sec) (dB) Coefficient Lommer-Seeliger F=500( Hz ) -60 -40 2 3 10 10 Frequency (Hz) -70 Figure 2. L-S Coefficients Derived from -80 Yellow Sea 96 Reverberation Data F=1500( Hz ) -60 -90 RL(dB)

-100 -70

-110 -80

-120 -90 5 10 15 20 25 30 35 40 Time(sec) RL(dB) F=800( Hz ) -100 -60

-110 -70

-120 -80 5 10 15 20 25 30 35 40 Time(sec)

-90 Figure 3. Reverberation in the Yellow Sea 96

RL(dB) Experiment at 1500 Hz. Dashed Line: L-M Law Solid

-100 Line: L-S Law

-110 REFERENCES 1. P.H. Rogers, J.X. Zhou, X.Z. Zhang and F.H. Li, in -120 5 10 15 20 25 30 35 40 Experimental Acoustic Inversion Methods for Exploration of Time(sec) the Shallow Water Environment, pp. 219-234, edited by A. Figure 1. Reverberation in the Yellow Sea 96 Caiti, J.P. Hermand, S.M. Jesus and M.B. Porter (Kluwer Experiment at 200 Hz (top), 500 Hz (Middle), and Academic Publishers, 2000). 800 Hz (Bottom). Dashed: L-M law Solid L-S law. 2. D.D. Ellis, J. Acoust. Soc. Am. 97, 2804-2814 (1995). 3. A.V. Bunchuk and Yu. Yu. Zhitkovskii, Sov. Phys. For frequencies that are higher than 700 Hz, the Acoust. 31, 363-370 (1980). 4. K.V. Mackenzie, J. Acoust. Soc. Am. 33, 1498-1504 long-range reverberation data in the Yellow Sea (>15s) (1961). decay slower than predictions by the two seabottom 5. A.N. Ivakin and Yu. P. Lasanov, Sov, Phys. Acoust. 27, scattering laws. This might be due to water-column 61-63 (1981). scattering contributions, for example, bio-scatters, fine 6. A.N. Ivakin and Yu. P. Lasanov, Sov. Phys. Acoust. 31, structure and turbulence in the thermocline and internal 236-237 (1985). Transmission Loss and Ambient Noise Measurements with Sonobuoys Moored in Shallow Water

C. de Moustier, S. Wiggins, G. D’Spain, and J. Murray

Marine Physical Laboratory, Scripps Institution of Oceanography, 9500 Gilman Drive, La Jolla CA 92093-0205, USA

A series of concurrent underwater ambient noise and acoustic transmission loss measurements were conducted in about 100 m of water depth, offshore Southern California, using calibrated sound sources and sonobuoys. Measurements were made in summer and winter conditions which are mostly differentiated by the presence and/or depth of a surface mixed layer in profiles of sound speed vs. depth. The signals consisted of a sequence of short duration tones ranging from 3 kHz to 30 kHz interspersed with silent gaps. The silent gaps allowed measurements of short term reverberation and omni-directional ambient noise levels. Transmitted sound pressure levels were limited to 195 dB re 1 µPa/m by the requirement to monitor presence of marine mammals in the survey area, and resulted in extinction distances between 4.5 and 5.5 km depending on the local topography and water depth.

INTRODUCTION were used for the experiments. For the transmission loss runs, the sound source was an ITC1007 resonant The Southern California Offshore Range (SCORE) at about 18 kHz. Its emitted sound pressure level was is a designated US Navy range located 60 nm west of monitored with a reference broadband omni- San Diego, California, and bound by San Clemente directional hydrophone (ITC 1042) located 3 m away Island to the east and Cortes and Tanner Banks to the from the source. Source and hydrophone were towed west, with San Nicholas Basin in the middle. Water on a drogue line attached to a batwing tow body depths range from 1700 m in the basin to the shoreline equipped with a pressure sensor to monitor the depth of the San Clemente Island and emerging rocks on the of the source. This arrangement was meant to banks[1]. approximate free field conditions to the greatest extent possible. It allowed us to tow the source at 5 knots in To improve environmental and tactical models of the and below the surface mixed layer at depths ranging ocean in the SCORE, a series of environmental and from 15 m to 50 m . underwater acoustics measurements were conducted at two shallow water sites and in the deep water basin. Unlike continuous wave transmissions commonly used Environmental measurements included profiles of in transmission loss experiments, we used repeated conductivity and temperature vs. depth, and recording sequences of 16 short pure tone pulses stepping in 1 of current speed and direction with shipborne and kHz increments from 3 kHz to 12 kHz and 3 kHz bottom moored acoustic Doppler current profilers. increments from 12 kHz to 30 kHz. Pulses lasted 10 ms and were separated by 90 ms, with a 5 s gap before In this paper, we focus on the measurements of transmitting the next 1.6 s transmission sequence. acoustic transmission loss and ambient noise at the two This sequence was designed to provide concurrent shallow water sites. We describe the methodology and measurements of transmission loss, ambient noise and the constraints imposed by the environment and the reverberation along each run. requirements of the Marine Mammal Protection Act of 1972 [2], and we present first order results. We used passive calibrated low frequency analysis and recording (LOFAR AN/SSQ-57B), and directional frequency analysis and recording (DIFAR AN/SSQ- 53B) sonobuoys [3] as receivers. The sonobuoys were METHODOLOGY set to transmit the acoustic data they received via radio waves for up to 8 h. The standard deployment depths of 27, 122 or 305 m for the LOFAR, and 27 or 122 m Sound sources and monitor hydrophones calibrated for the DIFAR were inadequate for the shallow water and operated by SPAWAR-TRANSDEC in San Diego environments in which we used them, so we modified loss runs. The pulse sequence and reverberation tails their deployment mechanisms to place the receiving behind each pulse stand out clearly from the elements in (e.g. 15 m) or below (e.g. 60 m) the mixed background noise. At the time of this writing data are surface layer. still being processed and will be presented more fully at the ICA2001 conference in September, 2001. In addition, to avoid uncertainties caused by drifting However, we have established that under the prevaling buoys, we tethered the sonobuoys to a mooring at the ambient noise, with a maximum source level of 195 two shallow water sites. The mooring included a dB re 1 µPa/m and an average receive sensitivity of hand-held GPS receiver to monitor the position of the –115 dB re 1V/µPa for the LOFAR sonobuoys in the recievers for the duration of the source tows, and four 3-30 kHz frequency band, the signal excess reaches 0 sonobuoys daisy-chained on the tether. Two of these dB at ranges of 4.5 to 5.5 km. Shorter ranges are buoys were LOFAR whose hydrophone was deployed influenced by local topography such as Tanner Bank. in and below the surface mixed layer. The third buoy was a DIFAR deployed in the mixed layer, and the fourth was a vertical line-array DIFAR (VLAD SSQ- 77A) deployed below the mixed layer. The four channels of our digital audio tape recorder limited the number of sonobuoys that we could deploy and monitor simultaneously.

ENVIRONMENTAL CONSTRAINTS

Although measurements were conducted in December 2000, February and June 2001, there was relatively little seasonal variation in oceanic conditions, and the acoustic propagation environment seemed to be mostly regulated by turbulent mixing of the surface layer by the prevaling 18-25 knots NW winds. During FIGURE 1. Spectrogram of two transmission prolongued calm periods in June 2001, the surface sequences received on an AN/SSQ-57B sonobuoy mixed layer disappeared and the thermocline extended deployed in the mixed layer in 120 m water depth. from the surface to 30-50 m depth. However one windy day was sufficient to reestablish a well developed mixed layer extending from the surface to about 30 m depth. ACKNOWLEDGMENTS The requirements of the Marine Mammals Protection P. Taylor and G. Wilkes of the US Naval Act imposed an important environmental constraint Oceanographic Office funded this work under grant that limited the transmitted sound pressure level (SPL) N00014-94-01-0279. We thank the captain and crew to a maximum of 195 dB re 1 µPa/m. This level of R/V New Horizon and the scientific parties of the provided an exclusion sphere, centered on the source three data collection cruises. and 56 m in radius, beyond which the SPL dropped below the Level B harassment for mysticetes. Consequently, acoustic transmissions were restricted to daylight hours when observers aboard the vessel REFERENCES could watch for marine mammals entering the exclusion sphere, at which time the sound source was 1. K.O. Emery, W.S. Butcher, H.R. Gould, and F.P. turned off until the mammals left the area. Shepard, “ Submarine geology off San Diego, California”, J. Geol. 60, 511-548 (1952).

2. Marine Mammal Protection Act of 1972 (P.L. 92-522; 16 USC 1361, et seq), , amended in 1994 (PL 104-297, FIRST ORDER RESULTS 105-18, 105-42, 105-277).

Figure 1 shows an example of the spectrograms 3. G.W. Wolf, “US Navy Sonobuoys – Key to antisubmarine derived from the data recorded during the transmission warfare”, Sea Technology, 39(11), 41-44, (1998). Space-Time Sound Fluctuations Caused by Internal Solitons in Shallow Water

B. Katsnelson a, S. Pereselkov a,K.Sabininb

a Physics Department, Voronezh State University, Universitetskaya pl.1, Voronezh, 394693 Russia. b Andreev Acoustics Institute, Russian Academy of Sciences, ul. Shvernika 4, Moscow, 117036 Russia.

Space-time structure of sound fluctuations caused by internal solitons in shallow water is considered. This structure depends on ori- entation of acoustical track relatively wave front of solitons In particular it can be manifested as resonance absorption of the sound waves passing across wave front of internal waves or as horizontal anisotropy of the sound field and even the forming of waveguide in horizontal plane. Some analytical estimations and numerical results are presented, experimental setup is discussed as well.

Range ( ÿ ) INTRODUCTION 0 500 1000

0 ) D ÿ

Internal solitons are often observed hydrodynamic ( 5 phenomenon in shallow water [1]. They transform wa- ζ 10 ter layer stratification significantly and cause a strong F perturbations of sound field. In [2,3] the spectrum and Sound speed (m/s) statistical properties of the broadband sound signal 1530 1520 1510 1500

crossing packet of solitons are studied on the base of 0 modal technique. The other acoustical effect is horizontal anisotropy of the sound field and even the forming of waveguide in horizontal plane. On the basis of 25 the approaches “vertical modes and horizontal rays”

and its generalization “vertical modes and parabolic Depth (m) 50 equation in horizontal plane” distribution of the sound intensity in horizontal plane is analyzed in the pa- 75 per[4].Presented paper is extension of the research in 0 250 500 750 1000 relation of space-time structure of the sound fluctua- Range (m) tions. This work was supported by RFBR, grant 00-05- FIGURE 1. Shallow water model. Plane of figure is per- 64752. pendicular to the wave front of solitons

SHALLOW WATER MODEL Here, δc is the sound speed variation caused by the displacement of the constant-density interface, Let us represent the oceanic medium as a three- 1 2 = ( ρ−1 ρ ) dimensional underwater waveguide in the X , Y , Z N(z) g d dz is the buoyancy frequency de- coordinate system. The waveguide consists of a water termined by the mean density stratification of the water ρ ρ layer with the density w (z) and the squared refractive layer, is the water density, g is the acceleration of 2 index n2 (z) + µ(x, y, z,t) , where n2(z) corresponds to gravity, Q ≈ 2.4 s m is a constant determined by the the mean equilibrium stratification of the layer (the physical properties of water, and ζ is the vertical dis- corresponding sound speed profile is c(z) )and placement of the water layers. µ(x, y, z,t) characterizes the changes in the acoustic properties of the layer under the effect of the train of MODELING RESULTS internal waves. The water layer is bounded by the pressure-release surface at z = 0 and a homogeneous ab- In view of the focusing and defocusing effects, let us sorbing halfspace at z = H , i.e., by the sea floor with calculate the temporal fluctuations of the sound field ρ intensity for the case at hand, when the train of internal the density 1 and the squared refractive index waves crosses the fixed path. To be more accurate, we 2 + α = α n1 (1 i ) , where n1 c(H )/ c1 and the factor de- use the PE method in the horizontal plane with vertical termines the absorptive properties of the bottom. (In waveguide modes. Received sound field can be repre- numerical calculations, we specified H = 75 m, sented as ρ = 2 g/cm3, c =1750 m/s, and α = 0.02 .). µ(x, y, z,t) M 1 1 P()rÿ, z = F ()()x, y ψ rÿ; z exp(iq(0)x) (2) is determined by the parameters of the train ÿ m m m m=0 where F ()x, y is the smoothly varying amplitude δ m µ = − 2 c(x, y, z,t) = − 2 ζ (x, y, z,t) 2QN (z) (x, y, z,t) (1) ∂ ∂ << (0) (0) c(z) ( Fm x qm Fm )and qm is the real part of the eigenvalue for the waveguide without internal waves. First, the amplitude variations are much higher in the () Then we have for the function Fm x, y : transverse propagation than in the longitudinal one. Second, the spectrum of the variations is much broader ∂ ∂2 (0) Fm = i Fm + iqm ()2()− nq x, y 1 Fm (3) for the transverse propagation than for the longitudinal ∂x (0) ∂ 2 2 2qm y one. In other words: high-intensity internal waves crossing a fixed path at right angle cause high- where n ()x, y = q ()x, y q(0) . Because the characteris- q m m frequency variations of the sound field, which are ab- tic time scale of the variations of the refractive index sent when the internal waves propagate along the path. (1) due to the internal wave motion is much greater To conclude with, we emphasize once again that, in than the time of the sound propagation along the path, the shelf zones, the internal waves strongly affect the the quasi-static approximation can be used to calculate low-frequency sound field, and the magnitude of this the time dependence P(rÿ, z,t) for the received sound effect depends on both the amplitude of internal waves field. In this calculation, the eigenfunctions and eigen- and the direction of their propagation. The greater the values can be assumed to depend on time in a paramet- angle between the propagation directions of the inter- ric way nal and sound waves, the greater the amplitude varia- Figure 2 shows the dependences of the relative am- tions of the sound field. plitudes A ( A = P(t) P(t) ) of the sound field calcu- Sound Field 0.027 0.023 0.018 0.014 0.009 0.004 0.000 lated for different depths of reception (eleven horizons of reception, from 5 to 55 m with a step of 5 m). Here 0 and below, the angular brackets stand for averaging over the reception depths and the overbar indicates the -25 time averaging. According to Fig. 2, the internal waves perpendicularly crossing the fixed path lead to intense Depth (m) variations of the sound field. The variations are caused -50 both by the changes in the interference pattern in the 0 10203040 waveguide and by the aforementioned focusing and Time (min) defocusing effects. The variations remain considerable FIGURE 2. Space-time distribution of the sound field ampli- even if the sound field is averaged in vertical. The sec- tude A for internal waves crossing acoustic track. ond situation corresponds to the train of internal waves Sound Field traveling along the path with the velocity 0.2 m/s; in 0.27 0.23 0.18 0.14 0.09 0.05 0.00 other words: the path is assumed to be nearly perpen- 0 dicular to the coastline. The dependence on the transverse coordinate can be neglected. The amplitudes of -25 the "local" modes change in distance, which testifies to

the interaction (coupling) of the modes. The aforemen- Depth (m) -50 tioned horizontal refraction is absent, and the wave train remains parallel to itself in the horizontal plane. -75 Figure 3 shows the calculated variations of the sound 0 50 100 150 200 field amplitude A for the case of the train moving along Time (min) FIGURE 3. Space-time distribution of the sound field the path. In our situation of a relatively short path and a amplitude A for solitons moving along acoustic track. relatively broad spatial spectrum of the soliton train, a simultaneous interaction of many modes takes place. Mathematically, the calculation consists in solving the REFERENCES system of a large number of ordinary differential equations that describe the interaction of the modes. It is 1. K. V. Konyaev and K. D. Sabinin, Waves within advantageous to use the well-known method of a PE the Ocean (Gidrometioizdat, St. Petersburg, 1992) (in the vertical plane) in this case. Figure 3 presents the 2. Katsnelson B.G. and Petnikov V.G. “Shallow wa- depth-averaged amplitude. As previously, averaging ter acoustics” – M.: Nauka, 1997. 191 p. was performed over eleven horizons. Note that, this 3. B. G. Katsnelson and S. Pereselkov, Acoustical. time, averaging leads to a nearly total smoothing of the Physics. 44, 786-792 (1998)] sound field variations. 4. B. G. Katsnelson and S. Pereselkov, Acoustical By comparing the calculations carried out for the Physics,.46, 684-691 (2000) two limiting cases of longitudinal and transverse propagation of the internal waves, we arrive at the two main conclusions. A Coupled Mode-PE Nx2d Reverberation Model Fenghua Li, Zhaohui Peng and Renhe Zhang

National Laboratory of Acoustics, Chinese Academy of Sciences, P.O.Box 2712, Beijing, 100080, China

In shallow water, the predominant interference for active sonar is often the reverberation from seabed. It is therefore important to be able to predict the bottom reverberation. The ray-mode reverberation model is one of the most widely used models in the range-independent environment. However, most areas have considerable space variability. In this paper, based on a normal mode-PE hybrid model, which is called Coupled Mode-Parabolic Equation (CMPE) method, and the bottom scattering model, an NX2D reverberation model is introduced. The effects of uneven bottom and seamount are discussed by numerical calculations in this paper. Some illustrations of directionality of the experimental reverberation data from a horizontal line array are also presented.

φ ()()()()ϕ ℘ ϕ INTRODUCTION t+τ  m zs Tm,n r, Dn r n,i r,  R()t,ϕ =  2πctdtdϕ ∫t ∑∑∑∑ × () (ϕ )φ ( ) mn i j U i r Ti, j r, j zr  Full simulation of reverberation involves not only (3) the local scattering processes, but also the accurate where ℘ ()r,ϕ is the scattering coefficient that propagation model. Several reverberation codes have m,n couples the field of nth incident mode with the field of been developed based on Ray, Normal mode, Ray- mth scattered mode. Mode, or PE. The extension of reverberation model to The reverberation time series () from all a range-dependent shallow water described here was R t developed by combining the coupled-mode direction is: 2π parabolic-equation (CMPE) propagation code for a R()t = ∫ R (t,ϕ )dϕ (4) range-dependent environment and the Ray-mode 0 reverberation model. Some numerical and experimental results of the reverberation directionality were also NUMERICAL EXAMPLES presented. The reverberation model was used to calculate the THEORY reverberation directionality in a shallow water shown in Fig. 1. The environment consists of an ideal slope The pressure ()at position ()due to an with the water depth increased linearly from 65 to p r, z s , z r, z 135m. The source and the receiver were located at acoustic source located at position ()0, z in a 0 (50m,0km,0km) and (20m,0km,0km) respectively. range-dependent shallow water can be written as: ()= φ ()()()ϕ φ (1) p r, zs , z ∑∑ m z0 Tm,n r, n r, z nm where ()ϕ is a function of the mode coupling Tm,n r, coefficient that couples the field of nth mode with the field of mth mode in the direction of ϕ , φ ()is the m z0 eigenfunction at the position (),and φ ()is the 0, z0 n r, z eigenfunction at the position ()r, z . In this paper, the ()ϕ is calculated by the coupled-mode Tm,n r, parabolic-equation (CMPE) method[1]. It has been discussed in Reference [1] that CMPE has fast computing speed and high accuracy. FIGURE 1 Geometry for numerical example 1. Decomposing the nth normal mode at position ()r, z [2] into the up-doing and down-going plane waveform : The numerical results of the reverberation from diffirent φ ()= ()if ()z + ()−if ()z (2) n r, z U r e D r e directions was shown in Fig. 2. The Lambert bottom For a narrowband signal pulse of duration τ ,the scattering model was used, σ = ℘ 2 = []− + ()θ ()θ . It indicated reverberation time series from ϕ direction R()t,ϕ is: mn m,n 27 10log10 sin m sin n dB from Fig. 2 that the received reverberation is asymmetric. The revererbation level from the direction with deeper water is samller.

FIGURE 4 Configuration of the bottom surface.

Seamount FIGURE 2 The directionarity of the reverberation in a slop.

EXPERIMETNAL RESULTS

In Fig 3 was shown the received beam power in dB vs reverberation time by a horizontal line array in a shallow water reverberation experiment. The omnidirectional source and receivers are located ar depths 39m and 10m. It is indicated from Fig 3 that there is a bright spot in the 40o direction at the reveberation time of 21s. A reasonable explanation of this phenomenon is due to a seamount. The configuration of the bottom surface from the map was shown in the figure 4, where a seamount was existed. The numerical prediction of the received beam power FIGURE 5 Numerical prediction of the directionarity of was shown in Fig. 5, where Lambert scattering model was reverberation. used. CONCLUSIONS Seamount A method base on couple mode-PE propagation model and ray-mode reverberation model has been presented for predicting range-dependent reverberation in shallow water. Some numerical and experimental results are also shown. The comparison of the numerical results to real data shows some correspondences.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China. ( Grant No. 10074070)

FIGURE 3 Received Beam power in dB vs reverbearion REFERENCES time by a horizontal line array. Frequency is 800Hz.

1. Peng,Z.andLi,F.,ScienceinChina(SeriesA)(inChinese), 31(2), 165-172 (2001) 2. Zhang, R., and Jin, G., Journal of Sound and Vibration, 119, 215-223 (1987) Numerical Analysis of Acoustical Propagation in Shallow Water with Sediment by FD-TD Method

T. Tsuchiyaa, Y. Tanakaa, N. Endoha and T. Tsuchiyab a Department of Electrical, Electronics and Information Engineering, Kanagawa University,221-868, Yokohama, Japan b Japan Marine Science and Technology Center, 237-0061, Yokosuka, Japan

Recently, the Acoustic thermometry of the ocean is being planned in shallow water. The characteristics of sound propagation in shallow water are influenced by the sediment material, because sound propagation is affected by boundary condition of water-sediment. Since many kind of sediment material exist in shallow water, not only longitudinal wave but also shear wave are generated in sediment layer. In this paper is to provide an accurate computational method of acoustical propagation problems in shallow water. In order to clear the characteristic of sound propagation in shallow water, we calculated sound pressure by Finite Difference Time Domain (FDTD) method. The calculation of the model area is 300 m by 4 km and the frequency is 25Hz. It is assumed that the two transducers are placed at 100m in depth. It is shown that we have to take account sound wave propagation in shallow water.

INTRODUCTION ∂v ∂p −=+ρηx v (2) ∂∂txx Recently, Ocean Acoustic Tomography (OAT)[1] is being planned in shallow water. The sound ∂v ∂p −=+ρηy v (3) propagation in shallow water is influenced by the ∂∂ y sediment material, because sound propagation in ty shallow water is affected by the boundary condition of water-sediment. In this paper, we provide an accurate where p is sound pressure, v is the particle velocity, K computational method of acoustical propagation is the bulk modulus, ρ is the density and t is time. An problems in shallow water by Finite Difference Time attenuation of the medium cased by the absorption is Domain (FDTD) method. The FDTD method is the taken account in the second part of the right hand side famous calculation method in the electromagnetic field in eqs. (2) and (3). The velocity of sound c, bulk [2]. The rapid development of computer system modules and resistance coefficient η are obtained as enables the FDTD method that requires tremendous shown in eqs. (4) to (6) computer resources to calculate accurately sound propagation problem. In order to clear the =−ωγ22 γ c 12 (4) characteristic of sound propagation in shallow water, we calculated sound propagation by the FDTD K =−ωρ222() γ γ (5) method varing sound speed and density in sediment. 12

2γγ ηρ= 12 c (6) γγ22− CALCULATION OF SOUND 12 PROPAGATION IN OCEAN where γ1 and γ2 is wave number and attenuation constant. The finite differential equations are obtained The basic equations taken account of attenuation as a function of discrete position x, y in space and in the x-y plane are given as follows [3], discrete time t. 1 ∂p ∂v ∂v −=+x y (1) Κ∂txy ∂ ∂

Sea surface CALCULATION MODEL 0[m] Water ρ =1000[kg/m3] Source 1 Figure 1 shows the calculation model of shallow 100[m] c =1500[m/s] 1

water with flat bottom. The depth of bottom is 200 m 25[Hz] Receiver

and the frequency is 25Hz. The calculation area of the 200[m] Seabed model is 300 m in depth and 4 km long. It is assumed Sediment ρ2 c2 that the projector and receiver are placed at 100m in 300[m] depth. The calculated spatial grid size are ∆x = ∆y = 1 Analysis domain 0 [km] 4 [km] m and time grid size is ∆t = 1 ms. For taking account of sediment material, the sediment of sound speed FIGURE 1. Geometry of the calculation model with varied from 1500 to 1700 m/s. In addition, the sediment in shallow water. 3 sediment of density varied from 1000 to 1200 kg/m . Attenuation coefficient in sediment is 0.5 dB/λ. Figure

2 shows the projected Gaussian pulse waveform given 1.0 as follows, 0.5

 22 sin() 2π ftt()−⋅ exp() −()() 4 / t tt − ; 0 ≤≤ t 2 t 0.0 = 0000 st()  (7) Amplitude  < -0.5 0 ; 2tt0

-1.0 We have to research about characteristics of 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 propagated sound waveform pass through waveguide Time [s] in shallow water. FIGURE 2. Projected Gaussian pulse sound. Pulse length is 0.2 s and Frequency bandwidth is 50 Hz. CONCLUTION RESULTS 30

Figure 3 shows the calculation results of ] (a) -3 propagated sound waveform as a function of sound 10 speed and density. The direct pulse is received at 2.8 s 0 as shown in Fig. 3 (a). It is shown that the pulse -10 Amplitude [x10 amplitude in (a) is smaller than in (c), because the -20 mismatch of acoustic characteristic impedance -30 between water and sediment increases. Additionally, 2.6 2.8 3.0 3.2 3.4 the reflect pulse received at 3.0 s. The pulse amplitude and pulse length increase because critical angle 60 40 decrease. It is shown that the propose method can be ] (b) -3 calculate sound propagation in shallow water 20 accurately. 0

-20

Amplitude [x10 -40

-60 ACKNOWLEDGMENTS 2.6 2.8 3.0 3.2 3.4

This work was partially supported by a 2001 Grant-in- 60 Aid for Encouragement of Young Scientists from the 40 (c) ] -3 Ministry of Education Culture, Sports, Science and 20

Technology. (Grant No. 13750400), Japan. 0

-20 Amplitude [x10 REFERENCES -40

-60 1. W.Munk et. al.,Ocean Acoustic Tomography, Cambridge 2.6 2.8 3.0 3.2 3.4 Univ. Cambridge, 1995, pp. 31-83 Time [s] FIGURE 3. Received waveform when sound speed and 2. K. S. Yee, IEEE trans. Ant. Prop., 14, 302. (1966) 3 density of sediment is (a) ρ2=1000 kg/m , c2=1500 m/s , 3 3 3. F. Iijima el. al., Jpn.J.Apl.Phys., 39, 3200-3204 (2000) (b) ρ 2=1200 kg/m , c2=1600 m/s , (c) ρ 2=1500 kg/m , c2=1700 m/s Platform Motion Compensation for Bistatic Synthetic Aperture Sonar Joseph R. Edwards and Henrik Schmidt Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

Synthetic apertures have long been used to improve along-track resolution in radar systems. A central problem in the extension of synthetic aperture techniques to sonar has been platform motion estimation, as a result of the relatively high platform velocity to sound speed ratio. In the monostatic case, a displaced phase center antenna (DPCA) approach has been shown to effectively counteract distortions attributable to both platform and medium motion. However, bistatic imaging geometries can be advantageous in the detection and classiﬁcation of buried targets in the seabed. Recent advances in underwater vehicle technology have established the autonomous underwater vehicle (AUV) as a viable bistatic imaging platform in littoral environments. In order to utilize this technology fully, a robust bistatic platform motion estimation method for extending the physical aperture is required. In this paper, the monostatic DPCA approach is extended to the bistatic case for a randomly rough insoniﬁed seabed. [Work supported by ONR and SACLANTCEN]

INTRODUCTION PROBLEM FORMULATION

Synthetic aperture sonar (SAS) applications have typ- A fundamental part of the sonar motion compensation ically been limited by platform motion compensation is- problem is simply a matter of geometry. The platform sues. One common approach to this problem has been the motion is estimated by travel times and the assumed or extension of the displaced phase center antenna (DPCA) known properties of the medium and seafloor. Motion method, which has proven to be successful in recent compensation for monostatic synthetic aperture sonars is years. The construction of displaced phase centers, how- generally reduced to a two-dimensional problem for prac- ever, inherently invokes the monostatic to bistatic equiv- tical reasons, with the cross-track motion assumed to be alence theorem (MBET), which is only applicable in limited to the slant-range plane. Extending to the bistatic quasi-monostatic operations. Bistatic operations will also case, a choice of coordinate system must first be made. To not in general include the reciprocal source/receiver loca- parallel the work done in the monostatic case and to align tions that are utilized in monostatic operations for self- with the compensation plane, each receiver is given its navigation. For fully bistatic operations, the motion com- own local coordinate system. The along-track axis is then pensation algorithm must be adapted to eliminate the re- the direction of the receiver at time 0, just as in traditional liance on such reciprocal measurements. The current monostatic motion compensation. The slant-range plane, work focuses on this task, but considering only horizontal however, is not as simple as in the monostatic case, as it linear arrays moving primarily in the horizontal direction varies as a function of receiver position and aspect with above a nearly flat surface. respect to the insonified patch. The other cross-track axis, referred to hereafter as pitch, will rotate correspondingly. The geometry used in this paper is shown in Figure 1. The time of arrival and the spatial correlation maxima are used to accomplish the sub-wavelength positioning. With these tools, an effective two dimensional micronavigation can be achieved with compensation in both the along-track and the slant range dimensions. The third dimension, pitch, is generally ignored, and would in fact require a three-dimensional array to fully estimate [1]. This method has proven very effective for high frequency, shallow grazing angle, monostatic micronavigation for synthetic aperture imaging on a flat seabed [2]. Micron- avigation is a relative navigation system, so the position FIGURE 1. The source (SRC) insonifies a patch in the xy plane. at time 0 is assumed to be known. For bistatic opera-

The local along-track, sway and pitch unit vectors for the re- tions, we also assume that the position of the source and

ceiver element are given by av, as and ap, respectively. insonified patch are known, and the aspect of the receiver relative to the center of the patch is known or estimated each ping. Because the random surface is a realization by beamforming. of its statistical distribution, the statistics of the surface may not directly indicate the statistics of the measured field. The reciprocity of the correlated receptions are THE STATIONARY SOURCE PROBLEM exploited in monostatic SAS to avoid this difficulty, but such measurements are unavailable in general bistatic op- The simplest abstraction from the monostatic geom- erations. However, the broadband nature of typical sonar etry is the case of a stationary source and a moving re- systems provides the opportunity to average over inde- ceiver. With such a configuration, the overlap of the pendent frequency bins to create an ensemble measure of physical array is the redundant measurement. No reci- the received signal, which has been shown in radar appli- procity or MBET is necessary for relating the correlated cations to effectively enhance the stability of the scattered signals. This type of system corresponds to synthesiz- field [3] and elicit the ensemble characteristic known (for ing a large array to sample a static scattered field. The a 1-D surface) as the “memory line” [4]. The memory receiver in this scenario can move a maximum of the re- line can in turn be used to provide the consistent basis ceiver length L per interping interval, as opposed to the for micronavigation. The 1-D memory line analysis pre- L 2 limit imposed by traditional SAS. Aside from these dicts that the best correlated returns will occur at points differences, the micronavigation follows as in the mono- described by: static scenario. We first consider a single element at ping

n, which is matched with an element of ping n ¡ 1 located

¤ ¤

n n 1 n n 1

cosθ cosθ cosθ cosθ (2)

∆ ∆ ∆ r r £ ¡ ¡

¢ i i

¥ ¦ ¤ ¥ ¦ ¤ ¥ ¦ at a distance of dx vn ¤ 1av n sn 1as n pn 1ap n, where the axes are the local coordinate system of the re- where the angles θ are grazing angles, the subscripts ceiver at ping n. Then the one-way range from the center refer to i)ncident or r)eceived, and the superscripts refer of the insoniﬁed patch to the receiver at ping n is approx- to the ping number. With this basis, the motion compen- imately:

sation follows as in the stationary source case. ¨

¨ ∆ 2 ∆ 2

∆ 1 vn ¤ 1 pn 1 ¡ ¡

§ ¤

Rn ¤ 1 Rn sn 1 (1) ¡ ∆ 2 R1 sn ¤ 1 CONCLUSIONS For slant-range imaging operations, the time of arrival difference is assumed to be ∆s, which means that the last An extension of the DPCA linear array platform mo- term in ( 1) becomes the error in the slant-range position estimation technique has been developed for general tion estimate. The positional error could become signifi- bistatic configurations with a stationary source and for the cant with this assumption, but the phase error of the sig- 1-D case with a moving source. These methods can be nals remains small near the center of the insonified patch. applied to free the receiver from the source in sonar ap- However, for general bistatic and particularly for multi- plications, allowing angular diversity of the target field to platform operations, true navigation is desired rather than be exploited fully with multi-platform technologies. phase compensation. Some improvement on the physical location estimate of the receiver can be achieved through the use of the ( 1) and the amplitude of the maximum REFERENCES correlation coefficient. Noting that the error term on ∆s is quadratic, it appears that the best slant-range position 1. Y. Doisy, IEEE J. Oceanic Eng. 23, 127-140 (1998). estimate for a linear array is the tangent of the estimated 2. M.A. Pinto, A. Bellettini, S. Fioravanti, S. Chapman, D.R. sway curve along the array. The along-track motion is Bugler, Y. Perrot and A. Hetet, MTS/IEEE Oceans'99 Con- well-estimated by a properly sampled array, so ∆v will ference Proceedings: Riding the Crest into the 21st Cen- be small. The pitch motion, ∆p, can then be estimated tury, 2, 916-22, Piscataway, NJ, (1999). through the value of the maximum correlation coefficient, 3. G. Zhang, L. Tsang and Y. Kuga, IEEE Trans. Geosci. Re- given that the correlation length of the seabed is on the or- mote Sensing 35, 444-452 (1997). der of the interelement separation. 4. T.R. Michel and K.A. O’Donnell, J. Opt. Soc. Amer. 9 1374-1384 (1992). THE MOVING SOURCE PROBLEM

When the source is moving, the overlapping section of the random surface is insoniﬁed from a different angle at Geo-Acoustic Model and Acoustic Reflection Properties of Fluid Mud Layers in Estuaries

S. Y. Zhang, T. Yang and Z. T. MA

Shanghai Acoustics Laboratory, Academia Sinica,, Shanghai 200032, China

A generalized geo-acoustic model of a fluid mud layer in estuaries of East China Sea has been derived from a large amount of field measurements of the bulk-density profiles of the layer, and of lab measurements of the acoustic velocities and attenuation coefficients of the fluid mud samples with different values of bulk-density for the frequencies of 100, 150, 500, and 1500 kHz. Based on the geo-acoustic model, the simulations of the acoustic reflection property of the fluid mud layer have been done by using the ray theory. The results confirm that the bulk-density profile of a fluid mud layer can be estimated and the effective water-depth for navigation in estuaries, which is defined by the criterion that the bulk-density of the fluid mud is less than 13 kN/m3, can be determined by using echo sounding techniques.

INTRODUCTION out in lab. The mud samples were collected from the The technology of underwater geo-acoustic detection fluid mud layers both in Changjiang Estuary and in has been progressing from the first stage of topographic Hangzhou Bay with a pump respectively. The results detection (seabed geo-mapping or profiling) to the show that for every frequency f , the variation of c is second stage of qualitative detection (seabed geological slight with ρ(about ±1.5%) in the range of ρ= 10 - 15 classification) and to the third stage of quantitative kN/m3, and that a minimum of 1460 m/s for the detection (seabed acoustic parameter estimation). In Changjiang Estuary sample at ρ= 14.5 kN/m3 or 1440 recent years much work on these subjects has been doing m/s for the Hangzhou Bay sample at ρ= 13.5 kN/m3 in the Shanghai Acoustics Laboratory, Academia Sinica exists in the 100 and 150 kHz measurements. Whenρ>15 [1]. kN/m3, c increases quickly with ρ. As shown in FIG. 1, A typical subject with great significance in channel the linear relationship between βand ρ or between βand f dredging is to estimate the bulk-density profile of fluid mud in the benthic boundary layer, because this is a key parameter to determining an effective water-depth for navigation in estuaries. To solve such a significant problem, some basic research on the acoustic reflection property of the fluid mud layer has been done through setting up an appropriate geo-acoustic model.

GEO-ACOUSTIC MODEL OF A FLUID MUD LAYER To set up a typical geo-acoustic model in a certain area, a large amount of measurements need to be done both in field and in lab. The Shanghai Institute of Waterways had applied the “γ-ray bulk-density meter” to measure the bulk-density profiles of the fluid mud layers both in Changjiang Estuary and in Hangzhou Bay for many years. The results show that the bulk-density is confirmed for ρ= 10 - 15 kN/m3. profiles are different from each other at different times and at different sites (mainly caused by the variations of FIG. 1, Acoustic attenuation coefficient versus bulk- wing and tide), and that a common feature of all the density of fluid mud at 100,150, 500 and 1500 kHz measured profiles can be expressed as follows: the bulk- (Changjiang Estuary and Hangzhou Bay) density ρ increases linearly with a gradient k1 from the upper boundary of the fluid mud layer to a certain So far, the geo-acoustic model of a fluid mud layer in subsurface (called a “knee” ) where ρis equal to 12 - 13 estuaries of East China Sea (i.e. the vertical profile of kN/m3, then ρincreases linearly with a different gradient ρc and βin the direction of depth z) can be set up and k2 , which can be greater or less than k1, to a value about generally illustrated by FIG. 2 (same as the profile of 15 kN/m3, after that, the fluid mud layer quickly ρ). For simplicity, the values of ρc and βin the ooze transforms to an ooze layer (ρ≥18 kN/m3 ). layer and in water are assumed to be a constant. The measurements of the acoustic velocity c and the ACOUSTIC REFLECTION PROPERTY OF acoustic attenuation coefficient βof fluid mud for the A FLUID MUD LAYER frequencies of 100, 150, 500, and 1500 kHz were carried Based on the geo-acoustic model in FIG.2, the simulations of acoustic reflection properties of a fluid from the sound source (at z = 0 ) to the upper boundary of the fluid mud layer is z0 = 3 m, the thickness of the layer is equal to z1 + z2 = 1.2 + 1.2 = 2.4 m, and the knee is in the middle of the layer.

(k1, k2 – the gradients of increases of ρc with z ) FIG. 2, Generalized geo-acoustic model of a fluid mud layer mud layer can be done by using the ray theory [2], because the signal frequency is high enough. In the simulations, the whole fluid mud layer is divided into many thin parallel layers with a same thickness ∆z = λ/ 5 (the wavelength λ= c / f, and c = 1500 m/s). and the sound source p0 ( t ) is defined as

2 p0 ( t ) = P0 sin (2π f t ) exp[-ζ( t – m /2 f ) ], t [0, n /2f ] FIG. 4, P3 / P0 (dB) versus k2 and P2/ P0 (dB) versus k2 / k1 P0 – the amplitude of the sound source where P0 = 1, f = 100 kHz (so λ= 1.5 cm), ζ= 20, m = 0.5 and n = 2.0. P2 – the amplitude of the second echo p2; Corresponding to five typical geo-acoustic models of P3 – the amplitude of the third echo p3. different k , the results of the simulations are illustrated 2 It can be seen from FIG. 3 and FIG. 4: 1, three clear by FIG.3 (where k1 is constant ), the distance echoes ( p1, p2 and p3 ) are successively generated at the upper boundary, at the sub-surface where the knee appears and at the lower boundary of the fluid mud layer; 2, the greater the k2, the greater the P3 (the amplitude of p3 ); 3, when k2 / k1.= 1, P2(the amplitude of p2 ) = 0, and the greater ( or the smaller ) the k2 / k1 , the greater the P2; 4, the polarity of p2 is positive for k2 / k1> 1, and vice versa. CONCLUSION In the bulk-density profile of a fluid mud layer, a knee (gradient change) exists at the depth whereρ= 12 - 13 kN/m3. And three echoes can be successively generated at the upper boundary, at the knee and at the lower boundary of the layer for a normally incident sound signal. So, it is confirmed that the bulk-density profile of a fluid mud layer can be estimated and the effective water depth for navigation in estuaries, which is defined by the criterion that the bulk-density of the fluid mud is less than 13 kN/m3, can be determined by using echo–sounding techniques. FIG. 3, Typical geo-acoustic models and the corresponding REFERENCES results of the acoustic reflection simulations [1], S. Y. Zhang, Acoustics Australia, 24(2), 47-519(1996). p1 - the first echo from the upper boundary; [2], D. .P. Knoblesand and P. J. Vidmar, J. Acoust. Soc. Am. p2 - the second echo from the subsurface at the knee; 79(6), 1760 –1766(1986). p3 - the third echo from the lower boundary. The peculiarities of the diffraction of sound waves by lumped inhomogeneity in shallow waveguide

V. G. Petnikova, A. V. Grigor’evb, V. M. Kuz’kina

aWave Research Center of the General Physics Institute, 38 Vavilov St., 119991 Moscow, Russia bVoronezh State University,1 Universitetskaya sq., 394693 Voronezh, Russia

An approximate approach for the calculation of sound field scattered by an object in a shallow waveguide is proposed. The approach is based on representation of the waveguide mode scattering matrix in terms of the scattering amplitude in free space. The calculated space-time structure of sound field scattered by liquid-filled spheroid in waveguide is presented and discussed. This model of scatterer enables us to simulate forward sound scattering from the different types of whales in shallow water. The acoustic monitoring of the sea mammals by using scattered sound field is discussed as well.

(r) INTRODUCTION scattered field Ps R . To calculate the scattered sound At present for whale conservation there is need to field we use the following integral expression [1]: create acoustic borderlines to control whale migration r = r′ r r′ r′ Ps ((1)R) ∫ v(R )G(R,R )dR in dangerous area of shallow water. To test the r feasibility of the borderlines from the physical point of where ν (R′) is the density of fictitious sources, r r view we should solve the problem of wave diffraction distributed over scattered volume. G(R, R′) is the by soft spheroid (model of whale body) in a waveguide r and demonstrate the possibility of detection of Green function. The unknown function ν (R′) is scattered waves. With this in mind in this paper we determined by the condition for sound field at the simulate forward sound scattering from whales by surface of scatterer Sˆ : using approximate technique for the solution of the r r r r [P ()R = P ()R , ρ ∂P ()R ∂n = ρ ∂P ()R ∂n]r (2) diffraction problem. + − s + − R∈Sˆ where P± are sound field out and inside of scatterer. TECHNIQUE OF THE CALCULATION The basis of our technique is assumption that the OF DIFFRACTION FIELD characteristics of medium are varied smoothly in the neighborhood of the scatterer and the Green function Suppose that the waveguide represents a water r r′ layer with depth H resting on absorbing half-space coincides with the Green function G0 (R,R ) of free ρ r with density 1 , sound speed c1 and refractive index space. In this case the function of sources ν (R′) = ()()() + α ρ n c H c1 1 i / 2 . (z) and c(z) are density corresponds to the solution of the diffraction problem r and sound speed in water layer correspondingly. Let us for free space ν (R′) . Note that for this problem it is () 0 introduce a frame of reference X ,Y , Z coupled to the also convenient to use the scattering amplitude which r waveguide. The Z -axis is pointed downward. Say the connected with the ν (R′) in the following way: sound source and the receiver are located respectively 0 r r = ()π −1 r r′ ()− r r′ r′ () () F(ki ,k s ) 4 v0 (k i , R ) exp ik s R dR (3) at points 0,0,z0 and x,y, z . Denote the radius- ∫ r vector of the receiving point by R . We also introduce r r where are wave vectors of incident and scattered () ki , ks a frame of reference x', y', z' , coupled to the r r scatterer. For this system the origin of the coordinates waves. F(k i ,k s ) can be expressed in terms of the () θ ϕ located in the scatterer center xs ,ys ,zs . Denote the angles and in the spherical frame of reference radius-vector of the scatterer and the receiver in coupled to the scatterer. The angles determine the r r direction of incident and scattered plane waves.. horizontal plane by rs and r respectively. Our interest ()r The sound pressure in the waveguide is sought in the is the sound field P R at the reception point, which form: r can be written as sum of the primary field P (R) and exp[iq r] 0 = ψ m []− γ P(r, z) ∑ Am m (z) exp m r 2 (4) m qm r ψ ξ where m (z) and m are the eigenfunctions and We assume that the scatterer crosses the baseline eigenvalues of the Sturm-Liouville problem connecting the sound source and the receiver with γ ()ξ =q +iγ 2 . For a point source of power W the speed v and at the angle . The moment of the m m m 0 = interaction is equal to ti 0 s. One result of the coefficients Am are equal to calculations is shown in Fig.1. A = ρ(z )c(z )W e iπ 4ψ (z ) . Then using (1-3) we m 0 0 0 m 0 0.04 can write the following expression for scattered field ° γ=90 (For more details, see [2,3]): 0.02

= π ψ ψ Ps (r, z) i 8 ∑ S µ ,m Am m (z s ) µ (z) 0 µ ,m , Pa P []()+ r − r  γ + γ r − r  ∆ exp i q r q µ r r r µ r r (5) -0.02 * m s s exp− m s s  r −  2  qm rs qµ r rs   -0.04 where Sµ ,m is the scattering matrix which has the form 0.04 γ ° = π [ + + (r + r − )+ + − (r + r + ) =60 Sµm 4 amaµ F km ,kµ amaµ F km ,kµ 0.02 (6) + − + ()r − r − + − − ()r − r + ] amaµ F km , kµ am aµ F km ,kµ

, Pa 0 where P ∆   -0.02 ± 1 dψ dz r ± a = ψ (z) ± m  ,σ = k 2 (z ) − q 2 , k m 2 m iσ m s m m -0.04  m  z=z s -1000 -500 0 500 1000 are wave vectors with horizontal and vertical время, с r ±σr components (qm , m ) , k is wave number. FIGURE 1. Sound field variations due to the diffraction. It is necessary to stress that the described approach For this testing numerical calculations we suppose that γ = ° ° = = = is valid when multiple scattering effects are weak and 90 and 60 , W0 500 w, H 40 m, r 10 km, the medium is homogeneous in the scatterer vicinity. In r ≅ 5 km, f = 300 Hz, c = 1480 m/s, ρ = 1 g/cm3, other words the scattering body should be offset from s c = 1540 m/s, ρ =1.05 g/cm3, l = 10 m, d = 3 m the waveguide boundary at a distance h exceeding the s s = = body horizontal size l ()h ≥ l and the variation of (typical size of gray whale), z0 40 m, zs 20 m, σr = ∆ = + − vertical wave vector m along the z axis should be z =20 m, v 1 m/s, P P0 Ps P0 . small at the distance equaled the body vertical size. As indicated by Fig.1 the pronounced variations of sound field take place when model scaterrer crosses the SOFT SPHEROID (WHALE) AS line between source and receiver. These variations SCATTERING BODY have complex form. When γ ≠ 90° they are not To simulate sound scattering by whale we use the symmetric about the time ti . The value of variations is scattering amplitude of a soft spheroid [4]: comparable to the usual level of acoustic noise (r ± r ± )= F k m , k µ ≅ 0.01 Pa. Additional computer modeling ∞ ∞ 2i ± ± ± ± demonstrated that this variations can be detected on the = ε S ()χ, cosθ S ()()χ, cosθ cos[]n ϕ −ϕ ∑∑ n nl m nl µ m µ background of noise by using match signal processing k nn=0 l = − ′ ′ [5] when the reference signal is calculated with the m 1 R (1) (χ,ϑ)R (1) (χ ,ϑ) − R (1) (χ,ϑ)R (1) (χ ,ϑ) * s nl nl s nl nl s (7) technique described above. −1 (1)′ χ ϑ (3) χ ϑ − (3)′ χ ϑ (1) χ ϑ m s Rnl ( s , )Rnl ( , ) Rnl ( , )Rnl ( s , ) ε ()1 ()3 ACNOWLEDGMENTS Here n is the Neuman symbol, Snl , Rnl , Rnl are prolate angular and radial spheroidal functions of the This work was supported by Russian Foundation for first and third kind (prime at radial function symbols Basic Research, project no. 99-02-17671. means a derivative with respect to ϑ ), m = ρ ρ , s s REFERENCES χ = ()2 − 2 χ = ()2 − 2 k 2 l d , s ksc 2 l d , 1. F. Ingenito, J. Acoust. Soc. Am. 82, 2051 (1987) 2. A. Sarkissan, J. Acoust. Soc. Am. 102, 825 (1997) = π ϑ = 2 − 2 ( ksc 2 f cs f - sound frequency), l l d . 3. V. A. Grigor’ev, B. G. Katsnelson, V. M. Kuzkin, Here d and l are minor and major spheroid axes, c V. G. Petnikov, Acoust. Phys. 47, 35 (2001) s 4. E. P Babilov, V. A. Kanevskii, Sov. Phys. Acoust., 34, 11 (1988) ρ and s are sound speed and density inside of spheroid 5. V. A. Zverev, A. L. Matveev, V. V. Mitygov, Acoust. Phys. 41, respectively. 518 (1995) Sound Fluctuation by Internal Waves in Shallow Water

M. Li, G. Tianfu, H. Tao, Y. Shun and C. Yaoming

Institute of Acoustics, Chinese Academy of Science, Beijing, P.R.China

The internal wave data obtained during the experiments in the offshore areas of the china seas are presented. It is shown that large amplitude, long internal waves occur in the seasonal thermoclines. The internal waves have asymmetric waveforms and so they are nonlinear. Then sound fluctuation have nonlinearity too. The experiment data show the attenuation rates of the power spectra of sound fluctuation is between –1.1and –1.7. The fluctuation amplitude are about between –20dB and 20dB. Based on the observations and the analyses, a model for the shallow-water internal waves is developed. Comparison of the model with the data shows reasonable agreement.

INTRODUCTION THEORY

Internal gravity waves propagating in any stably The KdV equation is well know as an appropriate stratified fluid medium are generated by the restoring physical model for the description of the nonlinear and effect of buoyancy force on water particles displaced dispersive properties of internal wave . Using a from their original equilibrium levels. An interfacial perturbation expansion in the fundamental wave arising between two superposed fluids of hydrodynamics equations, neglecting rotational effects, different density is a familiar phenomenon in nature. and assuming weakly nonlinear finite-amplitude plane The GM model is based on linear theory and progressive waves propagating in a specific direction, available midlatitude, deep ocean observations, the equation is derived. representing an average or steady-state spectrum away For arbitrary vertical stratification of ocean from the direct influence of sources, sinks or density and background shear flow, the KdV equation boundaries. The synthesis is purely empirical. Except is written as ∂ η ∂ η ∂ η ∂ 3η for inertial waves and tides, this model is believed to + c + αη + β = 0 (1) reflect the spectral features of the deep-ocean internal ∂ t ∂ x ∂ x ∂ x 3 wave climate and possess a certain global validity. where η(x, t) is the vertical displacement of the Most data are in good agreement with the model or can pycnocline, x is the horizontal coordinate, and t is be incorporated by slight modifications. time. the parameters α,β ,c are coefficients of However, the situations in shallow water are entirely nonlinearity dispersion, and phase speed of linear long different from those in the deep ocean. Internal solitary internal waves, respectively. waves on the continental shelf are readily observed by The internal soliton of the KdV equation (1) is aircraft and satellite synthetic aperture radar well-known (SAR).Oceanographically, shallow water can show 2 significant energy in both linear and nonlinear internal η = Λ sec h [(x − Ct) / ∆] (2) waves. In most cases, these waves are generated by the where Λ is the amplitude factor. The solition has a interaction of the tide with topographic features. Their nonlinear characteristic width spectral properties are not successfully reproduced by ∆ = (12β ) /(αΛ) (3) the GM model, as some basic assumptions of this and propagates with a nonlinear phase speed: model are violated. The major isotropy assumption, especially in the distribution of sources, sinks and C = c +αΛ/3 (4) boundaries due to bottom topography, is not satisfied in Both the soliton characteristic width and phase speed shallow water. The GM spectral model has been widely depend on the soliton amplitude. The implication is recognized to reflect rather adequately the real that the larger the amplitude, the faster the soliton situations in the deep ocean, but only as averaged over propagates and the narrower or steeper the soliton is. seasons, regions, etc. Of course, this model is not The cnoidal solution is written as: 2 related to the nonlinear part of the internal wave field. η = Hcn [2K(x − Ct) / L] (5) Moreover, linear internal waves in shallow water are where H is the wave height, and K(m) is the not necessarily characterized by simple GM spectrum. complete elliptic integral of the first kind and often Therefore, more internal wave observations are needed shown as the function of the parameter k with m = k 2 as well as a new model to replace the GM model for the shallow-water case. . The wave length L and phase speed C are given by L = 2K (12βm) /(αH ) (6) strong fluctuation in sound transmission are the areas of strang internal waves. The fluctuation amplictude C = c +αH (−m + 2 − 3E / K) /(3m) (7) are about between –20dB and 20dB. where E(m) is the complete elliptic integral of the second kind. It is assumed that the internal wave displacement field is composed of two components: a dominant, deterministic background component due to nonlinear internal wave packets and a stochastic plane wave component. The vertical displacement field η(x, z, t) can be written in the form:

η(x, z, t) = ηn (x. z, t) +ηl (x, z, t) (8) where ηn represents the nonlinear wave component, and ηl describes the linear diffuse contribution.

The diffuse field component ηl is represented as a statistical mixture of plane wave. This representation is obtained by expanding ηl in a complete orthonormal set of internal wave eigenfunctions that are obtained from solving the linearized Navier-Stokes equation for an inviscid, incompressible, stratified fluid. In this manner, the diffuse field can then be expressed as a weighted double sum over mode number and wave frequency

η l = ∑∑Al (ω , j)ψ (ω , j, z ) ω j (9) ∗ cos[ k (ω , j) x − ω t ] 2 −1.5 with Al ∝ ω in shallow water. The second component is the nonlinear wave displacement field, representing an example of the nonlinear interaction of oceanic tides with bathymetric feature. The isopycnal displacement for this component can be written in the form (10) η n = ∑ A n ( x , j)ψ (ω , j, z ) j where An is the modal coefficient describing the temporal and horizontal structure.

CONCLUSIONS

The Yellow Sea internal waves are statistically nonlinear. The cnoidal solution is suited to modeling the internal waves. The internal wave vertical- displacement field is composed of two components: a dominant, deterministic background component, corresponding to several cnoidal waves that may be coupled to each other, and a stochastic linear wave component, representing a statistical mixture of random plane waves. In shallow water sound fluctuation have nonlinearity too. The experiment data show the attenuation rates of the power spectra of sound fluctuation is between –1.1 and –1.7.The attenuation rates are the same as the power spectra of the internal waves. The areas of Curve Cluster Transformation for Extracting the Moving Targets

Fuquan Wang, Lianghao Guo, Renhe Zhang, Ling Xiao, Zaixiao Gong

National Lab of Acoustics, Institute of Acoustics Chinese Academy of Science, Beijing, 100080, CHINA

An approach for tracking moving targets is proposed in the article. This approach is based on the curve model for the target motion. The Curve Cluster Transformation for the curve model constructs the state of the target motion. The moving targets are extracted from the transformation result. The tracking process of the moving targets is then implemented by dynamically linking the extracted targets. Theoretically, the Curve Cluster Transformation can be considered as an extension of the traditional Radon transformation. The curve cluster transformation can eliminate the effects due to the noise and the target motion. It can get robust tracking result for the moving targets in real experiment. Finally, a shallow water experiment is conducted in 2000 to show the effectiveness of the proposed method.

INTRODUCTION tracing of one moving target can be considered as serials of bright dots, combining a shape of curve. θ Tracing moving objects is important in many cases. Written down the curve as =f(t,p1,p2,…,pn). Here, Many years, researchers have developed many trace p1,p2,…,pn corresponding the parameters of the curve. algorithms [1-8]. For this work, two important We call the curves with the parameters (p1,p2,…,pn), difficulties need to be solved. One difficult is that there belonging to a curve cluster. For example, if f takes the θ exists variability error for short time’s DOA estimation, form t=p1+p2* , then the curve reduce to a line in the especially when the DOA estimation comes from t-θ image. modern high-resolution method such as MUSIC 0°θ 180° method. Another difficulty is that when more than one t object come across, the objects tend to become one 0 C B A point in the DOA-time figure and then trend to divide into several parts. If the DOA-time picture is considered as an image, it is reasonable to use the image processing method to t overcome the above two difficulties. The Radon-transformation is famous in extracting the linear texture for 2-dimension image. In DOA-time figure t0 +d t during a short period, the trace of a object shows to be a curve. If the period is short enough, this curve can be FIGURE 1. Line traces in DOA time figure. approximately considered as a linear segment. This satisfies the conditions for using of Radon transfor- Consider the transformation of the 2-dimension mation. image B(θ,t) as following In this paper, we proposed a general formula for the + curve transformations. This transformation delimits the θ = t 0 dt T p1,..., pn (B( ,t)) ∫ B( f (t, p1,..., pn),t)dt (1) variability by integrating along the trace. It can also t 0 distinguish multi-objects even from the multi- parameters combinations of different curve traces when where θ in (0,180A) and t in (t0,t0+dt). Then in the n- these objects overlap. dimensional space of (p1,p2,…,pn), In 2000, an experiment is conducted to test the T … (B(θ ,t)) (2) curve cluster transformation. We will simply describe Tp1,p2, ,pn the experiment result. is a local maximal point where p1,…,pn is a group of parameters for one moving target. θ TRANSFORMATION When we use the curve cluster t=p1+p2* ,the local maximal point of the curve cluster transformation θ result of Figure 1 can be briefly described as in Figure Supposed the beamforming at time t0 is B( ,t0) 2. The three targets trace A, B, C are then transformed where θ is the degree of arrivals. At most time, the into the three maximal point A, B and C. Theoretically, of the beamforming. when we used curve cluster t=p1+p2*θ, it is just the Using the curve cluster f=p1+p2*θ,wherep1 traditional Radon-transformation in image processing. corresponding the current degree of the target, p2 p corresponding the velocity of the moving target’s 1 bearing. We get the curve cluster transformation’s result. The local maximal points are shown in Table 1. B Table 1. Local maximal of the transformation p 2 A No. of Object p1(current angle) p2(velocity) (90,0) A 72 -0.05 C B 92 -0.05 C 92 -0.88 D 107 -0.93

p1 FIGURE 2. Transformation of Figure 1.

EXPERIMENT p2 (90,0) A(72,-0.05) An experiment is conducted in 2000, and data from B(92,-0.05) HLA is used for analysis and test the efficiency of C(107,-0.93) curve cluster transformation in the experiment. A C(92,-0.88) cooperated ship is used for passive DOA estimation and tracing. This ship is about 90Aduring the whole FIGURE 5. Distribution of the local maximal points experiment area. A 16-sensors uniform line array is used, and the interval between two sensors is 1 m. The hint figure of Table 1 is shown in Figure 5. It shows that the curve cluster transformation can distinguish the multiple moving objects, even when Cooperate they come to the same direction. Ship And since the transformation is calculated by integrating, the estimation’s variability can be greatly Other Ships Other deduced if we use enough samples. Thus the Ships transformation process can be considered more robust than a single DOA picture.

1m ACKNOWLEDGMENTS 16 sensors ULA FIGURE 3. Experiment in 2000. This work is supported by the National NSF of 0°θ 180° China under Grant No.10023004. t 0 A REFERENCES

D 1. Ianniello J.P., IEEE signal processing magazine 15, 27-40 (1998).

t Cooperate 2. Alfred H., IEEE signal processing magazine 15,24-28 B Ship (1998). 3. Johnson, D.H., Proc. IEEE 70, 1018-1028 (1982). C t0 +d t 4.Nuttall, A.H., Wilson J.H., J. Acoust. Soc. Am. 108, 2256- 2265 (2000). FIGURE 4. Beamforming result 5. Li F., Vaccaro R.J., IEEE T-AES 26, 976-985 (1990). 6. Schmidt R.O., IEEE Trans. Antennas Propag. 34, 276-280 The received data between 200Hz-300Hz is (1986). analysed. The beamforming result of the DOA 7. Zhou Y.,Yip P.,Leung H., IEEE T-SP 47,2655-2666 (1999). estimation, gotten by modified EV method and then 8. Sastry C.R., Kamen E.W., Simaan M., IEEE T-SP 39, 242- sum up each frequency data. Figure 4 is a sketch map 246 (1991). Autofocussing procedures for high-quality acoustic images generated by a synthetic aperture sonar. P.T. Gough, M.P. Hayes, H.J. Callow, S.A. Fortune, a aDepartment of Electrical and Electronic Engineering, University of Canterbury, Christchurch, NEW ZEALAND

A sea-going synthetic aperture sonar (SAS), configured for either stripmap or spotlight operation in shallow waters, has the potential to produce optical-like images of the seafloor from acoustic data much in the same way as a synthetic aperture radar (SAR) produces images of the earth’s surface. Unfortunately, the potential of SAS to produce high-quality images is seldom realized because of unavoidable errors in the path trajectory. For diffraction-limited imagery, the path trajectory of the sonar should not stray more than a fraction of a wavelength from a perfect straight line. This submission outlines just two autofocussing algorithms that take the shallow-water acoustic data and produces an image of the seafloor as well as estimates of the path trajectory necessary to bring the image into focus. Some algorithms work with the raw data whereas others work with a partly processed low-quality image. Results presented show how some potentially attractive algorithms work well in simulated scenarios but fail to work when applied to real experimental data thus emphasizing the importance of modeling the seafloor correctly when testing potential algorithms. Structured session: Shallow-water acoustics

INTRODUCTION ERRORS IN THE DATA COLLECTION

When a section of the seaﬂoor, called the object Unless the sonar is constrained to traverse a ﬁxed

straight underwater rail, the sonar platform (typically a ¢ f f x ¡ y , is imaged by a sidelooking sonar, the imaging system has a point spread variant impulse reponse towfish) sways, heaves, surges, rolls, pitches and yaws; where many reflecting points on the seafloor contribute unfortunately these random errors in the supposedly to a sample of time and space in the data collection ma- “straight” flight-path inject errors into the data as col-

lected. Luckily, however, a single projector-single hy- ¢ trix which we call ss t ¡ u . The geometry is such that the cross-track coordinate x is mapped to delay time from the drophone sonar is mostly affected only by sway; that is,

side to side movement as it wobbles down the “straight”

start of a speciﬁc pulse t and the along-track coordinate

¢ ¦ ¡ ¢¨§

∆ ﬂight-path. So now instead of ss t ¡ u we record ss t u

¡ ¢

y is mapped to position along the track u. In ss t u , t

¢ ¡ ¢ ¢ is the time sampling interval and ∆u corresponds to the ss t © 2X u c u where X u is the displacement from distance moved by the sonar between transmitted pings. the straight ﬂight path at position u and c is the speed of sound.

Simple narrow beamwidth sidelooking sonars produce an

¦ ¢

approximate image of the seaﬂoor by rescaling delay time If ss t ¡ u is used as input to the SAS imaging algo-

rithm, the image is no longer diffraction-limited but a new

¢¤£ ¡ ¢

t as range r so that ss r¡ u f f x y . As a point spread

¡ ¢

variant imaging system, the greater x, the worse the ap- distorted estimate f f x y . It is the intent of all autofo-

¢ ¡ ¢

proximation and so sidelooking images have the recog- cussing proceedures to take either ss t ¡ u or f f x y and

¡ ¢ nisable feature that the image ﬁdelity degrades with range produce the diffraction-limited image ¥ f f x y . Realisti- r (and equivalently position x). cally there will be remnant errors, so that what we actu- ally produce is our best estimate of the diffraction-limited

Synthetic aperture sonars (SAS) however take this raw

image which we call f f x ¡ y . ¢

data matrix ss t ¡ u and process it to produce an im-

¡ ¢ age ¥ f f x y which is a diffraction-limited image of the true seaﬂoor reﬂectivity limited only by the beamwidths and the bandwidths of the sonar system. There are RAW-DATA AUTOFOCUS

several well-known block processing (i.e., efﬁcient) al-

¢ ¥ ¡ ¢ gorithms that start with ss t ¡ u and produce f f x y : One of the simplest sway estimation techniques for a

these would include the range-Doppler, wavenumber and single hydrophone SAS is based on ping to ping correla-

¡ ¢ chirp-scaling algorithms[1]. Unfortunately this is an ide- tion of the raw data ss¦ t u . The sucess of this “shear av- alised situation and diffraction limited images are seldom eraging” [2] technique is very dependent on the aperture u achieved without further processing. being “oversampled” and that the seafloor is an equiprob- able distribution of Rayleigh scatterers. Consequently, 0 when the sonar travels at the maximum allowable veloc- 5 ity or there is a strong cultural target somewhere in the 10 frame, the shear averaging technique fails. Modifications 15 to the basic shear averaging algorithm include weighting 20 25 the sway estimate for sections of the aperture adjacent to 30 strong targets. The results of the modified algorithm is 35 shown in figures1 to 4. 40

45 0

50 5 −20 −15 −10 −5 0 5 10 15 20

15 FIGURE 3. Real image from seaﬂoor on Sydney harbour.

20 0 25 5 30 10 35 15 40 20 45 25 50 −20 −15 −10 −5 0 5 10 15 20 30

FIGURE 1. Simulated scene before autofocus where the hori- 40 zontal ordinate is in metres from the centre of the area of interest 45 and the vertical ordinate is metres from nadir. 50 −20 −15 −10 −5 0 5 10 15 20

0 FIGURE 4. The same image after modiﬁed shear averaging.

10 15 that works well on the processed image is constraint- 20 based autofocus where the algorithm attempts to max- 25 imise some image quality parameter such as “sharpness”. 30 The computational load is high so this appears best em- 35

40 plyed off-line [6].

50 −20 −15 −10 −5 0 5 10 15 20 REFERENCES

FIGURE 2. The same image after modiﬁed shear averaging. 1. P.T. Gough and D.W. Hawkins, Int. J. Imaging Sci. and Techn. 8, 343-357, (1997). 2. K.A. Johnson, M.P.Hayes and P.T.Gough, IEEE PROCESSED IMAGE AUTOFOCUS Ocean. Eng. 20, 258-267, (1995).

The most common SAR autofocussing algorithms are 3. D.E Wahl, P.H. Eichel, D.C.Ghiglia and C.V.

Jakowatz, IEEE Aero. Elec. Sys. 30, 827-

¢ based on the processed distorted image f f x ¡ y and rely

on the assumption that 835,(1994).

¡ ¢ £¥ ¡ ¢ ¢ ¢ f f x y f f x y y exp jkX u where y is a 4. P.T. Gough, M.P. Hayes and H.J. Callow, Proc. 5th

convolution in the y (i.e., in the along track) direction, European Conf. on Underwater Acoustics, Lyon, is a Fourier transform[3]. Although this approxi- France, July 2000, pp.413-418. mation is often true for SAR (especially spotlight SAR), it doesnt work well for SAS. Variations on this algorithm 5. D.E.Wahl, C.V.Jakowatz and P.A. Thompson, Sixth more suitable for strip map SAR and SAS have been IEEE DSP Workshp. 1994, pp.53-56. written by us and others [4,5] but this has yet to prove 6. P.T. Gough, and R.G. Lane, J. Acoust. Soc. Am., useful on real SAS images although they work sucess- 103, p2859, (1998). fully on simulated SAS images. An alternative technique An Underwater Frame for an Acoustic Survey of Marine Vegetation

R. Bozzanoa, A. Siccardia, R. Mantovania and L. Castellanob

aCNR Istituto per l'Automazione Navale, Via de Marini 6, 16149 Genoa, Italy ([email protected]) bAcquario di Genova S.p.A., Area Porto Antico - Ponte Spinola, 16128 Genova, Italy

Aquatic vegetation analysis relates to plenty of applications ranging from ecological, up to biological and practical aspects. Moreover, sustainability and biodiversity of marine environments is becoming a more and more important subject, thus new investigation methodologies for an effective environmental analysis must be investigated. This paper describes the tests carried out for the preliminary acoustic assessment of marine vegetation by means of a very high frequency sector scanning sonar carried by a simple underwater frame. Some tests have been conducted along the eastern coast close to Genoa on a very low depth gradient bottom populated by significant vegetation settlements. It was possible to recover very meaningful data by fusing information of depth with the acoustic signals, hence providing a truthful representation of the sea bottom and of the benthic flora living upon it. Future experiments will be devoted to improve the performance of the system and to study in depth the acoustic backscattering of marine vegetation at sea.

marine animals and other species of plants and algae [4]. This plant is very sensitive to natural changes INTRODUCTION (temperature rise, turbid water, solar radiation, etc.), anthropogenic activities (dikes, excavation, discharge Stimulated by powerful acoustic devices of sewage and industrial waste, trawling, etc.), availability, acoustic-based approaches are emerging in competition with more robust algae, and meadows recent years as effective and suitable methods for regressions or disappearances is a topical problem. aquatic vegetation assessment, providing also some These items constitute a valid justification for more refined information about the spatial extent of monitoring the marine ecosystem and for investigating plant settlement with respect to other older 'direct' new and more and more effective technologies to do techniques. that. Some literature exists about the phenomenology of acoustic waves scattering by submerged vegetation especially regarding long and wide types of algae [1] METHODOLOGY and some species of European [2] and North-American seagrasses [3]. It can be noted that a global and The acoustic data about the seabed vegetation were exhaustive study about vegetation scattering is still acquired by means of high frequency sector scanning missing and mechanism of acoustic scattering (i.e., sonar from Tritech Int. Ltd. This monostatic unit is dependence on grazing angle or frequency) from characterised by narrow pencil beam (0.9° at the –3 dB seabed vegetation is largely unknown. point), variable frequency (selectable from few kHz up As a part of the European Union project MAUVE, to 2.0 MHz) and pulse duration (up to 500 ms). high frequency backscattering measurements about Being able to continuously scan the whole or a marine vegetation were carried out since 1996. The portion of the full sector in either direction, this low- purpose of the work was to develop and test a suitable cost sonar performs better than echosounders providing equipment and methodology for marine vegetation the full backscattered echoes along several directions. assessment. The performance of the unit are bounded by the In this work, attention is focused on the endemic high transmission loss due to the very high frequency Mediterranean Phanerogam Posidonia oceanica: its used, by the near-field conditions, and by the inherent meadows are the most important ecosystem for the life limitation of the device able to acquire only 1500 bins cycle of benthic coastal areas playing a fundamental per scanline providing a maximum range of about 7 role in the primary production in the photic zone and meters. These factors compel users to operate the unit providing an important habitat for several fish species, close to the sea bottom, preventing its installation on the boat hull. Taking into account these restrictions and in order to investigate the capabilities of the head, a simple underwater frame was developed, conceived only as a cheaper and simpler solution, with respect to underwater vehicles, to carry the sonar very close to the bottom. In addition to the described sonar, some other devices were installed on-board the frame such as a pressure transducer, a two-axis inclinometer, a fiber optic fluorometer, two echosounder, one for measuring the distance from the bottom and the other for obstacle avoidance purposes. Moreover, an underwater camera was also used to record real sea bottom characteristics into video sequences for ground-truthing purposes.

PRELIMINARY RESULTS

A preliminary test phase have been carried out along the eastern coast of Genoa, above very low depth gradient sea bottom. The frame was deployed into the water and trailed by a small boat. While travelling, the head insonified the seafloor at very high grazing angle (almost vertical). The sonar measurements can be viewed as a sequence of individual scanlines acquired while the unit sweeps its sensor axis through the user- defined sector. A kind of slice through the water column can be obtained by placing side-by-side in a vertical arrangements the scanlines. At the same time, information by the other sensors was stored together with the video sequences, allowing real-time ground- FIGURE 1. (up) Raw and (down) processed data. truthing for the acoustic data. Figure 1-up shows a sequence of raw acoustic data 25 seconds long. The sea bottom, clearly visible under ACKNOWLEDGMENTS the vegetation leaves, is detected and tracked in order to reconstruct the real bathymetry. Moreover, the data, The authors would like to thank H. Braithwaite and M. except those samples related to the ringing of the Cardew from System Technologies (Ulverston, UK) transmitted pulse, are corrected for attenuation and who provided valuable information about the sonar. some system bias (Figure 1-down). Acquired data clearly show the vegetation growing upon the sea bottom. REFERENCES

1. Shenderov, E.L., Journal of the Acoustical Society of CONCLUSIONS America, 104, 791-800 (1998). 2. Lyons, A.P., and Pouliquen, E., "Measurements of high Preliminary results demonstrate that this frequency acoustic scattering from seabed vegetation", in methodology can provide more detailed and significant Proceedings of the International Conference on data with respect to other types of equipment operating Acoustics, 1998, pp. 1627-1628. with lower resolution and at higher distance. 3. Sabol, B., and Burczinski, J., "Digital echo sounder system for characterising vegetation in shallow-water The described work has to be viewed as a environments", in Proceedings of the 4th European preliminary study about marine vegetation Conference on Underwater Acoustics, 1998, pp. 165-171. backscattering that has to be finalised into a system for 4. Cinelli, F., Fresi, E., Lorenzi, C., and Mucedola, A., La vegetation classification. Further work has also to be Posidonia oceanica, Roma, Rivista Marittima, 1995 done about the modelling and the variability over time (both in Italian and English). of the vegetation backscattering. Generalized Adiabatic Modes in Shallow Water as Solution of Parabolic Equations

B. Katsnelson, S. Pereselkov

Physics Department, Voronezh State University, 394693 Russia, Voronezh, Universitetskaya pl.1

The approach of normal mode of sound field in shallow water is generalized for the case of irregular waveguide in our paper. The purpose is the developing approach for sound field description which has not famous drawback of the coupled modes approach. We introduce the conception of the generalized adiabatic (uncoupled), normal modes (GAM) for the irregular waveguide. These modes satisfies parabolic equation (PE) and can be used in the irregular waveguide likewise traditional modes in regular one. In the paper the approach of GAM is analyzed both analytically and numerically..

INTRODUCTION 2 + α tion index nb (1 i ) , which corresponds to sound α At present time the approach of coupled modes is the speed cb .Here is defined by bottom absorption. most prevalent in the shallow water acoustics Refs. [1- 3]. Within the framework of this approach the sound CONCEPTION OF ADIABATIC MODES field in irregular waveguide is presented as superposition of the waveguide eigen functions (local modes) The complex sound field Ψ(r, z) of frequency f with range-dependent coefficients (modal amplitudes). (sound wavenumber k = 2πf c ) is defined by: These modal amplitudes are determined by set of cou- 0 pled differential linear equations. The initial conditions 1 ∂()r ∂Ψ ∂r ∂2Ψ + + k2n2(r, z)Ψ = 0 , (1) are defined by the type and position of source. In our r ∂r ∂z2 opinion such approach has the following drawback: the modification of source type or its position obliges to As known, the solution of Eq. (1) is presented as sum recalculate the set of differential equations. of coupled local modesϕ (r, z ) with range-dependent The purpose of our paper is the developing of the ap- n proach for sound field description which has not draw- amplitudesCn(r ) : back mentioned above. With this purpose we introduce r Ψ = ξ −1 2 ϕ ξ τ τ the conception of the generalized adiabatic (uncoupled), (r, z) ÿ( nr) Cn(r) n(r, z)exp(i n( )d ) , (2) normal modes of the irregular waveguide in shallow n 0 water Refs. [4,5]. These modes can be used in the ir- where local modes satisfy to boundary problem: regular waveguide likewise traditional modes in regular one. This research is supported by RFBR, grants 00-05- ∂2ψ n []2 2 64752, 99-02-17671. + k (r, z) −ξn (r)ψn = 0 , (3) ∂z2 ϕ = 0 , ϕ (r, z) = ϕ , SHALLOW WATER MODEL n z=0 n z=H −0 n z=H +0 ()∂ϕ ∂z = ()ρ ρ ()∂ϕ ∂z Let us consider the following model of 2D waveguide n z=H −0 w b n z=H +0 in shallow water (see Fig.1). In contrast to approach mentioned above, solution of Eq. (1) is presented as superposition of some functions - Φ “generalized adiabatic modes” (GAM)n(r, z ) which Φ Φ = δ δ are normalized n mdz nm ( nm is Kronecker’s symbol): r Ψ = η −1 2 Φ η τ τ (r, z) ÿ ( nr) An n (r, z) exp(i n ( )d ) , (4) n 0

FIGURE 1. Shallow water model. It should be emphasized that coefficients An are sup- Water layer with densityρ (z ) andsquaredrefrac- posed to be range-independent and are determined by w just source type and its depth. One can derive, that func- 2 Φ tion index n (r, z) , which corresponds to sound speed tionsn(r, z ) in (4) must satisfy the following PE: profile c(r, z) . This water layer has depthH (r ) and is ∂Φ i ∂2Φ iη (r) n = n + n (n2 −1)Φ , (5) limited by free surface atz = z (r ) and homogeneous 2 n n s ∂r 2ηn(r) ∂z 2 ρ absorbing bottom with density b andsquaredrefrac- with the boundary conditions: One can see that as far as removing from source the Φ = 0 , Φ = Φ , contribution of second local modeϕ (r, z ) increases n z=0 n z=H −0 n z=H +0 2 ()∂Φ ∂ = ()ρ ρ ()∂Φ ∂ but contribution of first one decreases. This process n z w b n z z=Hb −0 z=Hb +0 leads to the changing depth distribution of GAM = η Φ (r, z) . The depth dependence ofΦ (r, z ) is pre- Here nn(r, z) kn(r, z) n(r) . 1 1 sented on the Fig.3 for case under review.

COMPUTING OF ADIABATIC MODES 1.2 1.0 0.8 0.6 0.4 0.2 0.0 There is some arbitrariness in selection of initial form of GAM at source location ( r = 0 ). That is why we suppose that initial form of GAM coincides with one of 0.00 Φ = ϕ η = ξ local moden(0, z) n(0, z ) andn(0) n(0 ) .

One of possible ways to computing of GAM for -100.00 acoustic trace can consist of the solving Eq.(5) by using wide angle PE algorithm. The other way is in presenta- ϕ tion of AM as superposition of local modesm(r, z ) : -200.00 Φ = n ϕ n(r, z) am(r) m (r, z) , (6) ÿ 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 m Here are modal amplitudes which are defined by set FIGURE 3. Space-distribution of absolute value of first adia- of coupling equations: batic mode Φ1(r, z) . n dam = ()ξ −ξ n − n i m n am ÿVmpap , (7) CONCLUSION dr p ∂ψ We are thinking that developed approach for descrip- = ψ m tion of sound field in irregular shallow water waveguide where coupling coefficients Vnm n dz are ∂r can be effective for diverse acoustic problems. We determined by type of waveguide irregularity. Taking mean such problem as: source localization, modeling of into account initial condition at source location ( r = 0 ) the space-time fluctuations of sound field caused by one can obtain that initial conditions for coupled equa- moving local object in shallow water; etc. In these prob- tions set (7): lems the multiple calculations of sound field are needed. a n (0) = δ , (8) Within framework of the developed approach once m mn computed GAM can be used repeatedly. So in mentioned problems the developed approach allows de- As example we present GAM for the coastal slope: crease amount of calculations significantly. = − H (r) H0 er , (9) REFERENCE = = −2 with constants H0 250m , e 0,025m , 1. Keller J.B. and Papadakis J.S. Wave Propagation f = 250Hz , c = 1500m s , c = 1750m s . w b and Underwater Acoustics. Springer-Verlag, Berlin- Φ The first adiabatic mode1(r, z ) expansioninalo- Heidelberg-New-York, 227 pp., 1979 , ϕ cal modes of waveguidem(r, z ) isshownonFig.2. 2. A.T.Abawi, W.A.Kuperman, M.D.Collins Journal Acoust. Soc.Am 102 (1) 233-238, (1997) 1.0 1 3. O.A.Godin “ Journal Acoust. Soc.Am. 103 (1) 159- 168, (1998) 4. A.V. Gurevich, E.E. Tsedilina “Super long-range 2 propagation of short radio waves” – M.: Nauka, 1979. 248 p. modal amplitudes 3 0.0 5. Katsnelson B.G., Petnikov V.G. “Shallow water 0369 acoustics” – M.: Nauka, 1997. 191 p. range ( km )

FIGURE 2. The first adiabatic mode expansion in a local modes of waveguide. Modal Dispersion Curve Measurements for the Robust Inversion of Shallow Water Seabed Parameters B.T. Coxa and P. Josephb

aArup Acoustics, 8 St. Thomas St., Winchester, SO23 9HE, UK bInstitute of Sound and Vibration Research, University of Southampton, Southampton, SO17 1BJ, UK

Matched-Field Inversion is often used to determine seabottom parameters in a shallow water waveguide from measurements of the acoustic field. The estimates of the parameters obtained using this method are very sensitive to mismatch between the water depth used in the model and the actual water depth. It is therefore difficult to achieve robust parameter estimates. This paper describes a method that separates the part of the acoustic field that is less sensitive to the water depth (the low order modes) from the part that is more sensitive and hence causes the mismatch problem (the higher order modes). The measured variation of horizontal wavenumber with frequency for the low order modes, the dispersion curves, are used in a matched-field type algorithm to estimate the required parameters with much reduced sensitivity to water depth mismatch. Because this technique matches theoretical (model-based) and measured dispersion curves it is called Matched Dispersion Curve Inversion. It is inherently multi-frequency and, in theory, can invert for any parameters that affect the seabed reflection coefficient. Moreover, the technique is independent of source and receiver depth, and the necessary measurements easily made by Hankel transforming the acoustic pressure measured over a horizontal line array of hydrophones.

WATER DEPTH MISMATCH where n is the mode number, krn are discrete complex modal wavenumbers, and An denotes complex modal Matched-field inversion is often used to pressure amplitudes. The real and, in principle, determine seabed parameters in a shallow water imaginary parts of the modal wavenumber can be waveguide from measurements of the acoustic field measured as a function of frequency by Hankel [1]. The estimates of the parameters obtained using transforming the acoustic pressure measured over a standard matched-field processors are very sensitive to horizontal line array of hydrophones [3]. The modal mismatch, in particular between the water depth used wavenumbers plotted as a function of frequency are in the model and the actual water depth [2] and, to a called modal dispersion curves. By comparing these lesser extent, to the accuracy of the receiver and source dispersion curves with those calculated from a model positions. It is therefore difficult to achieve robust [4], it is possible to obtain parameter estimates in a parameter estimates without performing the inversion way directly analogous to matched-field inversion. over all parameters that may be mismatched, which is The advantage of this method over matched-field extremely computer intensive, even if it is assumed inversion, which uses the whole acoustic field, is that that the mismatches are independent. It has been it is possible to choose the number of modes used in shown elsewhere that, for the hard bottomed the inversion. As the lower order modes interact less waveguide described below, a mismatch of just 3 % in with the seabed than do the higher order modes, the water depth can result in errors in the seabed wave performing an inversion using the lower order modes speeds of greater than 500 m/s when inverting using alone may be less sensitive to water depth mismatch traditional matched-field inversion [3]. than traditional matched-field methods. Also, as modal dispersion curves are characteristic of the waveguide MODAL FIELD IN SHALLOW WATER alone, any source or receiver depth mismatch is also removed. Traditionally, in matched-field inversions, the measured and predicted acoustic fields have been MATCHED DISPERSION CURVE compared as a function of position. In a shallow water INVERSION waveguide the acoustic field as a function of range p(r) in the far-field of a source can be accurately The hypothesis that an inversion performed using approximated by the sum of N discrete proper modes: only the lowest order mode will be less sensitive to water depth mismatch than one in which a higher order 1 N mode is also used was tested using synthetic data. A ikrnr p(r) An e set of modal dispersion curves were obtained, using r n1 the method described in Ref. 4, for a shallow water FIGURE 1. Matched Dispersion Curve Inversion, using FIGURE 2. Matched Dispersion Curve Inversion, using modes 1 and 5, for compressional wave speed in the seabed, only mode 1, for compressional wave speed in the seabed, showing the effect of water depth mismatch. showing the effect of water depth mismatch. Comparing this figure with Fig. 1 shows that using only lower order modes waveguide of depth d = 100 mm, with a seabed in the inversion reduces the sensitivity to water depth modelled as a semi-infinite half-space characterised by mismatch in this case. a shear wave speed of 2766 m/s, compressional wave speed of 4409 m/s and a density of 2000 kg/m³. No In this paper, only the real part of the attenuation was included in the model. (This model wavenumbers were compared in the Matched was used as it corresponds to our experimental tank.) Dispersion Curve Inversion, so only parameters which The range of frequencies f was 1 kHz – 100 kHz. (As affect the phase of the reflection coefficient of the seabed could have been inverted for. In principle both the water sound speed c = 1467 m/s, and k 2 f / c , the real and imaginary parts of the wavenumbers could the range of frequencies expressed as the non- be used, and so this method may be used to invert for dimensional frequency kd was from 0.428 to 42.830.) any parameter that affects the seabed reflection Using modes 1 and 5, where mode 1 is the lowest coefficient. order mode, an inversion was performed in order to The preliminary result presented here suggests determine the compressional wave speed, given the that separating the acoustic field into those parts that other parameters, for a range of water depths from 90 are very sensitive to depth mismatch (high order mm to 110 mm (i.e. mismatch of ± 10 %). Figure 1 modes) and those less so (low order modes) and using shows that for the correct water depth the squared only the less sensitive parts of the field as input data error between the real parts of the correct and could be one way to reduce ambiguity and improve modelled dispersion curves goes to zero, as expected. accuracy of estimates of geoacoustic parameters For water depth mismatches as small as 2%, the obtained from shallow water inversions. ambiguity of the estimate is considerably increased, as can be seen by the flatter lines in Fig. 1, and it is ACKNOWLEDGMENTS difficult to determine the correct wave speed. (For the sake of clarity the results for values of the water depth Much of this work was sponsored by EPSRC. mismatch from –10 % to 0 % are shown in the figures. Similar results were obtained for values from 0 to +10%.) REFERENCES The same inversion was performed, this time using only the lowest order mode. As can be seen in 1. Tolstoy, A., Matched Field Processing for Underwater Acoustics, World Scientific, Singapore, 1993. Figure 2, the ambiguity in the estimates is 2. Chapman, N.R., Ozard, K.S., and Yeremy, M.L., J. considerably reduced and the estimates of the wave Comp. Acoust. 7, 1-13 (1989). speed are accurate to within 50 m/s even at a mismatch 3. Cox, B.T., Geoacoustic Inversion in Shallow Water, of 8 % in the water depth. PhD Thesis, Institute of Sound and Vibration Research, Southampton University, UK, 1999. 4. Tindle, C.T., and Chapman, N.R., J. Acoust. Soc. Am. 96, 1777-1782 (1994).