⇦Chinese Physics Letters, 2017, Vol. 34, No. 9, Article code 094301 Geoacoustic Inversion Using Time Reversal of Ocean Noise * Ji-Xing Qin(秦继兴)1**, Boris Katsnelson2, Oleg Godin3, Zheng-Lin Li(李整林)1 Affiliations 1State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190 2Department of Marine Geosciences, School of Marine Sciences, University of Haifa, Haifa 31905, Israel 3Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, Colorado 80309, USA Received 26 May 2017 *Supported by the National Natural Science Foundation of China under Grant Nos 11434012 and 41561144006.
**Corresponding author. Email: qjx@mail.ioa.ac.cn Citation Text: Qin J X, Katsnelson B, Godin O and Li Z L 2017 Chin. Phys. Lett. 34 094301 Abstract We present a passive geoacoustic inversion method using two hydrophones, which combines noise interferometry and time reversal mirror (TRM) techniques. Numerical simulations are firstly performed, in which strong focusing occurs in the vicinity of one hydrophone when Green's function (GF) is back-propagated from the other hydrophone, with the position and strength of the focus being sensitive to sound speed and density in the bottom. We next extract the GF from the noise cross-correlation function measured by two hydrophones with 8025-m distance in the Shallow Water '06 experiment. After realizing the TRM process, sound speed and density in the bottom are inverted by optimizing focusing of the back-propagated GF. The passive inversion method is inherently environmentally friendly and low-cost. DOI:10.1088/0256-307X/34/9/094301 PACS:43.30.Pc, 43.30.Ma, 43.30.Nb, 43.60.Tj © 2017 Chinese Physics Society Article Text Wave propagation in oceans is usually influenced significantly by bottom properties, especially for shallow water or transitional areas. Due to the difficulty and high cost of direct measurement for the bottom parameters, geoacoustic inversion as an important kind of indirect method has received considerable attention in underwater acoustics. A variety of inversion methods have been developed in recent years,[1-8] and most of them are based on active schemes. In the active inversion methods, physical properties of the environment affecting acoustic propagation can be retrieved from observations of signals generated by powerful controlled sound sources.[9] Passive acoustic inversion method employs the ubiquitous ambient noise as a replacement of the designated probing signals.[10] For the passive method, a critical issue is Green's function (GF) retrieval. The process by which approximations to GFs between two locations are estimated by cross-correlating time series of ambient noise recorded at those locations is widely referred to as noise interferometry (NI). The underlying theory has been well developed.[11-14] It is well known that if a pulse signal is radiated at one point and the field is recorded at multiple distant locations, then retransmitting the time-reversed recorded signals at those locations results in a wave field that focuses at the original sound generation point.[15-17] This process is referred to as implementation of a time reversal mirror (TRM). Roux and Kuperman[18] firstly demonstrated that the GFs obtained from noise cross-correlation functions (NCCFs), rather than measured responses to active source transmissions, can be used to successfully implement a TRM. The time reversal of ocean noise makes one of the receivers act as a virtual source. In this Letter, we combine the NI and TRM techniques to invert ocean bottom parameters passively. Firstly, numerical simulations are performed to verify that bottom parameters can be determined from the requirement that the TRM focuses the wave field at the position of the sound source or, by extension, of the virtual source created through NI. Secondly, we extract the GF from the NCCF measured by two single hydrophones in the Shallow Water '06 (SW06) experiment.[19] Thirdly, combined with the extracted GF, the TRM is used to search for the optimal sound speed and density in the bottom.
cpl-34-9-094301-fig1.png
Fig. 1. Geometry of the ocean environment between SHRU 1 and SHRU 2 in the SW06 experiment.
We consider the ocean environment as shown in Fig. 1, which is the same as one part of the SW06 experiment. In the experiment, five single hydrophone receiving units (SHRUs) were positioned on the across shelf path. We choose the waveguide between SHRU 1 and SHRU 2 to analyze. The water depth at the position of SHRU 1 is 85 m, and that at the position of SHRU 2 is 107 m. We assume that the bathymetry between the two receivers varies linearly. Both of the SHRUs are located 7 m above the bottom, and the horizontal distance between them is 8025 m. The bottom is modeled as a uniform fluid halfspace in this work. The averaged sound speed profile measured in the experiment is used in the following simulations. Let a point sound source be located at the position of SHRU 1, to emit a signal $s_0(t)$ with a spectrum $S(\omega)$. The spectrum has the form $$ S(\omega)=\begin{cases} \! 1, & 10\,{\rm Hz}\leq\omega/2\pi\le70\,{\rm Hz},\\\! 0, & {\rm elsewhere}. \end{cases}~~ \tag {1} $$ In the frequency domain, the acoustic pressure at the position of SHRU 2 is given by $$ P({\boldsymbol r}_2,\omega)=S(\omega)G(\omega),~~ \tag {2} $$ where $G(\omega)$ is the frequency-domain GF between the points of SHRUs 1 and 2. Next, reverse the received time-domain signal and reradiate it. The acoustic pressure received at the position of SHRU 1 is $$ P({\boldsymbol r}_1,\omega)=S^\ast(\omega)G^\ast(\omega)G(\omega),~~ \tag {3} $$ where $\ast$ denotes the complex conjugation. The focusing field is expected at the point of SHRU 1 if there are sufficient multi-paths connecting the two points. We calculate the frequency-domain acoustic pressure $P(r, z, \omega)$ using a wide-angle parabolic equation model RAM.[20] Subsequently, time-domain pressure $p(r, z, t)$ is Fourier-synthesized from $P(r, z, \omega)$. We define $E(r,z)=|\max\limits_{t>0}[p(r, z, t)]|^2$. The normalized peak intensity $J(r,z)=-10\lg[1-0.99E(r,z)/E_0]$, with $E_0=\max\limits_{r,z}[E(r,z)]$, is given in the dashed rectangular area around SHRU 1 as shown in Fig. 1 in the following results. Figure 2(a) shows the simulation result using the bottom parameters with the sound speed of 1750 m/s, the density of 1.9 g/cm$^3$, and the attenuation of 0.02 dB/wavelength. A sharpened focus can be observed in Fig. 2(a) exactly at the position of SHRU 1. If the bottom parameters for wave propagating from SHRU 1 to SHRU 2 are different from those for back-propagating, the main focus will shift and blur, or the spurious additional foci will become more pronounced. From Figs. 2(b)–2(d), we can see that the main-focus shift of the back-propagating wave is sensitive to mismatches of sound speed and density in the bottom. The simulation results suggest that bottom parameters can be estimated from the position of focusing sound field generated by the TRM. It should be emphasized that the focusing position is insensitive to the bottom attenuation coefficient, which is considered as a constant of 0.02 dB/wavelength in this study.
cpl-34-9-094301-fig2.png
Fig. 2. Sensitivity for the position shift of focusing wave field generated by the TRM to the bottom parameters. The sound speed is 1750 m/s and the density is 1.9 g/cm$^3$ in the bottom for forward wave propagating. The sound speed and density for back-propagating are (a) 1750 m/s and 1.9 g/cm$^3$, (b) 1700 m/s and 1.9 g/cm$^3$, (c) 1850 m/s and 1.9 g/cm$^3$, and (d) 1750 m/s and 1.5 g/cm$^3$. In each panel, the black dot denotes the position of the sound source, and the bathymetry is indicated by a thick black line.
For noise data recorded by SHRUs 1 and 2 in the SW06 experiment, we evaluate the NCCF from a Fourier transform of the cross spectrum, which is calculated by summating over a large number of data segments in 5.7 d. There are 10% data segments with the highest noise level that are discarded to suppress contributions of strong, localized and transient sources. To equalize contributions of various sources, the noise spectra are normalized in each data segment. Figure 3(a) shows the final result in the frequency band of 10–70 Hz, in which there are two peaks around the time delays of $\pm$5.5 s, respectively. The NCCF is approximately proportional to the sum of forward and backward GFs between SHRU 1 and SHRU 2, i.e., $C(t)=A[G(t)+G(-t)]$, where $A$ is a constant. An unexpected smaller peak also appears in Fig. 3(a) because some signals are probably treated as noise. In the following we choose the negative time delay part of NCCF as GF, which is the waveform in the dashed box in Fig. 3(a). The fine structure of the backward GF is given in Fig. 3(b). In principle, we could obtain the same GF from the positive time delay part of NCCF if the noise field is perfectly diffuse.
cpl-34-9-094301-fig3.png
Fig. 3. The noise cross-correlation function (NCCF) for SHRUs 1 and 2 in the SW06 experiment (a) and the fine structure of negative time delay part (b). The frequency band is in the range of 10–70 Hz.
In the following we realize a passive TRM using the GF retrieved from the ambient noise to invert bottom parameters. The process of implementing TRM is almost the same as the above numerical simulations. The only difference is the absence of a source in the waveguide. Instead, SHRU 1 serves as a virtual source. At the position of SHRU 2, the retrieved GF is firstly time-reversed, then we reradiate the reversed signal and make it propagate toward SHRU 1 by calculating the backward GF numerically. Next the quantity $J(r,z)$ is plotted around SHRU 1 to find a focus. We model the bottom as a uniform fluid halfspace and search for the bottom parameters that minimize the displacement of main focus from the virtual sound source. In the geoacoustic inversion, the searching region for bottom sound speed is from 1650 to 1900 m/s. For a given sound speed $c_{\rm b}$, the corresponding density $\rho_{\rm b}$ is obtained by the Hamilton sediment empirical relationship for continental terrace[21] $$ c_{\rm b}=2330.4-1257.0\rho_{\rm b}+487.7\rho_{\rm b}^2.~~ \tag {4} $$ Figure 4 gives the displacements of main focus from the virtual sound source SHRU 1, which are caused by deviations of bottom parameters from their true values. The minimum appears at the sound speed of 1770 m/s, which is the optimal value for the environment between SHRU 1 and SHRU 2. The optimal density is 2.0 g/cm$^3$ according to the empirical relationship of Eq. (4).
cpl-34-9-094301-fig4.png
Fig. 4. Displacement of main focus from the virtual sound source versus bottom sound speed.
cpl-34-9-094301-fig5.png
Fig. 5. Time reversal of GF retrieved from NCCF in the SW06 experiment. The GF is back-propagated in the environments with different bottom parameters. Normalized peak intensity of the back-propagated acoustic field in the vertical cross-section of the waveguide is shown by color. Sound speed and density in the bottom are (a) 1770 m/s and 2.0 g/cm$^3$, (b) 1650 m/s and 1.8 g/cm$^3$, (c) 1700 m/s and 1.9 g/cm$^3$, and (d) 1900 m/s and 2.2 g/cm$^3$. In each panel, the black dot denotes the position of the virtual sound source SHRU 1, and the bathymetry is indicated by a thick black line.
The normalized peak intensity $J(r,z)$ of the back-propagated field for the optimal bottom parameters is shown in Fig. 5(a). Remarkably, back propagation of the measured NCCF from the location of SHRU 2 gives a field with a pronounced focus in the vicinity of SHRU 1. The focusing quality of time-reversed NCCF in the experiment is comparable to that achieved in back-propagation of the simulated GF (Fig. 2(a)). The normalized peak intensity of the back-propagated field for other bottom parameters are also given in Figs. 5(b)–5(d). As in numerical simulations, the position of the main focus of the back-propagated NCCF proves to be sensitive to the bottom parameters. A mismatch between the actual bottom parameters and the parameters assumed in back-propagating the retrieved GF shifts and blurs the main focus, while making the spurious additional foci more pronounced. The corresponding bottom densities in Fig. 5 obtained from Eq. (4) are 2.0, 1.8, 1.9 and 2.2 g/cm$^3$, respectively. A uniform fluid halfspace bottom model is used in the inversion method, which includes three parameters: sound speed, density and attenuation. As discussed in Ref. [22], the equivalent single-layer bottom model has the same effect on the underwater acoustic field as the multiple-layer models within some range-frequency domain of interest. Furthermore, the Hamilton sediment empirical relationship between sound speed and density is utilized to reduce the dimension of unknown parameters. As a result, this inversion method could avoid the multiple-solution problem, which often appears in some other geoacoustic inversion methods. It should be emphasized that the inversion method combining NI and TRM techniques can also be applied to more complex bottom models. The additional parameters will lead to a considerable increase of computation time for searching optimal solutions, and the multiple-solution problem may appear. In summary, a passive geoacoustic inversion method combining NI and TRM techniques has been presented, in which ambient noise recorded on only two hydrophones is used. In numerical simulations, strong focusing occurs in the vicinity of one hydrophone when the GF is back-propagated from the other hydrophone, with the position and strength of the focus being sensitive to sound speed and density in the bottom. We extract the GF from the NCCF measured by two single hydrophones in the SW06 experiment. After performing the TRM process, values of sound speed and density in the bottom are estimated by optimizing focusing of the back-propagated GF. Compared with active techniques, the passive inversion method does not contribute to noise pollution in the ocean, and consequently is inherently environmentally friendly. Moreover, this is a low-cost method because only two hydrophones are necessary. References Hybrid geoacoustic inversion of broadband Mediterranean Sea dataTomographic inversion for sediment parameters in shallow waterQuantifying uncertainty in geoacoustic inversion. I. A fast Gibbs sampler approachBenchmarking geoacoustic inversion methods for range-dependent waveguidesReverberation Vertical Coherence and Sea-Bottom Geoacoustic Inversion in Shallow WaterGeoacoustic inversion for sediments in the South China Sea based on a hybrid inversion schemeGeoacoustic Inversion Based on Modal Dispersion Curve for Range-Dependent EnvironmentAn overview of matched field methods in ocean acousticsA passive fathometer technique for imaging seabed layering using ambient noiseOn the emergence of the Green’s function in the correlations of a diffuse fieldRetrieving the Elastodynamic Green's Function of an Arbitrary Inhomogeneous Medium by Cross CorrelationRecovering the Acoustic Green’s Function from Ambient Noise Cross Correlation in an Inhomogeneous Moving MediumRetrieval of Green’s functions of elastic waves from thermal fluctuations of fluid-solid systemsPhase conjugation in underwater acousticsTime-reversed acousticsAn initial demonstration of underwater acoustic communication using time reversalTime reversal of ocean noiseShallow Water '06: A Joint Acoustic Propagation/Nonlinear Internal Wave Physics ExperimentSound velocity and related properties of marine sedimentsA Broadband Geoacoustic Inversion Scheme
[1] Fallat M R and Nielson P L 2000 J. Acoust. Soc. Am. 107 1967
[2] Potty G R, Miller J H, Lynch J F and Smith K B 2000 J. Acoust. Soc. Am. 108 973
[3] Dosso S E 2002 J. Acoust. Soc. Am. 111 129
[4] Chapman N R, Chin-Bing S, King D and Evans R B 2003 IEEE J. Oceanic Eng. 28 320
[5] Zhou J X, Zhang X Z, Rogers P H, Simmen J A, Dahl P H, Jin G L and Peng Z H 2004 IEEE J. Oceanic Eng. 29 988
[6]Li F H and Zhang R H 2000 Acta Acust. 25 298 (in Chinese)
[7] Li Z L and Li F H 2010 Chin. J. Oceanol. Limnol. 28 990
[8] Guo X L, Yang K D, Ma Y L and Yang Q L 2015 Chin. Phys. Lett. 32 124302
[9] Baggeroer A B, Kuperman W A and Mikhalevsky P N 1993 IEEE J. Oceanic Eng. 18 401
[10] Siderius M, Harrison C H and Porter M B 2006 J. Acoust. Soc. Am. 120 1315
[11] Lobkis O I and Weaver R L 2001 J. Acoust. Soc. Am. 110 3011
[12] Wapenaar K 2004 Phys. Rev. Lett. 93 254301
[13] Godin O A 2006 Phys. Rev. Lett. 97 054301
[14] Godin O A 2009 J. Acoust. Soc. Am. 125 1960
[15] Jackson D R and Dowling D R 1991 J. Acoust. Soc. Am. 89 171
[16] Fink M, Cassereau D, Derode A, Prada C, Roux P, Tanter M, Thomas J L and Wu F 2000 Rep. Prog. Phys. 63 1933
[17] Edelman G F, Akal T, Hodgkiss W S, Kim S, Kuperman W A and Song H C 2002 IEEE J. Oceanic Eng. 27 602
[18] Roux P and Kuperman W A 2005 J. Acoust. Soc. Am. 117 131
[19] Tang D J, Moum J N, Lynch J F, Abbot P, Chapman R, Dahl P H, Duda T F, Gawarkiewicz G, Glenn S, Goff J A, Graber H, Kemp J, Maffei A, Nash J D and Newhall A E 2007 Oceanography 20 156
[20]Collins M D User's Guide for RAM Versions 1. 0 and 1.0p (Washington DC: Naval Research Laboratory)
[21] Hamilton E L and Bachman R T 1982 J. Acoust. Soc. Am. 72 1891
[22] Li Z L and Zhang R H 2004 Chin. Phys. Lett. 21 1100