Multistep Matched-Field Inversion for Broad ... - Ocean Engineering

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Multistep Matched-Field Inversion for Broad-Band Data From ASIAEX2001 Kunde Yang, Yuanliang Ma, Chao Sun, Member, IEEE, James H. Miller, Member, IEEE, and G. R. Potty

Abstract—This paper discusses the results of geoacoustic inversion carried out using explosive charge data from the Asian Seas International Acoustic Experiment (ASIAEX) East China Sea (ECS) Experiment. A multifrequency incoherent matched-field inversion processor and a genetic algorithm (GA) are used for the inversion. A multistep matched field inversion approach is presented, which makes use of the varying sensitivities of wave fields at various frequencies to reduce the inversion problem into a sequence of smaller inversions with fewer unknowns to estimate at each stage. Different parameters are estimated using data at different frequencies according to their sensitivities. Inversion results for different areas in the ECS region are summarized and compared with core data. Index Terms—Genetic algorithms (GAs), geoacoustic inversion, matched-field inversion.

I. INTRODUCTION

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NVERSION by matched-field processing (MFP) can be considered as a complex nonlinear optimization problem [1]–[11]. In general, the complexity of the problem increases with the number of unknown parameters, because of the presence of many local minima in the multidimensional parameter space, which makes the search for the global minimum more tedious. The accuracy with which a parameter can be inverted effectively depends mainly on the extent of its influence on the acoustic field. Sensitive parameters can be estimated more accurately and quickly as compared with less sensitive parameters. Since the sensitivity of parameters plays an important role in matched-field processing, many investigators have studied this aspect [1]–[6]. Ratilal et al. [2] divided the parameter vector into two subspaces—geometric parameters and bottom parameters—and inverted them using an iterative-subspace approach with high- and low-frequency data, respectively. Knobles et al. [3] used multiple acoustic data samples to decouple the original multidimensional problem into several smaller dimensional subsets and applied a nonlinear least squares approach to estimate parameters in each one. Stephan et al. [4] presented different neural network approaches for geoacoustic inversion and used a hierarchical approach in which the most sensitive parameters were estimated before the least sensitive. Ainslie et al. [5] described an iterative MFP scheme for efficient inversion

Manuscript received August 19, 2003; revised March 30, 2004. This work was supported by the Chinese National Foundation of Sciences under Grant 10304015 and by the Developing Program for Outstanding Persons, in Northwestern Polytechnical University, Xi’an, China. K. Yang, Y. Ma, and C. Sun are with Northwestern Polytechnical University, Xi’an, Shanxi Province 710072, China. J. H. Miller and G. R. Potty are with the University of Rhode Island, Narragansett, RI 02882 USA. Digital Object Identifier 10.1109/JOE.2004.835211

Fig. 1.

Shallow-water scenario assumed for the sensitivity analysis.

of geoacoustic parameters in shallow water using a vertical receiving array at three frequencies in the range of 50–500 Hz. Taroudakis et al. [6] studied the varying response of a Bartlett processor to changes in the values of geoacoustic parameters in different frequencies and ranges from source and developed a two-stage algorithm that searches for certain sets of parameters. This paper proposes a new inversion strategy based on the sensitivity of different parameters for the typical shallow-water environment in the East China Sea (ECS). This inversion scheme is then applied to explosive charge data from the Asian Seas International Acoustic Experiment (ASIAEX) in the ECS to estimate the bottom properties. Section II discusses the sensitivity analysis and presents the sensitivity index for various parameters at different frequencies. The multistep inversion approach is introduced in Section III and Section IV discusses the results of geoacoustic inversion using ASIAEX2001 data. Finally, the findings of this study are summarized in Section V. II. SENSITIVITY INDEX FOR MODEL PARAMETERS In this section, a sensitivity index is introduced to define the sensitivity of various model parameters. Fig. 1 shows a typical parameter model in shallow water, which can be used to describe the environment in the ECS [12], [13]. A range-independent scenario is assumed for sensitivity study and the shear effects in the bottom are also neglected. The unknown parameter set consists of the following twelve parameters: five geometric parameters (water depth, source depth, range, receiver depth, and array tilt); four sediment parameters (sediment density, attenuation, thickness, and sound speed); and three subbottom parameters (density, attenuation, and sound speed). The sensitivity study helps to numerically compare the influence of each model parameter and to provide information to select a suitable data set for the inversion. Many investigators have

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Fig. 2. Sensitivity of water depth at different frequencies.

studied this topic [1]–[6]. Although parameter coupling usually makes the sensitivity fuzzy, most investigators are in favor of getting an idea about the sensitivities without considering it. In addition, because the mean signal-to-noise ratio (SNR) for explosive charge data used in this study is greater than 10 dB, noise is not considered in sensitivity analysis. Our sensitivity study was based on the environmental model shown in Fig. 1. The synthetic acoustic field corresponding to an assumed true parameter value is calculated using SACLANTCEN normal-mode acoustic propagation (SNAP) [14]. The replica fields are generated by varying one parameter in the search space, while keeping all other parameters fixed. Finally, the correlation between the replica fields and the synthetic field is calculated and a curve showing the variation of the Bartlett power with various parameter values is obtained. In this way, the sensitivity of different parameters can be studied at different frequencies. For example, Fig. 2 shows the sensitivity of water depth at four frequencies. It can be seen that the MFP power varies sharply at high frequencies as compared to low frequencies. Based on this sensitivity curve, it can be concluded that water depth might be inverted more effectively using high frequencies. In order to quantify the sensitivity of model parameters, a sensitivity index is defined as (1) is MFP power for true value , which is alwhere ways one with noise-free data, and is MFP power for boundary value in the search space. Due to the dependence of on the frequency, the sensitivity index is a function of frequency. Nevertheless, it must be kept in mind that this method is numerical and depends mainly on the range of variation of the parameters, i.e., a very influential parameter restricted to a short range of variation may be found to be less important than another parameter given a wide range of variation. The bounds for determining the sensitivity index (SI) are roughly chosen as the parameter values where most of the MFP power curve values are low. As for the plots in Fig. 2, the search bounds are selected as 100 and 110 m and the corresponding

Fig. 3. Sensitivity index for 12 parameters at 40, 210, 470, and 670 Hz. (a) Geometric parameters. All parameters are more sensitive at higher frequencies. Range and water depth are more sensitive at 40 Hz compared with source depth, receiver depth, and array tilt. (b) Sediment parameters: sediment sound speed is more sensitive at 470 Hz and sediment thickness is more sensitive at 210 Hz. (c) Subbottom parameters: subbottom sound speed is more sensitive at 40 Hz.

SI values at four frequencies are shown in the second group in Fig. 3(a). The true values and bounds for all 12 parameters used

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invert for source range, water depth, sediment thickness, sediment sound speed, and subbottom sound speed. In the final step, the least sensitive parameters are inverted for using lower frequencies. These three steps are repeated two or three times, until the results converge. After each step, initial guesses are updated with the optimal results from the previous cycle and the search spaces for the parameters are correspondingly narrowed. After many simulations, it is found that reducing the search bounds by about one-third of the previous bounds works well. MS-MFI has following advantages compared with direct all-parameters matched-field inversion (DAP-MFI).

Fig. 4.

MS-MFI scheme.

in a sensitivity study are chosen as the mean values and ranges of the horizontal coordinates in Fig. 9. According to this definition, higher SI represents stronger sensitivity. Fig. 3 shows the SIs for the 12 parameters at four frequencies: 40, 210, 470, and 670 Hz. The results of the sensitivity study can be summarized as follows. • Parameters including source range, source depth, water depth, receiver depth, array tilt, and sediment sound speed are more sensitive at frequencies higher than 210 Hz. Hence, these parameters can be estimated more accurately at higher frequencies. • Sediment thickness is more sensitive at lower frequencies and, hence, can be estimated using data at these frequencies. Subbottom sound speed is sensitive only at very low frequencies (less than 40 Hz) and lower frequencies should be used for inversion. • The following four parameters in search spaces have very low SIs at all range of frequencies: sediment density, sediment attenuation, subbottom density, and subbottom attenuation. This indicates that they are very difficult to be inverted for unless other parameters have already been estimated accurately.

III. MULTISTEP MATCHED-FIELD INVERSION Based on the sensitivity study outlined in Section II, a new broad-band inversion scheme, namely multistep matched-field inversion (MS-MFI), is introduced in this section. The various steps involved in this scheme are schematically shown in Fig. 4. The following three steps are executed after initializing the inversion scheme. The first step uses the data at several higher frequencies to invert for the six parameters that have higher sensitivities. In the second step, data at hybrid frequencies (several low frequencies and a few high frequencies) are used to

• The MS-MFI scheme separates the unknown parameters into different subsets according to their sensitivity indexes and different frequencies are used to invert for them. Hence, it agrees with the global optimization principle that unknown parameters with similar sensitivities might yield better performance. • Inverting the parameters in steps and starting with parameters with strong sensitivity ensure that the most sensitive parameters are optimized more efficiently. The computational efforts can be concentrated on the least sensitive parameters once the most sensitive parameters are estimated in the former step. This offers more chances for the least-sensitive parameters to be estimated efficiently. • It simplifies the global optimization problem involving many unknowns (12 in this study) to a multistep approach with a subset of the original set of unknowns in each step. Also the search spaces are narrowed after each step. These steps increase the probability for converging to the global minimum. • Global searching for many parameters, with wide search spaces involving many frequencies, as in the case of DAP-MFI using genetic algorithms (GAs), requires larger population size, a larger number of generations, and more forward model runs. Since each MS-MFI step involves only a subset of the parameter vector and only few frequencies are involved, it is possible to reduce the amount of forward model calculations. This reduces the total computation time for MS-MFI as compared to DAP-MFI. In essence, as other methods based on parameter sensitivity [2]–[6], MS-MFI makes use of the varying sensitivities of wave fields at various frequencies to reduce the inversion problem into a sequence of smaller inversions with fewer unknowns to estimate at each stage. MS-MFI has some differences compared to the iterative-subspace approach proposed by Ratilal et al. [2]. This approach splits the parameter vector into two subspaces, namely, geometric parameter subspace and bottom parameter subspace, and implements the scheme with two iterative steps. However, MS-MFI divides the parameter vector into three subspaces based on the sensitivity index and operates in three steps. Sediment sound speed, which is sensitive at high frequency, is estimated in the first step. Source range and water depth, which are sensitive at low frequency, are estimated in the second step. The least sensitive parameters are estimated at last. These considerations may increase the possibility for converging to global minimum.

YANG et al.: MULTISTEP MATCHED-FIELD INVERSION FOR BROAD-BAND DATA FROM ASIAEX 2001

Fig. 5. Locations of the WBS deployments. Each asterisk indicates at least two shots that are very closely deployed. R/V Shiyan 3 was holding station approximately 0.5 nm NE of position M and the R/V Melville was holding station approximately 2.0 nm SW of postion M.

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Fig. 6. Acoustic signals from one of the WBS charges received at the VLA (shot 10).

As usual, we minimize an objective function for finding the most likely set of environmental parameters . The incoherent broadband MFI objective function is defined as (2) where is the complex transpose. The and are pressure vectors over the array of sensors. The replica field is computed using SNAP [14]. If the change of the objective function is very small in successive steps of MS-MFI, it is considered that the search has converged to the optimum point. This MS-MFI scheme has been proven to be very effective in a synthetic test case with a similar environment model [15]. In this study, we apply this scheme to geoacoustic inversion using field data obtained from the ASIAEX ECS Experiment. The details of this inversion are presented in Section IV. IV. INVERSION RESULTS FROM ASIAEX 2001 Two major field experiments were conducted in the ECS and South China Sea (SCS) as part of the ASIAEX in 2001. The first experiment was conducted in the SCS with a major focus on cross-shelf acoustic propagation. The study in this paper concentrates on the data from the second experiment conducted in the ECS [13]. A key phase of the experiment occurred from June 2–5, 2001, when 38- and 1000-g explosive charges, known as wide-band sources (WBS) were deployed from Chinese research vessels R/V Shiyan 2 and R/V Shiyan 3. Fig. 5 shows the locations (indicated by asterisks) where the WBS charges were deployed. Larger asterisks represent the locations where bigger (1000 g) charges were deployed and smaller ones represent the 38-g charges. Charges were deployed in three different patterns. 1) Circular pattern with R/V Melville and R/V Shiyan 3 near the center: the radius of this circle is approximately 30 km. 2) Radial line from the center of the circle to southwest corner of the experimental area.

Fig. 7.

Bathymetry along ME and FG segments.

3) A line of charges along the diameter nearly perpendicular to the radial line and extending beyond the circle to a water depth of approximately 1000 m. Data from these charges were recorded on a vertical line array (VLA) deployed from R/V Melville. The VLA provided by APL–UW (Applied Physics Laboratory–University of Washington) had 14 elements at 4-m spacing, sampling the water column with depths of 34.6–86.6 m. The data-acquisition system designed by the University of Rhode Island Narragansett collected data at a sampling rate of 2048 Hz. Data from all shots along the ME segment and several shots near points F and G were used for inversion. Fig. 6 shows the typical time series of acoustic data from one of the WBS charges recorded on the VLA at 5-km range. A. Range-Independent Inversion The bathymetry and sound speed in the water column along the ME segment is approximately range independent. The water depth along the ME segment is about 105 m (Fig. 7). The sound

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Fig. 8. Sound-speed profile (SSP) in the water column for inversion. The left panel shows SSP for ME segment, the right panel shows SSP for range-dependent inversion.

speed in the water column is downward refracting (Fig. 8). The unknown parameters are shown in Fig. 1. The search is carried out by a GA with incoherent objective function defined by (2). In order to find the optimum number of frequencies to be used in the broad-band incoherent MFP, inversion is carried out on the same shot data with different number of frequencies [7]. Shot 10 is chosen as a typical example to implement range-independent inversion. It was deployed at 5-km range from the VLA along the ME segment (Fig. 5). The acoustic signals from the shot recorded on the VLA are shown in Fig. 6. After estimating the relative amplitude and phase with fast Fourier transform (FFT) only for the higher energy part of the signals, data vectors at 22 frequencies with higher powers are selected. The average SNR for all the phones at frequencies lower than 450 Hz is greater than 10 dB. The 12 unknown parameters are estimated using different number of frequencies ranging from 3 to 22. By this approach it was found that, for a frequency number greater than about 10, the inversion results are relatively stable. Hence, all the inversions presented in this study are based on more than ten frequencies. For shot 10, data at 11 frequencies with higher SNR were finally used; namely, 48.4, 63.3, 76.3, 81.9, 96.8, 245.7, 258.7, 307.1, 355.5, 390.9, and 426.2 Hz. In DAP-MFI, data at all 11 frequencies were used. For MS-MFI presented in Fig. 4, data at six higher frequencies were used in the first step. Then, data at five lower frequencies and at two higher frequencies, namely, 355.5 and 426.2 Hz, were applied in the second step. Finally, data at five lower frequencies were used to estimate the leastsensitive parameters in the third step. The GA parameters were similar to [8] and [9]: the reproduction rate was 0.5; the permutation probability was 0.05; and the crossover rate was 0.8. When carrying out the optimization directly by a general software package SAGA (Seismo Acoustic inversion using Genetic Algorithms) [16] for DAP-MFI, 20 parallel runs, each sampling 2000 models with a population size of 64, were used. However, when carrying out the optimization by modified SAGA for MS-MFI, ten parallel runs, each sampling 1000 models with a population size of 64, were used.

Fig. 9. Marginal probability distributions for the 12 parameters using DAP-MFI.

From a Bayesian point of view, the solution to an inverse problem is fully characterized by a posteriori probability distributions of the unknown parameters [7]–[11]. Information about these parameters is assessed by moments of the a posteriori distribution, such as the mean, covariance, and marginal distributions. The marginal distributions are the most important in interpreting the inverse result. However, in order to calculate the moments, the multidimensional integration must be carried out. Gerstoft [8] first used the final generations from several GA inversions as the model sample and a semi-empirical probability weighting to compute marginal distributions for the geoacoustic inverse problem. The advantage of this scheme is that it works irrespective of the stochastic model for the data or likelihood function used. In an important work, Gerstoft and Mecklenbräuker [9] developed a rigorous likelihood-based approach to estimate the a posteriori probability distributions more efficiently. Adopting the likelihood-based formulation, Dosso [10], [11] applied a Gibbs sampler approach to estimate the distributions with unbiased and asymptotically convergent properties and developed a fast Gibbs sampler algorithm to reduce computation time. However, often the likelihood function is not available and then a practical weighting of the objective function is

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TABLE I MEAN INVERSION RESULTS FOR ASIAEX 2001

Fig. 10. Marginal probability distributions for the 12 parameters using MS-MFI.

performed to give an estimate of the a posteriori distribution [8], [9]. Furthermore, although the approaches provided by Gerstoft may introduce an unknown bias into the estimates and the convergent properties of GA likely overestimate the a posteriori probability distribution values around near-optimal models [9], [10], for the present study we apply them to assess the uniqueness and uncertainty of the inversion result for using the SAGA [16] code conveniently. Due to this ad hoc weighting, the a posteriori probability should be interpreted with care. The marginal probability distributions for the 12 parameters for the two cases (DAP-MFI and MS-MFI) are shown in Figs. 9 and 10, respectively. The horizontal axes show the search spaces, the vertical axes indicate probability distributions with total area of one, and the vertical lines are positions corresponding to optimal values of the parameters with minimum MFI power. It is noted that the search bounds for receiver depth are from 83 to 87 m, because of the tilt in the VLA during the experiment. The five geometric parameters with higher sensitivity index converge to the global optimum with high probabilities near the optimum values (Fig. 9). On the other hand, for sediment density, sound speed, thickness, subbottom attenuation, and density,

the probabilities near optimum values are lower because of their weak sensitivities. Furthermore, sediment attenuation and subbottom sound speed reach the boundary values. It can be noted from the probability distributions that the inversion is greatly influenced by the geometric parameters when using DAP-MFI. The convergence probabilities for the multiple-step method show some differences, as indicated in Fig. 10. The five geometric parameters with higher sensitivity index, the convergence probabilities are similar to the direct inversion method, but without bias for range and receiver depth. Sediment sound speed, thickness, and subbottom sound speed converge near the optimum values. The global convergence probabilities for the least-sensitive parameters, sediment density and attenuation, and subbottom density and attenuation show some improvement. From the viewpoint of a posteriori probability distribution, the multistep inversion strategy provides more chances for the least-sensitive parameters to contribute to the objective function and results in better inversion performance. However, because the search spaces have been reduced in size after each step and iteration, the GA is sampling only a reduced portion of the search spaces, which may create a bias in the a posteriori probability distribution estimate. In addition, there is a very interesting correlation or interaction between the estimates for range and water depth in the two types of inversions shown in Figs. 9 and 10. The range and water depth estimated using DAP-MFI are 5500 and 108 m (Fig. 9). However, when only the high frequencies are used to invert for these parameters, the estimated range and water depth are 5000 and 106 m. These results show the mirage effect that the estimates of range and water depth are correlated [17]. When all frequencies are used in DAP-MFI, it is not surprising that the low frequencies will sense the impedance change at the deeper value and the depth estimate likely represents the water depth plus the thin sediment. For the MS-MFI case, the high frequencies are able to sense the impedance contrast at the sea bed; hence, the water-depth estimate may not include any of the thin sediment layers. The estimated water depth using MS-MFI differs from the corresponding DAP-MFI estimation roughly by the estimated sediment thickness. Also, the estimated range is smaller, according to the correlation effect. Using the MS-MFI approach, inversions were carried out using data from 26 shots deployed along ME segment. The mean geoacoustic inversion results are listed in Table I. The GA search gives the optimum estimates and the a posteriori

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Fig. 12. Acoustic signals received at the VLA for the shots deployed on the NW and SE side of the experimental area. (a) Shot 84. (b) Shot 148 [20].

Fig. 11.

MFP localization results: (a) range and (b) depth.

distribution analysis provides the maximum probability values [8], [9], [16]. The values for the southwestern (SW) part in Table I are average optimum estimates obtained from the 26 shot data. For each parameter, the error bar is selected to denote the maximum difference between the average value and all estimated values. Fig. 11 shows broad-band MFP localization results using the inverted geoacoustic parameters. The range estimates agree well with the GPS values and the shot depth estimates fluctuate around 50 m, which was the preset deployment depth. B. Range-Dependent Inversion In order to compare the inversion results using WBS charges from the ME segment with those from northwestern (NW) and southeastern (SE) portion of the study area, some shots near points F and G (Fig. 5) are chosen to invert for the geoacoustic properties at these locations. Fig. 7 shows the water depth along FG segment. Water depth at the receiving VLA, F, and G points are approximately 105, 97, and 118 m respectively. The sound speeds in water column near F and G point shown in Fig. 8 are measured by Expendable Bathythermograph (XBT) deployed

from R/V Shiyan 2. It can be seen that there is a considerable range variation in the environment along the track. It has been observed that the mode-arrival structures show significant difference for shots deployed on the NW and SE sides of the experimental area (Fig. 12). The signals shown in Fig. 12 were recorded at depth of 50.6 m. Both shots are 38-g WBS charges deployed at 50-m depth at 30 km away from the VLA. Shot 84 is on the NW side of the experimental area, where the sediment is the soft mud/sand type. Shot 148 is on the SE side, where high-speed sandy sediments present [12], [13]. The energy at lower frequencies is stronger in Shot 84, whereas the energy in higher frequency is more prominent in Shot 148. In addition, the multipath effects in Shot 148 are stronger than those in Shot 84. The ASIAEX site in the ECS contains two regions of different surficial sediment types: low sound speed mud/sand to the NW and higher speed sand to the SE. This was first discovered by Niino and Emery in 1961 [18] and confirmed by gravity core data in ASIAEX 2000, shown in Fig. 13 [12], [19]. Data from approximately 20 core stations show that there is a conto siderable spatial variation in the sound speed in the top m of the sediments (the average core length). There also is a broader scale change in the properties of the top meter of sediments, which is displayed as a contour map of the vertical average sound speed of the cores in Fig. 13. For range-dependent inversions the replica field is calculated by the range-dependent SNAP version [14], [16] based on adiabatic normal mode theory. The parameter model is similar to that shown in Fig. 1. The geoacoustic properties are assumed to be range independent, whereas the water depth and sound speed in the water column are range dependent. Because the known sound-speed profile (SSP) along FM and GM segment (Figs. 5 and 13) is measured by XBT just near the F and G point; two range sections are used for replica field calculation in present study. The sound speed in the water column and water depth in the VLA is assumed to be known and the water depth in the source point is to be inverted. Therefore, the unknown parameters are similar to the range-independent condition, which in-

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consisting of three layers of sediment over a subbase. Their results for the southwest segment [20] show similar values for compressional wave speed and that the compressional wave speed increases from 1600 m/s at the sea bed to 1650 m/s at 2 m. This compares well with the present inversion of 1630 m/s in the SW region. Potty et al. inversion shows that below this surface layer compressional wave speed value is 1630 m/s down to 20-m depth increasing to 1675 m/s in the subbase. This is different from the present inversion (1887 m/s). It should be noted that only low frequencies are ( 50 Hz) sensitive at these depths and the quality of the inversions starts to degrade at depth approximately 30–40 m. V. SUMMARY AND CONCLUSION

Fig. 13. Gravity core data in ASIAEX 2000. The shot trace along ME and FG segment is also shown. The thick solid line is the boundary for high- and low-speed sediment types [19].

clude source range, source depth, water depth at source point, receiver depth, array tilt, and the seven geoacoustic parameters shown in Fig. 1. The average geoacoustic inversion results and error bars for the six shots near points F and G are also listed in Table I. C. Comparison of Inversion Results The inversions carried out in the present study provide a comparison of the geoacoustic properties in the experiment region. • The sediment thickness values were estimated as 3.1, 1.03, and 4.84 m in the SW, NW, and SE regions, respectively, which compare well with the values obtained from surveys [19]. The values obtained from these surveys are 3, 0.5, and 4.5 m in the SW, NW, and SE regions, respectively. • The sediment sound speed varies considerably in the three regions. The sediment sound speeds are approximately 1630 and 1643 m/s in the SW and SE sides. However, it is considerably different (1594 m/s) in the NW side. These values compare well with the results from ASIAEX2000 sediment core data shown in Fig. 13. • The attenuation coefficients in the sediment, estimated by the inversions are 0.33, 0.425, and 0.32 dB/ for SW, NW, and SE sides, respectively. The error bars are relatively large for attenuation due to their weak sensitivities. • The sediment density estimated for NW part is 1.82 g/cm , which is different from the value (1.9 g/cm ) inverted for the SW and SE areas. • The inversion results for subbottom sound-speed values are 1887, 1956, and 1804 m/s for the SW, NW, and SE areas, respectively. Inversions for subbottom attenuation and density are comparatively less reliable due to their lower sensitivities and need to be verified by further studies. Potty et al. [20] used the same WBS data for their long-range sediment tomography technique [1] using a sediment model

The complexity of multidimensional broad-band MFI can be simplified by a careful study on the propagation characteristics of the acoustic field in a given environment. The sensitivity information of different parameters in high and low frequencies can be incorporated into the MS-MFI scheme in which data for inversion are selected based on the frequency. The MS-MFI scheme presented in this study is ideal for complex geoacoustic models involving large number of unknowns. The total parameter space can be divided into a few subspaces and inversion can be performed in each of them. The wide-band explosive charge data from ASIAEX2001 in the ECS are analyzed. Data from 26 shots in the range-independent ME segment and 12 typical shots in the range-dependent FH segment are used to invert for the environmental parameters with particular emphasis on geoacoustic properties. Future work will concentrate on the verification of the geoacoustic parameters including subbottom properties. ACKNOWLEDGMENT The authors would like to thank the U.S. Office of Naval Research and J. Simmen, the Ocean Acoustics Program Manager, and J. Zhou, Georgia Institute of Technology, Atlanta, for all their efforts to make the ASIAEX 2001 East China Sea experiment possible. They would also like to thank R. Zhang, Chief Scientist onboard the R/V Shiyan 3, and P. Dahl, Chief Scientist onboard the R/V Melville, for their successful coordination in ASIAEX 2001. They also appreciate the insightful comments of the anonymous referees. REFERENCES [1] G. Potty, J. H. Miller, J. F. Lynch, and K. B. Smith, “Tomographic inversion for sediment parameters in shallow water,” J. Acoust. Soc. Amer., vol. 108, no. 3, pp. 973–986, 2000. [2] P. Ratilal, P. Gerstoft, and J. T. Goh, “Subspace approach to inversion by genetic algorithms involving multiple frequencies,” J. Comput. Acoust., vol. 6, pp. 99–115, 1998. [3] D. P. Knobles, R. A. Koch, E. K. Westwood, and T. Udagawa, “The inversion of ocean waveguide parameters using a nonlinear least squares approach,” J. Comput. Acoust., vol. 6, no. 1/2, pp. 83–97, 1998. [4] Y. Stephan, X. Demoulin, and O. Sarzeaud, “Neural direct approaches for geoacoustic inversion,” J. Comput. Acoust., vol. 6, no. 1/2, pp. 151–166, 1998. [5] M. A. Ainslie, R. M. Hamson, G. D. Horsley, A. R. James, R. A. Laker, M. A. Lee, D. A. Miles, and S. D. Richards, “Deductive multi-tone inversion of seabed parameters,” J. Comput. Acoust., vol. 8, no. 2, pp. 271–284, 2000.

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[6] M. I. Taroudakis and M. G. Markaki, “Bottom geoacoustic inversion by matched field processing: A sensitivity study,” Inverse Problems, vol. 16, pp. 1679–1692, 2000. [7] G. Haralabus and P. Gerstoft, “Source localization in shallow water using multi-frequency processing of shot data,” SACLANT Undersea Res. Center, La Spezia, Italy, 1997. SACLANTCEN Rep. SR-253. [8] P. Gerstoft, “Inversion of seismoacoustic data using genetic algorithms and a posteriori probability distribution,” J. Acoust. Soc. Amer., vol. 95, no. 2, pp. 770–781, 1994. [9] P. Gerstoft and C. F. Mecklenbräuker, “Ocean acoustic inversion with estimation of a posteriori probability distributions,” J. Acoust. Soc. Amer., vol. 104, no. 2, pp. 808–819, 1998. [10] S. E. Dosso, “Quantifying uncertainty in geoacoustic inversion. I. A fast Gibbs sampler approach,” J. Acoust. Soc. Amer., vol. 111, no. 1, pp. 129–142, 2002. [11] S. E. Dosso and P. L. Nielsen, “Quantifying uncertainty in geoacoustic inversion. II. Application to broadband, shallow-water data,” J. Acoust. Soc. Amer., vol. 111, no. 1, pp. 143–159, 2002. [12] J. Lynch, “ASIAEX 2000 east china sea cruise report 2000,” presented at the ASIAEX 2000 Workshop, Kona, HI, 2000. [13] P. H. Dahl, R. Zhang, J. H. Miller, L. R. Bartek, Z. Peng, S. R. Ramp, J. Zhou, C. Chiu, J. H. Lynch, J. A. Simmen, and R. C. Spindel, “Overview of Results from the Asian Seas International Acoustics Experiment in the East China Sea,” IEEE J. Ocean Eng., vol. 29, pp. 920–928, Oct. 2004. [14] F. B. Jensen and F. C. Ferla, “SNAP: The SACLANTCEN normal-mode acoustic propagation model,” SACLANT Undersea Res. Center, La Spezia, Italy, 1979. SACLANTCEN Rep. SM-121. [15] K. D. Yang and Y. L. Ma, “Shallow water broadband matched field inversion with multi-step strategy,” presented at the 3rd Int. Acoustics Conf., Harbin, China, 2002. [16] P. Gerstoft, SAGA users guide 2.0, An inversion software package, SACLANT Undersea Res. Center, La Spezia, Italy, 1997. SACLANTCEN Rep. SM-333. [17] G. L. D’Spain, J. J. Murray, W. S. Hodgkiss, N. O. Booth, and P. W. Schey, “Mirages in shallow water matched field processing,” J. Acoust. Soc. Amer., vol. 105, no. 6, pp. 3245–3265, 1999. [18] H. Niino and K. O. Emery, “Sediments of shallow portions of east China sea and South China Sea,” Geol. Soc. Amer. Bull., vol. 72, pp. 731–762, 1961. [19] J. Miller, L. Bartek, G. Potty, D. Tang, J. Na, and Y. Qi, “Sediments in the East China Sea,” IEEE J. Oceanic. Eng., vol. 29, pp. 940–951, Oct. 2004. [20] G. Potty, J. Miller, P. Dahl, and C. Lazauski, “Geoacoustic inversion results from the ASIAEX East China Sea experiment,” IEEE J. Oceanic. Eng., vol. 29, pp. 1000–1010, Oct. 2004. Kunde Yang received the B.S., M.S., and Ph.D. degrees in underwater acoustic engineering from Northwestern Polytechnical University (NPU), Xi’an, China, in 1996, 1999, and 2003, respectively. He has been with the College of Marine Engineering, Northwestern Polytechnical University, since 2003. His research interests include array signal processing, ocean acoustic modeling, and matched field localization and inversion.

Yuanliang Ma was born in Sichuan Province, China, in 1938. He received the B.S. degree in underwater acoustics from Northwestern Polytechnical University (NPU), Xi’an, China, in 1961. He has been working on underwater acoustics and signal processing, mainly at NPU, since 1961. From 1981 to 1983, he was a visiting scholar with the Department of Electrical and Electronic Engineering, Loughborough University, Loughborough, U.K. In 1980, he became an Associate Professor and Full Professor in 1985 at NPU. He has published books on underwater acoustic transducers and on adaptive active noise control in addition to more than 200 journal and conference papers. His current research interests are in sensor array signal processing, ocean acoustic modeling and tomography, low-frequency transducer arrays, and acoustic signals processing. Mr. Ma is currently a Vice-President of the Acoustical Society of China and was elected as a Member of the Chinese Academy of Engineering. He is also a Member of the Acoustical Society of America.

Chao Sun (M’97) received the B.S. degree in applied electronics from Northwestern Polytechnical University, Xi’an, China, in 1986 and the Ph.D. degree in electrical engineering from Loughborough University, Loughborough, U.K., in 1992. She has been with the College of Marine Engineering, Northwestern Polytechnical University, since 1992. Her research interests include array signal processing, parameter estimation and high-resolution algorithms, and application of adaptive techniques.

James H. Miller (S’83–M’87) received the B.S. degree in electrical engineering from Worcester Polytechnic Institute, Worcester MA, in 1979, the M.S. degree in electrical engineering from Stanford University, Stanford, CA, in 1981, and the Ph.D. degree in oceanographic engineering from the Massachusetts Institute of Technology, Cambridge/Woods Hole Oceanographic Institution, Woods Hole, MA, joint program in 1987. He was a Member of the Faculty, Department of Electrical and Computer Engineering, Naval Postgraduate School (NPS), Monterey, CA, from 1987 to 1995. Since 1995, he has been a Member of the Faculty, Department of Ocean Engineering, University of Rhode Island (URI), Narragansett, where he holds the rank of Professor. He is a Founder of FarSounder, Inc., Providence, RI, a startup company that develops forward-looking sonar for vessels, underwater vehicles, and divers. He has authored more than 100 publications in the areas of acoustical oceanography, signal processing, and marine bioacoustics. He has served as Associate Editor for Underwater Sound for the Journal of the Acoustical Society of America, responsible for scattering, inverse methods, and fish acoustics. Dr. Miller was elected Fellow of the Acoustical Society of America in 2003 and is a Member of Sigma Xi, Tau Beta Pi, Eta Kappa Nu, the Acoustical Society of America, and the Marine Technology Society. From 2001 to 2003, he was a Member of the National Academy of Sciences Panel on Noise in the Ocean. He serves on the National Marine Fisheries Service Panel on Acoustic Criteria for Marine Mammals. He also serves on the Marine Mammal Commission Subcommittee on the Impacts of Acoustics on Marine Mammals. He received the NPS Menneken Faculty Award for Excellence in Scientific Research and the URI Marshall Award for Faculty Excellence in Engineering in 1993 and 1999, respectively.

Gopu R. Potty was born in Trivandrum, India. He received the Graduate Degree in civil engineering from the University of Kerala, Trivandrum, India, in 1985, the M.S. degree in ocean engineering from the Indian Institute of Technology, Madras, India, in 1987, and the Ph.D. degree in ocean engineering from the University of Rhode Island, Narragansett, in 2000. He was a Research Associate with the Indian Institute of Technology from 1987 to 1988. From 1988 to 1995, he was with the Department of Ship Technology, Cochin University of Science and Technology, Cochin, India. Since 2000, he has been with the University of Rhode Island. His research interests include nonlinear sediment inversion, time-frequency analysis techniques, and marine bioacoustics. Dr. Potty is a Member of the Acoustical Society of America.