A Multi-Objective Geoacoustic Inversion of Modal-Dispersion and Waveform Envelope Data Based on Wasserstein Metric
<p>Simulated geoacoustic model and sound speed profile obtained from SW06 experiment. The source depth is 22 m, and a single receiver is placed 7.0 km away from the source at depth 55 m. Note that the graph is not to scale.</p> "> Figure 2
<p>(Color online) Numerical signals. (<b>a</b>,<b>b</b>) show the received and corresponding warped signals, respectively. (<b>c</b>) The signal after warping (the continuous curves) and unwarping (the red circles). Keep in mind that the time axes of the two subfigures are not equivalent.</p> "> Figure 3
<p>(Color online) (<b>a</b>) Spectrogram of the warped signal. The white polygon shows the region of the TF mask applied to filter mode 3. (<b>b</b>) The frequency spectrum of the warped signal for the frequency band 0–50 Hz, and the embedded graph is warped mode 3. (<b>c</b>) Spectrogram of the received signal. White dotted lines represent the theoretical DCs for the first four modes. The estimated DCs are also displayed as red curves upon the time-frequency spectrogram (panel (<b>c</b>)).</p> "> Figure 4
<p>(Color online) Data fit achieved in inversions of DCs. Comparison between the observed modal-dispersion data (red solid lines) and the posteriori ensembles (blue dashed lines) obtained from DCs-BO inversion. The green dotted line represents the best model and the gray region is a 95% credible interval from the Bayesian sampling.</p> "> Figure 5
<p>(Color online) (<b>a</b>) The upper envelope (red line) and lower envelope (orange line) of the observed data. (<b>b</b>) Data fits achieved in FWH inversion. Comparison between the observed FWH data (blue solid lines) and the posteriori ensembles (purple dashed lines) obtained from FWH-BO inversion. The green solid line represents the best model and the gray region is the 95% credible interval from the Bayesian sampling.</p> "> Figure 6
<p>The posterior distribution of likelihood function in MOBO inversions, with black solid points representing the true values. (<b>a</b>,<b>b</b>) Likelihood distributions of DCs based on (<b>a</b>) L2 term and (<b>c</b>) Wasserstein metric. (<b>c</b>,<b>d</b>) Likelihood distributions of FWH based on (<b>c</b>) L2 term and (<b>d</b>) Wasserstein metric.</p> "> Figure 7
<p>Posteriori models based on L2-MOBO and corresponding data fits for (<b>b</b>) FWH and (<b>c</b>) DCs, along with marginal distributions of (<b>d</b>) sediment thickness, (<b>e</b>) sediment sound speed, (<b>f</b>) sediment density, (<b>g</b>) basement density, (<b>h</b>) sediment attenuation and (<b>i</b>) basement attenuation. (<b>a</b>) Models of sound velocity and sediment depth. The results are represented with different colors, indicating the probability of the models, from the best 20%, 50% (medium) and all. Black vertical lines mark the actual sound speed values in the sediment and basement. The horizontal dashed line and the patch show the true value and distribution interval of sediment depth, respectively. The black solid lines, red solid lines and blue dashed lines in (<b>b</b>,<b>c</b>) indicate the average inversion values, observed values, and misfits under the posterior, respectively. The grouping of the best and full models and the colors are consistent with (<b>a</b>). The grey uncertainty intervals in (<b>b</b>,<b>c</b>) represent the range of values that contains the mean of the data, with a 95% credible interval. Black vertical dashed lines in (<b>d</b>–<b>i</b>) represent the true value of parameters.</p> "> Figure 8
<p>Posteriori models based on Wasserstein-MOBO and corresponding data fits for (<b>b</b>) FWH and (<b>c</b>) DCs, along with marginal distributions of (<b>d</b>) sediment thickness, (<b>e</b>) sediment sound speed, (<b>f</b>) sediment density, (<b>g</b>) basement density, (<b>h</b>) sediment attenuation and (i) basement attenuation. (<b>a</b>) Models of sound velocity and sediment depth. The results are represented with different colors, indicating the probability of the models, from the best 20%, 50% (medium) and all. Black vertical lines mark the actual sound speed values in the sediment and basement. The horizontal dashed line and the patch show the true value and distribution interval of sediment depth, respectively. The black solid lines, red solid lines and blue dashed lines in (<b>b</b>,<b>c</b>) indicate the average inversion values, observed values, and misfits under the posterior, respectively. The grouping of the best and full models and the colors are consistent with (<b>a</b>). The grey uncertainty intervals in (<b>b</b>,<b>c</b>) represent the range of values that contains the mean of the data, with a 95% credible interval. Black vertical dashed lines in (<b>d</b>–<b>i</b>) represent the true value of parameters.</p> ">
Abstract
:1. Introduction
2. Individual Inversion Theories
2.1. DCs Inversion
2.1.1. Modal Propagation in a Single Receiver Context
2.1.2. Estimation of the DCs Using Time-Warping
2.2. FWH Inversion
3. Inversion Methods
3.1. Bayesian Inversion Theory
3.2. Cost Function Based on L2 Norm and Wasserstein Metric
3.3. Multi-Objective Bayesian Optimization
4. Simulation Results
4.1. Environmental Setup and Simulated Data
4.2. Comparison between Individual Inversions and Multi-Objective Inversions
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Units | True Values | Prior Bounds |
---|---|---|---|
Layer thickness 1 | m | 25.0 | [20, 30] |
Sediment sound speed | 1600.0 | [1440, 2500] | |
Sediment density | 1.7 | [1.3, 2.4] | |
Sediment attenuation | 0.15 | [0.05, 0.5] | |
Basement sound speed | 2100.0 | [1440, 2500] | |
Basement density | 2.5 | [1.3, 2.4] | |
Basement attenuation | 0.6 | [0.05, 0.7] | |
Time shift | — | [−1.0, 2.0] |
Parameter | NRMSE | |||||||
---|---|---|---|---|---|---|---|---|
L2-DCs | 24.5 (±2.9) | 1601.0 (±5.8) | 1.65 (±0.11) | 2260.0 (±119.7) | 2.58 (±0.16) | —— | —— | —— |
L2-FWH | 29.7 (±4.2) | 1619.5 (±13.6) | 1.89 (±0.15) | 2091.0 (±99.4) | 2.45 (±0.13) | 0.220 (±0.025) | 0.405 (±0.158) | 7.35 × 10−5 |
L2-MOBO | 26.3 (±2.4) | 1635.5 (±39.5) | 1.75 (±0.08) | 2077.5 (±122.0) | 2.55 (±0.12) | 0.160 (±0.025) | 0.628 (±0.125) | 7.32 × 10−5 |
Wasserstein-MOBO | 27.1 (±4.3) | 1605.5 (±6.5) | 1.75 (±0.08) | 2136.0 (±70.0) | 2.54 (±0.11) | 0.170 (±0.015) | 0.604 (±0.125) | 5.67 × 10−5 |
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Ding, J.; Zhao, X.; Yang, P.; Fu, Y. A Multi-Objective Geoacoustic Inversion of Modal-Dispersion and Waveform Envelope Data Based on Wasserstein Metric. Remote Sens. 2023, 15, 4893. https://doi.org/10.3390/rs15194893
Ding J, Zhao X, Yang P, Fu Y. A Multi-Objective Geoacoustic Inversion of Modal-Dispersion and Waveform Envelope Data Based on Wasserstein Metric. Remote Sensing. 2023; 15(19):4893. https://doi.org/10.3390/rs15194893
Chicago/Turabian StyleDing, Jiaqi, Xiaofeng Zhao, Pinglv Yang, and Yapeng Fu. 2023. "A Multi-Objective Geoacoustic Inversion of Modal-Dispersion and Waveform Envelope Data Based on Wasserstein Metric" Remote Sensing 15, no. 19: 4893. https://doi.org/10.3390/rs15194893