A Multi-Objective Geoacoustic Inversion of Modal-Dispersion and Waveform Envelope Data Based on Wasserstein Metric

The inversion of acoustic field data to estimate geoacoustic parameters has been a prominent research focus in the field of underwater acoustics for several decades. Modal-dispersion curves have been used to inverse seabed sound speed and density profiles, but such techniques do not account for attenuation inversion. In this study, a new approach where modal-dispersion and waveform envelope data are simultaneously inversed under a multi-objective framework is proposed. The inversion is performed using the Multi-Objective Bayesian Optimization (MOBO) method. The posterior probability densities (PPD) of the estimation results are obtained by resampling from the exploited state space using the Gibbs Sampler. In this study, the implemented MOBO approach is compared with individual inversions both from modal-dispersion curves and the waveform data. In addition, the effective use of the Wasserstein metric from optimal transport theory is explored. Then the MOBO performance is tested against two different cost functions based on the L2 norm and the Wasserstein metric, respectively. Numerical experiments are employed to evaluate the effect of different cost functions on inversion performance. It is found that the MOBO approach may have more profound advantages when applied to Wasserstein metrics. Results obtained from our study reveal that the MOBO approach exhibits reduced uncertainty in the inverse results when compared to individual inversion methods, such as modal-dispersion inversion or waveform inversion. However, it is important to note that this enhanced uncertainty reduction comes at the cost of sacrificing accuracy in certain parameters other than the sediment sound speed and attenuation.