Nonlinear Optimization Techniques for Geoacoustic Tomography

Abstract

Global optimization schemes such as Simulated Annealing (SA) and Genetic Algorithms (GA), which rely on exhaustive searches, have been used increasingly in recent times for the inversion of underwater acoustic signals for bottom properties. Local optimization schemes such as the Levenberg-Marquardt algorithm (LM) and Gauss-Newton methods which rely on gradients, can compliment the global techniques near the global minimum. We use hybrid schemes which combine the GA with LM and Differential Evolution (DE) to invert for the geoacoustic properties of the bottom. The experimental data used for the inversions are SUS charge explosions acquired on a vertical hydrophone array during the Shelf Break Primer Experiment conducted south of New England in the Middle Atlantic Bight in August 1996. These signals were analyzed for their time-frequency behavior using wavelets. The group speed dispersion curves were obtained from the wavelet scalogram of the signals. Hybrid methods mentioned earlier are used for the inversion of compressional wave speeds in the sediment layers. An adiabatic normal mode routine was used to construct the replica fields corresponding to the parameters. Comparison of group speeds for modes 1 to 9 and for a range of frequencies 10 to 200 Hz was used to arrive at the best parameter fit. Error estimates based on the Hessian matrices and a posteriori mean and covariance are also computed. Resolution lengths were also calculated using the covariance matrix. The inverted sediment compressional speed profile compares well with in situ measurements.