Uncertainty and Resolution in Full-Waveform, Continuous, Geoacoustic Inversion

Abstract

The ocean geoacoustic inverse problem is the estimation of physical properties of the ocean bottom from a set of acoustic receptions in the water column. The problem is considered in the context of equipment and spatial scales relevant to naval sonar. This dissertation explores uncertainty, resolution, and regularization in estimating (possibly piece-wise) continuous profiles of ocean bottom properties from full-waveform acoustic pressure time-series in shallow-water experiments. Solving for a continuous solution in full-waveform seismic and acoustic problems is not in itself new. But analyses of uncertainty, resolution, and regularization were not included in previous works in this category of ocean geoacoustic problem. Besides quantifying the quality of individual inversion results, they also provide an important tool: Methods and details in these topics build to a pre-experiment design analysis based on the problem resolution, which can be estimated without measurements (i.e. before the experiment takes place). The resolution of the bottom inversion is calculated as a function of array configuration, source depth, and range. Array configurations include 40-element horizontal line arrays (HLAs) from 200-1200m long towed at 10m depth, with source range defined as that to closest HLA element, and single and multiple vertical line arrays (VLAs) which cover the water depth. Monte Carlo analyses of the inversion within the local minimum show the extent to which the linear descriptions of uncertainty and resolution used in the experiment design analysis are valid approximations. Since full-waveform geoacoustic inversion is a nonlinear inverse problem, the resolution analysis results are dependent on the choice of bottom model for which they are calculated. Resolution analyses for six widely differing bottom profiles are compared, and at the geometries and frequencies considered in this dissertation, the results and conclusions from the point of view of experiment design decisions are in fact largely similar, with the exception of the presence of a low velocity zone in the bottom model (from which acoustic energy does not return to the receivers). The techniques and conclusions in this work are appropriate when inverting for P-wave velocity profiles in shallow (200m) water, at relatively short (<=3km) range with flat bottom, and at low frequency (~100Hz).