The numerical synthesis and inversion of acoustic fields using the Hankel transform with application to the estimation of the plane wave reflection coefficient of the ocean bottom

Abstract

The plane wave reflection coefficient is an important geometry independent mean of specifying the acoustic response of a horizontally stratified ocean bottom. It is an integral step in the inversion of acoustic field measurements to obtain parameters of the bottom and it is used to characterize an environment for purposes of acoustic imaging. This thesis studies both the generation of synthetic pressure fields through the plane wave reflection coefficient and the inversion of measured pressure fields to estimate the plane wave reflection coefficient. These are related though the Sommerfeld integral which is in the form of a Hankel transform. The Hankel transform is extensively studied in this thesis and both theoretical properties and numerical implementations are considered. These results have broad applications. When we apply them to the generation of synthetic data, we obtain hybrid numerical-analytical algorithms which provide extremely accurate synthetic fields without sacrifising computational speed. These algorithms can accurately incorporate the effects of trapped modes guided by slow speed layers in the bottom. We also apply these tools to study the inversion of measured pressure field data for the plane wave reflection coefficient. We address practical issues associated with the inversion procedure including removal of the source field, sampling, field measurements over a finite range, and uncontrolled variations in source-height. A phase unwrapping and associated interpolation scheme is developed to handle improperly spaced data. A preliminary inversion of real pressure field data is performed. In parallel, an inversion of a synthetically generated field for similar bottom parameters is also performed and the results of processing the real and synthetic data are compared. The estimate for the depth dependent Green's function obtained from the real data shares many features with the depth dependent Green's function estimated from the synthetic data, suggesting that the total inversion to obtain the plane wave reflection coefficient will soon be possible. Errors in the present estimate of the plane wave reflection coefficient are associated with uncontrolled source-height variations during the acquisition of data.