Analysis of modal evolution caused by a weakly range-dependent seabed in shallow water and its application to inversion for geoacoustic properties

Abstract

In a shallow water ocean environment, the range-dependent variation of the geoacoustic properties of the seabed is one of the crucial factors affecting sound propagation. Since the local modes of propagation depend on the spatial changes in the bottom sediments, the local eigenvalues of these modes are useful as tools for examining the range dependence of the sediment properties. In order to extract the local eigenvalues from measurements of the pressure field in a laterally inhomogeneous waveguide, the zero-order asymptotic Hankel transform with a short sliding window is utilized. The local peak positions in the output spectra differ from the local eigenvalues due to both the range variation of the local modes and the interference of adjacent modes. The departure due to the former factor is evaluated analytically by using the stationary phase method. In order to reduce the error induced by the latter factor, mode filtering is utilized by incorporating data from a fixed vertical array of receivers. The use of the above zero-order Hankel transform in a three-dimensionally varying waveguide results in an underestimate of the local eigenvalues due to the effect of horizontal refraction. Thus a general asymptotic Hankel transform with a 2-D sliding window is used to correct for the underestimated amount. By expanding the latter transform with respect to the azimuthal angle, it can also be shown that the first term in the Taylor series corresponds to the former transform; the rest of the terms account for the value difference between the underestimated and actual local eigenvalues. In order to obtain the spatial variation of the sediment properties from the rangedependent variation of the extracted local eigenvalues, the analytical relationship between these two variations is derived by using a perturbation method in a horizontally varying, multi-layered bottom model. Upon use of the n2-linear profile in each layer, the relationship can be obtained in closed form. As a result, the range variation of the local eigenvalues may be separated into terms that depend on each geoacoustic parameter. Based on this relation, an inversion method for determining the range-dependent geoacoustic parameters is developed. The methods developed in this thesis are applied to simulated pressure field data as well as experimental field data. It is shown that the evolution with range of the local modes as well as the range-dependent geoacoustic properties can be successfully estimated.