Use of Galerkin's method using variable depth grids in the parabolic equation model

Abstract

Choice of a depth grid affects the accuracy of a parabolic equation (PE) propagation model, as well as the speed of execution. Choice of a fine grid step may result in lower discretization errors, but will lengthen computation times. Moreover, application of a sampling requirement (e.g. N samples per wavelength) to the water column results in oversampling in the bottom. Since an artificial absorbing later in the bottom is often employed, a large part of the computational domain is oversampled. Fine depth sampling is only needed in the region about the water sediment interface. Hence, Galerkin’s method using a variable depth grid is implemented. This is demonstrated to achieve the same error as a uniform grid with fine spacing over the entire depth domain, while taking a fraction of the run time. This is particularly important in models where nested PE models are required, as with noise models (so called N by 2D runs), full 3D, or broadband models. The variable grid Galerkin’s method is also used in an elastic PE model, in which sampling requirements for low-shear speed sediments require much finer sampling than that in the water column.