Numerical considerations in ray tracing and ray expansions of the acoustics wavefield

Abstract

In separable geometries (range‐independent sound speed profile, flat bottom) the reduced wave equation may be solved using the WKB technique. The resulting integral expression is a plane wave or ray expansion the acoustic wavefield. In nonseparable geometries the Maslov technique provides an expression of the same form. Use of the stationary phase technique reduces these integral expressions to standard ray theory. We focus our attention on numerical considerations associated with: (1) computing the geometric ray information which appears in these integral wavefield expressions; and (2) evaluating the integrals. Many commonly occurring problems associated with (1) (ray tracing) may be avoided by appropriately parametrizing the model and rewriting the travel time in terms of the phase integral, τ (sometimes referred to as the delay or intercept time). Problems associated with (2) are particularly troublesome when caustics are present. These may be avoided entirely by transforming to the time domain. [Work supported by ONR.]