Approximate Calculation of Scattered Field From Three-Dimensional Narrow Cracks

Abstract

An approximate and efficient formulation is presented for calculating the scattered field from a three-dimensional narrow crack in a ground plane illuminated by a plane wave. This formulation is based on a quasi-static approximation supplemented with terms that include the effect of traveling waves. It is shown that for shallow cracks, only the first dominant traveling-wave mode needs to be included to render an accurate solution. However, when a crack is deep enough, the second mode must be considered. The accuracy of the calculation is demonstrated by several numerical examples.