An Outer Boundary Integral Equation Applied to Transient Wave Scattering in an Inhomogeneous Medium

Abstract

The transient scattering of waves by an island surrounded by a locally variable water depth is solved by a finite-difference integration in the inhomogeneous region terminated at an outer boundary, beyond which the medium is infinite and homogeneous. At this outer boundary, an exact relationship between wave heights and velocities is used in the form of a Kirchhoff time-retarded integral equation. Examples are given for a constant depth, to check against other solutions, and for a parabolic depth with two forms of incident waves, a ramp-step, and a Gaussian.