Series solution for scattering of plane SH-waves by multiple shallow circular-arc canyons

Abstract

The analytical method is used for the problem of scattering of plane SH-waves by multiple shallow circular-arc cangons. The solution of multiple scattering of plane SH-waves is first expressed as the sum of series of solutions in each of local coordinates using separation of variables and is then converted into the form of dual infinite series of a local coordinate sytem by Graf's addition formula suitable for the interior and exterior problems. The solution of the problem is finally reduced to solving a set of infinite algbraic equations. Numerical results of scattering influence on the motion on the earth surface are presented for the two adjacent shallow circular-are canyons with the same diameter and variable depth-to-width ratio, and the effect of screening and interaction between canyons are discussed in the paper.