The spurious resonance disease and how to cure it: application to the seismic response of a canyon

Abstract

Three types of boundary integral equation (BIE) methods are employed to obtain closed-form solutions of a wave-scattering problem which are compared to the exact, closed-form (reference), solution deriving from the separation-of-variables technique. The problem involves either Dirichlet (D) or Neumann (N) boundary conditions (BC) for a scatterer that is a circular cylinder submitted to one or two incident waves. The three BIE methods lead to different expressions for the traction (for D-BC) or boundary displacement (for N-BC) by which numerous resonances are predicted whose frequency of occurrence differs from one method to another. This is interpreted as being the sign that the three methods are generally-defective and the resonances are 'spurious'. This 'disease' is cured by combining two BIE into one in such a way that the resulting BIE gives rise to a closed-form solution identical to the exact reference solution devoid of spurious resonances.