An improved version of an algorithm due to Takeuchi and Saito

Abstract

Takeuchi & Saito (1972) discussed several numerical techniques for the computation of Love and Rayleigh waves. In particular, they suggested an algorithm which is based on a fixed-step size fourth-order Runge-Kutta-Gill (RKG) method to compute Love and Rayleigh waves in a layered medium which has a piecewise continuous shear modulus and density. In this note we present a single example to demonstrate that this algorithm cannot accurately compute higher-mode Love and Rayleigh waves for frequencies greater than 0.5 Hz. We also show how to modify Takeuchi & Saito's algorithm in a simple fashion so that th'ese higher-mode Love and Rayleigh waves can be accurately computed. We first review the algorithm suggested by Takeuchi & Saito for the computation of Rayleigh waves in a layered piecewise continuous medium. The equation numbers which we reference are equation numbers which appear in Takeuchi & Saito (1972). We assume that the reader is familiar with this paper.