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Calculation of the surface motion of a layered half-space by the method of Laplace transform

DEPARTMENT OF APPLIED MATHEMATICS QUEEN MARY COLLEGE UNIVERSITY OF LONDON, MILE END ROAD LONDON E1 4NS, England

Abstract

A new method is presented for calculating the surface response of a horizontally stratified system of N homogeneous, isotropic, linearly anelastic layers with radiation damping, when subjected to a normally incident plane wave of arbitrary profile.

The method used is that of Laplace transform and contour integration. In the case N = 1, the radiation damping coefficient is found to be – [tanh^–1I₁]/s₁ for an elastic layer (where I₁ is the impedance ratio between the layer and underlying bedrock and s₁ is the time thickness of the layer). A solution, valid for low input frequencies, is also found for the damping coefficients and damped natural frequencies when viscous damping is present in the layer. For N > 1, the damping coefficients and damped natural frequencies are calculated numerically from an N-term recurrence relation.

The method may have computational advantages over some existing methods of solution.