Love waves in nonuniform wave guides: Finite difference calculations

Abstract

A simple finite difference approximation to the elastic equations of motion is successfully used to solve various wave-propagation problems possessing analytical solutions. On this basis the method is extended to the problem of Love waves propagating across an ocean-continent type boundary. Numerical propagation of an initial transient solution results in seismograms at various distances. The Fourier transforms of these seismograms are used to calculate phase velocity, group delay, and amplitude-transfer coefficients for various seismometer combinations across the transition region. Some results are' the transition zone can have a small but noticeable effect on phase velocities measured between stations situated away from the zone; a phase-velocity anisotropy exists for waves propagating in opposite directions across the same array. In general, waves propagating into the region of thinning have anomalously high-phase velocities and vice versa. This is especially noticeable for velocities measured over the zone of transition, where the perturbations of the phase velocity of continent-to-ocean waves from the expected local phase velocity can exceed the variations expected from the continent-ocean structural differences. The behavior at a distance from the boundary justifies the well-established method of calculating effective group velocities by means of inverse averages of regional group velocities and also indicates a simple correction for the effect of the ocean-continent boundary that can be applied to calculations of earthquake-source mechanisms based on the method of amplitude equalization.