Finite-difference time-domain method for modelling of seismic wave propagation in viscoelastic media

A finite difference formulation for the equations of SH waves in viscoelastic media has been developed and applied to the problem of an infinite half space with a buried source emitting a compressional pulse. A dispersion relation has been developed by employing the finite difference (FD) method, which has been used to discuss the stability criteria and also for obtaining the relation for phase and group velocities in viscoelastic media. Furthermore, the effect of variation of stability parameter on phase and group velocities; effect on the wave propagation with increase in dispersion parameter; and change in the wave propagation at different locations from the source have also been studied. The SH waves are found to be dispersive in viscoelastic media. The phase velocity increases with decrease in stability parameter. Furthermore, the location of the source has an important effect on the strength of the wave propagation in that the intensity of wave and therefore its longevity is inversely proportional to the distance from the source, implying that the wave will progressively die out exponentially.