Numerical simulation of transient waves in a heterogeneous soil layer

The passage of elastic waves through the upper soil strata is modeled by a rather simple solution based on freely propagating waves in a continuously heterogeneous material with amplitude dependence on a single coordinate corresponding to the direction of propagation. Specifically, pseudo-dilational and pseudo-rotational waves are developed for an elastic medium with position-dependent density and thus position-dependent pressure (P) and shear (S) wavespeeds, although in a strict sense these no longer exist as such due to coupling through the material heterogeneity. Time harmonic conditions are assumed to hold at the fundamental solution level and transient signal generation is achieved through Fourier synthesis. Numerical examples for the square root of linear in the depth coordinate wavespeed profiles are used in modeling the passage of impulsively-generated signals in a soft soil deposit under two-dimensional conditions.