High-Gradient Modeling for Love Wave Propagation in Geological Materials

Abstract

Based on a microstructural approach, geological material, owing to its discrete nature, can be represented by an equivalent continuum of the high-gradient type. The high-gradient continuum differs from the perfectly elastic continuum by having a characteristic length scale that is an intrinsic property of the material. Using the high-gradient stress-strain relationship, we formulate a fourth-order wave equation to describe the propagation of a Love-wave in a two-layer medium. We employ Hamilton's principle to derive the additional boundary conditions involved in the differential equation. The differential equation is then solved to study the effects of characteristic length on the wave propagation in geological material. Comparisons are made between the predicted and observed wave velocities in a two-layer geological medium during an earthquake.