Seismic Wave Scattering By InhomogeneousGeological Deposits With Cracks

Abstract

In this work, we study seismic wave scattering by cracks in inhomogeneous geological continua with depth-dependent material parameters and under conditions of plane strain. A restricted case of inhomogeneity is considered, with Poisson’s ratio equal to 0.25 and with both shear modulus and density profiles varying proportionally. Also, time-harmonic conditions are assumed to hold. For this type of material, elastic wave speeds remain macroscopically constant and it becomes possible to recover exact Green functions for the crack-free inhomogeneous continuum by using an algebraic transformation proposed in earlier work [1] as a first step. Subsequently, the complete elastodynamic fundamental solution, along with its spatial derivatives and an asymptotic expansion for small argument, are all derived in closed-form using the Radon transform [2]. Next, a non-hypersingular, traction-based boundary element formulation (BEM) is implemented for solving the plane boundary-value problem (BVP) with internal cracks [2]. This formulation is used for computing stress intensity factors (SIF) and scattered wave displacement field amplitudes for the case of an inclined line crack in a continuously inhomogeneous medium swept by either pressure (P) waves or vertically polarized shear (SV) waves at an arbitrary angle of incidence. The numerical results show substantial differences between homogeneous and inhomogeneous materials containing a crack in terms of their dynamic response, with the latter case being a more realistic representation for geological deposits. Finally, these types of results are useful within the context of earthquake engineering, since they can account for the influence of geological cracks in modifying seismically-generated ground motions.