Scattering of SH waves by a shallow rectangular cavity in an elastic half space

Scattering of plane SH waves by a rectangular cavity embedded at shallow depth in an elastic half-space is investigated using a method that is a combination of the wave-function expansion and the weighed residual methods. The proposed method consists of partitioning the half-space using an auxiliary circle that encloses tightly the cavity, representing the motion in each region by a convenient expansion, and determining the coefficients of expansion by imposing continuity of stresses and displacements on the auxiliary circle, which is a transparent boundary. In the four regions inside the circle, representations are used in local coordinate systems such that satisfy automatically the zero-stress condition on the cavity walls, and in the outer region, such that satisfies the radiation condition. The coefficients of expansion are determined approximately, by projecting the displacement and stress residuals along the auxiliary circle onto a set of orthogonal weight functions on [−π,π] and setting all projections simultaneously to zero in the least squares sense. The method is verified by comparison with Finite Element Method solutions obtained using ANSYS, and then used to study the effects of the model parameters, such as embedment depth, cavity aspect ratio, frequency and angle of incidence, on the ground surface and cavity wall displacements. While restricted to rectangular cavity shape and still approximate, this method is computationally much more efficient than the Finite Element Method, and therefore is convenient for parametric studies of scattering of seismic waves by rectangular cavities.