A 2D equivalent linear inversion model of bedrock motions in a layered transversely isotropic half-space

Inversion is the process that evaluates input motion on the bedrock from surface motions, primarily for use as input excitation for site seismic response or soil-structure interaction analyses. The paper presents a twodimensional (2D) equivalent linear inversion model for bedrock motion in a multi-layered transversely isotropic (TI) half-space. Based on the exact dynamic stiffness matrices of TI soil layer and bedrock half-space, an inversion objective function is established from both horizontal and vertical surface acceleration records, and the optimization method is adopted to update the control parameters for the inversion process. Moreover, an equivalent linear method is used to account for the TI soil nonlinearity, thus realizing the nonlinear inversion for bedrock motion and incident angle. The inversion procedure is verified by using a single-layered TI soil profile model with three different materials. The numerical results demonstrate that the bedrock motion and the incident angle in the TI medium can be accurately inversed according to the surface motions and the TI site characteristics, indicating that the inversion method can be used for reliable engineering applications in the TI medium.