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 two-dimensional (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.

中文翻译：

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层状横观各向同性半空间基岩运动二维等效线性反演模型


反演是根据表面运动评估基岩输入运动的过程，主要用作现场地震响应或土壤-结构相互作用分析的输入激励。本文提出了多层横观各向同性 (TI) 半空间中基岩运动的二维 (2D) 等效线性反演模型。基于TI土层和基岩半空间的精确动刚度矩阵，根据水平和垂直地表加速度记录建立反演目标函数，并采用优化方法更新反演过程的控制参数。此外，采用等效线性方法考虑TI土壤非线性，从而实现基岩运动和入射角的非线性反演。通过使用具有三种不同材料的单层 TI 土壤剖面模型来验证反演过程。数值结果表明，根据地表运动和TI场地特征，可以准确反演TI介质中的基岩运动和入射角，表明该反演方法可以在TI介质中进行可靠的工程应用。