There is a need to estimate complex seismic input motions in a near-surface domain, without resorting to the hypocenter, from restricted seismic measurement data. Thus, engineers can replicate responses within structures and soils after an earthquake occurrence by using the estimated seismic inputs and evaluate the impact of an earthquake on the built environment. To date, there has been no robust numerical method that can identify complex seismic input motions in a solid, truncated by a wave-absorbing boundary condition. Existing methods are limited to large-scale seismic-source inversion approaches and deconvolution. To fill this gap, a new inversion modeling method is presented for reconstructing complex, incoherent SH wave input motions in a two-dimensional (2D) domain that is truncated by a wave-absorbing boundary condition (WABC), using a partial differential equation (PDE)constrained optimization method. In a set of numerical examples, targeted, dynamic traction at the WABC mimics seismic incident wavefield. The discretize-then-optimize (DTO) approach is used in the mathematical modeling and numerical implementation, and the finite element method (FEM) is applied to solve state and adjoint problems. The numerical results indicate that the presented inversion algorithm can reconstruct incident, inclined plane waves. Second, the accuracy of our inversion solver is not compromised by the material complexity of a background domain. Lastly, the minimizer suffers less from solution multiplicity when it identifies lower frequency traction (e.g., a realistic seismic signal).
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