Abstract

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).

Abstract

Shock tracking, as an alternative method to shock capturing, aims to generate a mesh such that element faces align with shock surfaces and other non-smooth features to perfectly represent them with the inter-element jumps in the solution basis. These methods have been shown to enable high- order approximation of high-speed flows and do not require extensive refinement in non-smooth regions because, once the non-smooth features are tracked by the mesh, the solution basis approximates the remaining smooth features. In previous work, we introduced an implicit shock tracking framework that re-casts the geometrically complex problem of generating a mesh that conforms to all discontinuity surfaces as a PDE-constrained optimization problem. In this talk, we present a number of extensions to the implicit shock tracking method aimed at improving robustness for complex problems.