Inversion of an Effective Seismic Force at a Domain Reduction Method (DRM) Boundary and Reconstruction of Wave Responses inside the DRM Boundary

Resumo

A new inverse modeling is presented for reconstructing an SH wave input motion (i.e., its corresponding
effective seismic force vector) in a 2D domain that is truncated by a wave-absorbing boundary condition (WABC).
The domain reduction method (DRM) is utilized to model seismic input motions coming from the outside domain
of the WABC. The partial differential equation (PDE)-constrained optimization method aims at reconstructing
a targeted effective seismic force vector, corresponding to targeted incident wavefields, at the DRM boundary.
The presented method includes the discretize-then-optimize (DTO) approach, the finite element method (FEM),
which is used for solving state and adjoint problems, and the conjugate-gradient scheme, determining the desired
search path throughout a minimization process. The numerical results show that an effective force vector at a
DRM boundary is accurately reconstructed when a regularization, aimed at suppressing wave energy in an exterior

domain outside a DRM boundary, is utilized in conjunction with a typical misfit functional. By using such a regu-
larization term, the presented algorithm can minimize the kinetic energy associated with scattered wave responses

outside the DRM boundary and, eventually, improve the inversion performance. It is also shown that our inverse
modeling can accurately reconstruct the wave responses within a domain inside the DRM boundary.