Seismic input motion identification in a heterogeneous halfspace

This paper presents a new time domain method for reconstructing unknown incident seismic input waves entering into a truncated heterogeneous soil domain from a soil surface response. The problem is cast into a partial differential equation (PDE)-constrained optimization problem where a misfit between a measured response at a sensor on the ground surface induced by a target signal and a computed wave solution induced by an estimate signal is minimized. Using this method allows for fast and accurate evaluation of the sensitivity of a misfit functional (i.e., gradient or Fréchet derivative) with respect to control parameters. Both forward and adjoint problems are solved by using the finite-element method (FEM). The numerical results prove that the presented method can identify a targeted incident seismic input signal into a truncated soil domain without providing the numerical optimizer with any hint about the target. In presence of noise in measurement, this inversion process recovers a target signal more accurately than the deconvolution does.