On the reconstruction of the near-surface seismic motion

Assessing the built environment's seismic risk relies increasingly on numerical simulations of the response of infrastructure components to seismic motion. Since forecasting earthquake-induced motion is difficult, if not impossible, subjecting the infrastructure to seismic motion from past earthquakes remains the most potent way to assess the infrastructure's risk and resilience. However, such simulations require a rupture-to-rafters modeling approach that entails complex inversion procedures and ultra-scale computations. In this work, we discuss a systematic methodology that attempts to reconstruct the earthquake-induced wavefield only within the near-surface deposits, using ground surface recordings of seismic motion. The methodology improves on alternative approaches by bypassing the need for either seismic source inversion or joint seismic-source-and-material-model inversion, relying instead on a priori knowledge of the soil properties for only the near-surface deposits, thus realizing significant computational savings. The methodology takes advantage of a state-of-the-art, near-surface, seismic wave motion simulation framework rooted in the Domain Reduction Method (DRM), which relies on a reduced computational domain containing the near-surface deposits only, including possible topographic features and even accounting for materially-nonlinear response. The reduced domain is surrounded by an artificial boundary - the DRM boundary -, onto which the seismic input is typically prescribed in forward seismic motion simulations. A narrow wave-absorbing buffer exterior to the DRM boundary completes the computational domain. It is the aim of this work to reconstruct the DRM seismic input from ground-surface records using an inversion approach rooted in partial differential equation (PDE)-constrained optimization, without having to appeal to fault rupture inversion or joint inversions. To this end, we use the DRM, enhanced with a Complex-Frequency-Shifted (CFS) Perfectly-Matched-Layer (PML), to address the forward wave simulation, and an adjoint approach to address the inversion of the DRM seismic input. Our numerical experiments demonstrate the versatility of the methodology in reconstructing the near surface seismic motion from sparse surface motion records, almost irrespective of the azimuthal coherency of the incoming motion.