Full-Waveform Inversion of Seismic Input Motions in a Truncated Domain

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Under this award a new full-waveform inversion method will be developed for the identification of the seismic input motion on the truncation surface of a computational domain, using existing sparse seismic records. This new method will allow engineers to reconstruct the spatial and temporal distribution of the seismic input motion, without the need to resort to the reconstruction of the seismic event at the hypocenter, as is typically the case. Then, by using the reconstructed seismic motion, it will be possible to study the effect of an earthquake on the built environment, including subsurface systems (soil, foundations, and underground structures). Therefore, the method will serve as a tool to assess holistically the impact of earthquakes on the built environment during seismic events. The proposed research will present the mathematical and computational modeling of the new seismic-input identification method, as well as numerical results showing the accuracy, scalability, and efficiency of the method. The computer code, input data, and tutorials, necessary for using the new seismic-input identification method, will be disseminated through the DesignSafe Cyberinfrastructure. These materials will help informed users to easily follow the research and extend it. Participating graduate students will gain broad knowledge and experience on wave propagation analyses and inverse problems. Moreover, hands-on projects will be used to motivate high school students, from underrepresented groups, to pursue STEM careers during the planned outreach program ``How do waves work?: watch, feel, and analyze waves??.To date, there has been no robust numerical method that can identify complex, incoherent seismic input motions in a solid, truncated by a wave-absorbing boundary. Existing methods are limited to either simplified deconvolution techniques or large-scale seismic-source inversion approaches that can identify the seismic source parameters (however simple or complicated the adopted seismic source model may be) at the hypocenter. However, there are many complexities, inaccuracies, and uncertainties associated with the large-scale inversion approach that render it impractical for near-surface simulations. It is the aim of this research to bypass the complexities associated with the large-scale seismic source inversion by targeting the seismic-motion reconstruction near the surface. Specifically, this research will focus on the reconstruction of effective seismic input motion at the Domain Reduction Method (DRM) boundary, using a partial differential equation-constrained optimization method. The semi-infinite extent of the computational domain will be truncated by using Perfectly-Matched-Layers, and state and adjoint wave equations will be solved using the finite element method. The new seismic-input identification method will be the most accurate and efficient method for inferring seismic input motions in soil-structure systems. This method can accommodate arbitrary soil heterogeneity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.