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

根据该奖项，将开发一种新的全波形反演方法，用于使用现有的稀疏地震记录识别计算域截断表面上的地震输入运动。这种新的方法将允许工程师重建地震输入运动的空间和时间分布，而不需要像通常情况那样在震源处重建地震同相轴。然后，通过使用重建的地震运动，可以研究地震对建筑环境的影响，包括地下系统（土壤，地基和地下结构）。因此，该方法将作为一种工具，以全面评估地震对建筑环境的影响，在地震事件。拟议的研究将提出新的地震输入识别方法的数学和计算建模，以及数值结果显示的准确性，可扩展性和效率的方法。使用新的地震输入识别方法所需的计算机代码、输入数据和教程将通过DesignSafe Cyberinfrastructure传播。这些材料将帮助知情的用户轻松地跟踪研究并扩展它。参与的研究生将获得波传播分析和逆问题的广泛知识和经验。此外，动手项目将被用来激励高中生，从代表性不足的群体，追求干的职业生涯在计划外展计划``波如何工作？：观察、感受和分析波浪。到目前为止，还没有一个强大的数值方法，可以识别复杂的，非相干的地震输入运动的固体，截断波吸收边界。现有的方法局限于简化的反褶积技术或大规模的震源反演方法，可以识别震源参数（无论采用的震源模型是简单的还是复杂的）。然而，有许多复杂性，不准确性和不确定性与大规模的反演方法，使其不切实际的近地表模拟。本研究的目的是通过针对地表附近的地震运动重建来绕过与大规模震源反演相关的复杂性。具体而言，本研究将集中在重建的有效地震输入运动域缩减方法（DRM）的边界，使用偏微分方程约束的优化方法。计算区域的半无限范围将通过使用完美匹配层来截断，并且状态和伴随波动方程将使用有限元法来求解。新的地震输入识别方法将是最准确和有效的方法推断地震输入运动的土壤结构系统。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.