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

根据这一奖项，将开发一种新的全波形反演方法，用于利用现有的稀疏地震记录识别计算域截断面上的地震输入运动。这种新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下那样在震中重建地震事件。然后，通过使用重建的地震运动，可以研究地震对包括地下系统(土壤、基础和地下结构)在内的建筑环境的影响。因此，该方法将作为一种工具，在地震事件期间对地震对建成环境的影响进行全面评估。提出的研究将给出新的地震输入识别方法的数学和计算模型，以及显示该方法的准确性、可扩展性和效率的数值结果。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网络基础设施传播。这些材料将帮助有见识的用户轻松跟踪研究并扩展它。参加课程的研究生将在波传播分析和反问题方面获得广泛的知识和经验。此外，实践项目将被用来激励高中生，来自代表性不足的群体，在计划的外联计划`‘波是如何工作的？：观察、感觉和分析波？’‘期间追求STEM职业生涯。到目前为止，还没有强有力的数值方法来识别被吸收波边界截断的固体中复杂的、不连贯的地震输入运动。现有的方法要么局限于简化的反褶积技术，要么局限于能够识别震源参数的大规模震源反演方法(无论所采用的震源模型有多简单或复杂)。然而，与大尺度反演方法相关的许多复杂性、不准确性和不确定性使得它不适用于近地表模拟。这项研究的目的是绕过大规模震源反演的复杂性，以地表附近的地震运动重建为目标。具体地说，这项研究将集中于利用偏微分方程约束最优化方法重建区域归约方法(DRM)边界上的有效地震输入运动。计算区域的半无限范围将用完全匹配层截断，状态方程和伴随波动方程将用有限元方法求解。这种新的地震输入识别方法将是推断土-结构体系地震输入运动最准确、最有效的方法。这种方法可以适应任意的土壤非均质性。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.