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

根据该合同，将开发一种新的全波形反演方法，用于识别计算域截断面上的地震输入运动，使用现有的稀疏地震记录。这种新方法将使工程师能够重建地震输入运动的时空分布，而不需要像通常的情况那样，在震源处重建地震事件。然后，通过使用重建的地震运动，将有可能研究地震对建筑环境的影响，包括地下系统（土壤，基础和地下结构）。因此，该方法将作为一种工具，在地震事件中全面评估地震对建筑环境的影响。提出的研究将展示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，实践项目将用于激励来自弱势群体的高中生在计划的推广项目“波浪如何工作？”中追求STEM职业。观察、感受和分析波浪。迄今为止，还没有一种可靠的数值方法可以识别由吸波边界截断的固体中复杂的非相干地震输入运动。现有的方法仅限于简化的反褶积技术或大规模震源反演方法，这些方法可以识别震源参数（无论所采用的震源模型是简单还是复杂）。然而，与大规模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合近地表模拟。本研究的目的是绕过大尺度震源反演的复杂性，以近地表的地震运动重建为目标。具体而言，本研究将侧重于使用偏微分方程约束优化方法在域约简法（DRM）边界处重建有效地震输入运动。用完全匹配层截断计算域的半无限范围，用有限元法求解状态方程和伴随波方程。这种新的地震输入识别方法将是推断土-结构体系中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异质性。该奖项反映了美国国家科学基金会的法定使命，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.