Passive seismic inversion of SH wave input motions in a truncated domain
Passive seismic inversion of SH wave input motions in a truncated domain
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截断域内 SH 波输入运动的被动地震反演
DOI：
10.1016/j.soildyn.2022.107263
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发表时间：
2022
影响因子：
4
通讯作者：
Jeong, Chanseok
中科院分区：
文献类型：
--
作者：
Guidio, Bruno;Jeremić, Boris;Guidio, Leandro;Jeong, Chanseok
本文介绍了一种新的反演方法，利用偏微分方程约束优化方法，在被吸波边界条件截断的区域重构复杂非相干SH入射波场。在数值算例中，WABC处的动力牵引模拟了地震入射波场。估计的牵引力在空间和时间上离散化，离散化后的值利用域顶面的传感器和垂直阵列稀疏的地震运动数据进行重建。在数学建模和数值实现中采用离散再优化（DTO）方法，并采用有限元法求解状态和伴随问题。数值计算结果表明，在垂直阵列上安装传感器和在顶部安装传感器都可以重建入射斜平面波。如果没有垂直阵，通过垂直阵的倾斜波的特定部分的反演精度会下降。无论入射波的主导频率、时间信号的复杂性以及它们在均匀或分层背景域中的角度如何，垂直阵列都能观察到这种有效性。其次，优化器在识别低频牵引力（例如，实际地震信号）时，会经历较轻的解多重性。第三，必须使用足够多的传感器来提高算法的反演性能。当入射波的波长减小时，每单位长度所需的传感器数量增加。第四，由于有限元解波器固有的低通滤波，高主导频率重构牵引反演误差的大值不一定转化为计算域中相应重构波响应的相同数量级的误差。第五，我们提出的反演算法的精度不受背景域材料复杂性的影响。最后，当测量数据中加入较大水平的噪声时，重构牵引力的误差和相应的波响应误差都增大，但比例不同。通过将所提出的方法扩展到现实的3D环境中，该算法可以指出地震事件期间建筑环境和感兴趣区域的土壤中出现大振幅应力波（即弱点）的位置。
This paper introduces a new inversion method for the reconstruction of complex, incoherent SH incident wavefield in a domain that is truncated by a wave-absorbing boundary condition (WABC), using a partial differential equation (PDE)-constrained optimization method. In numerical examples, dynamic traction at the WABC mimics seismic incident wavefield. Estimated traction is discretized over space and time, and the discretized values are reconstructed by using seismic motion data that are sparsely made by sensors on the top surface of a domain and a vertical array. The discretize-then-optimize (DTO) approach is used in the mathematical modeling and numerical implementation, and the finite element method (FEM) is applied to solve state and adjoint problems. The numerical results show that incident, inclined plane waves can be reconstructed if sensors are located both on the top surface and at a vertical array. Without the vertical array, the accuracy to invert for the particular part of the inclined waves that pass the vertical array declines. Such effectiveness of the vertical array is observed regardless of the dominant frequencies of incident waves, the complexity of their time signals, and their angles in a homogeneous or layered background domain. Second, the optimizer undergoes less severe solution multiplicity when identifying lower-frequency traction (e.g., realistic earthquake signal). Third, a sufficiently large number of sensors must be employed to improve the algorithm’s inversion performance. The desired number of sensors per unit length increases as the wavelength of the incident waves decreases. Fourth, a large value of the inversion error in the reconstructed traction of a high dominant frequency does not necessarily translate to an error of the same order of magnitude in the corresponding reconstructed wave responses in the computational domain because of the intrinsic low-pass filtering of the FEM wave solver. Fifth, our presented inversion algorithm’s accuracy is not compromised by the material complexity of a background domain. Lastly, the error in the reconstructed traction and the error in the corresponding wave responses grow when the noise of a larger level is added to the measurement data, but not in the same proportion. By extending the presented method into realistic 3D settings, this algorithm can indicate where large amplitudes of stress waves (i.e., weak points) occur in built environments and soils in a domain of interest during seismic events.