Seismic Tomography with Random Batch Gradient Reconstruction
Seismic Tomography with Random Batch Gradient Reconstruction
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DOI：
10.1137/21m1452342
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
Yixiao Hu;L. Chai;Zhongyi Huang;Xu Yang
中科院分区：
文献类型：
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作者：
Yixiao Hu;L. Chai;Zhongyi Huang;Xu Yang
地震层析成像解决了高维优化问题，以成像地球的地下结构。在本文中，我们建议使用随机批处理方法来构造梯度用于迭代地震层析成像。具体来说，我们使用冻结高斯近似计算地震波的传播，然后构造随机梯度的随机批处理方法。该方法继承了随机梯度下降法求解高维优化问题的思想。所提出的想法是通用的，因为它不依赖于冻结高斯近似的使用，并且可以用任何其他有效的波传播求解器来代替它，例如，高斯光束法和谱元法。我们证明了在均方意义下的随机批处理方法的收敛性，并显示所提出的方法的数值性能的二维和三维的例子基于波动方程的走时反演和全波形反演，分别。作为一个副产品，我们还证明了收敛的加速全波形反演使用动态小批量和谱元素方法。
Seismic tomography solves high-dimensional optimization problems to image subsurface structures of Earth. In this paper, we propose to use random batch methods to construct the gradient used for iterations in seismic tomography. Specifically, we use the frozen Gaussian approximation to compute seismic wave propagation, and then construct stochastic gradients by random batch methods. The method inherits the spirit of stochastic gradient descent methods for solving high-dimensional optimization problems. The proposed idea is general in the sense that it does not rely on the usage of the frozen Gaussian approximation, and one can replace it with any other efficient wave propagation solvers, e.g., Gaussian beam methods and spectral element methods. We prove the convergence of the random batch method in the mean-square sense, and show the numerical performance of the proposed method by two-dimensional and three-dimensional examples of wave-equation-based travel-time inversion and full-waveform inversion, respectively. As a byproduct, we also prove the convergence of the accelerated full-waveform inversion using dynamic mini-batches and spectral element methods.