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Parametric elastic full waveform inversion with convolutional neural network

Guo Keting, Zong Zhaoyun, Yang Jidong, Tan Yuanyuan

Acta Geophysica

2024

Vol. 72, no. 2

673--687

Elastic full waveform inversion (EFWI) is a powerful tool for estimating elastic models by reducing the misfit between multi-component seismic records and simulated data. However, when multiple parameters are updated simultaneously, the gradients of the loss function with respect to these parameters will be coupled together, the effect exacerbate the nonlinear problem. We propose a parametric EFWI method based on convolutional neural networks (CNN-EFWI). The parameters that need to be updated are the weights in the neural network rather than the elastic models. The convolutional kernel in the network can increase spatial correlations of elastic models, which can be regard as a regularization strategy to mitigate local minima issue. Furthermore, the representation also can mitigate the cross-talk between parameters due to the reconstruction of Frechét derivatives by neural networks. Both forward and backward processes are implemented using a time-domain finite-difference solver for elastic wave equation. Numerical examples on overthrust models, fluid saturated models and 2004 BP salt body models demonstrate that CNN-EFWI can partially mitigate the local minima problem and reduce the dependence of inversion on the initial models. Mini-batch configuration is used to speed up the update and achieve fast convergence. In addition, the inversion of noisy data further verifies the robustness of CNN-EFWI.

Elastic full waveform inversion based on equivalent staggered grid FDM and inter-parameter trade-off mitigation

Li Qingyang, Wu Guochen

Acta Geophysica

2022

Vol. 70, no 6

2555--2579

Elastic full waveform inversion (EFWI) has increasingly been applied in seismic exploration as computer performance improves. EFWI significantly improves calculation efficiency, but requires very large computer storage space and suffers interparameter trade-off and local minima problems. Preconditioning the gradients based on elastic wave mode decomposition can effectively mitigate inter-parameter trade-offs, but the decomposition-based scheme may further increase the memory usage, which limits EFWI application. The equivalent staggered grid (ESG) scheme in acoustic medium requires less memory usage and generates results numerically equivalent to those using the standard staggered grid (SSG) scheme. In this paper, we extend the ESG scheme to second-order elastic wave equations in terms of velocity, producing results numerically equivalent to the SSG ones based on first-order velocity–stress wave equations while reducing memory usage by 45% compared with the SSG scheme. We then apply the ESG scheme to EFWI and derive the formula of the preconditioned gradient of the S-wave velocity. Finally, three numerical examples demonstrate that applying the ESG scheme to decomposition-based EFWI can significantly reduce computer memory usage and mitigate the trade-offs between the P- and S-wave velocities.