A Physics-Based Neural-Network Way to Perform Seismic Full Waveform Inversion

Yuxiao Ren,Senlin Yang,Xinji Xu,Yangkang Chen,Lichao Nie

doi:10.1109/access.2020.2997921

Abstract

Seismic full waveform inversion is a common technique that is used in the investigation of subsurface geology. Its classic implementation involves forward modeling of seismic wavefield based on a certain type of wave equation, which reflects the physics nature of subsurface seismic wavefield propagation. However, obtaining a good inversion result using traditional seismic waveform inversion methods usually comes with a high computational cost. Recently, with the emerging popularity of deep learning techniques in various computer vision tasks, deep neural network (DNN) has demonstrated an impressive ability in dealing with complex nonlinear problems, including seismic velocity inversion. Now, extensive efforts have been made in developing a DNN architecture to tackle the problem of seismic velocity inversion, and promising results have been achieved. However, due to the dependence of a labeled dataset, i.e., the barely accessible true velocity model corresponding to real seismic data, the current supervised deep learning inversion framework may suffer from limitations on generalization. One possible solution to mitigate this issue is to impose the governing physics into this kind of purely data-driven method. Thus, following the procedures of traditional seismic full waveform inversion, we propose a seismic waveform inversion network, namely SWINet, based on wave-equation-based forward modeling network cells. By treating the single-shot observation data and its corresponding shot position as training data pairs, the inverted velocity model can be obtained as the trainable network parameters. Moreover, since the proposed seismic waveform inversion method is performed in a neural-network way, its implementation and inversion effect could benefit from some built-in tools in Pytorch, such as automatic differentiation, Adam optimizer and mini-batch strategy, etc. Numerical examples indicate that the SWINet method may possess great potential in resulting a good velocity inversion effect with relatively fast convergence and lower computation cost.

Highlights

Seismic full waveform inversion plays an important role in the estimation of subsurface properties, such as geology, lithology, rock mass quality, etc., and it has been of significant interest to exploration geophysicists for decades [1]–[5]
After theoretically proving the equivalence of two gradient calculation methods, i.e., the adjoint state method in traditional seismic waveform inversion and the automatic differentiation widely used in deep learning, in a discrete matrix form, we choose the latter due to its guarantee of adjointness and the convenient implementation in Pytorch
Numerical experiments with the Adam optimizer and mini-batch strategy indicate that popular ideas from the deep learning community can be beneficial to seismic full waveform inversion and result in an improvement in the perspective of convergence speed and computation cost

Summary

Introduction

Seismic full waveform inversion plays an important role in the estimation of subsurface properties, such as geology, lithology, rock mass quality, etc., and it has been of significant interest to exploration geophysicists for decades [1]–[5]. The associate editor coordinating the review of this manuscript and approving it for publication was Wei Liu. seismic full waveform inversion (FWI) in its conventional form is to reconstruct the velocity model that is capable of matching the actual recorded data by minimizing the data residual between synthetic data and actual data in a L2 norm [6]–[8]. Seismic full waveform inversion (FWI) in its conventional form is to reconstruct the velocity model that is capable of matching the actual recorded data by minimizing the data residual between synthetic data and actual data in a L2 norm [6]–[8] This inverse problem is usually ill-posed and sensitive to initial model. Due to the large amount of model parameters (usually between 104 in 2D and 1010 in 3D) to invert, the computation cost is another constraining factor that requires consideration in the research and practical application of this method [9]

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Discussion

Conclusion