A theory-guided deep-learning formulation and optimization of seismic waveform inversion

Sun, Jian; Niu, Zhan; Innanen, Kristopher A.; Li, Junxiao; Trad, Daniel

doi:10.1190/geo2019-0138.1

Cited by 172 publications

(49 citation statements)

References 56 publications

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“…A time-domain acoustic wave ISP is solved in [33], which develops a theory-designed RNN. It finds that training such a network and updating its weights amount to a solution of the ISP and the process is equivalent to a gradient-based full-waveform inversion.…”

Section: Other Approachesmentioning

confidence: 99%

See 1 more Smart Citation

A Review of Deep Learning Approaches for Inverse Scattering Problems (Invited Review)

Chen¹,

Wei²,

Li³

et al. 2020

PIER

216

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In recent years, deep learning (DL) is becoming an increasingly important tool for solving inverse scattering problems (ISPs). This paper reviews methods, promises, and pitfalls of deep learning as applied to ISPs. More specifically, we review several state-of-the-art methods of solving ISPs with DL, and we also offer some insights on how to combine neural networks with the knowledge of the underlying physics as well as traditional non-learning techniques. Despite the successes, DL also has its own challenges and limitations in solving ISPs. These fundamental questions are discussed, and possible suitable future research directions and countermeasures will be suggested.

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Section: Other Approachesmentioning

confidence: 99%

“…A summary of papers that solve inverse scattering problems using deep learning schemes. Note that [32] and [33] that belong to "other approaches" are not listed in the figure.…”

Section: Other Approachesmentioning

confidence: 99%

A Review of Deep Learning Approaches for Inverse Scattering Problems (Invited Review)

Chen¹,

Wei²,

Li³

et al. 2020

PIER

216

View full text Add to dashboard Cite

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“…As for the network hyper-parameters, we follow the discussion in [34] and set the learning rate lr = 40 for the Adam optimizer with the number of epochs equal to 50. Note that there is no activation function or normalization applied in the SWINet, a larger learning rate will benefit the convergence of the Adam optimizer.…”

Section: A Dataset and Training Parameter Setupmentioning

confidence: 99%

“…On the other hand, the promising inversion performance of traditional FWI in synthetic and actual complex models, indicates the great power of considering the governing wave equation in seismic inversion. Thus, another possible solution to generalize the seismic deep learning inversion to large complex models is to incorporate the relevant physical nature rules into the purely data-driven methods and form a physicsbased deep learning concept [33], [34]. In this concept, a seismic forward modeling operator needs to be designed and imposed into the deep learning inversion architecture, which will relate the basic generation rules and features of seismic observation data with the learning process, and as a result, may lead the optimization of network parameters to a more stable and reasonable direction.…”

Section: Introductionmentioning

confidence: 99%

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

Ren

Yang

et al. 2020

IEEE Access

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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 minibatch 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. INDEX TERMS acoustic wavefield modeling, deep learning inversion, seismic waveform inversion

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“…Therefore the complexity of NML in both theoretical and computational aspects will increase when the latent space dimension increases. Hughes et al (2019) and Sun et al (2020) showed that the wave-equation modeling is equivalent to the recurrent neural network (RNN) and the FWI gradient can be automatically calculated by the AD. Because CAE training also relies on the AD, therefore the AD is a perfect tool to numerically connect a CAE architecture to the wave-equation inversion.…”

Section: Hybrid Machine Learning Inversionmentioning

confidence: 99%

Seismic inversion by Newtonian machine learning

Chen

Schuster

2020

GEOPHYSICS

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We present a wave-equation inversion method that inverts skeletonized seismic data for the subsurface velocity model. The skeletonized representation of the seismic traces consists of the low-rank latent-space variables predicted by a well-trained autoencoder neural network. The input to the autoencoder consists of seismic traces, and the implicit function theorem is used to determine the Fréchet derivative, i.e., the perturbation of the skeletonized data with respect to the velocity perturbation. The gradient is computed by migrating the shifted observed traces weighted by the skeletonized data residual, and the final velocity model is the one that best predicts the observed latent-space parameters. We denote this as inversion by Newtonian machine learning (NML) because it inverts for the model parameters by combining the forward and backward modeling of Newtonian wave propagation with the dimensional reduction capability of machine learning. Empirical results suggest that inversion by NML can sometimes mitigate the cycle-skipping problem of conventional full-waveform inversion (FWI). Numerical tests with synthetic and field data demonstrate the success of NML inversion in recovering a low-wavenumber approximation to the subsurface velocity model. The advantage of this method over other skeletonized data methods is that no manual picking of important features is required because the skeletal data are automatically selected by the autoencoder. The disadvantage is that the inverted velocity model has less resolution compared with the FWI result, but it can serve as a good initial model for FWI. Our most significant contribution is that we provide a general framework for using wave-equation inversion to invert skeletal data generated by any type of neural network. In other words, we have combined the deterministic modeling of Newtonian physics and the pattern matching capabilities of machine learning to invert seismic data by NML.

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A theory-guided deep-learning formulation and optimization of seismic waveform inversion

Cited by 172 publications

References 56 publications

A Review of Deep Learning Approaches for Inverse Scattering Problems (Invited Review)

A Review of Deep Learning Approaches for Inverse Scattering Problems (Invited Review)

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

Seismic inversion by Newtonian machine learning

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