Seismic inversion by multi-dimensional Newtonian machine learning

Chen, Yuqing; Saygin, Erdinc; Schuster, Gerard T.

doi:10.1190/segam2020-3425975.1

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…Compared with the connective function assumption proposed by Chen and Schuster (2020) and Chen et al. (2020), AD can compute the exact solution of

\frac{\partial z^{p r e d}}{\partial boldv}

and the computation cost remains almost the same regardless of the dimension of the LS. Figure 4a shows the architecture for HML inversion, where a velocity model

boldv

and a source wavelet

boldf

are included in the wave‐equation modeling to generate the predicted data

d^{p r e d}

.…”

Section: Methodsmentioning

confidence: 99%

“…Combined with the implicit function theorem, it is possible to compute the velocity gradient with respect to the LS feature misfit. However, the problem with the connective function assumption is that the computation cost increases dramatically as the latent space dimension increases (Chen et al., 2020). To mitigate this computational problem, instead of using the connective function assumption, we use automatic differentiation (AD) (Rall & Corliss, 1996) to connect the perturbation of the LS features with the velocity perturbation.…”

Section: Introductionmentioning

confidence: 99%

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Seismic Inversion by Hybrid Machine Learning

Chen

Saygin

2021

JGR Solid Earth

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We present a hybrid machine learning (HML) inversion method, which uses the latent space (LS) features of a convolutional autoencoder (CAE) to estimate the subsurface velocity model. The LS features are the effective low‐dimensional representation of the high‐dimensional seismic data. However, no equations exist to describe the relationship between the perturbation of an LS feature and the velocity perturbation. To address this problem, we use automatic differentiation (AD) to connect the two terms. Following this step, we use the wave‐equation inversion to invert the LS features for the subsurface velocity model. The HML misfit function measures the LS feature differences between the observed and predicted seismic data in a low‐dimensional space, which is less affected by the cycle‐skipping problem compared to the waveform mismatch in a high‐dimensional space. A low dimensional LS feature mainly contains the kinematic information of seismic data, while a large dimensional LS feature can also preserve the dynamic information of seismic data. Therefore, the HML inversion can recover the subsurface velocity model in a multiscale approach by inverting the LS features with different dimensions. Based on the different ways of utilizing AD to compute the velocity gradient, we propose full‐ and semi‐automatic approaches to solve this problem. These two approaches are mathematically equivalent; the former is easier to implement, while the latter is computationally more efficient. Numerical tests show that the HML inversion method can effectively recover both the low‐ and high‐wavenumber velocity information by inverting the LS features with different dimensions.

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“…Compared with the connective function assumption proposed by Chen and Schuster (2020) and Chen et al. (2020), AD can compute the exact solution of

\frac{\partial z^{p r e d}}{\partial boldv}

and the computation cost remains almost the same regardless of the dimension of the LS. Figure 4a shows the architecture for HML inversion, where a velocity model

boldv

and a source wavelet

boldf

are included in the wave‐equation modeling to generate the predicted data

d^{p r e d}

.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Seismic Inversion by Hybrid Machine Learning

Chen

Saygin

2021

JGR Solid Earth

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Review of physics-informed machine-learning inversion of geophysical data

Schuster,

Chen,

Feng

2024

GEOPHYSICS

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We review five types of physics-informed machine learning (PIML) algorithms for inversion and modeling of geophysical data. Such algorithms use the combination of a data-driven machine learning (ML) method and the equations of physics to model and/or invert geophysical data. By incorporating the constraints of physics, PIML algorithms can effectively reduce the size of the solution space for machine learning models, enabling them to be trained on smaller datasets. This is especially advantageous in scenarios where data availability may be limited or expensive to obtain.In this review we restrict the {\it physics} to be that from the governing wave equation, either as a constraint that must be satisfied or by using numerical solutions to the wave equation for both modeling and inversion.#xD;This approach ensures that the resulting models adhere to physical principles while leveraging the power of machine learning to analyze and interpret complex geophysical data.#xD;The key challenge with PIML methods is to strike a balance between computational efficiency and predictive accuracy. While PIML algorithms may offer computational advantages over standard numerical methods, their accuracy must justify the trade-off. In cases where PIML models are efficient but somewhat inaccurate, they can still serve valuable purposes, such as providing initial velocity models for more accurate techniques like Full Waveform Inversion (FWI).

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Seismic inversion by multi-dimensional Newtonian machine learning

Chen

Saygin

Schuster

2020

SEG Technical Program Expanded Abstracts 2020

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Newtonian machine learning (NML) inversion has been shown to accurately recover the low-to-intermediate wavenumber information of subsurface velocity models. This method uses the wave-equation inversion kernel to invert the skeletonized data that is automatically learned by an autoencoder. The skeletonized data is a one-dimensional latent-space representation of the seismic trace. However, for a complicated dataset, the decoded waveform could lose some details if the latent space dimension is set to one, which leads to a low-resolution NML tomogram. To mitigate this problem, an autoencoder with a higher dimensional latent space is needed to encode and decode the seismic data. In this paper, we present a waveequation inversion that inverts the multi-dimensional latent variables of an autoencoder for the subsurface velocity model. The multi-variable implicit function theorem is used to determine the perturbation of the multi-dimensional skeletonized data with respect to the velocity perturbations. In this case, each dimension of the latent variable is characterized one gradient and the velocity model is updated by the weighted sum of all these gradients. Numerical results suggest that the multidimensional NML inverted result can achieve a higher resolution in the tomogram compared to the conventional singledimensional NML inversion.

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Seismic inversion by multi-dimensional Newtonian machine learning

Cited by 3 publications

References 18 publications

Seismic Inversion by Hybrid Machine Learning

Seismic Inversion by Hybrid Machine Learning

Review of physics-informed machine-learning inversion of geophysical data

Seismic inversion by multi-dimensional Newtonian machine learning

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