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Machine learning based prediction of regularization parameters for seismic inverse problems

Liu Shihuan, Zhang Jiashu

Acta Geophysica

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2021

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Vol. 69, no. 3

809--820

EN

Regularization parameter selection (RPS) is one of the most important tasks in solving inverse problems. The most common approaches seek the optimal regularization parameter (ORP) from a sequence of candidate values. However, these methods are often time-consuming because they need to conduct the estimation process on all candidate values, and they are always restricted to solve certain problem types. In this paper, we propose a novel machine learning-based prediction framework (MLBP) for the RPS problem. The MLBP frst generates a large number of synthetic data by varying the inputs with diferent noise conditions. Then, MLBP extracts some pre-defned features to represent the input data and computes the ORP of each synthetic example by using true models. The pairs of ORP and extracted features construct a training set, which is used to train a regression model to describe the relationship between the ORP and input data. Therefore, for newly practical inverse problems, MLBP can predict their ORPs directly with the pre-trained regression model, avoiding wasting computational resources on improper regularization parameters. The numerical results also show that MLBP requires signifcantly less computing time and provides more accurate solutions for diferent tasks than traditional methods. Especially, even though the MLBP trains the regression model on synthetic data, it can also achieve satisfying performance when directly applied to feld data.

2

Adaptive individual weight-gain AVO inversion with smooth nonconvex regularization

Du Siyuan, Zhang Jiashu, Zhang Sheng, Hu Guangmin

Acta Geophysica

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2021

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Vol. 69, no. 4

1199--1213

EN

Amplitude variation with ofset (AVO) inversion is a widely used approach to obtain reliable estimates of elastic parameter in the felds of seismic exploration. However, the AVO inversion is an ill-posed problem because of the band-limited characteristic of seismic data. The regularization constraint plays an important role in improving inversion resolution. Total variation (TV) class regularization based on L1 norm has been introduced in seismic inversion. But, these methods may underestimate the high-amplitude components and obtain low-resolution results. To tackle these issues, we propose to combine a smooth nonconvex regularization approach with adaptive individual weight-gain. Compared with the L1 norm regularizers, the proposed smoothed nonconvex sparsity-inducing regularizers can lead to more accurate estimation for high-amplitude components. Diferent from previous regularization methods, the proposed approach also assigns diferent weight regularization parameters for diferent strata, which we call adaptive individual weight-gain strategy. To ensure sufcient minimization of the constructed objective function, a spectral Polak–Ribière–Polyak conjugate gradient method with line search step size is used. Further, we prove that the proposed algorithm converges to a stationary point. The synthetic data tests illustrate that our approach has improved performance compared with the conventional TV class regularization methods. Field data example further verifes the higher resolution of the proposed approach.

3

A robust data driven AVO inversion with logarithm absolute error loss function

Du Siyuan, Zhang Jiashu, Hu Guangmin

Acta Geophysica

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2020

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Vol. 68, no. 2

445--458

EN

Amplitude variation with ofset (AVO) inversion is a widely used approach to obtain reliable estimates of elastic parameter. Tikhonov and total variation regularization are commonly used methods to address ill-posed problem of AVO inversion. However, these model-driven methods are only for special geological structure such as smoothness or blockiness. In this letter, a robust data-driven-based regularization method with logarithm absolute error loss function (DDI-Log) for AVO inversion is proposed. In DDI-Log, the information of well-log data and the complex geology are considered in a sparse representation framework. In pre-stack seismic data, outlier noise can negatively infuence inversion results. Thus, diferent from the previous data-driven inversion based on L2 norm loss function, we extend the logarithm absolute error function as the loss function. In the iteration, a new spectral PRP conjugate gradient method is used to solve the large-scale optimization problem. The synthetic data and feld data tests illustrate that the proposed approach is robust against outlier noise and that the resolution and accuracy of the solutions are improved.