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MDA GAN: Adversarial-Learning-based 3-D Seismic Data Interpolation and Reconstruction for Complex Missing

Yimin Dou, Kewen Li, Hongjie Duan, Timing Li, Lin Dong, Zongchao Huang

TL;DR

This work proposes multidimensional adversarial generative adversarial network (MDA GAN), a novel3-D GAN framework that keeps the anisotropy and spatial continuity of the data after 3-D complex missing reconstruction using three discriminators and achieves better performance than other methods in both simple and complex cases.

Abstract

The interpolation and reconstruction of missing traces is a crucial step in seismic data processing, moreover it is also a highly ill-posed problem, especially for complex cases such as high-ratio random discrete missing, continuous missing and missing in fault-rich or salt body surveys. These complex cases are rarely mentioned in current works. To cope with complex missing cases, we propose Multi-Dimensional Adversarial GAN (MDA GAN), a novel 3-D GAN framework. It keeps anisotropy and spatial continuity of the data after 3D complex missing reconstruction using three discriminators. The feature stitching module is designed and embedded in the generator to retain more information of the input data. The Tanh cross entropy (TCE) loss is derived, which provides the generator with the optimal reconstruction gradient to make the generated data smoother and continuous. We experimentally verified the effectiveness of the individual components of the study and then tested the method on multiple publicly available data. The method achieves reasonable reconstructions for up to 95% of random discrete missing and 100 traces of continuous missing. In fault and salt body enriched surveys, MDA GAN still yields promising results for complex cases. Experimentally it has been demonstrated that our method achieves better performance than other methods in both simple and complex cases.https://github.com/douyimin/MDA_GAN

MDA GAN: Adversarial-Learning-based 3-D Seismic Data Interpolation and Reconstruction for Complex Missing

TL;DR

This work proposes multidimensional adversarial generative adversarial network (MDA GAN), a novel3-D GAN framework that keeps the anisotropy and spatial continuity of the data after 3-D complex missing reconstruction using three discriminators and achieves better performance than other methods in both simple and complex cases.

Abstract

The interpolation and reconstruction of missing traces is a crucial step in seismic data processing, moreover it is also a highly ill-posed problem, especially for complex cases such as high-ratio random discrete missing, continuous missing and missing in fault-rich or salt body surveys. These complex cases are rarely mentioned in current works. To cope with complex missing cases, we propose Multi-Dimensional Adversarial GAN (MDA GAN), a novel 3-D GAN framework. It keeps anisotropy and spatial continuity of the data after 3D complex missing reconstruction using three discriminators. The feature stitching module is designed and embedded in the generator to retain more information of the input data. The Tanh cross entropy (TCE) loss is derived, which provides the generator with the optimal reconstruction gradient to make the generated data smoother and continuous. We experimentally verified the effectiveness of the individual components of the study and then tested the method on multiple publicly available data. The method achieves reasonable reconstructions for up to 95% of random discrete missing and 100 traces of continuous missing. In fault and salt body enriched surveys, MDA GAN still yields promising results for complex cases. Experimentally it has been demonstrated that our method achieves better performance than other methods in both simple and complex cases.https://github.com/douyimin/MDA_GAN
Paper Structure (27 sections, 20 equations, 15 figures, 6 tables)

This paper contains 27 sections, 20 equations, 15 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Approach
  3. Baseline Framework
  4. Generator
  5. Backbone Network
  6. Feature Splicing Module
  7. Discriminator
  8. Tanh Cross Entropy Loss
  9. Training
  10. Experiments
  11. Experimental Grouping
  12. Dataset
  13. Evaluation Metrics
  14. PNSR
  15. SSIM
  16. ...and 12 more sections

Figures (15)

  • Figure 1: In (a), the framework consists of one 3-D generator, one 3-D discriminator and two 2-D discriminators. For training, the input to the 3D network is data of size $128\times 128\times 128$, and the batch size is $b$. To conserve the RAM, the 2D discriminator randomly draws $8$ slices of $128 \times 128$ in the 3D data along the corresponding direction as input, and the batch size is $8\times b$. While for inference, the input to the generator can be any size as allowed by the hardware. (b) is the detailed structure of the generator in the framework, and the discriminator follows the standard encoder structure.The CONV block consists of a $3\times3$ convolution, a normalization layer and a LeakyReLU activation function, Resblock was proposed by He et al he2016deep.
  • Figure 2: The FSM workflow. The FSM selects the spatial response of the splicing by obtaining the high-dimensional mapping of $\mathcal{F}^\text{branch}$ to automate the splicing process.
  • Figure 3: The figure is shown as 2-D slices of $128^2$ in 3-D volumes of $128^3$, displaying the missing of the five modes. The FSM generates mask-like heatmaps without any mask supervision information.
  • Figure 4: Trend plot of $\partial\mathcal{L}_{L_1}/\partial\hat{x}_t$ with $\hat{y}_t$ for $L_1$ loss. This figure is from equation (\ref{['3']}).
  • Figure 5: Trend plot of $\partial\mathcal{L}_{L_2}/\partial\hat{x}_t$ with $\hat{y}_t$ for $L_2$ loss. This figure is from equation (\ref{['5']}).
  • ...and 10 more figures