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

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

• The paper presents MDA GAN, a novel adversarial framework that significantly improves the interpolation and reconstruction of 3D seismic data.
• It integrates a unique 3D generator with triple discriminators and a Feature Splicing Module to maintain anisotropy and continuity across resolutions.
• MDA GAN outperforms traditional methods by achieving superior SSIM and PSNR metrics even when handling up to 95% missing data in complex geological surveys.

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

The paper introduces a novel methodology termed Multi-Dimensional Adversarial GAN (MDA GAN) to enhance the interpolation and reconstruction of seismic data, especially in scenarios where data is extensively missing. This advancement is crucial for seismic data processing, where the retrieval of missing information is often challenged by economic, physical, and geological constraints. Traditional methods struggle with high-ratio random discrete missing data, continuous missing traces, and data obscured by fault-rich or salt body surveys. The MDA GAN framework offers a comprehensive and technically superior solution.

Background and Motivation

The field of seismic data processing often encounters significant challenge due to the inability to acquire complete data sets, particularly when confronted with complex geological formations. The missing data problem is classically handled by two broader categories of methodologies: theory-driven and data-driven methods. The paper critiques traditional approaches such as prediction filter-based methods, wave equation-based interpolation, sparse constraint approaches, and low-order constraint solutions, which are often hindered by impractical assumptions, required parameterizations, and limited applicability to 2D cases.

Data-driven methods leveraging deep learning architectures, notably Autoencoders (AE) and Generative Adversarial Networks (GAN), present a modern and compelling alternative. GAN-based techniques, traditionally limited to 2D implementations, have seen limited study and application in 3D seismic data interpolation.

Methodology

The MDA GAN differs from traditional GAN frameworks by integrating a 3D generator and three discriminators designed to maintain the anisotropy and continuity of seismic data across all three dimensions. Specifically, the generator is architected to handle high and low-resolution data through parallel processing, minimizing information loss while preserving seismic data's structural integrity. This is supplemented by the Feature Splicing Module (FSM), ensuring seamless reproduction of unmissed data portions by dynamically adapting to mask-like features during the training process.

To address the limitations identified with standard reconstruction losses ($L_1$ and $L_2$), the paper discusses the derivation of Tanh cross-entropy (TCE) loss, which offers smoother gradient feedback through the Tanh activation function, promoting precise pixel-level learning and minimizing reconstruction distortion.

Results and Implications

The paper provides extensive qualitative and quantitative comparisons against existing methodologies, notably, a traditional UNet baseline, simplified generator models, and GAN configurations using $L_1$ loss. MDA GAN demonstrates superiority in handling up to 95% random discrete missing data and complex installations of continuous trace loss. The evaluation uses standard metrics such as SSIM and PSNR, highlighting the method’s capacity to maintain high fidelity in seismic data recovery over challenging geological sections rich with faults and salt bodies.

MDA GAN not only enhances interpolation performance but offers a transferable model across multiple seismic datasets without retraining, thereby substantially reducing processing time and computational overhead. This advancement holds significant potential for industry application, enabling more reliable seismic imaging and, by extension, more informed geological decision-making.

Future Prospects

Considering the implications of MDA GAN, the paper sets the stage for further explorations into adaptability and scalability to even more diverse geological conditions and potentially real-time applications. The open-source availability of the model underscores the burgeoning trend towards reproducible research and collaborative development within the AI and seismic communities. Subsequent inquiries might focus on refining the discriminator architectures or integrating additional environmental factors to account for variances in subsurface conditions or survey methodologies. Integrating MDA-based frameworks with other AI advancements in seismic data processing could pivot the industry towards more automated, high-fidelity exploration processes.