Optimal Transport-Based Gradient Operators for Seismic Imaging: A Robust Approach for Subtle Structural Detection

Abstract In the complex landscape of seismic data, fault detection is the key to unlocking the secrets of geological structures and pinpointing oil and gas reservoirs, but traditional gradient operators like finite difference and Sobel filters often fall short, as they are highly susceptible to noise and struggle to reveal subtle structural features. Our innovative method, grounded in optimal transport theory, revolutionizes fault detection by leveraging Wasserstein distances to compute gradients in seismic imaging, envisioning seismic images as 2D mass distributions and calculating gradients based on the minimal transport cost required to align neighboring patches, making it inherently robust against noise and expertly identifying small structural changes, such as faults, fractures, and stratigraphic boundaries. With the incorporation of entropic regularization ensuring numerical stability and GPU acceleration empowering efficient processing of large datasets, our method outperforms traditional approaches in both synthetic and real datasets, demonstrating its superiority in fault detection and offering a reliable, practical solution for large-scale seismic imaging applications, ultimately unveiling hidden faults and providing a clearer understanding of the geological landscape.