Spectral structure-oriented filtering of seismic data with self-adaptive paths

We have developed an algorithm to perform structure-oriented filtering (SOF) in 3D seismic data by learning the data structure in the frequency domain. The method, called spectral SOF (SSOF), allows us to enhance the signal structures in the [Formula: see text]-[Formula: see text]-[Formula: see text] domain by running a 1D edge-preserving filter along curvilinear self-adaptive trajectories that connect points of similar characteristics. These self-adaptive paths are given by the eigenvectors of the smoothed structure tensor, which are easily computed using closed-form expressions. SSOF relies on a few parameters that are easily tuned and on simple 1D convolutions for tensor calculation and smoothing. It is able to process a 3D data volume with a 2D strategy using basic 1D edge-preserving filters. In contrast to other SOF techniques, such as anisotropic diffusion, anisotropic smoothing, and plane-wave prediction, SSOF does not require any iterative process to reach the denoised result. We determine the performance of SSOF using three public domain field data sets, which are subsets of the well-known Waipuku, Penobscot, and Teapot surveys. We use the Waipuku subset to indicate the signal preservation of the method in good-quality data when mostly background random noise is present. Then, we use the Penobscot subset to illustrate random noise and footprint signature attenuation, as well as to show how faults and fractures are improved. Finally, we analyze the Teapot stacked and depth-migrated subsets to show random and coherent noise removal, leading to an improvement of the volume structural details and overall lateral continuity. The results indicate that random noise, footprints, and other artifacts can be successfully suppressed, enhancing the delineation of geologic structures and seismic horizons and preserving the original signal bandwidth.