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Improving fault surface construction with inversion-based methods

Constructing fault surfaces is a key step for seismic structural interpretation and building structural models. We automatically construct fault surfaces from oriented fault samples scanned from a 3D seismic image. The main challenges of the fault surface construction include the following: Some fault samples are locally missing, the positions and orientations of the fault samples may be noisy, and surfaces may form complicated intersections with each other. We adopt the Poisson equation surface method (PESM) and the point-set surface method (PSSM) to automatically construct complete fault surfaces from fault samples and their corresponding orientations. Our methods can robustly fit the noisy fault samples and reasonably fill holes or missing samples, thus improving fault surface construction. By formulating fault surface construction as an inverse problem, we estimate a scalar function to approximate the fault samples in the least-squares sense. In PESM, we estimate the scalar function by solving a weighted Poisson equation. In PSSM, the scalar function is derived by fitting local algebraic spheres based on moving least-squares approximations. Then, the fault surfaces can be approximated by zero isosurfaces of the resulting scalar function. To handle complicated cases of crossing faults, we first classify the fault samples according to their orientations, and we take each class of samples as input of our inversion-based approaches to independently construct the crossing faults. We determine the ability of our methods in robustly building the complete fault surface using synthetic and real seismic images complicated by noise and complexly intersecting faults.