Structure-Constrained Direction-Orthogonalizing Radial Basis Function Fitting of Scattered Data.

The improvement of parameter estimation accuracy depends on the increase of information. The purpose of structure-constrained scattered data fitting is to build a more accurate field by incorporating structure into a few scattered data. This is important for exploration geophysics because only a few well data can be obtained, while a wide range of subsurface parameters need to be estimated. This article introduces a structure-constrained method named direction-orthogonalizing constraint (DOC), which makes directions parallel to the structure orthogonal to parameter gradients. The structure tensor is utilized to extract directions parallel to the structure from seismic images. Then, a DOC radial basis function (RBF) fitting method is developed. Scattered data are approximated by anisotropic RBFs, and DOC is used to bring in structure. Applications on Marmousi density model, 3-D overthrust model, and 3-D field data demonstrate the efficiency and effectiveness of DOC-RBF fitting.