Fitting stratum interface through regularized thin-plate spline function

The mechanical mechanism of formation of stratum interface geometry is very similar to that of thin-plate spline widely used mathematically, both follow the mechanical mechanism of bending deformation of stressed plate. This paper introduced the common methods of surface fitting and their deficiencies of fitting the sparse and discrete original sampling points, then a thin-plate spline function was proposed to construct stratum interface. First of all, the basic principle of the thin-plate spline was presented briefly. In some cases, fitting surface overshoots due to original sampling points are distributed unevenly in the study area and at the same time the original data are also noisy, a regularized thin-plate spline function was proposed to solve two problems. Taking the horizontal drilling data in an shale gas field for example, in order to construct stratum interface, the equilateral triangle mesh with optimal geometry was used to subdivide stratum interface and the value of mesh vertexes was fitted by the regularized thin-plate function. At last, the value of the regularization parameter was adjusted to make the visualization and precision of the fitting stratum interface meet the requirements.