An algorithm for Delaunay triangulation and contour generation under the constraints of fault surfaces

Key words:  fault constraint  Delaunay triangulation  α-shape algorithm  contour line  high precision interpolation

Abstract:

Two traditional contour algorithms are commonly used for generating contour maps. The first method involves generating contour lines before removing fault polygons, while the second method removes fault polygons first and then generates contour lines. Both of these approaches overlook the horizon information at the fault, leading to inaccuracies near the fault that don 't meet the requirements of modern oil and gas exploration. In this paper, the intersection of the fault plane and the interpretation horizon is processed meticulously. Initially, the precise control point sequence of the fault plane is obtained by subdividing and densifying the fault data. Then, using Clough-Tocher interpolation, the precise control point sequenceis interpolated to obtain the elevation of the layer point at the fault plane. This method effectively enhances the accuracy of the contour at the fault plane. The study explores Delaunay triangulation constrained by fault plane and designs a fast generation algorithm for smooth contours. A technology module for the automatic generation of horizon contours under the constraint of the fault plane is developed. The results show that this method not only improves the accuracy of contour drawing, but also effectively reduces the complexity of contour search and improves calculation efficiency.