A PRECISE METHOD FOR DETERMINING CONTOURED SURFACES

Abstract

Although the petroleum geologist is concerned with analysing three-dimensional data, he relies entirely on two-dimensional portrayals - cross-sections and particularly contour maps of all types. With the advent of digital computers, machine contouring has become increasingly common, but little attention has been directed to the limitations of the various algorithms that can be employed to generate contour maps from a set of control points. For example, it is not widely appreciated that contouring procedures which faithfully honour the value of original control points produce poor predictions at locations where no control is available. Contouring a published set of topographic data shows how this and other limitations lead to approximations and errors in machine-generated contours.A new method based on triangulation interpolation using Delaunay tessellations (deltri analysis) is superior to existing methods. Not only does the method give the most accurate and objective measurement and display of the contoured surface, but it is also computationally efficient. Rapid calculation of volume of closure over contoured structures is possible. The method also allows estimation of the adequacy of the data on which the contouring is based by introducing a measure of 'roughness' of the surface. This is achieved by analysing the directions of normals to triangles surrounding each control point.