Fracture Prediction using Gaussian Curvature Analysis

Richard J. Lisle and Julian M. Robinson

Gaussian curvature analysis (GCA) is a technique for identifying those portions of a geological structure that, on the basis of their geometrical attributes, are likely to be more fractured than surrounding regions. As simple paper folding experiments show, a layer which does not stretch or contract can be folded into a huge variety of shapes but these do not include those with double curvature, such as domes or saddles. The occurrence of geometries of the latter type, which have non-zero Gaussian curvature values, implies the presence of folding-related strains which could be expressed as fracturing. The new method involves the computation and display of Gaussian curvature values across a mapped structure, and serves to highlight those parts which are more likely to show a greater intensity of fracturing. Current developments of the GCA method concentrate on the quantification of local strains within a folded layer. A theoretical model of three-dimensional buckling is presented which allows the calculation of strain magnitudes from principal curvature values. Several examples of GCA will be discussed, including applications to structures associated with salt diapirs.

AAPG Search and Discover Article #91019©1996 AAPG Convention and Exhibition 19-22 May 1996, San Diego, California