Detection of Zones of Abnormal Strains in Structures Using Gaussian Curvature Analysis

Abstract

Whereas some folds, such as those produced by flexural slip, do not theoretically entail strain within the folded surfaces, any surface involving double curvature (such as domes and saddles) cannot form without some stretching or contraction of the bedding. Whether straining of the surfaces is required during folding depends on the three-dimensional fold shape and, in particular, on the Gaussian curvature at points on the folded surface. Using this as a basis, I present a method for detecting zones of anomalously high strain in oil-field structures from Gaussian curvature analysis (GCA) of natural structures. The new method of GCA is suitable for analyzing surfaces that have been mapped seismically. A Gaussian curvature map of the structure is a principal outcome of the a alysis and can be used to predict the density of strain-related subseismic structures, such as small-scale fracturing. The Goose Egg dome, near Casper, Wyoming, is analyzed and provides an example of GCA. In this structure, a relationship is observed between fracture densities and Gaussian curvature.