Abstract
Maps of the three-dimensional geometry of geologic surfaces show that structural curvature commonly varies with scale of observation: This fact can be viewed as superposition of structures at different wavelengths. Rock properties such as fracture density and orientation reflect the contribution of superimposed structures. For this reason, characterization of geologic surfaces is fundamentally different from purely geometrical characterization, for which local description of surface properties is sufficient. We show that measured curvature decays according to a power law with increasing size of measurement window, so short-wavelength curvatures do not obscure long-wavelength curvatures in the same data set. This property can be taken advantage of in a simple technique for automatically mapping multiwavelength curvatures. At each point on a surface, curvature is measured at a range of wavelengths. This curvature spectrum can be analyzed in map view or collapsed into a single value at each point in space. The results indicate that complex geologic surfaces can be characterized without any prior knowledge of structural wavelengths and orientation. The method should prove useful in applications requiring knowledge of spatial variation in rock properties from remotely sensed data, such as exploration for hydrocarbon reservoirs or nuclear waste repositories.
