Hypersurface Curvatures of Geological Features

Abstract

Reflector-normal angles and reflector-curvature parameters are the principal geometric attributes used in seismic interpretation for characterizing the orientations and shapes, respectively, of geological reflecting surfaces. Commonly, the input dataset for their computation consists of fine 3D grids of scalar fields representing either the seismic-driven reflectivities (e.g., amplitudes of 3D seismic migrated volumes) or model-driven reflectivities, computed, for example, from the derived elastic impedance parameters. Conventionally, the computation of curvature parameters at each grid point is based on analyzing the local change in the inline/crossline dips, considering the potential existence of a local quadratic reflecting surface in the vicinity of that point. This assumption breaks down for subsurface points in the vicinity of either complex reflecting surfaces (e.g., brittle/rough/tilted synclines/anticlines, ridges/troughs, and saddles) and/or sharp discontinuous geological features (e.g., fault edges/tips, pinch-outs, fracture systems, channels, small geobodies), where the values of the computed curvature become extremely high. While these high values can indicate the existence of non-reflecting objects, they do not deliver their specific geometric characteristics. We present a novel method that better characterizes the shapes of these complex geological features by extending the assumption of local surfaces (2D surfaces in 3D space) into hypersurfaces (3D hypersurfaces in 4D space), with their corresponding principal and effective curvature parameters. We demonstrate the advantages of our method by comparing the conventional dip-based surface curvature parameters with the hypersurface curvature parameters, using a synthetic model/image with different types and shapes of geological features and two seismic images of real data containing complex faults and hidden buried channels.