A Method to Estimate Volumetric Curvature Attributes in 3D Seismic Data

Volumetric curvature attributes can provide, for each volume sample, a measure of bends and breaks in seismic reflectors, capturing subtle variations caused by faults and folding that were not obvious in amplitude field. This paper aims to propose a new method to compute volumetric curvature attributes from 3D amplitude data. Seismic horizons can be understood as level surfaces described by some implicit function F. Such implicit function can be viewed as a local surface identifier, in sense that more probable surface samples are closer to some constant value. We propose three seismic attributes in order to describe seismic horizons as level surfaces: Adjusted instantaneous phase, vertical derivative and ridge/valley detector. For each attribute, partial derivatives provide a normal field for seismic horizons in 3D space. Using this normal field and differential geometry, we can obtain curvature measures such Gaussian curvature, mean curvature, and principal normal curvatures.