Dip Extraction from Three–dimensional Depth Images–Algorithms and Applications

The estimation of the slope of locally planar events in a seismic section has become a popular tool with many applications. In the time domain, locally planar events are estimated by considering them as plane wave solutions which satisfy the wave equation, and the time variable plays a special role. By contrast, in depth image domain there is no time variable and, strictly speaking, no wave equation or plane wave, but instead a reflectivity image which may be locally planar. The reflectivity image in depth depends on three spatial coordinates which are fully interchangeable, and dips may cover the full 360 degree angle range, including vertical and overhanging dips. Dip extraction on three-dimensional images can be conveniently carried out by a least-squares fitting of derivatives in the neighborhood of each image grid point. This allows recovery of dips of any orientation, including vertical ones. Multivariate B-spline representation of the image enables efficient inter- and extrapolation at any location together with efficient evaluation of the necessary derivatives.