Discontinuous seismic horizon reconstruction based on local dip transformation

We present a method to reconstruct a seismic horizon with a finite number of discontinuities due to oriented fault throws. Our approach requires the knowledge of the two points delimiting the horizon as well as the discontinuities orientations, locations and jumps. We deal with an accurate and noise robust global optimization technique based on a non-linear partial derivative equation relied on the local dip. The key point is the expression of the local dip in a basis in which the discontinuities are vertical. This basis is obtained by a bijective transformation composed of several transformations applied part-by-part in areas defined by the number and the sequence of the discontinuities. By exploiting a fault attribute, we finally propose an efficient method even when the discontinuities parameters are unknown.