Enhancing C2 and C3 coherency resolutions through optimizing semblance-based functions

Abstract

Apparent dips from 3–D reflectors are calculated by maximizing the semblance–based coherency (C2) by numerical optimization techniques. This maximization was done by means of searching through a tessellation of the apparent dips domain, and by optimization algorithms. We applied the simplex and Levenberg–Marquardt, whose performance was compared with those from the direct search techniques. According to numerical experiments with real data, the simplex algorithm enables not just important computing time savings, but provides the highest values from the objective function under all circumstances. This result implies that simplex achieves the maximization process more efficiently, while the other analyzed techniques converge towards the solution region but fail attaining the maxima. This result translates into a better contrast bettween coherent and non coherent features which implies higher resolution. The Levenberg–Marquardt algorithm provides the lowest values for the coherency. These results also found application to the calculation from normal C3 coherency (eigenstructure). This is achieved by slanting the traces with the apparent dips, previously obtained by optimizing the C2 slanted semblance with the simplex technique. The obtained dip corrected coherency show partially an enhanced resolution.