Métodos de otimização global aplicados na busca dos parâmetros SRC

Abstract

The Common Reflection Surface Stack (CRS) method provides the simulation of zerooffset (ZO) sections by means of the summing seismic events of the multicoverage data contained in the stacking surface. This method does not depend on the velocity macro-model of medium; it only requires a priori knowledge of the near-surface velocity. The simulation of ZO sections for this stacking method uses a hyperbolic second-order traveltime approximation of the paraxial rays to define the CRS stacking surface or CRS stack operator. For 2D media, this operator depends on three kinematic attributes of two hypothetical waves (N I P and N waves), observed in the point of emergency of the central ray with normal incidence, namely, the angle of emergency of the central ZO ray (β0), the radius of curvature of the Normal Incidence Point Wave (RN I P ) and the radius of curvature of the Normal Wave (RN ). Therefore, the optimization problem in the CRS method consists in the determination, from the seismic data, of the three optimal parameters (β0, RN I P , RN ) associated to each sample point of ZO section to be simulated. The simultaneous determination of these parameters can be made by means of multidimensional global search process (or global optimization), using as objective function some coherence criterion. The optimization problem in CRS method is very important for the good performance with respect to quality of the results and mainly to computational cost, compared with the methods traditionally used in the seismic industry. There are several search strategies to determine these parameters, based on systematic searches and using optimization algorithms, where only one parameter at each time can be estimated, or the two or three parameters simultaneously. Taking in to account the search strategy by means of the application of global optimization, these three parameters can be estimated through of procedures: in the first case the three parameters can be simultaneously estimated and in second case initially two parameters can be determined simultaneously (β0, RN I P ), and subsequently the third parameter (RN ), using the values of the two parameters already known. In this work it is presented the application and comparison of four algorithms of global optimization to find the CRS optimal parameters: Simulated Annealing (SA), Very Fast Simulated Annealing (VFSA), Differential Evolution (DE) and Controlled Random Search – 2 (CRS2). As importants results of the application of each optimization method, as well as between the methods regarding the effectiveness, efficiency and reliability to determine the best CRS parameters are presented. Subsequently, applying the global search strategies for the determination of these parameters, by means of the optimization method VFSA that presented the best performance, the CRS stacking was applied to the Marmousi dataset, one stacking using two parameters (β0, RN I P ), estimated by global search, and another CRS stacking using the three parameters (β0, RN I P , RN ), also estimated by global search.