A GLOBAL OPTIMIZATION ALGORITHM APPLIED TO THE COMMON REFLECTION SURFACE (CRS) PROBLEM

摘要

The Common Reflection Surface (CRS) method is a powerful extension of the classical Common Midpoint (CMP) method in two ways: (a) it considers supergathers of source-receiver pairs, which are arbitrarily located around a reference point and (b) it uses general (multiparametric) hyperbolic moveouts to stack along the supergathers. These characteristics are to be contrasted with the CMP method, which considers gathers of source-receiver pairs symmetrically located around the reference (CMP) point and single-parameter normal moveouts (NMO) for stacking. In the 2D situation envisaged in this paper, the number of CRS parameters is three. Extraction of traveltime parameters in both CMP and CRS are carried out by direct application of coherence measures to the seismic data. As a consequence, more involved procedures are required in the multiparametric CRS situation. The new attributes provide more information that can be used for better imaging, as well as for a better determination of the velocity model as needed, such as in migration. The conventional approach to obtain the three CRS parameters exploits the fact that within particular configurations of the data, say, common midpoint and common source, the number of parameters is reduced to one or two. This allows for a quick estimation of an initial value of the parameters, which can be subsequently refined by the use of a local optimization algorithm. A drawback of this approach is that a local maximum, instead of the desired global one, might arise. Therefore, there is the need to derive a search procedure that directly aims at the global maximum. In this work, we pose the simultaneous estimation of the three CRS parameters as a global optimization problem for which a strategy based on Lissajous curves to scan in the parameter domain is proposed. Because of the well-recognized difficulties that are inherent in the formulation and solution of global optimization problems, we focus our attention on a careful description of the approach we use, as well as on validation through a simple illustrative example. We do not address important practical issues such as efficient computational implementation and comparison to available conventional approaches. The test was successful and encourages us to continue this line of research, including the issues we did not address in the present implementation, with the aim of application to field data.