Restricted optimization : a clue to a fast and accurateimplementation of the Common Re ection Surface

For a xed, central ray in an isotropic elastic or acoustic media, traveltime moveouts of rays in its vicinity can be described in terms of a certain number of parameters that refer to the central ray only. The determination of these parameters out of multicoverage data leads to very powerful algorithms that can be used for several imaging and inversion processes. Assuming two-dimensional propagation, the traveltime expressions depend on three parameters directly related to the geometry of the unknown model in the vicinity of the central ray. We present a new method to extract these parameters out of coherency analysis applied directly to the data. It uses (a) fast one-parameter searches on di erent sections extracted from the multi-coverage data to derive initial values of the sections parameters, and (b) the application of a recently introduced Spectral Projected Gradient optimization algorithm for the nal parameter estimation. Application of the method on a synthetic example shows an excellent performance of the algorithm both in accuracy and e ciency. The results obtained so far indicate that the algorithm may be a feasible option to solve the corresponding, harder, full three-dimensional problem, in which eight parameters, instead of three, are required.