Restricted optimization: a clue to a fast and accurate implementation of the Common Reflection Surface Stack method

Abstract

For a fixed, 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 multi-coverage 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 different 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 (SPG) optimization algorithm for the final parameter estimation. Application of the method on a synthetic example shows an excellent performance of the algorithm both in accuracy and efficiency. 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.