Efficient spreading strategy for global solution search using a trust-region optimization method: An application to the common-reflection-surface stacking problem

Abstract

Some processes in seismic imaging can be formulated as a coherence-based problem, such as common-reflection-surface (CRS) stacking. The approach consists of obtaining the CRS attributes that provide the best-fitting CRS surface in the multicoverage data. The problem can be described as an optimization problem and is solved by an optimization algorithm. In general, quick convergent optimization algorithms are local solvers. To obtain a global solution, an efficient strategy has been developed to be used combined with a trust-region local optimization method. This strategy can be divided into two features: the sequential parameter search and the spreading solution. The idea is to first find solutions on a coarse output grid by a sequential parameter search. This feature is based on constructing splines to estimate the maxima of the objective function in one dimension. These estimated maxima are the initial approximations to the local solver. The optimization algorithm obtains the parameters by sequentially solving 1D, 2D, and 3D problems. Once the solutions are found on the coarse grid, useful information is propagated in the neighborhood to obtain the solutions on all output grids. Although the idea of spreading a solution seems easy, its implementation is complex. It is essential to consider the properties of the problem as well as the properties of the optimization algorithm. Through some numerical experiments, the results using this strategy are shown. The use of sequential parameter search and spreading solution provides an improvement not only in the parameters but also in computational time.