Optimization of common reflection surface (CRS) attributes based on hybrid method

The simultaneous estimation of Common Reflection Surface stack attributes considers a solution of a global non-linear minimization problem. We propose a hybrid method to solve this unconstrained optimization method. The approach comprises a conjugate direction method with its well known convergence properties and an iterative line search considering the strong Wolfe-Powell rule for the control of the step length. The use of the conjugate direction method leads to a highly efficient iterative search method to speed up the convergence rate while using Hessian is avoided. The iterative line search considering the strong Wolfe-Powell rule for the control of the step length prevents the premature convergence into local minima, without the need of computing the gradient. In the current version of the CRS code the Nelder-Mead optimization method is applied to estimate CRS stack attributes. This technique requires more iterations and is more time consuming than the hybrid method introduced here. Applications show that the method provides very good solutions particularly in the presence of several local minima.