SIMULATED ANNEALING WAVELET ESTIMATION VIA 4TH-ORDER CUMULANT MATCHING

The fourth-order cumulant matching method has been developed recently for estimating a mixed-phase wavelet from a convolutional process. Mat ching between the trace cumulant and the wavelet moment is done in a m inimum mean-squared error sense under the assumption of a non-Gaussian , stationary, and statistically independent reflectivity series. This leads to a highly nonlinear optimization problem, usually solved by te chniques that require a certain degree of linearization, and that inva riably converge to the minimum closest to the initial model. Alternati vely, we propose a hybrid strategy that makes use of a simulated annea ling algorithm to provide reliability of the numerical solutions by re ducing the risk of being trapped in local minima. Beyond the numerical aspect, the reliability of the derived wavelets depends strongly on t he amount of data available. However, by using a multidimensional tape r to smooth the trace cumulant, we show that the method can be used ev en in a trace-by-trace implementation, which is very important from th e point of view of stationarity and consistency. We demonstrate the vi ability of the method under several reflectivity models. Finally, we i llustrate the hybrid strategy using marine and held real data examples . The consistency of the results is very encouraging because the impro ved cumulant matching strategy we describe can be effectively used wit h a limited amount of data.