Research On The Application Of Non-linear Optimization Algorithm For Seismic Wavelet Estimation

Accurate seismic wavelet estimation is the base of deconvolution processing, inverse and forward models of seismic wave impedance, and it is significant in seismic exploration fields. Because the higher order statistic retains the phase information of the signal and is able to eliminate the Gaussian noise, it is studied extensively in the field of seismic wavelet estimation.In this thesis, on the assumption that seismic wavelet was mixed-phase and the noise was Gaussian, the wavelet estimation objective function was constructed via the fourth-order cumulants of seismic data matching the fourth-order moments of parametric wavelet model. In order to validate the uniqueness of the model solution, the wavelet estimation methods based on fourth-order cumulants were analyzed and studied according to the wavelet three-order spectral. Theoretical analysis demonstrated that this approach could estimate the wavelet model parameters precisely with some linear migration of the amplitude or the phase of the seismic wavelet, and the accuracy of the seismic wavelet estimated through this approach meets the requirement of seismic signal processing.The solution of the objective function leads to a multidimensional and multimodal non-linear optimization problem. The minimizing process of the objective function should able to search the parameter vectors globally, and the deep-searching ability is also the necessary characteristic of the optimization algorithm, this makes it difficult to get the global optimal via the general algorithm. The genetic algorithm perfectly balances the global searching capacity and the local search capability, but often gets premature in the late searching process. To overcome this flaw and get the optimal solution more effectively and stably, this paper did some reasearch on the measurement and maintenance of the population, the setting of the basic operaters, and the small neighborhood seaeching respectively. Then the improved Genetic Algorithm, which could overcome the premature and search the global optimal effectively, is proposed in this paper, simulation alse demonstrated this characteristic of this algorithm.Chaos optimization algorithm is also absorbed for further improvement of the mutation ability of this algorithm. The characteristics of Logistic mapping, Tent mapping and Arnold mapping are discussed in the view of the egodicity and the computational efficiency of the chaotic mapping or the distribution of the chaotic sequence. Then the Arnold mapping is absorbed in the Genetic Algorithm to extract the wavelet. The high dimensional function simulation demonstrated that this algorithm could improve the searching ability and get the global optimal effectively and stably. The application of seismic data processing results demonstrated that the novel chaos genetic algorithm is able to estimate the accuracy seismic wavelet fastly and effectively.