Research On Seismic Wavelet Modeling And Parameter Estimation Method Based On High-Order Statistic

The accurate extraction of the seismic wavelet is the base of wave impedance inversion and forward model, and has profound significance for high precision seismic data processing. Recently, the high-order statistical method of seismic wavelet extraction achieved comprehensive application in real seismic data processing. These methods reveal potential power in the accurate estimation of seismic wavelet, for the seismic data processed by these methods need not restrict to the usual hypothesis that the wavelet is minimum phase or the additive noise is white Gaussian distribution. Based on the convolution model, this thesis thoroughly studied the accurate model of seismic wavelet modeling and the application of high-order statistic in mixed-phase sesmic wavelet extraction.For the cumulant based ARMA (autoregressive moving average ) model seismic wavelet extraction method could not only retain the pahse information of the seismic wavlet while eliminating the colored Gaussian noise, but also provide a parsimonious, more efficient modeling in fitting seismic trace than MA (moving average)model does, the ARMA model is utilized to describe the seismic wavelet. The seismic wavelet extraction method with ARMA model description available is the cumulant-based matrix-equation approach. In this thesis, the cumulant-based matrix-equation approach is discussed through theoretic analysis and numerical simulation, which demonstrate that this approach is not as stable as the formula proved when been applied to extract seicmic wavelet from seismic record that is short or contaminated by strong additive noise, for it only applies the special-slice information of the trace cumulant. To solve this problem, the ARMA cumulant matching method was exploited to estimate the wavelet parameters, which was deduced from the ARMA model cumulant matching theorem and the seismic convolution model. The seismic extraction simulations demonstrate that this method is not so sensitive to the data amount or noise intension, and could estimate the wavelet parameters accurately and stably, because more information of the trace cumulant is applied. But this method also leads to a highly nonlinear optimization problem: the objective function is very sensitive to the parameters, which makes the solution of this method dependent on the valid of the parameter initialization.To offset those limitations of linear or nonlinear parametric estimation methods, this paper proposed a parametric estimation approach which synthesized both the linear (matrix equation) and nonlinear (cumulant matching) methods. In this approach, the ARMA cumulant matching method was exploited to evaluate the validity of the initialization, and the matching error was feedback to adjust the threshold value of matrix-equation method. Then the parameter space is reinitialized from adjusted matrix-equation method, and the accurate parameter estimation is obtained from cumulant matching method. Theoretic analysis and numerical simulation demonstrate the feasibility of this approach. Compared with the potential computational error of the linear methods, this approach can improve parameter estimation precision. Moreover, it extracts wavelet with high computational efficiency by reducing the complexity of initial guess via ARMA model matching approach.