Research On The Order Determination Of The Parameterized Seismic Wavelet Estimation Model

In the oil and gas exploration field, high-resolution seismic wavelet extraction technology is the important research project, which is urgent to be solved. The seismic wavelets estimated by the current wavelet extraction technology have low resolution and the computing cost is high. View of the defects of current methods, this thesis researched on the seismic record characteristics, assumptions and boundary constraints, analyzed various attributes and characteristics of seismic wavelet, broke through the seismic wavelet extraction technology based on Moving Average (MA) model, proposed an parsimonious parameters Autoregressive Moving Average (ARMA) model which was used to model the parameterized seismic wavelet accurately, and studied the order determination of seismic wavelet ARMA model mainly. The author determined the Average (AR) part order using SVD method based on autocorrelation firstly, and then proposed a new MA order determination method which introduced information theoretic criteria function into MA order determination based on higher-order cumulant. In the premise of ensuring the accuracy of seismic wavelet, reduced the model order as much as possible so as to obtain high-efficiency and high-precision seismic wavelet model order determination.Higher order cumulant can completely suppress Gaussian noise theoretically, and keep signal phase information and so on. But the higher order cumulant are sensitive to the special slice, AR order determination converted to solving a special matrix constructed by special cumulant slice. At this moment the slice is difficult to be chosen and the results of AR order determination are unstable. Compared with the method based on higher order cumulant, the SVD method based on autocorrelation is mature and easy to operate. Theoretical analysis and numerical simulations demonstrated that the computing cost was low and the method could be used with moderate noises.As the higher order cumulant estimation is satisfied with sufficient data samples, but the actual data are always limited, MA order determination based on high order cumulant is unstable. This thesis proposed a new MA order determination method which combined the information theoretic criteria method based on autocorrelation with cumulant based method so as to correct the order bias caused by high-order cumulant. Numerical simulations demonstrated that the new method could effectively improve the stability and accuracy of MA model order determination.On the basis of order determination, AR parameters and MA parameters were estimated by SVD-TLS method and cumulant-based method respectively. As MA order determination and parameters estimation would deviate from the real value with short time data, and the anti-causal part order determination maybe unstable. So the author optimized the model parameters corresponding to model order, using the non-linear optimization algorithm in order to improve the accuracy of model parameters.