Kurtosis Based Seismic Wavelet Estimation And Avo Inversion Algorithms And Applications

AVO technology uses seismic trace record to compute the parameter and to detect the oil and gas area by analyzing the relationship between the amplitude and offset. The seismic wavelet estimation and AVO inversion are two main focuses of AVO technology, and are also the two aspects of our research works.The thesis firstly introduces the research status of wavelet estimation and inversion problems. By conducting research on the existing methods and problems occurred in them, we propose some corresponding solutions, that is,Wavelet estimation problems, based on convolution model, can be regarded as system identification problems from the perspective of signal processing. Then the method of adaptive filtering can be utilized by combining the wavelet estimation problems with the filtering problems. Aiming the problem that the least mean kurtosis (LMK) will be deteriorated in an impulsive environment, an improved variance estimation LMK (IVE-LMK) method is proposed, which uses a median operator for the variance estimation and consequently can remove the effect of the impulsive noise and improve the performance of the method. The simulation results demonstrate the effectiveness of the new method in dealing with impulsive noise.Secondly, aiming the problems that the computation complexity in the update equation is large and the fixed step size will lead to a slow convergence rate, a variable step size signed least mean kurtosis (VSS-SLMK) is proposed. Signed method using a sign operator instead of the multiplication and other operations can effectively reduce the computation complexity of the method. In addition, the step size derived from the gradient descent method is iteratively updated by using the information of the input and error signal in every iteration, and can improve the convergence rate of the method while ensuring the lower steady state error. And the step size for the convergence of the method in the sense of mean square is also presented. The simulation results demonstrate its fast convergence rate and good steady state performance.Finaly, aiming at the problem that AVO inversion faces difficulties when applied to seismic data contaminated by many kinds of noises, this thesis propose a new AVO inversion method. Inspired by the least mean kurtosis algorithm, a robust tool for Gaussian noises, we introduce it into the inversion field and construct an inversion objective function. Simultaneously a smooth operator is also included to obtain robustness to outliers. The simulation results demonstrate its effectiveness in reducing the effect of Gaussian noise and outliers. Meanwhile it provides a new approach for other geophysical inverse problems.