The Former Nonlinear / Non-gaussian Stack Seismic Inversion Theory And Applications

Alpha stable distribution processes which has greater applicability than the ideal Gaussian distribution attracts a great deal of attention of signal processing experts and scholars in the past less than twenty years'time. And now, people begin to try to re-examine and improve signal processing methods in the new perspective of non-Gaussian. While pre-stack seismic inversion is an important application in the field of signal processing, and the purpose of seismic inversion is to deduce the required deep geological information and lithology parameters from seismic records and a small amount of available logging information. As it is known, accurate geological information and lithology parameters are of vital importance for the reservoir identification and hydrocarbon detection, especially, on the hidden reservoir exploitation, requiring more precise and accurate inversion result than general application. To address the issue with signal processing methods, effectively inversion theory must be improved.First of all, the dissertation studies suchαstable distribution characteristic as theoretical basis, property, influence of key parameters on the distribution and some important numerical characteristic, and then, differences between non-Gaussianαstable distribution processing and the ideal Gaussian distribution are extracted.After that, pre-stack inversion theory as well as basic elastic impedance inversion, extended elastic impedance inversion and generalized elastic impedance inversion are studied, pre-stack seismic inversion steps are established.In the last part of this dissertation,αstable distribution signal processing theory is applied to pre-stack seismic inversion, and a new pre-stack seismic inversion algorithm based on fractional lower order statistics theory is proposed. The algorithm proposed in the dissertation was performed in practical pre-stack seismic inversion application successfully, which demonstrat the algorithm is practical and effective in pre-stack seismic inversion.The dissertation abandoned the traditional assumption that seismic signal obeys the ideal Gaussian distribution, and successfully appliedαstable distribution to pre-stack seismic inversion. The main achievements of the dissertation can be summarized as follows:⑴Proposed a method of observing dynamic sample variance curve to determine whether the seismic signal obeys Gaussian distribution or non-Gaussianαstable distribution. As non-Gaussianαstable distribution signal does not own limited dynamic sample variance value theoretically, comparing the the dynamic sample variance curves of Gaussian distribution and non-Gaussianαstable distribution is a convenient way to distinguish them. In fact, real seismic data subjects to non-Gaussian stable distribution rather Gaussian distribution.⑵Proposed a new pre-stack seismic inversion algorithm based on the assumption that seismic signal subjects to non-Gaussianαstable distribution. Different from Gaussian distribution, non-Gaussianαstable distribution does not have a second order moment, the classic signal processing methods such as least sequares algorithm do not work at all. Combining fractional lower order statistic theory and the convolution theory, this dissertation established a new objective function with least average l p norm of the inversion error, on this basis, proposed non-Gaussian stable distribution inversion algorithm and implementation steps.