Research On Non-gaussian Three-term AVO Inversion Algorithm And Its Application

With the developing of the oil and gas exploration techniques, the emphasis of the present oil and gas exploration has shifted from structural reservoirs to lithologic reservoirs. Compared with the traditional structural reservoirs, the lithologic reservoirs have greater invisibility, more complex forming rules, which require us to describe reservoirs more accurate in order to obtain more reliable information on the reservoir. That is important of reducing the risk of oil and gas exploration.AVO (Amplitude Variation with Offset) inversion is an important way to extract hidden lithological parameters from the pre-stack seismic data, and is also one of the frontier research topics of the current seismic signal processing and explain. Conventional l2 norm based seismic inversion algorithms, which assume the noise obeys the Gaussian distribution, are used more out of mathematical convenience than for sound physical reasons. Under the Gaussian noise assumption, the existing algorithms have a good performance on the post-stack seismic inversion which has a relatively high signal-to-noise ratio (SNR). However, the Gaussian assumption may cause inaccurate of the algorithm, and even divergent in the pre-stack seismic inversion which has a relatively low SNR, especially for the complex reef reservoirs. So, from the view of performance loss of the inversion algorithms, a more accurate non-Gaussian model is urgently necessary to provide a more reliable basis for seismic interpretation. In this thesis, we discuss the non-Gaussian property of the noise in the actual pre-stack seismic data and iterative residual error in the inversion algorithm, and furtherly study the non-Gaussian three-term AVO inversion to improve the precision and robustness of the pre-stack seismic inversion.Based on the analysis of the non-Gaussian property of the noise in the actual pre-stack seismic data and iterative residual error in the inversion algorithm, we analyze the commonly used non-Gaussian models and study the non-Gaussian three-term AVO inversion method under different noise models. Based on the more accurate model, the inversion results provide a more precision description of the reservoirs and a more reliable basis for interpretation. The research work is mainly includes:(1) For the widely use of the "Gaussian distribution hypothesis of the noise" in the pre-stack seismic inversion problems, we study the non-Gaussian characteristics of the noise in the actual pre-stack seismic data and iterative residual error in the inversion algorithm. Furthermore, we verify this assumption using the actual pre-stack seismic data, which laid the theoretical foundation of the study of non-Gaussian inverse algorithm in this thesis.(2) Amplitude Variation with Offset (AVO) inversion is very sensitive to noise and other uncertainties which are often far from Gaussian in the actual pre-stack seismic data, sometimes causing AVO inversion to give poor results. Since the generalized extreme value (GEV) distribution can efficiently fit any distributions with different parameters, to obtain steady and rational AVO inversion results, we use GEV distribution to model the distribution of the iterative residual error in the AVO inversion. The maximum likelihood method is used to re-evaluate the GEV distribution parameters of each iterative residual error to efficiently fit its non-Gaussian property and reduce the sensitivity of AVO inversion to non-Gaussian residual error. Quasi-Newton based Conjugate Gradient (QCG) AVO algorithm is derived from adaptive adjusted parameters GEV distribution to make sure the direction is always a descent direction for the objective function.(3) The l1 norm minimization gives more robust solutions than the l2 norm does because it is less sensitive to spiky and high-amplitude noise, however, it is singular where any residual component vanishes, which leads to instability in numerical minimization. To take advantages of the l1 norm and constraint on the deviation between two adjacent solutions, a variable step size-normalized sign gradient algorithm (VSS-NSGA) is proposed to obtain a more rational inversion result. It not only reduces the computational cost of the large scale seismic inversion problems but also avoids the instability of the l1 norm solution using the iteratively reweighted least squares (IRLS) algorithm. Furthermore, the variable step size is introduced to overcome the contradiction of the fast convergence rate and small steady-state error brought by fixed step size.(4) Under the analysis of the advantages and disadvantages of the different weighted norms in the IRLS algorithm, an IRLM algorithm, which uses the Hampel’s function as the misfit measure, is proposed for robust AVO inversion. The Hampel’s function improves the performance of the inversion algorithm by combining the advantages of the Huber norm and Biweght norm, which behaves like l2 norm for small residuals, l1 norm for large residuals and Biweight norm when the proportion of outliers increases.(5) For the non-Gaussian characteristics of the noise in the pre-stack seismic data, we propose an mixed l1/l2 norm algorithm that combines the benefits of the 12 norm and the l1 norm to deal with various non-Gaussian noises. Meanwhile, the well logging constraint is added in the objective function to improve the stability of the inversion.(6) Based on the study of the mixed l1/l2 norm algorithm, an adaptive mixed l1/l2 norm algorithm is proposed where the weight of the l1 and l2 norms are adjusted adaptive by a generalized likelihood ratio test (GLRT) function of the iterative residual error. The proposed algorithm improves the ability of suppressing the non-Gaussian noise in the pre-stack seismic inversion adaptively.(7) The l2 norm has a better performance in the super-Gaussian noise and Gaussian noise environment while the l4 norm has a better performance in sub-Gaussian noise environment, however, either the l2 norm or l4 norm are very sensitive to the assumed noise model that will limit their utility. Herein, we propose an adaptive mixed-norm algorithm that combines the benefits of the l2 norm for Gaussian and super-Gaussian noises and the l4 norm for sub-Gaussian noise to deal with various non-Gaussian noises. In addition, to improve the resolution of the inversion results, an adaptive regularization strategy which uses l1 norm regularization for the non-smooth regions and l2 norm regularization for the smooth regions according to a non-smooth detection matrix is proposed.