Robust Avo Inverse Algorithms And Their Applications

Because the seismic exploration objectives is from structural reservoir into lithologic reservoir, the traditional post-stack inversion technique has been difficult to meet exploration needs and the increasing demand for oil and gas. Prestack seismic data contains abundant parameter information, and using AVO technology to procese can get more accurate inversion result. Since the noise in the actual pre-stack seismic data is complex and dose not meet the Gauss distribution, and the inverse results based on the tradition Gauss distribution can not accord with the real data, non-Gauss or robustness issues become the focus of research. Now there are not many robust inverse algorithms and they are traditional algorithms. In order to cope with the demands of the continuous development of inversion technology, we need to modify traditional robust inversion algorithm to find more effective inversion algorithm.The thesis studies the robust inverse algorithm for outliers or non-Gauss distribution. It focuses on inverse algorithms for solving the robust objective function inversion algorithms and their application in AVO inversion.First of all, this paper introduces the basic principle of AVO algorithm and the corresponding basic flow, and then gives the basic process of a common inverse algorithm for AVO inverse problem. Finally summarizing the existing robust inversion algorithms and their respective advantages and disadvantages, it provides the basic theory knowledge for the future research and innovation.In order to solve these problems that l1-norm in non-Gaussian noise has singularity, large amount of calculation, and the IRLS inverse method has ill-condition matrix inversion and the weighted matrix is not easy to choose when solving l1-norm objective function. A new method based on the l1-norm and l2-norm is introduced, and it uses the property that l1-norm is insensitivity for abnormal values or more stable for non-Gaussian noise. Then we take the l2-norm of the increment of the model parameters as the constraint condition to reduce the singularity effect and the amount of calculation. Finally under the new objective function, by using Lagrange multiplier and basic gradient optimization algorithm we obtain a new inverse algorithm called sign gradient inverse algorithm. The algorithm effectively reduces the large amount of calculation problem caused by swing in extreme point when solving the l1norm and reduces its singularity effect. And in the process of updating algorithm requiring only error sign vector, it can be more simple and easy to implement.Secondly this paper analyzes the influence of the step-size selection of inverse algorithm on the inversion results, gives a adaptive variable step size algorithm based on the Taylor expression of error. This step size can be applied in different robust inversion algorithms, avoid the complex process of solving step size by using the exact search. In each iteration, the step size adaptive adjusts its size to minimize the error between the inverse solution and the real data by using the error information. At the same time the step size relative to other step size under the robust norm is simpler, lower computational complexity, and the experimental results have a better convergence property and more satisfactory inversion result.Finally, through the analysis of the rapid convergence of quasi-Newton algorithm and combining the property of conjugate gradient algorithm, the paper gives a new conjugate gradient algorithm. The algorithm uses the approximate inverse matrice of Hessian matrice to obtain a new fast search direction, and then use the properties of conjugate gradient algorithm based on robust norm to get a new parameters. Finally compared with the traditional nonlinear conjugate gradient inverse algorithm in robust norm, the proposed algorithm has better convergence properties, and shows validity by the artificial data and real data.