Methodologies Of Non-convex L_1-2 Regularized Seismic Inversion

Using the seismic data and combining the known information of geology,drilling,and well-log data,seismic inversion is a very important technique in the field of oil and gas exploration and development.It allows us to estimate the spatial structure and physical properties of the subsurface.However,seismic inversion is a typical ill-posed problem with the features of ill-condition,unstable and uncertain.This problem is generally added a constrained prior information and approximately solved by the regularization method.At present,Tikhonov regularization and L₁ regularization methods are commonly used in seismic inversion.But Tikhonov regularization method obtains smooth solutions and fails to preserve boundary information.Furthermore,L₁regularization method can not obtain the sparest solution when the inverse problem is seriously ill-condition.Hence,we develop a set of seismic inversion method based on non-convex L_1-2regularization method and propose a novel high-resolution seismic inversion method for deep reservoirs and complex structure reservoirs,which provides a theoretical basis and technical support for the prediction of reservoirs exactly.This study includes:1)Under the framework of Bayesian theory,we propose a new seismic impedance inversion method with low-frequancy and sparse constrains.Firstly,according to DCT method,we design a low pass filter matrix for seismic inversion and improve the conventional low-frequancy constraint item.Then,he inversion objective functions are built based on the dipole reflection coefficient decomposition method and Kolsky-Futterman model respectively.And they are solved by non-convex L_1-2 regularization method.Hence,the proposed method can improve the accuracy and stability of the inversion methods.2)The far angle gathers seismic data in pre-stack inversion are collected very difficultly.To deal with this problem,we employ non-convex L_1-2regularization for simultaneous P-and S-impedance inversion from pre-stack seismic data.We firstly derive the forward problem with multi-angles and set up the inversion objective function with constraints of a priori low-frequency information obtained from well-log data.Then,we introduce non-convex L_1-2 regularization to solve this objective function,then P-and S-impedance inversion can be estimated by the proposed method.3)Based on the above content,we extend non-convex L_1-2 regularization to three-terms AVO inversion.Under the framework of Bayesian theory,the proposed method incorporates a covariance matrix to constrain P-impedance and S-impedance and density.Then,a priori low-frequency information is built by using well-log data and added into the inversion objective function.Finally,this inversion objective function is also solved by non-convex L_1-2 regularization.Then,the inverdion objective function of 1).2).and 3)are respectively decomposed into two convex subproblems via the difference of convex algorithm(DCA),and each subproblem is solved by the alternating direction method of multipliers(ADMM).Finally,the synthetic experiments and field-data application show that the proposed methods enhance the lateral continuity and the vertical resolution of inversion results,which can effectively characterize the boundary layer.And,the nonstationary acoustic-impedance inversion method can improve the resolution of inversion results.These results provide a theoretical basis and technical support for the prediction of structurally complex reservoirs.