弹性阻抗反演的后验正则化方法

岩石的脆性指数是页岩气藏评价的关键参数之一。相对于叠后声波阻抗反演和AVO反演方法，弹性阻抗反演能得到更为丰富、稳定、可靠的弹性参数反演结果，有利于页岩敏感性脆性指数的选取。但是，弹性阻抗反演为Hadamard意义下的不适定问题，即不能同时满足解的存在性、唯一性和稳定性的要求，需要利用正则化方法并辅之以适当的最优化技巧来提高解的稳定性和准确度。为克服弹性阻抗反演问题的不适定性，本文建立基于L₂范数约束的Tikhonov正则化反演最优化模型，辅以后验最优正则参数选取方法，并提出求解极小化问题的双滤波因子正则化算法。理论模型和实际数据的数值试验表明双滤波因子正则化算法是可行和有应用前景的。

A posteriori regularization method for elastic impe-dance inversion

The rock brittleness index is one of the key factors for shale gas reservoir evaluation.In comparison with the post stack acoustic impedance inversion and AVO inversion,the elastic impedance inversion can obtain more abundant,stable and reliable inversion results of elastic parameters,which is beneficial to the selection of shale sensitivity brittleness index.However,the elastic impedance inversion is an ill posed problem in the sense of Hadamard,that is,the existence,uniqueness and stability of the solution cannot be met at the same time.It is necessary to use the regularization me-thod and with appropriate optimization techniques to improve the stability and accuracy of solutions.In order to overcome the ill-posedness of the elastic impedance inversion,a Tikhonov regularization inversion optimization model based on L₂ norm constraint is established,which is supplemented by a posteriori optimal regular parameter selection method,and a dual filter factor regularization algorithm for minimizing problems is proposed.Nume-rical experiments on theoretical model and real data show that the dual filter regularization algorithm is feasible and promising.