基于正交匹配追踪算法的叠前地震反演方法

Prestack seismic inversion based on orthogonal matching pursuit algorithm

为了给地质解释提供更为有利的反演数据,本文提出一种基于正交匹配追踪算法的叠前稀疏反演方法。采用正交匹配追踪算法先搜索稀疏的反射系数位置再计算大小,利用L0范数对反射系数的稀疏性进行约束,构建基于正交匹配追踪算法的叠前地震反演目标函数,并加入模型约束以增强反演的稳定性。由于L0范数具有较强的稀疏性,反演结果界面块化,地层界面清晰。反演得到的反射系数可通过积分的方式转化为地层弹性信息。模型测试表明该方法稳定可靠,抗噪能力强。实际地震数据反演的井旁道与测井资料匹配较好,与常规反演方法相比,提升了反演结果对地层的分辨能力。

This study proposes a new prestack seismic inversion method based on orthogonal matching pursuit algorithm to generate the blocky layers with high resolution and provide more advantageous data for geological interpretation.The strategy of the proposed inversion method is to seek the location of reflections firstly,and then re-estimate the value of coefficients at each iteration step.This is an improved version of match pursuit(MP)algorithm called orthogonal match pursuit(OMP)algorithm.This paper adds the regularization term by utilizing the L0 norm to constraint the reflectivity sparsity,and establishes the objective function of prestack inversion based on OMP algorithm.And it is necessary to utilize the model constraint to enhance the stability of inversion.Because of the strong sparsity of the L0 norm constraint,the inversion results will be expressed as blocky or the step stairs.The method is performed in a synthetic example and a field example.In both of them,the proposed orthogonal matching pursuit prestack seismic inversion method works well with credible results compared with the true model and the well log data.The inverted results from the field data are blocky layers with higher resolution.