叠后地震数据自适应正则化参数稀疏约束反演方法

Sparse constrained post-stack seismic data inversion with adaptive selection of regularization parameters

在叠后地震数据的稀疏脉冲反演中,正则化约束参数的选取是一个非常关键的问题.目前,最常用的正则化参数选取方法为质量控制法与L曲线法.二者都需要根据大量的试验来确定合适的正则化参数,工作量十分巨大,并且存在很大的经验性与局限性.针对这个问题,本文采用基于广义Stein无偏风险估计的正则化参数求取方法.该方法的具体思路是通过求解广义Stein无偏风险估计函数,在叠后地震数据的反演求解过程中自适应地求取正则化参数.模型测试与实际数据反演结果表明,相比于目前常用的质量控制法与L曲线法,自适应法得到的正则化参数是更合适的,同时降低了正则化参数求取的工作量.

The selection of regularization parameters is a very key issue in the sparse constrained post-stack seismic data inversion. At present, the most common used existing methods to determine the regularization parameters are quality control and L-Curve. Both of the above two methods are based on trails which are very work-consuming. In addition, these methods are very empirical and circumscribed. To address this problem, this paper uses an alternative method for regularization parameters selection based on the Generalized Stein’s Unbiased Risk Estimate(G-SURE). Its specific idea is to solve the G-SURE function and adaptively to estimate the regularization parameters in the process of post-stack seismic data inversion. Results of the model numerical tests and real seismic data indicate that the adaptive method can estimate the more appropriate regularization parameters compared to the common used quality control method and L-Curve method. In addition, the workload of selection of regularization parameters is greatly reduced.