基于α稳定分布的地震反演方法  

Seismic inversion method with α-stable distribution

作　　者：岳碧波[1] 彭真明[1] 张启衡[2] 

机构地区：[1]电子科技大学光电信息学院,成都610054 [2]中国科学院光电技术研究所,成都610209

出　　处：《地球物理学报》2012年第4期1307-1317,共11页Chinese Journal of Geophysics

基　　金：国家自然科学基金(40874066;40839905);国家科技重大专项(2008ZX05019-006);中央高校基本科研业务费专项资金(ZYGX2011YB021)资助

摘　　要：本文介绍了α稳定分布的统计特征,并对比分析了实际地震信号与α稳定分布的动态样本方差特征,提出地震信号服从非高斯α稳定分布的假设.在此基础上,利用地震记录估计误差的p阶统计量作为代价函数,提出了基于非高斯α稳定分布的最小p范数地震反演方法.将该方法应用到单道反射系数理论模型及实际叠前弹性阻抗反演实例中,均取得了良好的反演效果.实际反演结果验证了本文提出的地震信号服从非高斯α稳定分布假设的合理性,以及最小p范数地震反演方法的可行性和有效性.This paper briefly introduced the statistic characteristics of α-stable distribution,analyzed the dynamic sample variance of α-stable distribution and seismic signals comparatively,and proposed that seismic signals follow α-stable distribution.Based on this,the cost function was built with the p-order statistics of seismic data estimated error.The least p-norm seismic inversion algorithm was proposed and applied to single-channel reflectivity inversion and real pre-stack elastic impedance inversion.Both of the applications obtained good results,which demonstrated that the seismic signals follow non-Gaussian α-stable distribution and the least p-norm seismic inversion algorithm was efficient and feasible.

关 键 词：Α稳定分布 非高斯 反演 p范数 

分 类 号：P631[天文地球—地质矿产勘探]