基于贝叶斯一稀疏约束正则化方法的地震波形反演  

Seismic waveform inversion based on Bayesian-sparsity constraint regularization method

作　　者：毛衡[1] 王薇[1] 韩波[2] 

机构地区：[1]复旦大学数学科学学院,上海200433 [2]哈尔滨工业大学理学院,哈尔滨150001

出　　处：《应用数学与计算数学学报》2012年第3期285-297,共13页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(41074088)

摘　　要：将稀疏约束正则化方法应用于地震波形反演问题.为了减弱对稀疏约束项的光滑性要求,引入贝叶斯推断,产生一组收敛于后验分布的采样点.通过数值算例记录了采样点的条件期望、方差、置信区间等具有统计意义的结果.数值结果表明,在没有光滑性的要求下,稀疏约束正则化方法对孔洞模型和分层模型中的介质边缘有良好的识别能力.特别地,当减少观测数据时,稀疏约束正则化方法仍能获得较好的反演结果.The regularization method is applied with sparsity constraints to seis- mic waveform inversion in this paper. To weaken the smoothness requirement of the sparsity constraints, the Bayesian inference is introduced and a series of samplings which satisfies the posterior distribution are generated. In numerical examples, sta- tistically significant results of samplings such as conditional expectation, variance and confidence interval are recorded. Numerical results are presented to illustrate that, without requirement of smoothness, the regularization method with sparsity constraints has a good ability to identify the edge of the media with cavity and lay- ered models. Especially, when the observation data are reduced, the regularization method with sparsity constraints can still provide reasonable inversion results.

关 键 词：地震波形反演 稀疏约束正则化 贝叶斯推断 马尔可夫链蒙特卡罗(MCMC)方法 

分 类 号：O212.8[理学—概率论与数理统计] P631.4[理学—数学]