应用数学与计算数学学报
應用數學與計算數學學報
응용수학여계산수학학보
COMMUNICATION ON APPLIED MATHEMATICS AND COMPUTATION
2012年
3期
285-297
,共13页
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
地震波形反縯%稀疏約束正則化%貝葉斯推斷%馬爾可伕鏈矇特卡囉(MCMC)方法
지진파형반연%희소약속정칙화%패협사추단%마이가부련몽특잡라(MCMC)방법
seismic waveform inversion%regularization with sparsity constraints%Bayesian inference%Markov chain Monte Carlo (MCMC) method
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．
將稀疏約束正則化方法應用于地震波形反縯問題．為瞭減弱對稀疏約束項的光滑性要求，引入貝葉斯推斷，產生一組收斂于後驗分佈的採樣點．通過數值算例記錄瞭採樣點的條件期望、方差、置信區間等具有統計意義的結果．數值結果錶明，在沒有光滑性的要求下，稀疏約束正則化方法對孔洞模型和分層模型中的介質邊緣有良好的識彆能力．特彆地，噹減少觀測數據時，稀疏約束正則化方法仍能穫得較好的反縯結果．
장희소약속정칙화방법응용우지진파형반연문제．위료감약대희소약속항적광활성요구，인입패협사추단，산생일조수렴우후험분포적채양점．통과수치산례기록료채양점적조건기망、방차、치신구간등구유통계의의적결과．수치결과표명，재몰유광활성적요구하，희소약속정칙화방법대공동모형화분층모형중적개질변연유량호적식별능력．특별지，당감소관측수거시，희소약속정칙화방법잉능획득교호적반연결과．
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.
