Adaptive multiple subtraction method based on hybrid L1/L2 norm
XIONG Fan-Sheng1, HUANG Xin-Wu1, ZHANG Di1, LI Rong-Xian2, WANG Peng3
1. School of Engineering and Technology, China University of Geosciences, Beijing 100083, China;
2. Construction Engineering Corporation of Yunnan Province, Kunming 650041, China;
3. Yantai Geological Prospecting Branch Institute of Shandong Province, Yantai 264002, China
One of the most important steps of surface-related multiple elimination (SRME) is subtraction of the matching multiple waves from the original data. The L2-norm adaptive multiple subtraction method applies to the situation in which the energy of primary wave is very low; however, the L1-norm adaptive multiple subtraction method could apply to the situation in which the energy of primary wave is strong. To obtain a more ideal method, the authors built a mathematical model to combine L2-norm and L1-norm adaptive multiple subtraction method by means of weighted array, and proposed the method for determination of weight coefficient. In addition, the method which combines synthetic data with field data was illustrated, and the results between using the hybrid L1/L2-norm and using L2-norm and L1-norm alone were comparatively studied. The results show that using the hybridL1 /L2-norm adaptive multiple subtraction method can not only suppress the multiple wave better, but also keep the primary wave well.
[1] Verschuur D J.地震多次波去除技术的过去现在和未来[M].陈浩林,张保庆,刘军,等,译.北京:石油工业出版社,2010,12:109-121.[2] 刘光.压制自由表面相关多次波的自适应减方法研究及应用[D].北京:中国地质大学,2009:25-52。[3] Kennett B L N.The suppression of surface multiples on seismic records[J].Geophysical Prospecting,1979,27:584-600.[4] Riley D C,Claerbout J F.2-D multiple reflections[J].Geophysics,1976,41:592-620.[5] Berkhout A J.Seismic migration:imaging of acoustic energy by wavefield exploration:2nd edit[M].Amsterdam:Elsevier Science Publ Co Inc,1982:211-218.[6] Verschuur D J.Surface-related multiple elimination:an inversion approach[D].Delft:University of Technology,1991.[7] Verschuur D J,Berkhout A J.Estimation of multiple scattering by iterative inversion,partⅠ:theoretical considerations[J].Geophysics,1997,62(5):1586-1595.[8] 牛滨华,沈操,黄新武.波动方程多次波压制技术的进展[J].地球物理学进展,2002,17 (3):480-485.[9] 陆文凯,骆毅,赵波,等.基于独立分量分析的多次波自适应相减技术[J].地球物理学报,2004,47(5):886-891.[10] 李钟晓,陆文凯,庞廷华,等.基于多道卷积信号盲分离的多次波自适应相减方法[J].地球物理学报,2012,55(4):1325-1334.[11] 黄新武,孙春岩,牛滨华,等.基于数据一致性预测与压制自由表面多次波—理论研究与试处理[J].地球物理学报,2005,48(1):173-180.[12] Guittonand A,Verschuur D J.Adaptive subtraction of multiples using the L1-norm[J].Geophysical Prospecting,2004,52(3):27-38.[13] BudeK P,Langan R T.Hybrid L1/L2 minimization with applications to tomography[J].Geophysics,1997,62(4):1183-1195.[14] Gersztenkorn A,BeeBednar J,Lines L R.Robust iterative inversion for the one-dimensional acousticwave equation[J].Geophysics,1986,51(2):357-368.[15] 李学聪,刘伊克,常旭,等.均衡多道1范数匹配多次波衰减的方法与应用研究[J].地球物理学报,2010,53(4):963-973.[16] 李鹏,刘伊克,常旭,等.均衡拟多道匹配滤波法在波动方程法压制多次波中的应用[J].地球物理学报,2007,50(6):1844-1853.[17] 武银婷,刘伊克,常旭,等.改进的1范数匹配滤波法及在南海深水盆地的应用[J].地球物理学报,2012,55(3):1007-1016.[18] 刘华锋,李庆春,王立明.利用改进的扩展多道匹配相减法压制多次波[J].石油地球物理勘探,2009,44(3):270-275.[19] 李振春,刘建辉,郭朝斌,等.基于扩展伪多道匹配的保幅型多次波压制方法[J].石油地球物理勘探,2012,46(2):207-210.[20] 石颖,王建民,井洪亮,等.多道自适应匹配滤波方法压制表面多次波[J].地球物理学进展,2013,28(2):785-792.[21] Long Y,Han L G,Han L,et al.L1 norm optimal solution match processing in the wavelet domain[J].Applied Geophysics,2012,9(4):451-458.[22] 陆文凯.基于L1范数多项式拟合的多次波消除方法[J].石油地球物理勘探,2011,46(3):386-389.[23] Pang T H,Lu W K,Ma Y J.Adaptive multiple subtraction using a constrained L1-norm method with lateral continuity[J].Applied Geophysics,2009,6(3):241-247.[24] Guitton A.Huber solver versus IRLS algorithm for quasi L1inversion[J].Stanford Exploration Project,2000,103:205~266[25] Guitton A.Implementation of a nonlinear solver for minimizing the Huber norm[J].103:281-289.[26] Darche G.Iterative L1 deconvolution[J].SEP Annual Report,1989(61):281-301.[27] Claerbout J F,Muit F.Robust modeling with erratic data[J].Geophysics,1973,38(4):820-844.[28] 黄新武,牛滨华,刘光,等.基于数据一致性原理预测与压制自由表面多次波的效果分析[J].石油地球物理勘探,2009,44 (4):409-416.
