Elastic full-waveform inversion of land single-component seismic data based on optimal transport theory
LI Qingyang1,2, WU Guochen1,2, WANG Yumei3, SHEN Guoqiang3, DUAN Peiran1
1. School of Geosciences, China University of Petroleum(East China), Qingdao, Shandong 266580, China; 2. Laboratory for Marine Mineral Resources, Pilot National Laboratory for Marine Science and Technology(Qingdao), Qingdao, Shandong 266071, China; 3. Geophysical Research Institute of Shengli Oilfield, SINOPEC, Dongying, Shandong 257022, China
Abstract：The single-component seismic data collected from land only contains P-wave information without S-wave. Acoustic full-waveform inversion (AFWI) is the most commonly used method to invert the P-wave velocity and density with P-wave data. However, it ignores the elastic AVO characteristics of single-component data and the existence of converted P-waves. To tackle this problem, this paper derives a new pseudo-pressure elastic wave equation based on the elastic medium assumption. The numerical simulation result of the equation is still a scalar wavefield but contains elastic AVO characteristics and converted P-wave information, which indicates the change of S-wave velocity. Then we build a theoretical framework of full-waveform inversion (FWI) to invert elastic para-meters using P-wave data. Besides, due to the high non-linearity of the FWI, modeling accurate initial velocity is crucial. In view of this, we introduce the quadratic Wasserstein distance (W2-norm) based on the optimal transport theory to optimize the convexity of objective function and overcomes the local minima caused by periodic skipping without increasing calculations. On this basis, the conventional L2-norm inversion (W2 + L2 inversion) is carried out, which eliminates the dependence on the initial model. The test using the Marmousi model after resampling verifies the effectiveness of the method in inverting P/S-wave velocities with only P-wave data, as well as its advantages in avoiding periodic skipping. Finally, this method is applied to actual seismic data of Area M in eastern China, and the inversion results illustrate the practicability and stability of the proposed method.
李青阳, 吴国忱, 王玉梅, 慎国强, 段沛然. 基于最优输运原理的陆上单分量资料弹性波全波形反演[J]. 石油地球物理勘探, 2021, 56(5): 1060-1073.
LI Qingyang, WU Guochen, WANG Yumei, SHEN Guoqiang, DUAN Peiran. Elastic full-waveform inversion of land single-component seismic data based on optimal transport theory. Oil Geophysical Prospecting, 2021, 56(5): 1060-1073.
Virieux J, Operto S. An overview of full-waveform inversion in exploration geophysics[J]. Geophysics, 2009, 74(6):WCC1-WCC26.
[2]
Tarantola A. Inversion of seismic reflection data in the acoustic approximation[J]. Geophysics, 1984, 49(8):1259-1266.
[3]
Tarantola A. A strategy for nonlinear elastic inversion of seismic reflection data[J]. Geophysics, 1986, 51(10):1893-1903.
[4]
Mora P. Elastic wave-field inversion of reflection and transmission data[J]. Geophysics, 1988, 53(6):750-759.
[5]
Köhn D, De Nil D, Kurzmann A, et al. On the influence of model parametrization in elastic full waveform tomography[J]. Geophysical Journal International, 2012, 191(1):325-345.
[6]
Jeong W, Lee H. Min D J. Full waveform inversion strategy for density in the frequency domain[J]. Geophysical Journal International, 2012, 188(3):1221-1242.
[7]
Ren Z, Liu Y. A hierarchical elastic full-waveform inversion scheme based on wavefield separation and the multistep-length approach[J]. Geophysics, 2016, 81(3):R99-R123.
[8]
Wang T, Cheng J. Elastic full waveform inversion based on mode decomposition:the approach and mechanism[J]. Geophysical Journal International, 2017, 209(2):606-622.
[9]
Raknes E, Arntsen B, Weibull W. Three-dimensional elastic full waveform inversion using seismic data from the Sleipner area[J]. Geophysical Journal International, 2015, 202(3):1877-1894.
Sears T J, Singh S C, Barton P J. Elastic full waveform inversion of multi-component OBC seismic data[J]. Geophysical Prospecting, 2008, 56(6):843-862.
[12]
Li Q, Wu G, Wu J, et al. Finite difference seismic forward modeling method for fluid-solid coupled media with irregular seabed interface[J]. Journal of Geophysics and Engineering, 2019, 16(1):198-214.
[13]
李青阳, 吴国忱, 吴建鲁. 非均匀流-固边界耦合介质多参数全波形反演方法[J]. 地球物理学报, 2019, 62(9):3557-3570.LI Qingyang, WU Guochen, WU Jianlu. A multi-parameter full waveform inversion method for a heterogeneous medium with a fluid-solid coupled boundary[J]. Chinese Journal of Geophysics, 2019, 62(9):3557-3570.
[14]
Brossier R, Operto S, Virieux J. Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion[J]. Geophysics, 2009, 74(6):WCC105-WCC118.
[15]
Barnes C, Charara M. The domain of applicability of acoustic full-waveform inversion for marine seismic data[J]. Geophysics, 2009, 74(6):WCC91-WCC103.
[16]
刘立彬, 李振春, 张云银, 等. 一种时间域全波形反演中的地震子波估计方法[J]. 地球物理学进展, 2019, 35(3):987-994.LIU Libing, LI Zhenchun, ZHANG Yunyin. Seismic wavelet estimation for full-waveform inversion in time domain[J]. Progress in Geophysics, 2019, 35(3):987-994.
[17]
Li Q, Wu G. 2D multi-parameter waveform inversion of land reflection seismic data obtained from the particle-motion response from the vertical geophone[J]. Acta Geophysica, 2020, 68(2):377-388.
[18]
王毓玮, 董良国, 黄超, 等. 降低弹性波全波形反演强烈非线性的分步反演策略[J]. 石油地球物理勘探, 2016, 51(2):288-294.WANG Yuwei, DONG Liangguo, HUANG Chao, et al. A multi-step strategy for mitigating severe nonli-nearity in elastic full-waveform inversion[J]. Oil Geo-physical Prospecting, 2016, 51(2):288-294.
[19]
Wu Z, Alkhalifah T. Selective data extension for full-waveform inversion:An efficient solution for cycle skipping[J]. Geophysics, 2018, 83(3):R201-R211.
[20]
吴彦, 马玥, 刘玉金, 等.全走时反演及其应用[J]. 石油物探, 2017, 56(1):50-56.WU Yan, MA Yue, LIU Yujin, et al. Full-traveltime inversion and its application[J]. Geophysical Prospecting for Petroleum, 2017, 56(1):50-56.
Wu R, Luo J, Wu B. Seismic envelope inversion and modulation signal model[J]. Geophysics, 2014, 79(3):WA13-WA24.
[23]
Xu S, Wang S, Chen F, et al. Full waveform inversion for reflected seismic data[C]. Extended Abstracts of 74th EAGE Conference & Exhibition, 2012, W024.
[24]
Warner M, Guasch L. Adaptive waveform inversion[J]. Geophysics, 2016, 81(6):R429-R445.
[25]
Yang Y, Engquist B, Sun J. Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion[J]. Geophysics, 2018, 83(1):R43-R62.
[26]
Métivier L, Brossier R, Mérigot Q, et al. Measuring the misfit between seismograms using an optimal transport distance:Application to full waveform inversion[J]. Geophysical Journal International, 2016, 205(1):345-377.
[27]
石玉梅, 张研, 姚逢昌, 等. 基于声学全波形反演的油气藏地震成像方法[J]. 地球物理学报, 2014, 57(2):607-617.SHI Yumei, ZHANG Yan, YAO Fengchang, et al. Methodology of seismic imaging for hydrocarbon re-servoirs based on acoustic full waveform inversion[J]. Chinese Journal of Geophysics, 2014, 57(2):607-617.
[28]
Tang C, McMechan G. Multidirectional-vector-based elastic reverse time migration and angle-domain common-image gathers with approximate wavefield decomposition of P- and S-waves[J]. Geophysics, 2017, 83(1):S57-S79.
[29]
牛滨华, 孙春岩. 半空间介质与地震波传播[M]. 北京:石油工业出版社, 2002.
[30]
Plessix R. A review of the adjoint-state method for computing the gradient of a functional with geophysical applications[J]. Geophysical Journal Internatio-nal, 2006, 167(2):495-503.
