ZHANG Pan,
HAN LiGuo,
GONG XiangBo et al
.2018.Multi-source elastic full waveform inversion based on the anisotropic total variation constraint.Chinese Journal Of Geophysics,61(2): 716-732,doi: 10.6038/cjg2018L0122
基于各向异性全变分约束的多震源弹性波全波形反演
张盼, 韩立国, 巩向博, 孙宏宇, 毛博
吉林大学地球探测科学与技术学院, 长春 130026
Multi-source elastic full waveform inversion based on the anisotropic total variation constraint
ZHANG Pan, HAN LiGuo, GONG XiangBo, SUN HongYu, MAO Bo
College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China
Abstract:The multi-source encoding technology can improve the calculation efficiency of the full waveform inversion, but the crosstalks caused by the source aliasing can reduce the quality of inversion results. The total variation (TV) constraint can suppress the noise within the layer and sharp the model interfaces. The combination of TV constraint and multi-source technology can not only greatly improve the calculation efficiency of the elastic full waveform inversion, but also ensure the inversion quality. In this paper, an efficient dynamic multi-source full waveform inversion strategy is proposed, which can disperse the crosstalks while ensuring uniform illumination. Then, we analyze the characteristics of the crosstalks, and establish the corresponding TV constraint elastic full waveform inversion method. To avoid cycle-skipping, we apply the low frequency reconstruction method based on the sparse constraint to elastic seismic data, and propose a new elastic multiscale inversion strategy. We also give the workflow for solving the anisotropic TV constraint full waveform inversion problem by the fast gradient projecting algorithm. The numerical tests show that our method can not only suppress the crosstalks caused by source aliasing, but also reduce the effect of the noise in observations on the final inversion results.
[1] Acar R, Vogel C R. 1994. Analysis of bounded variation penalty methods for ill-posed problems. Inverse Problems, 10(6): 1217-1229. [DOI:10.1088/0266-5611/10/6/003] [2] Anagaw A Y, Sacchi M D. 2011. Full waveform inversion with total variation regularization.//2011 CSPG CSEG CWLS Convention. Canada: 1-4. [3] Askan A, Akcelik V, Bielak J, et al. 2007. Full waveform inversion for seismic velocity and anelastic losses in heterogeneous structures. Bulletin of the Seismological Society of America, 97(6): 1990-2008. [DOI:10.1785/0120070079] [4] Beck A, Teboulle M. 2009a. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1): 183-202. [DOI:10.1137/080716542] [5] Beck A, Teboulle M. 2009b. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Transactions on Image Processing, 18(11): 2419-2434. [DOI:10.1109/TIP.2009.2028250] [6] Boonyasiriwat C, Valasek P, Routh P, et al. 2009. An efficient multiscale method for time-domain waveform tomography. Geophysics, 74(6): WCC59-WCC68. [DOI:10.1190/1.3151869] [7] Boonyasiriwat C, Schuster G T. 2010. 3D multisource full-waveform inversion using dynamic random phase encoding. //80th SEG Annual International Meeting, Expanded Abstracts. SEG: 1044-1049. [8] Brossier R, Operto S, Virieux J. 2009. Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion. Geophysics, 74(6): WCC105-WCC118. [DOI:10.1190/1.3215771] [9] Bunks C, Saleck F M, Zaleski S, et al. 1995. Multiscale seismic waveform inversion. Geophysics, 60(5): 1457-1473. [DOI:10.1190/1.1443880] [10] Burstedde C, Ghattas O. 2009. Algorithmic strategies for full waveform inversion: 1D experiments. Geophysics, 74(6): WCC37-WCC46. [DOI:10.1190/1.3237116] [11] Crase E, Pica A, Noble M, et al. 1990. Robust elastic nonlinear waveform inversion: Application to real data. Geophysics, 55(5): 527-538. [DOI:10.1190/1.1442864] [12] Crase E, Wideman C, Noble M, et al. 1992. Nonlinear elastic waveform inversion of land seismic reflection data. Journal of Geophysical Research, 97(B4): 4685-4703. [DOI:10.1029/90JB00832] [13] Esser E, Guasch L, van Leeuwen T, et al. 2015. Total variation regularization strategies in full waveform inversion for improving robustness to noise, limited data and poor initializations. Technical Report TR-EOAS-2015-5, 06 2015. [14] Gao K, Lin Y Z, Huang L J, et al. 2015. Anisotropic elastic waveform inversion with modified total-variation regularization. //85th SEG Annual Meeting, Expanded Abstract. SEG: 5158-5163. [15] Hu Y, Han L G, Zhang P, et al. 2016. Multistep full-waveform inversion based on waveform-mode decomposition. //86th SEG Annual Meeting, Expanded Abstract. SEG: 1501-1505. [16] Krebs J R, Anderson J E, Hinkley D, et al. 2009. Fast full-wavefield seismic inversion using encoded sources. Geophysics, 74(6): WCC177-WCC188. [DOI:10.1190/1.3230502] [17] Li X, Aravkin A Y, van Leeuwen T, et al. 2012. Fast randomized full-waveform inversion with compressive sensing. Geophysics, 77(3): A13-A17. [DOI:10.1190/geo2011-0410.1] [18] Lin Y Z, Huang L J. 2015. Acoustic- and elastic-waveform inversion using a modified total-variation regularization scheme. Geophysical Journal International, 200(1): 489-502. [19] Liu Y Z, Yang J Z, Chi B X, et al. 2015. An improved scattering-integral approach for frequency-domain full waveform inversion. Geophysical Journal International, 202(3): 1827-1842. [DOI:10.1093/gji/ggv254] [20] Liu Y F, Wang S D, Wang B F, et al. 2016. Simultaneous multisource full waveform inversion with total variation regularization in time domain. //78th EAGE Conference and Exhibition 2016. EAGE. [21] Lu X T, Han L G, Zhang P, et al. 2015. Direct migration method of multi-source blended data based on total variation. Chinese Journal of Geophysics (in Chinese), 58(9): 3335-3345, doi: 10.6038/cjg20150926. [DOI:10.6038/cjg20150926] [22] Lu X T. 2016. Research on regularized migration imaging methods of multisource blended data [Ph. D. thesis] (in Chinese). Changchun: Jilin University. [23] Luo Y, Schuster G T. 1991. Wave-equation traveltime inversion. Geophysics, 56(5): 645-653. [DOI:10.1190/1.1443081] [24] Moghaddam P P, Herrmann F J. 2010. Randomized full-waveform inversion: A dimensionality-reduction approach. //80th SEG Annual International Meeting, Expanded Abstract. SEG: 977-982. [25] Moghaddam P P, Keers H, Herrmann F J, et al. 2013. A new optimization approach for source-encoding full-waveform inversion. Geophysics, 78(3): R125-R132. [26] Mora P. 1987. Nonlinear two-dimensional elastic inversion of multioffset seismic data. Geophysics, 52(9): 1211-1228. [DOI:10.1190/1.1442384] [27] Mora P. 1988. Elastic wave-field inversion of reflection and transmission data. Geophysics, 53(6): 750-759. [DOI:10.1190/1.1442510] [28] Plessix R E. 2006. A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International, 167(2): 495-503. [DOI:10.1111/gji.2006.167.issue-2] [29] Prieux V, Lambaré G, Operto S, et al. 2013. Building starting models for full waveform inversion from wide-aperture data by stereotomography. Geophysical Prospecting, 61(S1): 109-137. [30] Qiu L Y, Chemingui N, Zou K H, et al. 2016. Full waveform inversion with steerable variation regularization. //86th SEG Annual Meeting, Expanded Abstract. SEG: 1174-1178. [31] Rudin L I, Osher S, Fatemi E. 1992. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena, 60(1-4): 259-268. [DOI:10.1016/0167-2789(92)90242-F] [32] Sears T J, Singh S C, Barton P J. 2008. Elastic full waveform inversion of multi-component OBC seismic data. Geophysical Prospecting, 56(6): 843-862. [DOI:10.1111/gpr.2008.56.issue-6] [33] Sheng J M, Leeds A, Buddensiek M, et al. 2006. Early arrival waveform tomography on near-surface refraction data. Geophysics, 71(4): U47-U57. [DOI:10.1190/1.2210969] [34] Sun H Y, Han L G, Han M, et al. 2015. Elastic full waveform inversion based on visibility analysis and energy compensation for metallic deposit exploration. Chinese Journal of Geophysics (in Chinese), 58(12): 4605-4616, doi: 10.6038/cjg20151222. [DOI:10.6038/cjg20151222] [35] Tarantola A. 1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics, 49(8): 1259-1266. [DOI:10.1190/1.1441754] [36] Tarantola A. 1986. A strategy for nonlinear elastic inversion of seismic reflection data. Geophysics, 51(10): 1893-1903. [DOI:10.1190/1.1442046] [37] Tarantola A. 1988. Theoretical background for the inversion of seismic waveforms including elasticity and attenuation. Pure and Applied Geophysics, 128(1-2): 365-399. [DOI:10.1007/BF01772605] [38] Van Leeuwen T, Aravin A Y, Herrmann F J. 2011. Seismic waveform inversion by stochastic optimization. International Journal of Geophysics, 2011: Article ID 689041, 1-18. [39] Vigh D, Starr E W. 2008. 3D prestack plane-wave, full-waveform inversion. Geophysics, 73(5): VE135-VE144. [DOI:10.1190/1.2952623] [40] Vigh D, Jiao K, Watts D, et al. 2014. Elastic full-waveform inversion application using multicomponent measurements of seismic data collection. Geophysics, 79(2): R63-R77. [DOI:10.1190/geo2013-0055.1] [41] Virieux J, Operto S. 2009. An overview of full-waveform inversion in exploration geophysics. Geophysics, 74(6): WCC1-WCC26. [DOI:10.1190/1.3238367] [42] Wang Y W, Dong L G, Huang C, et al. 2016. A multi-step strategy for mitigating severe nonlinearity in elastic full-waveform inversion. Oil Geophysical Prospecting (in Chinese), 51(2): 288-294. [43] Yuan S Y, Wang S X. 2013. Edge-preserving noise reduction based on Bayesian inversion with directional difference constraints. Journal of Geophysics and Engineering, 10(2): 1-10, doi: 10.1088/1742-2132/10/2/025001. [DOI:10.1007/s11770-015-0520-2] [44] Zhang P, Han L G, Zhou Y, et al. 2015. Passive-source multitaper-spectral method based low-frequency data reconstruction for active seismic sources. Applied Geophysics, 12(4): 585-597, doi:10.1007/s11770-015-0520-2. [DOI:10.1007/s11770-015-0520-2] [45] Zhang P, Han L G, Zhang F J, et al. 2016. Wavelet filter based low-frequency data reconstruction for time domain full waveform inversion. //78th EAGE Conference and Exhibition 2016. EAGE. [46] Zhang P, Han L G, Xu Z, et al. 2017. Sparse blind deconvolution based low-frequency seismic data reconstruction for multiscale full waveform inversion. Journal of Applied Geophysics, 139: 91-108. [DOI:10.1016/j.jappgeo.2017.02.021] [47] Zhou C X, Cai W Y, Luo Y, et al. 1995. Acoustic wave-equation traveltime and waveform inversion of crosshole seismic data. Geophysics, 60(3): 765-773. [DOI:10.1190/1.1443815] [48] 卢昕婷, 韩立国, 张盼等. 2015. 基于全变分原理的多震源混合数据直接偏移方法. 地球物理学报, 58(9): 3335-3345, doi: 10.6038/cjg20150926. [DOI:10.6038/cjg20150926] [49] 卢昕婷. 2016. 多震源混采数据正则化偏移成像方法研究[博士论文].长春: 吉林大学. [50] 孙宏宇, 韩立国, 韩淼等. 2015. 基于可视性分析与能量补偿的金属矿弹性波全波形反演. 地球物理学报, 58(12): 4605-4616, doi: 10.6038/cjg20151222. [DOI:10.6038/cjg20151222] [51] 王毓玮, 董良国, 黄超等. 2016. 降低弹性波全波形反演强烈非线性的分步反演策略. 石油地球物理勘探, 51(2): 288-294.