Review of seismic inverse scattering migration and inversion
-
摘要: 随着油气勘探领域逐渐向深层、复杂型、隐蔽性油气藏转移，油气资源的勘探难度越来越大，传统反射地震勘探技术难以满足日益增长的油气勘探需求，亟需发展适合复杂地质构造的地震波偏移反演新技术. 针对地球深部非均匀结构体引起的地震散射波，发展地震逆散射偏移反演理论和技术将有可能解决复杂构造成像反演的技术难题. 本文回顾地震波逆散射偏移反演理论的发展历史和基本原理，以逆广义Radon变换求解线性化逆散射问题为基础，介绍逆散射理论在介质结构成像、物性参数反演、多次波衰减等方面的技术延伸，同时将其应用到合成数据和实际数据资料，探讨地震勘探逆散射方法的技术优势和应用潜力.Abstract: With the shifting toward deeper, geologically more complex, and more subtle hydrocarbon reservoirs than before, the exploration of oil and gas resources is becoming more and more difficult. The traditional seismic reflection exploration technology can hardly meet the increasing demand for oil and gas, and it is urgent to develop new seismic migration and inversion technologies adapted to complex geological structures. In view of the seismic scattered waves caused by heterogeneous structures in the deep part of the earth, it is possible to solve the technical problems for imaging complex geological structures by developing the seismic inverse scattering migration inversion theory and technology. This paper reviews the development history and basic principles of seismic inverse scattering migration and inversion theory, based on the inverse generalized Radon transform to solve the linearized seismic inverse scattering problem, introduces the technical extension in the geological structure imaging, inversion for petrophysical parameters, multiple attenuation and so on. At the same time, the application to synthetic and real data is also presented, in which the technical advantages and application potential of the inverse scattering method are discussed.
-
Key words:
- inverse scattering /
- generalized Radon transform /
- migration /
- inversion
-
图 1 （a）常规GRT反演剖面；（b）角度域GRT反演剖面（修改自Li et al., 2018）
Figure 1. Inversion profiles for the layered model by using (a) conventional GRT inversion method and (b) angle-domain GRT inversion method (modified from Li et al., 2018)
图 2 常规GRT反演振幅曲线（黑色虚线）和真实扰动振幅（红色实线）对比图. 道集位置对应图1a中的白色虚线位置: （a）x=500 m；（b）x=800 m；以及（c）x=2000 m（修改自Li et al., 2018）
Figure 2. Comparison of true perturbations (red solid lines) and retrieved perturbations (black dashed lines) by conventional GRT inversion method at the distances (a) x=500 m ; (b) x=800 m ; and (c) x=2000 m in Fig. 1a (modified from Li et al., 2018)
图 3 与图2类似，角度域GRT反演振幅曲线与真实扰动振幅对比图（修改自Li et al., 2018）
Figure 3. Similar to Fig. 2, but for angle-domain GRT inversion method from Fig. 1b (modified from Li et al., 2018)
图 4 水平保幅情况.（a）常规GRT反演；（b）角度域GRT反演（修改自Li et al., 2018）
Figure 4. The retrieved amplitude curves picked along the reconstructed reflectors from (a) conventional GRT inversion profile and (b) angle-domain GRT inversion profile (modified from Li et al., 2018)
图 5 变密度水平层状模型角度域共成像点道集图（修改自Li et al., 2018）
Figure 5. ADCIGs calculated at the distance x=2 000 m (modified from Li et al., 2018)
图 6 （a）理论AVA特征曲线；（b）计算提取的AVA曲线（修改自Li et al., 2018）
Figure 6. (a) Theoretical AVA curves and (b) Picked AVA curves from the calculated ADCIGs panel (Fig. 5) (modified from Li et al., 2018)
图 7 散射序列示意图.（a）全波场散射示意图.（b）一阶Born近似散射示意图.（c）二阶Born近似散射示意图（李武群等, 2017）
Figure 7. Schematics of scattering series for (a) full order Born scattering, (b) first order scattering, and (c) second order scattering (Li et al., 2017)
图 8 局部二次散射示意图（李武群等，2017）
Figure 8. Schematics of second order scattering within a local area (Li et al., 2017)
图 9 不同速度扰动的单界面水平层状模型
Figure 9. Single interface horizontal layered model with different velocity perturbations
图 10 不同扰动模型Born近似误差变化曲线.（a）一阶Born近似误差.（b）二阶Born近似误差（李武群等，2017）
Figure 10. Error distribution curves from Born data of different perturbation. (a) First order Born approximate data error. (b) Second order Born approximate data error (Li et al., 2017)
图 11 GRT线性反演和非线性反演界面振幅归一化曲线图.（a）GRT线性反演；（b）GRT非线性反演（李武群等，2017）
Figure 11. Comparison of normalized inverted amplitudes from GRT linear and nonlinear inversion of different perturbation models. (a) GRT linear inversion. (b) GRT nonlinear inversion (Li et al., 2017)
图 12 （a）Sigsbee 2A速度模型及（b）非线性反演剖面（修改自Ouyang et al., 2014）
Figure 12. (a) the Sigsbee 2A model and (b) the nonlinear inversion profile (modified from Ouyang et al., 2014)
图 13 反演值（实线）与真实扰动（虚线）之间的比较.（a）线性反演值与真实扰动之间的比较.（b）非线性反演值与真实扰动的比较（修改自Ouyang et al., 2014）
Figure 13. Comparison between true perturbations (dotted line) and inverted perturbations (solid line). (a) Linear inversion. (b) Quadric nonlinear inversion (modified from Ouyang et al., 2014)
图 14 墨西哥湾某区ISS自由表面多次波去除应用示例（修改自Weglein et al., 2003）
Figure 14. The left panel is a stack of a field data set from the Gulf of Mexico. The right panel is the result of inverse-scattering free-surface multiple removal (modified from Weglein et al., 2003)
图 15 墨西哥湾某区ISS层间多次波去除应用示例（修改自Weglein et al., 2003）
Figure 15. An example of inverse-scattering internal multiple attenuation from the Gulf of Mexico (modified from Weglein et al., 2003)
图 17 2D SEAM 模型偏移成像结果.（a）逆散射成像；（b）高斯束成像
Figure 17. The migration results of the 2D SEAM model by (a) ISM, and (b) GBM
图 19 3D SEG/EAGE模型沿x方向剖面偏移成像结果.（a）和（b）分别原始速度模型.（c）和（d）为逆散射偏移成像结果.（e）和（f）为高斯束偏移成像结果
Figure 19. Migration results of the profiles along x direction. (a) and (b) are velocity models. (c) and (d) are ISM results. (e) and (f) are GBM results
图 20 3D SEG/EAGE模型沿y方向剖面偏移成像结果.（a）和（b）分别原始速度模型.（c）和（d）为逆散射偏移成像结果.（e）和（f）为高斯束偏移成像结果
Figure 20. Migration results of the profiles along y direction. (a) and (b) are velocity models. (c) and (d) are ISM results. (e) and (f) are GBM results
图 21 3D SEG/EAGE模型深度切片偏移成像结果. （a）为深度位置z=0.8 km切片上的速度模型. （b）为逆散射偏移成像结果. （c）为高斯束偏移成像结果
Figure 21. Migration results of the depth slice. (a) Velocity at slice z=0.8 km. (b) ISM result. (c) GBM result
图 24 逆散射偏移成像剖面（左）和局部放大区域（右）
Figure 24. The imaging result by Inverse scattering migration (left) and the zoomed one (right)
图 25 Kirchhoff偏移成像剖面（左）和局部放大区域（右）
Figure 25. The imaging result by Kirchhoff migration (left) and the zoomed one (right)
图 26 SEAM成像结果. （a），（b），（c）和（d）依次为速度场，上行波成像，下行波成像以及全波成像结果（修改自Li et al., 2019）
Figure 26. Imaging results of the SEAM 2D model (a). (b), (c) and (d) are the imaging results using primary, multiple and joint imaging condition, respectively (modified from Li et al., 2019)
表 1 常密度水平层状模型
Table 1. Horizontal layered model with constant density
层厚度/m 速度/(m·s–1) 密度/(kg·m–3) 300 2000 2500 300 2100 2500 300 2000 2500 300 2100 2500 300 2000 2500 300 2100 2500 
下载: 导出CSV
表 2 变密度水平层状模型
Table 2. Horizontal layered model with varying density
层厚度/m 速度/(m·s–1) 密度/(kg·m–3) 300 2000 2000 300 2100 2100 300 2000 2000 300 2100 2100 300 2000 2000 300 2100 2100
下载: 导出CSV
-
[1] Beylkin G. Imaging of Discontinuities in the Inverse Scattering Problem by Inversion of a Causal Generalized Radon-Transform[J]. Journal of Mathematical Physics, 1985, 26(1): 99-108. doi: 10.1063/1.526755 [2] Beylkin G. The inversion problem and applications of the generalized Radon transform[J]. Communications on pure and applied mathematics, 1984, 37(5): 579-599. doi: 10.1002/cpa.3160370503 [3] Beylkin G, Burridge R. Linearized inverse scattering problems in acoustics and elasticity[J]. Wave Motion, 1990, 12(1): 15-52. doi: 10.1016/0165-2125(90)90017-X [4] Bleistein N. On the imaging of reflectors in the earth[J]. Geophysics, 1987, 52(7): 931-942. doi: 10.1190/1.1442363 [5] Burridge R, De Hoop M V, Miller D E, et al., Multiparameter inversion in anisotropic elastic media[J]. Geophysical Journal International, 1998, 134(3): 757-777. [6] 陈小宏, 刘华锋. 预测多次波的逆散射级数方法与SRME方法及比较[J]. 地球物理学进展, 2012, 27(3): 1040-1050.Chen X H, Liu H F. Comparison between inverse scattering series method and SRME method in free surface related multiple prediction[J]. Progress in Geophys, 2012, 27(3): 1040-1050 (in Chinese). [7] Clayton R W, Stolt R H. A Born-WKBJ inversion method for acoustic reflection data[J]. Geophysics, 1981, 46(11): 1559-1567. doi: 10.1190/1.1441162 [8] Cohen J K. Bleistein N, An inverse method for determining small variations in propagation speed[J]. Siam Journal on Applied Mathematics, 1977, 32(4): 784-799. doi: 10.1137/0132066 [9] Cohen J K, Bleistein N. Velocity inversion procedure for acoustic waves[J]. Geophysics, 1979, 44(6): 1077-1087. doi: 10.1190/1.1440996 [10] De Hoop M V, Bleistein N, Generalized radon transform inversions for reflectivity in anisotropic elastic media[J]. Inverse Problems, 1997, 13(3): 669-690. doi: 10.1088/0266-5611/13/3/009 [11] De Hoop M V, Brandsbergdahl S. Maslov asymptotic extension of generalized Radon transform inversion in anisotropic elastic media: a least-squares approach[J]. Inverse Problems, 2000, 16(3): 519-562. doi: 10.1088/0266-5611/16/3/301 [12] De Hoop M V, Spencer C, Burridge R. The resolving power of seismic amplitude data: An anisotropic inversion/migration approach[J]. Geophysics, 1999, 64(3): 852-873. doi: 10.1190/1.1444595 [13] Dillon P B, A comparison between kirchhoff and grt migration on vsp data[J]. Geophysical Prospecting, 1990, 38(7): 757-777. doi: 10.1111/j.1365-2478.1990.tb01873.x [14] 丁科. 地震逆散射理论与深度成像[D].长沙: 中南大学, 2002.Ding K. Seismic inverse scattering theory and depth imaging[D]. Changsha: Central South University, 2002 (in Chinese). [15] 董兴朋, 滕吉文, 马学英, 等. 二阶Born近似有限频率走时敏感核[J]. 地球物理学报, 2016, 59(3): 1070-1081.Dong X P, Teng J W, Ma X Y, et al. Finite-frequency traveltime sensitivity kernel based on second-order Born approximation[J]. Chinese Journal of Geophysics, 59(3): 1070-1081 (in Chinese). [16] Fleury C, Vasconcelos I. Imaging condition for nonlinear scattering-based imaging: Estimate of power loss in scattering[J]. Geophysics, 2012, 77(1): S1-S18. [17] French W S. Two-dimensional and three-dimensional migration of model-experiment reflection profiles[J]. Geophysics, 1974, 39(3): 265-277. doi: 10.1190/1.1440426 [18] 符力耘. Born序列频散方程和Born-Kirchhoff传播算子[J]. 地球物理学报, 2010, 53(2): 370-384.Fu L Y. Born-series dispersion equation and Born-Kirchhoff propagators[J]. Chinese Journal of Geophysics, 2010, 53(2): 370-384 (in Chinese). [19] 符力耘, 杨慧珠, 牟永光. 非均匀介质散射问题的体积分方程数值解法[J]. 力学学报, 1998, 30(4): 488-494.Fu L Y, Yang H Z, Mu Y G. Volume integral equation method for scattering problems of inhomogeneous media [J]. Acta Mechanica Sinica, 1998, 30(4): 488-494 (in Chinese). [20] Ikelle L T. Using even terms of the scattering series for deghosting and multiple attenuation of ocean‐bottom cable data[J]. Geophysics, 1999, 64(2): 579-592. doi: 10.1190/1.1444565 [21] Ikelle L T, Amundsen L, Yoo S. An optimization of the inverse scattering multiple attenuation method for OBS and VC data[J]. Geophysics, 2002, 67(4): 1293-1303. doi: 10.1190/1.1500392 [22] 金德刚, 常旭, 刘伊克. 逆散射级数法预测层间多次波的算法改进及其策略 [J]. 地球物理学报, 2008, 51(4): 1209-1217.Jin D G, Chang X, Liu Y K. Algorithm improvement and strategy of internal multiples prediction based on inverse scattering series method [J]. Chinese Journal of Geophysics, 2008, 51(4): 1209-1217 (in Chinese). [23] Li W, Mao W, Li X, et al. Angle-domain inverse scattering migration/inversion in isotropic media[J]. Journal of Applied Geophysics, 2018, 154: 196-209. doi: 10.1016/j.jappgeo.2018.05.006 [24] Li W, Mao W, Liang Q. Joint imaging with primaries and multiples of VSP data by GRT migration[J]. Seg Technical Program Expanded Abstracts, 2019,18(10): 5325-5329. [25] 李武群, 毛伟建, 欧阳威, 等. 二阶Born近似及其在逆散射GRT反演中的应用[J]. 地球物理学进展, 2017, 32(2): 0645-0656.Li W Q, Mao W J, Ouyang W, et al. Second-order Born appoximation and its application to inverse scattering GRT inversion [J]. Progress in Geophysics, 32(2): 0645-0656 (in Chinese). [26] 李翔, 胡天跃. 逆散射级数法去除自由表面多次波[J]. 地球物理学报, 2009, 52(6): 1633-1640.Li X, Hu T Y. Surface-related multiple removal with inverse scattering series method [J]. Chinese Journal of Geophysics, 2009, 52(6): 1633-1640 (in Chinese). [27] Liang Q, Ouyang W, Mao W, et al. Scattering pattern analysis and true-amplitude generalized Radon transform migration for acoustic transversely isotropic media with a vertical axis of symmetry[J]. Geophysical Prospecting, 2020,68(4):1211-1227. doi: 10.1111/1365-2478.12921 [28] Liu F, Weglein A B, Innanen K A, et al. Multi-dimensional seismic imaging using the inverse scattering series[J]. Seg Technical Program Expanded Abstracts, 2006, 25(1): 3026-3030. [29] Mao W J, Ouyang W, Li X L. Nonlinear migration inversion with second-order born approximation[C]// 75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013, London, UK, 10-13 June 2013. [30] Matson K H. The relationship between scattering theory and the primaries and multiples of reflection seismic data[J]. Journal of Seismic Exploration, 1996, 5(1): 63-78. [31] Miller D, Oristaglio M, Beylkin G. A new slant on seismic imaging: Migration and integral geometry[J]. Geophysics, 1987, 52(7): 943-964. doi: 10.1190/1.1442364 [32] Moses H E. Calculation of the scattering potential from reflection coefficients[J]. Physical Review, 1956, 102(2): 559-567. doi: 10.1103/PhysRev.102.559 [33] Ouyang W, Mao W. Approximate nonlinear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media[J]. Geophysical Journal International, 2018, 214(1): 14-35. doi: 10.1093/gji/ggy106 [34] Ouyang W, Mao W, Li W, et al. Approximate non-linear multiparameter inversion with single and double scattering seismic wavefields in acoustic media[J]. Geophysical Journal International, 2017, 208(2): 767-789. doi: 10.1093/gji/ggw422 [35] Ouyang W, Mao W, Li X. Approximate solution of nonlinear double-scattering inversion for true amplitude imaging[J]. Geophysics, 2014, 80(1): R43-R55. [36] Prosser R T. Formal solutions of inverse scattering problems. III[J]. Journal of Mathematical Physics, 1969, 21(10): 2648-2653. [37] Protasov M, Tcheverda V. True/preserving amplitude seismic imaging based on Gaussian beams application[J]. Seg Technical Program Expanded Abstracts, 2006,25(1), doi: 10.1190/1.2369957. [38] Protasov M I, Tcheverda V A. True amplitude elastic Gaussian beam imaging of multicomponent walkaway vertical seismic profiling data[J]. Geophysical Prospecting, 2012, 60(6): 1030-1042. doi: 10.1111/j.1365-2478.2012.01068.x [39] Protasov M L. Tcheverda V A. True amplitude imaging by inverse generalized Radon transform based on Gaussian beam decomposition of the acoustic Green's function[J]. Geophysical Prospecting, 2011, 59(2): 197-209. doi: 10.1111/j.1365-2478.2010.00920.x [40] Ravasi M. Curtis A. Nonlinear scattering based imaging in elastic media: Theory, theorems, and imaging conditions[J]. Geophysics, 2013, 78(3): S137-S155. doi: 10.1190/geo2012-0286.1 [41] Raz S. Direct reconstruction of velocity and density profiles from scattered field data[J]. Geophysics, 1981, 46(6): 832-836. doi: 10.1190/1.1441220 [42] Thorbecke J W. Draganov D. Finite-difference modeling experiments for seismic interferometry[J]. Geophysics, 2011, 76(6): H1-H18. doi: 10.1190/geo2010-0039.1 [43] Weglein A B. How can the inverse‐scattering method really predict and subtract all multiples from a multidimensional earth with absolutely no subsurface information?[J]. Geophysics, 1999, 18(1): 132-136. [44] Weglein A B, Araujo F V, Carvalho P M, et al. Inverse scattering series and seismic exploration[J]. Inverse Problems, 2003, 19 (6):R27-R83. doi: 10.1088/0266-5611/19/6/R01 [45] Weglein A B, Gasparotto F A, Carvalho P M, et al. An inverse‐scattering series method for attenuating multiples in seismic reflection data[J]. Geophysics, 1997, 62(6): 1975-1989. doi: 10.1190/1.1444298 [46] Weglein A B. Gray S H. The sensitivity of Born inversion to the choice of reference velocity; a simple example[J]. Geophysics, 1983, 48(1): 36-38. doi: 10.1190/1.1441404 [47] 杨金龙, 朱立华. 逆散射级数层间多次波压制方法及其应用[J]. 石油物探, 2018, 57(6): 853-861.Yang J L, Zhu L H. Inverse scattering series internal multiple attenuation method and its application[J]. Geophysical Prospecting for Petroleum, 2018, 57(6): 853-861 (in Chinese). [48] Zhang H. Weglein A B. Direct nonlinear inversion of 1D acoustic media using inverse scattering subseries[J]. Geophysics, 2009a, 74(6): WCD29-WCD39. doi: 10.1190/1.3256283 [49] Zhang H, Weglein A B. Direct nonlinear inversion of multiparameter 1D elastic media using the inverse scattering series[J]. Geophysics, 2009b, 74(6): WCD15-WCD27. doi: 10.1190/1.3251271 -
点击查看大图
计量
- 文章访问数: 1625
- HTML全文浏览量: 851
- PDF下载量: 192
- 被引次数: 0
