基于复数波场分解的VSP逆时偏移方法研究
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摘要
相比地面地震勘探,垂直地震剖面(VSP)资料信噪比高,从VSP偏移结果中能够准确地识别井旁小的地质构造.在VSP偏移方法中,VSP逆时偏移方法基于双程波动方程,具有成像精确且无倾角限制、适应任意复杂速度模型等诸多优点,受到人们广泛关注.传统的VSP逆时偏移方法会在成像剖面上产生低频噪声,同时井中检波点分布位置附近会产生井轨迹噪声,严重影响了成像剖面的质量.在本文中,我们利用优化时空域频散关系求解差分系数,提高数值模拟精度;采用混合吸收边界条件压制边界反射,减少边界反射对成像的影响;通过Hilbert变换来构建复数波场,利用波场分解成像条件进行VSP逆时偏移成像,来压制低频噪声和井轨迹噪声.数值模型和实际资料测试表明,基于复数波场分解成像方法能够实现高精度的VSP逆时偏移,并且能够有效地压制VSP逆时偏移中的低频成像噪声和井轨迹噪声;相比地面地震逆时偏移,本文方法能够对井旁构造和盐丘下构造取得更清晰的成像结果.
Comparing with surface seismic data, VSP data has high signal to noise ratio and small geology structure can be identified from Vertical Seismic Profiling(VSP) migration result. VSP Reverse Time Migration, based on two-way wave equation, can produce accurate images. It shows great advantages in imaging dip reflectors and complex structures, which attracts the attention of researchers. Traditional VSP reverse time migration(RTM) can bring low-frequency noise, including the noise at the well location, which contaminates the imaging result. In this paper, we calculate finite-difference coefficients by optimizing time-space dispersion relation, to improve the modeling accuracy. Hybrid absorbing boundary is adopted to absorb the boundary reflection. We construct complex wavefield using Hilbert transform and implement VSP RTM with wavefield decomposition imaging condition. Numerical examples of Marmousi model and salt model show that our method can achieve high-accuracy VSP RTM images and reduce the above mentioned noise. Numerical examples and real data test demonstrate that our method can obtain clearer imaging near the well and under the salt dome than the surface RTM method.
Comparing with surface seismic data, VSP data has high signal to noise ratio and small geology structure can be identified from Vertical Seismic Profiling(VSP) migration result. VSP Reverse Time Migration, based on two-way wave equation, can produce accurate images. It shows great advantages in imaging dip reflectors and complex structures, which attracts the attention of researchers. Traditional VSP reverse time migration(RTM) can bring low-frequency noise, including the noise at the well location, which contaminates the imaging result. In this paper, we calculate finite-difference coefficients by optimizing time-space dispersion relation, to improve the modeling accuracy. Hybrid absorbing boundary is adopted to absorb the boundary reflection. We construct complex wavefield using Hilbert transform and implement VSP RTM with wavefield decomposition imaging condition. Numerical examples of Marmousi model and salt model show that our method can achieve high-accuracy VSP RTM images and reduce the above mentioned noise. Numerical examples and real data test demonstrate that our method can obtain clearer imaging near the well and under the salt dome than the surface RTM method.
引文
Baysal E, Kosloff D D, Sherwood J W C. 1983. Reverse time migration[J]. Geophysics, 48(11): 1514-1524, doi: 10.1190/1.1441434.
Baysal E, Kosloff D D, Sherwood J W C. 1984. A two-way nonreflecting wave equation[J]. Geophysics, 49(2): 132-141, doi: 10.1190/1.1441644.
Bérenger J P. 1994. A perfectly matched layer for the absorption of electromagnetic waves[J]. Journal of Computational Physics, 114(2): 185-200, doi: 10.1006/jcph.1994.1159.
Cai X H, Liu Y, Wang J M, et al. 2015. Full-wavefield VSP reverse-time migration based on the adaptive optimal finite difference scheme[J]. Chinese Journal of Geophysics (in Chinese), 58(9): 3317-3334, doi: 10.6038/cjg20150925.
Campbell A, Gross J, Walker B, et al. 2002. Evaluation of a near-salt reservoir with an offset VSP a case study in the Gulf of Mexico[C]. //2002 SEG Annual Meeting. Society of Exploration Geophysicists. Expanded Abstracts, 2353-2356.
Cassell B R, Alam M A, Millahn K O. 1984. Interactive VSP-CDP mapping in complex media[C]. //1984 SEG Annual Meeting. Society of Exploration Geophysicists. Expanded Abstracts, 842-845.
Chang W F, McMechan G A. 1986. Reverse-time migration of offset vertical seismic profiling data using the excitation-time imaging condition[J]. Geophysics, 51(1): 67-84, doi: 10.1190/1.1442041.
Chon Y T, Souza J, Planchart C, et al. 2003. Offset VSP imaging with elastic reverse time migration[C]. //2003 SEG Annual Meeting. Society of Exploration Geophysicists. Expanded Abstracts, 1079-1082.
Claerbout J F. 1971. Toward a unified theory of reflector mapping[J]. Geophysics, 36(3): 467- 481, doi: 10.1190/1.1440185.
Dillon P B, Thomson R C. 1984. Offset source VSP surveys and their image reconstruction[J]. Geophysical Prospecting, 32(5): 790-811, doi: 10.1111/j.1365-2478.1984.tb00739.x.
Du Q Z, Zhu Y T, Zhang M Q, et al. 2013. A study on the strategy of low wavenumber noise suppression for prestack reverse-time depth migration[J]. Chinese Journal of Geophysics (in Chinese), 56(7): 2391-2401, doi: 10.6038/cjg20130725.
Fei T W, Luo Y, Yang J R, et al. 2015. Removing false images in reverse time migration: The concept of de-primary[J]. Geophysics, 80(6): S237-S244, doi: 10.1190/geo2015- 0289.1.
Fletcher R P, Fowler P J, Kitchenside P, et al. 2006. Suppressing unwanted internal reflections in prestack reverse-time migration[J]. Geophysics, 71(6): E79-E82, doi: 10.1190/1.2356319.
Gao H W, Zhang J F. 2008. Implementation of perfectly matched layers in an arbitrary geometrical boundary for elastic wave modelling[J]. Geophysical Journal International, 174(3): 1029-1036, doi: 10.1111/j.1365-246X.2008.03883.x.
Gazdag J, Squazzero P. 1984. Migration of seismic data by phase shift plus interpolation[J]. Geophysics, 49(2): 124-131, doi: 10.1190/1.1441643.
Guitton A, Kaelin B, Biondi B. 2006. Least-squares attenuation of reverse-time-migration artifacts[J]. Geophysics, 72(1): S19-S23, doi: 10.1190/1.2399367.
Hornby B E, Yu J H, Sharp J A, et al. 2006. VSP: Beyond time-to-depth[J]. The Leading Edge, 25(4): 446- 452, doi: 10.1190/1.2193224.
Hu J T, Wang H Z. 2015. Reverse time migration using analytical time wavefield extrapolation and separation[J]. Chinese Journal of Geophysics (in Chinese), 58(8): 2886-2895, doi: 10.6038/cjg20150822.
Kang W, Cheng J B. 2012. Methods of suppressing artifacts in prestack reverse time migration[J]. Progress in Geophysics (in Chinese), 27(3): 1163-1172, doi: 10.6038/j.issn.1004-2903.2012.03.041.
Ke X, Shi Y. 2017. Forward simulation and reverse time migration imaging based on one step wavefield extrapolation[J]. Chinese Journal of Geophysics (in Chinese), 60(11): 4468- 4479, doi: 10.6038/cjg20171131.
Liu F Q, Zhang G Q, Morton S A, et al. 2011. An effective imaging condition for reverse-time migration using wavefield decomposition[J]. Geophysics, 76(1): S29-S39, doi: 10.1190/1.3533914.
Liu Q L, Luo Y. 1989. Prestack wave equation reverse-time migration of VSP data[J]. Oil Geophysical Prospecting (in Chinese), 24(3): 281-289.
Liu Y. 2013. Globally optimal finite-difference schemes based on least squares[J]. Geophysics, 78(4): T113-T132, doi: 10.1190/geo2012- 0480.1.
Liu Y, Sen M K. 2010. A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation[J]. Geophysics, 75(2): A1-A6, doi: 10.1190/1.3295447.
Loewenthal D, Mufti I R. 1983. Reversed time migration in the spatial frequency domain[J]. Geophysics, 48(5): 627-635, doi: 10.1190/1.1441493.
Loewenthal D, Stoffa P L, Faria E L. 1987. Suppressing the unwanted reflections of the full wave equation[J]. Geophysics, 52(7): 1007-1012, doi: 10.1190/1.1442352.
McMechan G A. 1983. Migration by extrapolation of time-dependent boundary values[J]. Geophysical Prospecting, 31(3): 413- 420, doi: 10.1111/j.1365-2478.1983.tb01060.x.
Neklyudov D, Borodin I. 2009. Imaging of offset VSP data acquired in complex areas with modified reverse-time migration[J]. Geophysical Prospecting, 57(3): 379-391, doi: 10.1111/j.1365-2478.2008.00745.x.
Shen P, Albertin U. 2015. Up-Down separation using Hilbert transformed source for causal imaging condition[C]. //2015 SEG Annual Meeting. Society of Exploration Geophysicists. Expanded Abstracts, 4175- 4179.
Shi Y, Wang Y H. 2016. Reverse time migration of 3D vertical seismic profile data[J]. Geophysics, 81(1): S31-S38, doi: 10.1190/geo2015- 0277.1.
Sun W B, Sun Z D. 2010. VSP reverse time migration based on the pseudo-spectral method and its applications[J]. Chinese Journal of Geophysics (in Chinese), 53(9): 2196-2203, doi: 10.3969/j.issn.0001-5733.2010.09.020.
Wang W H, Ke X, Pei J Y. 2013. Application investigation of perfectly matched layer absorbing boundary condition[J]. Progress in Geophysics (in Chinese), 28(5): 2508-2514, doi: 10.6038/pg20130529.
Whitmore N D. 1983. Iterative depth migration by backward time propagation[C]. //1983 SEG Annual Meeting. Society of Exploration Geophysicists. Expanded Abstracts, 382-385.
Wiggins J W. 1984. Kirchhoff integral extrapolation and migration of nonplanar data[J] Geophysics, 49(8): 1239-1248, doi: 10.1190/1.1441752.
Wyatt K, Wyatt S B. 1981. Determination of subsurface structural information using the vertical seismic profile[C]. //1981 SEG Annual Meeting. Society of Exploration Geophysicists. Expanded Abstracts.
Yoon K, Marfurt K J. 2006. Reverse-time migration using the Poynting vector[J]. Exploration Geophysics, 37(1): 102-107, doi: 10.1071/EG06102.
Zhang Y, Sun J. 2009. Practical issues in RTM: true amplitude gathers, noise removal and harmonic-source encoding[J]. First Break, 27(1): 53-59, doi: 10.3997/1365-2397.2009002.
蔡晓慧, 刘洋, 王建民, 等. 2015. 基于自适应优化有限差分方法的全波VSP逆时偏移[J]. 地球物理学报, 58(9): 3317-3334, doi: 10.6038/cjg20150925.
杜启振, 朱钇同, 张明强, 等. 2013. 叠前逆时深度偏移低频噪声压制策略研究[J]. 地球物理学报, 56(7): 2391-2401, doi: 10.6038/cjg20130725.
胡江涛, 王华忠. 2015. 基于解析时间波场外推与波场分解的逆时偏移方法研究[J]. 地球物理学报, 58(8): 2886-2895, doi: 10.6038/cjg20150822.
康玮, 程玖兵. 2012. 叠前逆时偏移假象去除方法[J]. 地球物理学进展, 27(3): 1163-1172, doi: 10.6038/j.issn.1004-2903.2012.03.041.
柯璇, 石颖. 2017. 基于一步法波场延拓的正演模拟和逆时偏移成像[J]. 地球物理学报, 60(11): 4468- 4479, doi: 10.6038/cjg20171131.
刘清林, 骆毅. 1989. VSP 资料的叠前波动方程逆时偏移[J]. 石油地球物理勘探, 24(3): 281-289.
孙文博, 孙赞东. 2010. 基于伪谱法的VSP逆时偏移及其应用研究[J]. 地球物理学报, 53(9): 2196-2203, doi: 10.3969/j.issn.0001-5733.2010.09.020.
王维红, 柯璇, 裴江云. 2013. 完全匹配层吸收边界条件应用研究[J]. 地球物理学进展, 28(5): 2508-2514, doi: 10.6038/pg20130529.
Baysal E, Kosloff D D, Sherwood J W C. 1984. A two-way nonreflecting wave equation[J]. Geophysics, 49(2): 132-141, doi: 10.1190/1.1441644.
Bérenger J P. 1994. A perfectly matched layer for the absorption of electromagnetic waves[J]. Journal of Computational Physics, 114(2): 185-200, doi: 10.1006/jcph.1994.1159.
Cai X H, Liu Y, Wang J M, et al. 2015. Full-wavefield VSP reverse-time migration based on the adaptive optimal finite difference scheme[J]. Chinese Journal of Geophysics (in Chinese), 58(9): 3317-3334, doi: 10.6038/cjg20150925.
Campbell A, Gross J, Walker B, et al. 2002. Evaluation of a near-salt reservoir with an offset VSP a case study in the Gulf of Mexico[C]. //2002 SEG Annual Meeting. Society of Exploration Geophysicists. Expanded Abstracts, 2353-2356.
Cassell B R, Alam M A, Millahn K O. 1984. Interactive VSP-CDP mapping in complex media[C]. //1984 SEG Annual Meeting. Society of Exploration Geophysicists. Expanded Abstracts, 842-845.
Chang W F, McMechan G A. 1986. Reverse-time migration of offset vertical seismic profiling data using the excitation-time imaging condition[J]. Geophysics, 51(1): 67-84, doi: 10.1190/1.1442041.
Chon Y T, Souza J, Planchart C, et al. 2003. Offset VSP imaging with elastic reverse time migration[C]. //2003 SEG Annual Meeting. Society of Exploration Geophysicists. Expanded Abstracts, 1079-1082.
Claerbout J F. 1971. Toward a unified theory of reflector mapping[J]. Geophysics, 36(3): 467- 481, doi: 10.1190/1.1440185.
Dillon P B, Thomson R C. 1984. Offset source VSP surveys and their image reconstruction[J]. Geophysical Prospecting, 32(5): 790-811, doi: 10.1111/j.1365-2478.1984.tb00739.x.
Du Q Z, Zhu Y T, Zhang M Q, et al. 2013. A study on the strategy of low wavenumber noise suppression for prestack reverse-time depth migration[J]. Chinese Journal of Geophysics (in Chinese), 56(7): 2391-2401, doi: 10.6038/cjg20130725.
Fei T W, Luo Y, Yang J R, et al. 2015. Removing false images in reverse time migration: The concept of de-primary[J]. Geophysics, 80(6): S237-S244, doi: 10.1190/geo2015- 0289.1.
Fletcher R P, Fowler P J, Kitchenside P, et al. 2006. Suppressing unwanted internal reflections in prestack reverse-time migration[J]. Geophysics, 71(6): E79-E82, doi: 10.1190/1.2356319.
Gao H W, Zhang J F. 2008. Implementation of perfectly matched layers in an arbitrary geometrical boundary for elastic wave modelling[J]. Geophysical Journal International, 174(3): 1029-1036, doi: 10.1111/j.1365-246X.2008.03883.x.
Gazdag J, Squazzero P. 1984. Migration of seismic data by phase shift plus interpolation[J]. Geophysics, 49(2): 124-131, doi: 10.1190/1.1441643.
Guitton A, Kaelin B, Biondi B. 2006. Least-squares attenuation of reverse-time-migration artifacts[J]. Geophysics, 72(1): S19-S23, doi: 10.1190/1.2399367.
Hornby B E, Yu J H, Sharp J A, et al. 2006. VSP: Beyond time-to-depth[J]. The Leading Edge, 25(4): 446- 452, doi: 10.1190/1.2193224.
Hu J T, Wang H Z. 2015. Reverse time migration using analytical time wavefield extrapolation and separation[J]. Chinese Journal of Geophysics (in Chinese), 58(8): 2886-2895, doi: 10.6038/cjg20150822.
Kang W, Cheng J B. 2012. Methods of suppressing artifacts in prestack reverse time migration[J]. Progress in Geophysics (in Chinese), 27(3): 1163-1172, doi: 10.6038/j.issn.1004-2903.2012.03.041.
Ke X, Shi Y. 2017. Forward simulation and reverse time migration imaging based on one step wavefield extrapolation[J]. Chinese Journal of Geophysics (in Chinese), 60(11): 4468- 4479, doi: 10.6038/cjg20171131.
Liu F Q, Zhang G Q, Morton S A, et al. 2011. An effective imaging condition for reverse-time migration using wavefield decomposition[J]. Geophysics, 76(1): S29-S39, doi: 10.1190/1.3533914.
Liu Q L, Luo Y. 1989. Prestack wave equation reverse-time migration of VSP data[J]. Oil Geophysical Prospecting (in Chinese), 24(3): 281-289.
Liu Y. 2013. Globally optimal finite-difference schemes based on least squares[J]. Geophysics, 78(4): T113-T132, doi: 10.1190/geo2012- 0480.1.
Liu Y, Sen M K. 2010. A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation[J]. Geophysics, 75(2): A1-A6, doi: 10.1190/1.3295447.
Loewenthal D, Mufti I R. 1983. Reversed time migration in the spatial frequency domain[J]. Geophysics, 48(5): 627-635, doi: 10.1190/1.1441493.
Loewenthal D, Stoffa P L, Faria E L. 1987. Suppressing the unwanted reflections of the full wave equation[J]. Geophysics, 52(7): 1007-1012, doi: 10.1190/1.1442352.
McMechan G A. 1983. Migration by extrapolation of time-dependent boundary values[J]. Geophysical Prospecting, 31(3): 413- 420, doi: 10.1111/j.1365-2478.1983.tb01060.x.
Neklyudov D, Borodin I. 2009. Imaging of offset VSP data acquired in complex areas with modified reverse-time migration[J]. Geophysical Prospecting, 57(3): 379-391, doi: 10.1111/j.1365-2478.2008.00745.x.
Shen P, Albertin U. 2015. Up-Down separation using Hilbert transformed source for causal imaging condition[C]. //2015 SEG Annual Meeting. Society of Exploration Geophysicists. Expanded Abstracts, 4175- 4179.
Shi Y, Wang Y H. 2016. Reverse time migration of 3D vertical seismic profile data[J]. Geophysics, 81(1): S31-S38, doi: 10.1190/geo2015- 0277.1.
Sun W B, Sun Z D. 2010. VSP reverse time migration based on the pseudo-spectral method and its applications[J]. Chinese Journal of Geophysics (in Chinese), 53(9): 2196-2203, doi: 10.3969/j.issn.0001-5733.2010.09.020.
Wang W H, Ke X, Pei J Y. 2013. Application investigation of perfectly matched layer absorbing boundary condition[J]. Progress in Geophysics (in Chinese), 28(5): 2508-2514, doi: 10.6038/pg20130529.
Whitmore N D. 1983. Iterative depth migration by backward time propagation[C]. //1983 SEG Annual Meeting. Society of Exploration Geophysicists. Expanded Abstracts, 382-385.
Wiggins J W. 1984. Kirchhoff integral extrapolation and migration of nonplanar data[J] Geophysics, 49(8): 1239-1248, doi: 10.1190/1.1441752.
Wyatt K, Wyatt S B. 1981. Determination of subsurface structural information using the vertical seismic profile[C]. //1981 SEG Annual Meeting. Society of Exploration Geophysicists. Expanded Abstracts.
Yoon K, Marfurt K J. 2006. Reverse-time migration using the Poynting vector[J]. Exploration Geophysics, 37(1): 102-107, doi: 10.1071/EG06102.
Zhang Y, Sun J. 2009. Practical issues in RTM: true amplitude gathers, noise removal and harmonic-source encoding[J]. First Break, 27(1): 53-59, doi: 10.3997/1365-2397.2009002.
蔡晓慧, 刘洋, 王建民, 等. 2015. 基于自适应优化有限差分方法的全波VSP逆时偏移[J]. 地球物理学报, 58(9): 3317-3334, doi: 10.6038/cjg20150925.
杜启振, 朱钇同, 张明强, 等. 2013. 叠前逆时深度偏移低频噪声压制策略研究[J]. 地球物理学报, 56(7): 2391-2401, doi: 10.6038/cjg20130725.
胡江涛, 王华忠. 2015. 基于解析时间波场外推与波场分解的逆时偏移方法研究[J]. 地球物理学报, 58(8): 2886-2895, doi: 10.6038/cjg20150822.
康玮, 程玖兵. 2012. 叠前逆时偏移假象去除方法[J]. 地球物理学进展, 27(3): 1163-1172, doi: 10.6038/j.issn.1004-2903.2012.03.041.
柯璇, 石颖. 2017. 基于一步法波场延拓的正演模拟和逆时偏移成像[J]. 地球物理学报, 60(11): 4468- 4479, doi: 10.6038/cjg20171131.
刘清林, 骆毅. 1989. VSP 资料的叠前波动方程逆时偏移[J]. 石油地球物理勘探, 24(3): 281-289.
孙文博, 孙赞东. 2010. 基于伪谱法的VSP逆时偏移及其应用研究[J]. 地球物理学报, 53(9): 2196-2203, doi: 10.3969/j.issn.0001-5733.2010.09.020.
王维红, 柯璇, 裴江云. 2013. 完全匹配层吸收边界条件应用研究[J]. 地球物理学进展, 28(5): 2508-2514, doi: 10.6038/pg20130529.