反射波层析反演速度建模方法
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摘要
我国油气地震勘探目标逐渐转向小尺度(薄互层)岩性油气藏,油气地震勘探技术也逐渐向单点高密度、宽带、宽方位("两宽一高")地震勘探方向转变。"两宽一高"的地震数据采集为宽带波阻抗成像提供了数据基础,精确的背景(偏移)速度建模是宽带波阻抗成像必不可少的环节。在实际应用中,反射波层析反演是主要的宏观速度建模技术,典型的方法如成像道集层析或立体层析等,但它们在反演精度及计算效率方面仍存在不足之处。在数据域中,反射波时差的精确测量仍然是一个颇具挑战性的问题。为解决这一难题,从叠前地震数据的稀疏表达与特征分解出发,利用特征波场分解和包络走时定义准则,提取叠前地震数据的运动学信息,并构造了特征数据体(包含地震波的斜率、走时及子波波形)。通过分析特征波在地下的聚焦特性,提出了一种反射波残差(时差或者地下偏移距)的自动测量方法,避免了地震波振幅对反射波运动学信息拟合的影响。基于反射波残差,提出了一种特征波反射层析反演(characteristic reflection inversion,简记为CRI)方法,通过极小化反射波时差或地下偏移距实现背景速度反演。理论分析可知:反射波时差测量方法仅适用于二维模型,而地下偏移距测量方法可以适用于二维和三维模型,因而其适用性更广。在数值计算方面,反射波残差目标泛函的梯度可以用波动理论计算,也可以用射线理论近似。出于计算效率的考虑,利用射线理论计算泛函梯度并结合梯度去噪方法,实现低波数的速度更新。数值实验表明:该方法无需长偏移距观测数据或低频信息,对初始模型依赖性低、计算效率高,且整个反演流程可以实现全自动化,可以为后续的宽波数带速度建模提供较为可靠的低波数背景速度模型。
As the target of oil exploration in China is changing toward the small-scale(thin-interbed) lithologic reservoirs,the seismic acquisition methods are being gradually upgraded to the broadband,wide-azimuth and high-density(BWH) techniques.Such new techniques permit broadband impedance imaging,which require an accurate background model(in terms of velocity,anisotropy,even Q).In exploration seismology,the macro-velocity model is often estimated using reflection tomography.Typical inversion methods,such as the Ray-based tomographic migration velocity analysis or the stereo-tomography,still suffer from low resolution and high computational costs.In the data domain,accurately measuring the difference in the reflection travel time between the observed and synthetic data remains a challenge.To address this problem,we begin with a sparse presentation and characterization of pre-stack seismic data,from which we extract kinematic information(slope,travel time,and waveform of the reflection event) using the characteristic wavefield decomposition method.Furthermore,by analyzing the focus property of a wavefield in the subsurface space,two reflection-misfit calculation strategies are proposed:the reflection travel time-residual and the subsurface-offset measurements.Consequently,the new reflection inversion method,which is referred to as the characteristic reflection inversion(CRI),is based on the minimization of reflection travel-time residuals or subsurface offsets.According to a theoretical analysis,the strategy for measuring the reflection travel time residual should be valid for any 2 D media,while the subsurface offset measurement method should be valid for both 2 D and 3 D media.The functional gradient can be calculated either by wave-equation linearization or by the ray theory.To increase the computational efficiency,the ray theory version of the gradient is calculated,followed by a denoising method in such a way that the low-wavenumber components of the velocity model can be updated.Numerical examples demonstrate that the CRI neither requires low-frequency seismic data nor long-offset acquisition.In addition,the CRI is computationally efficient,since it eliminates the need for calculating and saving the common image gathers and travel time picking.Furthermore,it is a fully automatic procedure,and is insensitive to the accuracy of the staring model,making it quite promising for automatic macro-velocity model building.
As the target of oil exploration in China is changing toward the small-scale(thin-interbed) lithologic reservoirs,the seismic acquisition methods are being gradually upgraded to the broadband,wide-azimuth and high-density(BWH) techniques.Such new techniques permit broadband impedance imaging,which require an accurate background model(in terms of velocity,anisotropy,even Q).In exploration seismology,the macro-velocity model is often estimated using reflection tomography.Typical inversion methods,such as the Ray-based tomographic migration velocity analysis or the stereo-tomography,still suffer from low resolution and high computational costs.In the data domain,accurately measuring the difference in the reflection travel time between the observed and synthetic data remains a challenge.To address this problem,we begin with a sparse presentation and characterization of pre-stack seismic data,from which we extract kinematic information(slope,travel time,and waveform of the reflection event) using the characteristic wavefield decomposition method.Furthermore,by analyzing the focus property of a wavefield in the subsurface space,two reflection-misfit calculation strategies are proposed:the reflection travel time-residual and the subsurface-offset measurements.Consequently,the new reflection inversion method,which is referred to as the characteristic reflection inversion(CRI),is based on the minimization of reflection travel-time residuals or subsurface offsets.According to a theoretical analysis,the strategy for measuring the reflection travel time residual should be valid for any 2 D media,while the subsurface offset measurement method should be valid for both 2 D and 3 D media.The functional gradient can be calculated either by wave-equation linearization or by the ray theory.To increase the computational efficiency,the ray theory version of the gradient is calculated,followed by a denoising method in such a way that the low-wavenumber components of the velocity model can be updated.Numerical examples demonstrate that the CRI neither requires low-frequency seismic data nor long-offset acquisition.In addition,the CRI is computationally efficient,since it eliminates the need for calculating and saving the common image gathers and travel time picking.Furthermore,it is a fully automatic procedure,and is insensitive to the accuracy of the staring model,making it quite promising for automatic macro-velocity model building.
引文
[1] 王华忠,郭颂,周阳.“两宽一高”地震数据下的宽带波阻抗建模技术[J].石油物探,2019,58(1):80-87WANG H Z,GUO S,ZHOU Y.Broadband acoustic impedance model building for broadband,wide-azimuth,and high-density seismic data[J].Geophysical Prospecting for Petroleum,2019,58(1):80-87
[2] WOODWARD M J,NICHOLS D,ZDRAVEVA O,et al.A decade of tomography[J].Geophysics,2008,73(5):VE5-VE11
[3] STORK C.Reflection tomography in the postmigrated domain[J].Geophysics,1992,57(5):680-692
[4] NEMETH T.Velocity estimation using tomographic migration velocity analysis[J].Expanded Abstracts of 55th Annual Internat SEG Mtg,1995:1058-1061
[5] WOODWARD M J,FARMER P,NICHOLS D,et al.Automated 3D tomographic velocity analysis of residual moveout in prestack depth migrated common image point gathers[J].Expanded Abstracts of 58th Annual Internat SEG Mtg,1998:1218-1221
[6] XIE X B,YANG H.The finite-frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis[J].Geophysics,2008,73(6):S241-S249
[7] BEVC D,FLIEDNER M M,BIONDI B.Wave path tomography for model building and hazard detection[J].Expanded Abstracts of 78th Annual Internat SEG Mtg,2008:3098-3102
[8] ZHANG S,SCHUSTER G,LUO Y.Wave-equation reflection traveltime inversion[J].Expanded Abstracts of 81st Annual Internat SEG Mtg,2011:2705-2710
[9] FLIEDNER M M,BEVC D.Automated velocity model building with wavepath tomography[J].Geophysics,2008,73(5):VE195-VE204
[10] GUILLAUME P,LAMBARé G,SIONI S,et al.Geologically consistent velocities obtained by high definition tomography[J].Expanded Abstracts of 81st Annual Internat SEG Mtg,2011:4061-4065
[11] SIONI S,GUILLAUME P,LAMBARé G,et al.High definition tomography brings velocities to light[J].Expanded Abstracts of 82nd Annual Internat SEG Mtg,2012:1-5
[12] SOUBARAS R,GRATACOS B.Velocity model building by semblance maximization of modulated-shot gathers[J].Geophysics,2007,72(5):U67-U73
[13] SYMES W W,VERSTEEG R.Velocity model determination using differential semblance optimization[J].Expanded Abstracts of 63rd Annual Internat SEG Mtg,1993:696-699
[14] SHEN P.Differential semblance velocity analysis via shot profile migration[J].Expanded Abstracts of 75th Annual Internat SEG Mtg,2005:2249-2253
[15] SYMES W W.Migration velocity analysis and waveform inversion[J].Geophysical Prospecting,2008,56(6):765-790
[16] SHEN P,SYMES W W.Automatic velocity analysis via shot profile migration[J].Geophysics,2008,73(5):VE49-VE59
[17] FEI W,WILLIAMSON P.On the gradient artifacts in migration velocity analysis based on differential semblance optimization[J].Expanded Abstracts of 80th Annual Internat SEG Mtg,2010:4071-4076
[18] YANG T,SHRAGGE J,SAVA P,Illumination compensation for image-domain wavefield tomography[J].Geophysics,2013,78(5):U65-U76
[19] ZHANG Y,SHAN G.Wave-equation migration velocity analysis using partial stack-power-maximization[J].Expanded Abstracts of 83rd Annual Internat SEG Mtg,2013:4847-4852
[20] SHEN P,SYMES W W.Horizontal contraction in image domain for velocity inversion[J].Geophysics,2015,80(3):R95-R110
[21] LUO Y,MA Y,WU Y,et al.Full-traveltime inversion[J].Geophysics,2016,81(5):R261-R274
[22] LIU L,WU Y,GUO B,et al.Near-surface velocity estimation using source-domain full traveltime inversion and early arrival waveform inversion[J].Geophysics,2018,83(4):R335-R344
[23] BISHOP T N,BUBE K P,CUTLER R T,et al.Tomographic determination of velocity and depth in laterally varying media[J].Geophysics,1985,50(6):903-923
[24] CHIU S K L,STEWART R R.Tomographic determination of three-dimensional seismic velocity structure using well-logs vertical seismic profiles and surface seismic data[J].Geophysics,1987,52(8):1085-1098
[25] FARRA V,MADARIAGA R.Non-linear reflection tomography[J].Geophysical Journal International,1988,95(1):135-147
[26] SWORD C H.Tomographic determination of interval velocities from picked reflection seismic data[J].Expanded Abstracts of 56th Annual Internat SEG Mtg,1986:657-660
[27] BIONDI B.Velocity estimation by beam stack[J].Geophysics,1992,57(8):1034-1047
[28] CHAURIS H,NOBLE M,LAMBARé G,et al.Migration velocity analysis from locally coherent events in 2D laterally heterogeneous media,Part I:Theoretical aspects[J].Geophysics,2002,67(4):1202-1212
[29] DUVENECK E.Velocity model estimation with data-derived wavefront attributes[J].Geophysics,2004,69(1):265-274
[30] BAUER A,SCHWARZ B,GAJEWSKI D.Utilizing diffractions in wavefront tomography[J].Geophysics,2017,82(2):R65-R73
[31] BILLETTE F,LAMBARé G.Velocity macro-model estimation from seismic reflection data by stereotomography[J].Geophysical Journal International,1998,135(2):671-690
[32] LAMBARé G.Stereotomography[J].Geophysics,2008,73(5):VE25-VE34
[33] TAVAKOLI F B,OPERTO S,RIBODETTI A,et al.Slope tomography based on eikonal solvers and the adjoint-state method[J].Geophysical Journal International,2017,209(3):1629-1647
[34] 杨锴,熊凯,王宇翔,等.联合结构张量与运动学反偏移的立体层析数据空间提取与反演策略研究I:理论[J].石油物探,2017,56(5):123-135YANG K,XIONG K,WANG Y X,et al.Inversion strategy and data space construction for stereo-tomography using structure tensor and kinematic demigration.I:Theory[J].Geophysical Prospecting for Petroleum,2017,56(5):694-706
[35] YANG K,SHAO W,XING F,et al.Stereotomography in triangulated models[J].Geophysical Journal of International,2018,214(2):1018-1040
[36] TAVAKOLI F B,OPERTO S,RIBODETTI A,et al.Matrix-free anisotropic slope tomography:Theory and application[J].Geophysics,2019,84(1):R35-R57
[37] MA Y,HALE D.Wave-equation reflection traveltime inversion with dynamic warping and full-waveform inversion[J].Geophysics,2013,78(6):R223-R233
[38] FENG B,WANG H Z.Data-domain wave equation reflection traveltime tomography[J].Journal of Earth Science,2015,26(4):487-494
[39] 李辉,殷俊锋,王华忠.高斯波包反射走时速度反演方法[J].地球物理学报,2017,60(10):3916-3933LI H,YIN J F,WANG H Z.Velocity inversion method with reflection travel-time based on Gaussian packet[J].Chinese Journal of Geophysics,2017,60(10):3916-3933
[40] FENG B,WANG H Z,WU R S.Automatic traveltime inversion via sparse decomposition of seismic data[J].Geophysics,2018,83(6):R659-R668
[41] LEEUWEN T,MULDER W A.A correlation-based misfit criterion for wave-equation traveltime tomography[J].Geophysical Journal International,2010,182(3):1383-1394
[42] BAEK H,CALANDRA H,DEMANET L.The failure mode of correlation focusing for model velocity estimation[J].Expanded Abstracts of 83rd Annual Internat SEG Mtg,2013:4704-4708
[43] TARANTOLA A.Inverse problem theory and methods for model parameter estimation[M].Philadelphia:Society for Industrial and Applied Mathematics (SIAM),2005:1-342
[44] VAN LEEUWEN T,HERRMANN F J.Mitigating local minima in full-waveform inversion by expanding the search space[J].Geophysical Journal International,2013,195(1):661-667
[45] 王华忠,冯波,王雄文,等.特征波反演成像理论框架[J].石油物探,2017,56(1):38-49WANG H Z,FENG B,WANG X W,et al.The theoretical framework of characteristic wave inversion imaging[J].Geophysical Prospecting for Petroleum,2017,56(1):38-49
[46] 王华忠,冯波,刘少勇,等.叠前地震数据特征波场分解、偏移成像与层析反演[J].地球物理学报,2015,58(6):2024-2034WANG H Z,FENG B,LIU S Y,et al.Characteristic wavefield decomposition,imaging and inversion with prestack seismic data[J].Chinese Journal of Geophysics,2015,58(6):2024-2034
[47] 冯波,王华忠,冯伟.基于特征波场分解的反射走时反演方法研究[J].地球物理学报,2019,62(4):1471-1479FENG B,WANG H Z,FENG W.Characteristic wavefield decomposition based reflection traveltime inversion[J].Chinese Journal of Geophysics,2019,62(4):1471-1479
[48] XIE X B,YANG H.The finite-frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis[J].Geophysics,2008,73(6):S241-S249
[49] XU W,XIE X B,GENG J.Validity of the Rytov approximation in the form of finite-frequency sensitivity kernels[J].Pure and Applied Geophysics,2015,172(6):1409-1427
[50] LUO Y,SCHUSTER G T.Wave-equation travel time inversion[J].Geophysics,1991,56(5):645-653
[51] 蔡杰雄.高斯束偏移与高斯束层析反演速度建模[J].石油物探,2018,57(2):262-273CAI J X.Gaussian beam operator-based migration and tomography[J].Geophysical Prospecting for Petroleum,2018,57(2):262-273
[2] WOODWARD M J,NICHOLS D,ZDRAVEVA O,et al.A decade of tomography[J].Geophysics,2008,73(5):VE5-VE11
[3] STORK C.Reflection tomography in the postmigrated domain[J].Geophysics,1992,57(5):680-692
[4] NEMETH T.Velocity estimation using tomographic migration velocity analysis[J].Expanded Abstracts of 55th Annual Internat SEG Mtg,1995:1058-1061
[5] WOODWARD M J,FARMER P,NICHOLS D,et al.Automated 3D tomographic velocity analysis of residual moveout in prestack depth migrated common image point gathers[J].Expanded Abstracts of 58th Annual Internat SEG Mtg,1998:1218-1221
[6] XIE X B,YANG H.The finite-frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis[J].Geophysics,2008,73(6):S241-S249
[7] BEVC D,FLIEDNER M M,BIONDI B.Wave path tomography for model building and hazard detection[J].Expanded Abstracts of 78th Annual Internat SEG Mtg,2008:3098-3102
[8] ZHANG S,SCHUSTER G,LUO Y.Wave-equation reflection traveltime inversion[J].Expanded Abstracts of 81st Annual Internat SEG Mtg,2011:2705-2710
[9] FLIEDNER M M,BEVC D.Automated velocity model building with wavepath tomography[J].Geophysics,2008,73(5):VE195-VE204
[10] GUILLAUME P,LAMBARé G,SIONI S,et al.Geologically consistent velocities obtained by high definition tomography[J].Expanded Abstracts of 81st Annual Internat SEG Mtg,2011:4061-4065
[11] SIONI S,GUILLAUME P,LAMBARé G,et al.High definition tomography brings velocities to light[J].Expanded Abstracts of 82nd Annual Internat SEG Mtg,2012:1-5
[12] SOUBARAS R,GRATACOS B.Velocity model building by semblance maximization of modulated-shot gathers[J].Geophysics,2007,72(5):U67-U73
[13] SYMES W W,VERSTEEG R.Velocity model determination using differential semblance optimization[J].Expanded Abstracts of 63rd Annual Internat SEG Mtg,1993:696-699
[14] SHEN P.Differential semblance velocity analysis via shot profile migration[J].Expanded Abstracts of 75th Annual Internat SEG Mtg,2005:2249-2253
[15] SYMES W W.Migration velocity analysis and waveform inversion[J].Geophysical Prospecting,2008,56(6):765-790
[16] SHEN P,SYMES W W.Automatic velocity analysis via shot profile migration[J].Geophysics,2008,73(5):VE49-VE59
[17] FEI W,WILLIAMSON P.On the gradient artifacts in migration velocity analysis based on differential semblance optimization[J].Expanded Abstracts of 80th Annual Internat SEG Mtg,2010:4071-4076
[18] YANG T,SHRAGGE J,SAVA P,Illumination compensation for image-domain wavefield tomography[J].Geophysics,2013,78(5):U65-U76
[19] ZHANG Y,SHAN G.Wave-equation migration velocity analysis using partial stack-power-maximization[J].Expanded Abstracts of 83rd Annual Internat SEG Mtg,2013:4847-4852
[20] SHEN P,SYMES W W.Horizontal contraction in image domain for velocity inversion[J].Geophysics,2015,80(3):R95-R110
[21] LUO Y,MA Y,WU Y,et al.Full-traveltime inversion[J].Geophysics,2016,81(5):R261-R274
[22] LIU L,WU Y,GUO B,et al.Near-surface velocity estimation using source-domain full traveltime inversion and early arrival waveform inversion[J].Geophysics,2018,83(4):R335-R344
[23] BISHOP T N,BUBE K P,CUTLER R T,et al.Tomographic determination of velocity and depth in laterally varying media[J].Geophysics,1985,50(6):903-923
[24] CHIU S K L,STEWART R R.Tomographic determination of three-dimensional seismic velocity structure using well-logs vertical seismic profiles and surface seismic data[J].Geophysics,1987,52(8):1085-1098
[25] FARRA V,MADARIAGA R.Non-linear reflection tomography[J].Geophysical Journal International,1988,95(1):135-147
[26] SWORD C H.Tomographic determination of interval velocities from picked reflection seismic data[J].Expanded Abstracts of 56th Annual Internat SEG Mtg,1986:657-660
[27] BIONDI B.Velocity estimation by beam stack[J].Geophysics,1992,57(8):1034-1047
[28] CHAURIS H,NOBLE M,LAMBARé G,et al.Migration velocity analysis from locally coherent events in 2D laterally heterogeneous media,Part I:Theoretical aspects[J].Geophysics,2002,67(4):1202-1212
[29] DUVENECK E.Velocity model estimation with data-derived wavefront attributes[J].Geophysics,2004,69(1):265-274
[30] BAUER A,SCHWARZ B,GAJEWSKI D.Utilizing diffractions in wavefront tomography[J].Geophysics,2017,82(2):R65-R73
[31] BILLETTE F,LAMBARé G.Velocity macro-model estimation from seismic reflection data by stereotomography[J].Geophysical Journal International,1998,135(2):671-690
[32] LAMBARé G.Stereotomography[J].Geophysics,2008,73(5):VE25-VE34
[33] TAVAKOLI F B,OPERTO S,RIBODETTI A,et al.Slope tomography based on eikonal solvers and the adjoint-state method[J].Geophysical Journal International,2017,209(3):1629-1647
[34] 杨锴,熊凯,王宇翔,等.联合结构张量与运动学反偏移的立体层析数据空间提取与反演策略研究I:理论[J].石油物探,2017,56(5):123-135YANG K,XIONG K,WANG Y X,et al.Inversion strategy and data space construction for stereo-tomography using structure tensor and kinematic demigration.I:Theory[J].Geophysical Prospecting for Petroleum,2017,56(5):694-706
[35] YANG K,SHAO W,XING F,et al.Stereotomography in triangulated models[J].Geophysical Journal of International,2018,214(2):1018-1040
[36] TAVAKOLI F B,OPERTO S,RIBODETTI A,et al.Matrix-free anisotropic slope tomography:Theory and application[J].Geophysics,2019,84(1):R35-R57
[37] MA Y,HALE D.Wave-equation reflection traveltime inversion with dynamic warping and full-waveform inversion[J].Geophysics,2013,78(6):R223-R233
[38] FENG B,WANG H Z.Data-domain wave equation reflection traveltime tomography[J].Journal of Earth Science,2015,26(4):487-494
[39] 李辉,殷俊锋,王华忠.高斯波包反射走时速度反演方法[J].地球物理学报,2017,60(10):3916-3933LI H,YIN J F,WANG H Z.Velocity inversion method with reflection travel-time based on Gaussian packet[J].Chinese Journal of Geophysics,2017,60(10):3916-3933
[40] FENG B,WANG H Z,WU R S.Automatic traveltime inversion via sparse decomposition of seismic data[J].Geophysics,2018,83(6):R659-R668
[41] LEEUWEN T,MULDER W A.A correlation-based misfit criterion for wave-equation traveltime tomography[J].Geophysical Journal International,2010,182(3):1383-1394
[42] BAEK H,CALANDRA H,DEMANET L.The failure mode of correlation focusing for model velocity estimation[J].Expanded Abstracts of 83rd Annual Internat SEG Mtg,2013:4704-4708
[43] TARANTOLA A.Inverse problem theory and methods for model parameter estimation[M].Philadelphia:Society for Industrial and Applied Mathematics (SIAM),2005:1-342
[44] VAN LEEUWEN T,HERRMANN F J.Mitigating local minima in full-waveform inversion by expanding the search space[J].Geophysical Journal International,2013,195(1):661-667
[45] 王华忠,冯波,王雄文,等.特征波反演成像理论框架[J].石油物探,2017,56(1):38-49WANG H Z,FENG B,WANG X W,et al.The theoretical framework of characteristic wave inversion imaging[J].Geophysical Prospecting for Petroleum,2017,56(1):38-49
[46] 王华忠,冯波,刘少勇,等.叠前地震数据特征波场分解、偏移成像与层析反演[J].地球物理学报,2015,58(6):2024-2034WANG H Z,FENG B,LIU S Y,et al.Characteristic wavefield decomposition,imaging and inversion with prestack seismic data[J].Chinese Journal of Geophysics,2015,58(6):2024-2034
[47] 冯波,王华忠,冯伟.基于特征波场分解的反射走时反演方法研究[J].地球物理学报,2019,62(4):1471-1479FENG B,WANG H Z,FENG W.Characteristic wavefield decomposition based reflection traveltime inversion[J].Chinese Journal of Geophysics,2019,62(4):1471-1479
[48] XIE X B,YANG H.The finite-frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis[J].Geophysics,2008,73(6):S241-S249
[49] XU W,XIE X B,GENG J.Validity of the Rytov approximation in the form of finite-frequency sensitivity kernels[J].Pure and Applied Geophysics,2015,172(6):1409-1427
[50] LUO Y,SCHUSTER G T.Wave-equation travel time inversion[J].Geophysics,1991,56(5):645-653
[51] 蔡杰雄.高斯束偏移与高斯束层析反演速度建模[J].石油物探,2018,57(2):262-273CAI J X.Gaussian beam operator-based migration and tomography[J].Geophysical Prospecting for Petroleum,2018,57(2):262-273
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