频率域波动方程菲涅尔带走时层析成像方法
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摘要
传统的走时层析反演都是依赖于射线理论,而实际地震资料的带限特征与射线理论无限高频的假设存在理论上的矛盾.针对传统的射线层析存在的上述问题,本文从频率域波动方程的Born和Rytov近似入手,推导出菲涅尔带走时层析敏感核函数,其与传统的射线层析方法的显著区别在于它建立在带限地震波与第一菲涅尔带的理论基础上.通过射线走时残差与Rytov近似走时残差的比较,本文提出了依据Rytov近似走时残差的菲涅尔层析反演方法.表层速度模型试算结果表明,相对于传统的射线走时层析,基于频率域波动方程的菲涅尔带走时层析成像方法具有更高的成像精度与分辨率.
In the traditional seismic imaging experiments,ray theory plays an important role in gaining the velocity construction.In reality,recorded wave signal is band-limited which is contradictive with the infinite-frequency assumption.We start from the Born and Rytov approximation of frequencydomain wave equation to derive the traveltime sensitivity kernels for Fresnel zone tomography.It is distinguished from the ray theory in that the sensitivity is established on the bandlimited wave signal and the first Fresnel zone. We present Fresnel zone tomography based on the Rytov approximation traveltime delay by comparing it with ray theory traveltime delay.We apply our method into the construction of the near surface velocity model.The inverted result proves that our method has a higher resolution and accuracy when comparing with the ray theory tomography.
In the traditional seismic imaging experiments,ray theory plays an important role in gaining the velocity construction.In reality,recorded wave signal is band-limited which is contradictive with the infinite-frequency assumption.We start from the Born and Rytov approximation of frequencydomain wave equation to derive the traveltime sensitivity kernels for Fresnel zone tomography.It is distinguished from the ray theory in that the sensitivity is established on the bandlimited wave signal and the first Fresnel zone. We present Fresnel zone tomography based on the Rytov approximation traveltime delay by comparing it with ray theory traveltime delay.We apply our method into the construction of the near surface velocity model.The inverted result proves that our method has a higher resolution and accuracy when comparing with the ray theory tomography.
引文
Al-Yahya K.1989.Velocity analysis by interactive profile migration[J].Geophysics,54(6):718-729.
Bian A F,Yu W H,Zhou H W.2010.Progress in the frequencydomain full waveform inversion method[J].Progress inGeophysics,25(3):982-993.
Bois P,La Porte M,Lavergne M,et al.1972.Well-to-well seismicmeasurements[J].Geophysics,37(3):471-48.
Dahlen F A,Hung S H,Nolet G..2000.Fréchet kernels for finitefrequency traveltimes——I.Theory.Geophysical JournalInternational,141:157-174.
Faye J P,Jeanot J P,Denelle E.1986.Prestack migration velocitiesfrom depth focusing analysis[J].Expanded Abstracts of the56th Annual Internat SEG Meeting,438-440.
Garotta R,Miehon D.1967.Continuous analysis of the velocityfunction and of the normal-moveout corrections[J].GeophysicalProspecting,15(4):584-597.
Jiang Y,Chen X F.2011.Review on the comparative study betweenfinite-frequency tomography and ray-theoretical tomography[J].Progress in Geophysics,26(5):1566-1575.
Jin S,Beydoun W.2000.2D multiscale non-linear velocityestimation[J].Geophysical Prospecting,48(1):163-180.
Jocker J,Spetzler J,Smeulders D,et al.2006.Validation of FirstOrder Diffraction Theory for the Traveltimes and Amplitudes ofPropagating Waves[J].Geophysics,71:167-177.
Ke B,Zhang J Z,Chen B,et al.2007.Fat-ray first arrival seismictomography and its application[J]:77th Annual InternationalMeeting,SEG,Expanded Abstracts,3354-3358.
Liu Y Z,Dong L G.2007.Analysis of influence factors of firstbreaks tomography[J].Oil Geophysical Prospecting,42(5):544-553.
Liu Y.Z,Dong L G,Wang Y W,et al.2009.Sensitivity kernelsfor Seismic Fresnel Volume Tomography[J].Geophysics,74(5):U35-U46.
Liu Y Z;Dong L G;Li P M,et al.2009.Fresnel volumetomography based on the first arrival of the seismic wave[J].Chinese J.Geophys.(in Chinese),52(9):2310-2320.
Liu Y Z,DONG L G.2012.Influence of wave front healing onseismic tomography[J].Sci China Earth Sci,42(5):784-794.
Luo Y,Schuster G T.1990.Wave equation traveltime inversion[J].Expanded Abstracts of the 60th Annual International SEGMeeting,1207-1210.
Marquering H,Nolet G,Dahlen F A.1998.Three-dimensionalwaveform sensitivity kernels[J].Geophysical Journal International,132:521-534.
Qin N,Li Z C,Yang X D,et al.2013.Pre-stack joint migrationvelocity modeling with multi-stage optimization[J].Progress inGeophysics,(1):320-328.
Qin N,Li Z C,Zhang K,et al.2013.Joint tomography inversion ofimage domain for elastic vector wavefield.Chinese JournalGeophysics,56(9):3109-3117.
Spetzler G.and Snieder R,2004,The fresnel volume andtransmitted waves[J].Geophysics,69,653-663..
Spetzler G,Snieder R.2001.The effect of small-scale heterogeneityon the arrival time of waves[J].Geophysical JournalInternational,145:786-796.
Snieder R,Lomax A.1996.Wavefield smoothing and the effect ofrough velocity perturbations on arrival times and amplitudes[J].Geophysical Journal International,125:796-812.
Xu X M;Shi D N;Li X F.2009.Research progress of the finitefrequency tomography method[J].Progress in Geophysics,24(2):432-438.
Zhang J Z,Zhao B and Zhou H W.2009.Fat ray tomography withoptimal relaxation factor[J].Expanded Abstracts of 2009SEGAnnual International Meeting..
Zhang M,Li Z C,Zhang K,et al.2011.Comparisons and analysesof prestack migration common-image point gathers[J].Progressin Geophysics,26(1):220-228.
Zhang K,Li Z C.2013.Tomographic velocity inversion methodwith dual-complexity[J].Progress in Geophysics,28(6):3001-3006.
Zhang Z G,Shen Y,Zhao L.2007.Finite-frequency sensitivitykernels for head waves[J].Geophysical Journal International,171:847-856
卞爱飞,於文辉,周华伟.2010.频率域全波形反演方法研究进展[J].地球物理学进展,25(3):982-993.
江燕,陈晓非.2011.有限频与射线层析成像比较研究综述[J].地球物理学进展,26(5):1566-1575.
刘玉柱,董良国,李培明,等.2009.初至波菲涅尔体地震层析成像[J].地球物理学报,52(9):2310-2320.
刘玉柱,董良国.2007.初至波层析影响因素分析[J].石油地球物理勘探,42(5):544-553.
刘玉柱,董良国.2012.波前弥合现象对地震层析成像的影响[J].中国科学地球科学,42(5):784-794.
秦宁,李振春,杨晓东,等.2013.叠前多级优化联合偏移速度建模[J].地球物理学进展,(1):320-328.
秦宁,李振春,张凯,等.2013.弹性矢量波成像域联合层析反演.地球物理学报,56(9):3109-3117.
徐小明;史大年;李信富.2009.有限频层析成像方法研究进展[J].地球物理学进展,24(2):432-438.
张凯,李振春.2013.双复杂条件下层析速度反演方法研究[J].地球物理学进展,28(6):3001-3006.
张敏,李振春,张凯,等.2011.叠前偏移共成像点道集的对比分析[J].地球物理学进展,26(1):220-228
Bian A F,Yu W H,Zhou H W.2010.Progress in the frequencydomain full waveform inversion method[J].Progress inGeophysics,25(3):982-993.
Bois P,La Porte M,Lavergne M,et al.1972.Well-to-well seismicmeasurements[J].Geophysics,37(3):471-48.
Dahlen F A,Hung S H,Nolet G..2000.Fréchet kernels for finitefrequency traveltimes——I.Theory.Geophysical JournalInternational,141:157-174.
Faye J P,Jeanot J P,Denelle E.1986.Prestack migration velocitiesfrom depth focusing analysis[J].Expanded Abstracts of the56th Annual Internat SEG Meeting,438-440.
Garotta R,Miehon D.1967.Continuous analysis of the velocityfunction and of the normal-moveout corrections[J].GeophysicalProspecting,15(4):584-597.
Jiang Y,Chen X F.2011.Review on the comparative study betweenfinite-frequency tomography and ray-theoretical tomography[J].Progress in Geophysics,26(5):1566-1575.
Jin S,Beydoun W.2000.2D multiscale non-linear velocityestimation[J].Geophysical Prospecting,48(1):163-180.
Jocker J,Spetzler J,Smeulders D,et al.2006.Validation of FirstOrder Diffraction Theory for the Traveltimes and Amplitudes ofPropagating Waves[J].Geophysics,71:167-177.
Ke B,Zhang J Z,Chen B,et al.2007.Fat-ray first arrival seismictomography and its application[J]:77th Annual InternationalMeeting,SEG,Expanded Abstracts,3354-3358.
Liu Y Z,Dong L G.2007.Analysis of influence factors of firstbreaks tomography[J].Oil Geophysical Prospecting,42(5):544-553.
Liu Y.Z,Dong L G,Wang Y W,et al.2009.Sensitivity kernelsfor Seismic Fresnel Volume Tomography[J].Geophysics,74(5):U35-U46.
Liu Y Z;Dong L G;Li P M,et al.2009.Fresnel volumetomography based on the first arrival of the seismic wave[J].Chinese J.Geophys.(in Chinese),52(9):2310-2320.
Liu Y Z,DONG L G.2012.Influence of wave front healing onseismic tomography[J].Sci China Earth Sci,42(5):784-794.
Luo Y,Schuster G T.1990.Wave equation traveltime inversion[J].Expanded Abstracts of the 60th Annual International SEGMeeting,1207-1210.
Marquering H,Nolet G,Dahlen F A.1998.Three-dimensionalwaveform sensitivity kernels[J].Geophysical Journal International,132:521-534.
Qin N,Li Z C,Yang X D,et al.2013.Pre-stack joint migrationvelocity modeling with multi-stage optimization[J].Progress inGeophysics,(1):320-328.
Qin N,Li Z C,Zhang K,et al.2013.Joint tomography inversion ofimage domain for elastic vector wavefield.Chinese JournalGeophysics,56(9):3109-3117.
Spetzler G.and Snieder R,2004,The fresnel volume andtransmitted waves[J].Geophysics,69,653-663..
Spetzler G,Snieder R.2001.The effect of small-scale heterogeneityon the arrival time of waves[J].Geophysical JournalInternational,145:786-796.
Snieder R,Lomax A.1996.Wavefield smoothing and the effect ofrough velocity perturbations on arrival times and amplitudes[J].Geophysical Journal International,125:796-812.
Xu X M;Shi D N;Li X F.2009.Research progress of the finitefrequency tomography method[J].Progress in Geophysics,24(2):432-438.
Zhang J Z,Zhao B and Zhou H W.2009.Fat ray tomography withoptimal relaxation factor[J].Expanded Abstracts of 2009SEGAnnual International Meeting..
Zhang M,Li Z C,Zhang K,et al.2011.Comparisons and analysesof prestack migration common-image point gathers[J].Progressin Geophysics,26(1):220-228.
Zhang K,Li Z C.2013.Tomographic velocity inversion methodwith dual-complexity[J].Progress in Geophysics,28(6):3001-3006.
Zhang Z G,Shen Y,Zhao L.2007.Finite-frequency sensitivitykernels for head waves[J].Geophysical Journal International,171:847-856
卞爱飞,於文辉,周华伟.2010.频率域全波形反演方法研究进展[J].地球物理学进展,25(3):982-993.
江燕,陈晓非.2011.有限频与射线层析成像比较研究综述[J].地球物理学进展,26(5):1566-1575.
刘玉柱,董良国,李培明,等.2009.初至波菲涅尔体地震层析成像[J].地球物理学报,52(9):2310-2320.
刘玉柱,董良国.2007.初至波层析影响因素分析[J].石油地球物理勘探,42(5):544-553.
刘玉柱,董良国.2012.波前弥合现象对地震层析成像的影响[J].中国科学地球科学,42(5):784-794.
秦宁,李振春,杨晓东,等.2013.叠前多级优化联合偏移速度建模[J].地球物理学进展,(1):320-328.
秦宁,李振春,张凯,等.2013.弹性矢量波成像域联合层析反演.地球物理学报,56(9):3109-3117.
徐小明;史大年;李信富.2009.有限频层析成像方法研究进展[J].地球物理学进展,24(2):432-438.
张凯,李振春.2013.双复杂条件下层析速度反演方法研究[J].地球物理学进展,28(6):3001-3006.
张敏,李振春,张凯,等.2011.叠前偏移共成像点道集的对比分析[J].地球物理学进展,26(1):220-228
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