煤层厚度变化时地震槽波理论频散曲线计算方法及频散特征分析
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摘要
槽波地震勘探利用槽波的频散特性反演煤层的结构特征,故理论频散曲线的计算是一个重要方面.使用水平层状模型假设下的面波频散曲线计算方法能够计算煤层厚度恒定模型地震槽波频散曲线;但当煤层厚度变化时该方法不再适用.基于前人水平层状均匀介质模型的面波理论频散曲线计算方法,对于含煤三层模型,本文发展了煤层厚度变化情况下的地震槽波理论频散曲线计算方法,并使用该方法计算分析了不同厚度函数模型的频散曲线形态特征.研究表明:与稳定厚度煤层相比,煤层厚度变化使得地震槽波群速度成为与频率及传播射线在水平面投影路径相关的二元函数;射线路径上煤层厚度的变化使得频散曲线在群速度方向上压缩,群速度变化范围变小,且使处于最小值位置的埃里相群速度增大;而煤层厚度的线性变化模型频散曲线只与射线首、尾处的煤层厚度有关,与煤层厚度恒定模型相比,曲线形态不发生改变;煤层厚度呈非线性变化时,频散曲线形态上可能发生改变.
In channel-wave seismic exploration,dispersion features are used to invert structures of coal seams.So calculation of theoretical dispersion curves is an important subject.We can calculate dispersion curves when the coal-thickness keeps unchanged by utilizing the calculation method for surface wave dispersion of a horizontal stratified model.But this method is inapplicable when the coal-seam thickness changes.For a coal-bearing three-layer model,this work proposes a calculation method for theoretical dispersion curves when the coal-seam thickness fluctuates,which is based on the calculation method for dispersion curves of horizontal stratified models.Wealso analyze the characteristics of dispersion curves for different models of varied coal-seam thickness.Our research shows that unlike unchangeable coal-thickness model,group velocity of a changeable coal-thickness model becomes a function related to frequency and projective ray paths in horizontal plane.The change of coal-seam thickness along the ray route leads to squeezing effect of dispersion curves in velocity′s direction,narrowing the range of group velocity and increasing the minimal group velocity at airy phase.The dispersion curve of the linearly changing coal-seam thickness model relates only to the thickness at the start and end of ray paths,while the curve shape does not change compared with the unchangeable coal-seam thickness model.The dispersion curve shape of a nonlinearly varied coal-seam thickness model may case change in the shape of dispersion curves with respect to the model with constant coal-seam thickness.
In channel-wave seismic exploration,dispersion features are used to invert structures of coal seams.So calculation of theoretical dispersion curves is an important subject.We can calculate dispersion curves when the coal-thickness keeps unchanged by utilizing the calculation method for surface wave dispersion of a horizontal stratified model.But this method is inapplicable when the coal-seam thickness changes.For a coal-bearing three-layer model,this work proposes a calculation method for theoretical dispersion curves when the coal-seam thickness fluctuates,which is based on the calculation method for dispersion curves of horizontal stratified models.Wealso analyze the characteristics of dispersion curves for different models of varied coal-seam thickness.Our research shows that unlike unchangeable coal-thickness model,group velocity of a changeable coal-thickness model becomes a function related to frequency and projective ray paths in horizontal plane.The change of coal-seam thickness along the ray route leads to squeezing effect of dispersion curves in velocity′s direction,narrowing the range of group velocity and increasing the minimal group velocity at airy phase.The dispersion curve of the linearly changing coal-seam thickness model relates only to the thickness at the start and end of ray paths,while the curve shape does not change compared with the unchangeable coal-seam thickness model.The dispersion curve shape of a nonlinearly varied coal-seam thickness model may case change in the shape of dispersion curves with respect to the model with constant coal-seam thickness.
引文
Abo-Zena A.1979.Dispersion function computations for unlimited frequency values.Geophysical Journal International,58(1):91-105.
Aki K,Richards P G.1980.Quantitative Seismology:Theory and Methods.San Francisco:W.H.Freeman and Company.
Buchanan D J.1987.Dispersion calculations for SH and P-SV waves in multilayered coal seams.Geophysical Prospecting,35(1):62-70.
Buchen P W,Ben-Hador R.2007.Free-mode surface-wave computations.Geophysical Journal International,124(3):869-887.
Chen X F.1993.A systematic and efficient method of computing normal modes for multilayered half-space.Geophysical Journal International,115(2):391-409.
Cheng J L.1994.Calculation of theoretical seismograms of Love channel waves.Journal of Shandong Mining Institute(in Chinese),13(4):349-353.
Cheng J Y,Ji G Z,Zhu P M.2012.Love channel waves dispersion characteristic analysis of typical coal models.Journal of China Coal Society(in Chinese),37(1):67-72.
Dunkin J W.1965.Computation of modal solutions in layered,elastic media at high frequencies.Bulletin of the Seismological Society of America,55(2):335-358.
Fan Y H,Chen X F,Liu X F,et al.2007.Approximate decomposition of the dispersion equation at high frequencies and the number ofmultimodes for Rayleigh waves.Chinese Journal of Geophysics(in Chinese),50(1):233-239.
Haskell N A.1953.The dispersion of surface waves on multilayered media.Bulletin of the Seismological Society of America,43:17-34.
Hu G H,Teng J W,Pi J L,et al.2013.In-seam seismic exploration techniques---ageophsical method predictting coal-Mine disaster.Progress in Geophysics(in Chinese),28(1):439-451,doi:10.6038/pg20130150.
Jose R S.1990.Seam waves:What are they?Part 1.The Leading Edge,9(4):19-23.
Kennett B L N.1974.Reflections,rays,and reverberations.Bulletin of the Seismological Society of America,64(6):1685-1696.
Kennett B L N.1980.Seismic waves in a stratified half space-II.Theoretical seismograms.Geophysical Journal International,61(1):1-10.
Knopoff L.1964.A matrix method for elastic wave problems.Bulletin of the Seismological Society of America,54(1):431-438.
Li G.2016.Transmission channel wave detection technology of coal seam thickness variation.Coal Mining Technology(in Chinese),21(5):11-13,55,doi:10.13532/j.cnki.cn11-3677/td.2016.05.004.
Liu H Y,Li Z X,Li S J,et al.2005.The characteristics of minitype structures and their influence on roof′s stability inYanzhou Coalfield.Coal Geology&Exploration(in Chinese),33(6):24-27,doi:10.3969/j.issn.1001-1986.2005.06.007.
Liu T F,Pan D M,Li D C,et al.1994.In-Seam Seismic Exploration.Xuzhou:China University of Mining and Technology Press.
Pan J T,Wu Q J,Li Y H,et al.2009.Group velocities computation of surface waves based on the fast generalized R/T coefficient method.Progress in Geophysics(in Chinese),24(6):2030-2035,doi:10.3969/j.issn.1004-2903.2009.06.013.
Pestel E G,Leckie F A.1963.Matrix Methods in Elasto-Mechanics.New York:McGraw Hill Company Inc.
Qian J W,Li D C.2013.A study on love mode channel wave basic characteristics.Coal Geology of China(in Chinese),25(9):52-54.
Rder D,Schott W,Dresen L,et al.1985.Calculation of dispersion curves and amplitude-depth distributions of Love channel waves in horizontally-layered media.Geophysical Prospecting,33(6):800-816,doi:10.1111/j.1365-2478.1985.tb00779.x.
Schott W,Waclawik P.2015.On the quantitative determination of coal seam thickness by means of in-seam seismic surveys.Canadian Geotechnical Journal,52(10):1496-1504,doi:10.1139/cgj-2014-0466.
Schwab F.1970.Surface-wave dispersion computations:Knopoff's method.Bulletin of the Seismological Society of America,60(5):1491-1520.
Thomson W T.1950.Transmission of elastic waves through a stratified solid medium.Journal of Applied Physics,21(2):89-93.
Thrower E N.1965.The computation of the dispersion of elastic waves in layered media.Journal of Sound and Vibration,2(3):210-226.
Wang S B,Guo H L.2005.Analysis on the coal seam thickness change and geological formation.Coal Technology(in Chinese),24(6):88,doi:10.3969/j.issn.1008-8725.2005.06.061.
Wang W,Gao X,Li S Y,et al.2012.Channel wave tomography method and its application in coal mine exploration:an example from Henan Yima Mining Area.Chinese Journal of Geophysics(in Chinese),55(3):1054-1062,doi:10.6038/j.issn.0001-5733.2012.03.036.
Wang Y L,Zhao M P,Wang G C,et al.1998.Prediction and classification of erosion zones in coal seams.Journal of Liaoning Technical University(Natural Science)(in Chinese),17(3):249-253.
Watson T H.1970.A note on fast computation of Rayleigh wave dispersion in the multilayered half-space.Bulletinof the Seismological Society of America,60(1):161-166.
Xu G M,Ni S D,Wang H B.1998.Eigen-equation of Rayleigh guide waves and its application.Journal of China Coal Society(in Chinese),23(2):124-129.
Yang X H,Li D C,Yu P F.2010.Analysis of Rayleigh channel wave dispersion in coal seam.Geophysical and Geochemical Exploration(in Chinese),34(6):750-752.
Yang Z,Feng T,Wang S G.2010.Dispersion characteristics and wave shape mode of SH channel wave in a 0.9m-thin coal seam.Chinese Journal of Geophysics(in Chinese),53(2):442-449,doi:10.3969/j.issn.0001-5733.2010.02.023.
Yuan L M,Fan Y H,Sun S R.2009.Making the calculation of generalized reflection-transmission coefficients dimensionless.Acta Seismologica Sinica(in Chinese),31(4):377-384.
程建远,姬广忠,朱培民.2012.典型含煤模型Love型槽波的频散特征分析.煤炭学报,37(1):67-72.
程久龙.1994.Love型槽波理论地震图的计算.山东矿业学院学报,13(4):349-353.
凡友华,陈晓非,刘雪峰等.2007.Rayleigh波的频散方程高频近似分解和多模式激发数目.地球物理学报,50(1):233-239.
胡国泽,滕吉文,皮娇龙等.2013.井下槽波地震勘探---预防煤矿灾害的一种地球物理方法.地球物理学进展,28(1):439-451,doi:10.6038/pg20130150.
李刚.2016.煤层厚度变化的透射槽波探测技术.煤矿开采,21(5):11-13,55,doi:10.13532/j.cnki.cn11-3677/td.2016.05.004.
刘海燕,李增学,李淑进等.2005.兖州煤田小构造发育特征及其对顶板稳定性的影响.煤田地质与勘探,33(6):24-27,doi:10.3969/j.issn.1001-1986.2005.06.007.
刘天放,潘东明,李德春等.1994.槽波地震勘探技术.徐州:中国矿业大学出版社.
潘佳铁,吴庆举,李永华等.2009.基于快速广义反射透射系数方法的面波群速度计算.地球物理学进展,24(6):2030-2035,doi:10.3969/j.issn.1004-2903.2009.06.013.
钱建伟,李德春.2013.Love型槽波的基本特性研究.中国煤炭地质,25(9):52-54.
王世彬,郭厚亮.2005.煤层厚度变化地质成因分析.煤炭技术,24(6):88,doi:10.3969/j.issn.1008-8725.2005.06.061.
王伟,高星,李松营等.2012.槽波层析成像方法在煤田勘探中的应用---以河南义马矿区为例.地球物理学报,55(3):1054-1062,doi:10.6038/j.issn.0001-5733.2012.03.036.
王宇林,赵明鹏,王国成等.1998.煤层冲刷带的分类及预测.辽宁工程技术大学学报(自然科学版),17(3):249-253.
徐果明,倪四道,王汉标.1998.瑞利型槽波的本征方程及其应用.煤炭学报,23(2):124-129.
杨小慧,李德春,于鹏飞.2010.煤层中瑞利型槽波的频散特性.物探与化探,34(6):750-752.
杨真,冯涛,Wang S G.2010.0.9m薄煤层SH型槽波频散特征及波形模式.地球物理学报,53(2):442-449,doi:10.3969/j.issn.0001-5733.2010.02.023.
尹晋平.2011.浅谈煤层冲刷带特征及预测研究.山西科技报.2011-11-10(015).
袁腊梅,凡友华,孙书荣.2009.广义反射-透射系数算法的无量纲化.地震学报,31(4):377-384.
张德亮.2015.煤层厚度变化的地质成因分析.内蒙古煤炭经济,(12):211-212,doi:10.3969/j.issn.1008-0155.2015.12.116.
Aki K,Richards P G.1980.Quantitative Seismology:Theory and Methods.San Francisco:W.H.Freeman and Company.
Buchanan D J.1987.Dispersion calculations for SH and P-SV waves in multilayered coal seams.Geophysical Prospecting,35(1):62-70.
Buchen P W,Ben-Hador R.2007.Free-mode surface-wave computations.Geophysical Journal International,124(3):869-887.
Chen X F.1993.A systematic and efficient method of computing normal modes for multilayered half-space.Geophysical Journal International,115(2):391-409.
Cheng J L.1994.Calculation of theoretical seismograms of Love channel waves.Journal of Shandong Mining Institute(in Chinese),13(4):349-353.
Cheng J Y,Ji G Z,Zhu P M.2012.Love channel waves dispersion characteristic analysis of typical coal models.Journal of China Coal Society(in Chinese),37(1):67-72.
Dunkin J W.1965.Computation of modal solutions in layered,elastic media at high frequencies.Bulletin of the Seismological Society of America,55(2):335-358.
Fan Y H,Chen X F,Liu X F,et al.2007.Approximate decomposition of the dispersion equation at high frequencies and the number ofmultimodes for Rayleigh waves.Chinese Journal of Geophysics(in Chinese),50(1):233-239.
Haskell N A.1953.The dispersion of surface waves on multilayered media.Bulletin of the Seismological Society of America,43:17-34.
Hu G H,Teng J W,Pi J L,et al.2013.In-seam seismic exploration techniques---ageophsical method predictting coal-Mine disaster.Progress in Geophysics(in Chinese),28(1):439-451,doi:10.6038/pg20130150.
Jose R S.1990.Seam waves:What are they?Part 1.The Leading Edge,9(4):19-23.
Kennett B L N.1974.Reflections,rays,and reverberations.Bulletin of the Seismological Society of America,64(6):1685-1696.
Kennett B L N.1980.Seismic waves in a stratified half space-II.Theoretical seismograms.Geophysical Journal International,61(1):1-10.
Knopoff L.1964.A matrix method for elastic wave problems.Bulletin of the Seismological Society of America,54(1):431-438.
Li G.2016.Transmission channel wave detection technology of coal seam thickness variation.Coal Mining Technology(in Chinese),21(5):11-13,55,doi:10.13532/j.cnki.cn11-3677/td.2016.05.004.
Liu H Y,Li Z X,Li S J,et al.2005.The characteristics of minitype structures and their influence on roof′s stability inYanzhou Coalfield.Coal Geology&Exploration(in Chinese),33(6):24-27,doi:10.3969/j.issn.1001-1986.2005.06.007.
Liu T F,Pan D M,Li D C,et al.1994.In-Seam Seismic Exploration.Xuzhou:China University of Mining and Technology Press.
Pan J T,Wu Q J,Li Y H,et al.2009.Group velocities computation of surface waves based on the fast generalized R/T coefficient method.Progress in Geophysics(in Chinese),24(6):2030-2035,doi:10.3969/j.issn.1004-2903.2009.06.013.
Pestel E G,Leckie F A.1963.Matrix Methods in Elasto-Mechanics.New York:McGraw Hill Company Inc.
Qian J W,Li D C.2013.A study on love mode channel wave basic characteristics.Coal Geology of China(in Chinese),25(9):52-54.
Rder D,Schott W,Dresen L,et al.1985.Calculation of dispersion curves and amplitude-depth distributions of Love channel waves in horizontally-layered media.Geophysical Prospecting,33(6):800-816,doi:10.1111/j.1365-2478.1985.tb00779.x.
Schott W,Waclawik P.2015.On the quantitative determination of coal seam thickness by means of in-seam seismic surveys.Canadian Geotechnical Journal,52(10):1496-1504,doi:10.1139/cgj-2014-0466.
Schwab F.1970.Surface-wave dispersion computations:Knopoff's method.Bulletin of the Seismological Society of America,60(5):1491-1520.
Thomson W T.1950.Transmission of elastic waves through a stratified solid medium.Journal of Applied Physics,21(2):89-93.
Thrower E N.1965.The computation of the dispersion of elastic waves in layered media.Journal of Sound and Vibration,2(3):210-226.
Wang S B,Guo H L.2005.Analysis on the coal seam thickness change and geological formation.Coal Technology(in Chinese),24(6):88,doi:10.3969/j.issn.1008-8725.2005.06.061.
Wang W,Gao X,Li S Y,et al.2012.Channel wave tomography method and its application in coal mine exploration:an example from Henan Yima Mining Area.Chinese Journal of Geophysics(in Chinese),55(3):1054-1062,doi:10.6038/j.issn.0001-5733.2012.03.036.
Wang Y L,Zhao M P,Wang G C,et al.1998.Prediction and classification of erosion zones in coal seams.Journal of Liaoning Technical University(Natural Science)(in Chinese),17(3):249-253.
Watson T H.1970.A note on fast computation of Rayleigh wave dispersion in the multilayered half-space.Bulletinof the Seismological Society of America,60(1):161-166.
Xu G M,Ni S D,Wang H B.1998.Eigen-equation of Rayleigh guide waves and its application.Journal of China Coal Society(in Chinese),23(2):124-129.
Yang X H,Li D C,Yu P F.2010.Analysis of Rayleigh channel wave dispersion in coal seam.Geophysical and Geochemical Exploration(in Chinese),34(6):750-752.
Yang Z,Feng T,Wang S G.2010.Dispersion characteristics and wave shape mode of SH channel wave in a 0.9m-thin coal seam.Chinese Journal of Geophysics(in Chinese),53(2):442-449,doi:10.3969/j.issn.0001-5733.2010.02.023.
Yuan L M,Fan Y H,Sun S R.2009.Making the calculation of generalized reflection-transmission coefficients dimensionless.Acta Seismologica Sinica(in Chinese),31(4):377-384.
程建远,姬广忠,朱培民.2012.典型含煤模型Love型槽波的频散特征分析.煤炭学报,37(1):67-72.
程久龙.1994.Love型槽波理论地震图的计算.山东矿业学院学报,13(4):349-353.
凡友华,陈晓非,刘雪峰等.2007.Rayleigh波的频散方程高频近似分解和多模式激发数目.地球物理学报,50(1):233-239.
胡国泽,滕吉文,皮娇龙等.2013.井下槽波地震勘探---预防煤矿灾害的一种地球物理方法.地球物理学进展,28(1):439-451,doi:10.6038/pg20130150.
李刚.2016.煤层厚度变化的透射槽波探测技术.煤矿开采,21(5):11-13,55,doi:10.13532/j.cnki.cn11-3677/td.2016.05.004.
刘海燕,李增学,李淑进等.2005.兖州煤田小构造发育特征及其对顶板稳定性的影响.煤田地质与勘探,33(6):24-27,doi:10.3969/j.issn.1001-1986.2005.06.007.
刘天放,潘东明,李德春等.1994.槽波地震勘探技术.徐州:中国矿业大学出版社.
潘佳铁,吴庆举,李永华等.2009.基于快速广义反射透射系数方法的面波群速度计算.地球物理学进展,24(6):2030-2035,doi:10.3969/j.issn.1004-2903.2009.06.013.
钱建伟,李德春.2013.Love型槽波的基本特性研究.中国煤炭地质,25(9):52-54.
王世彬,郭厚亮.2005.煤层厚度变化地质成因分析.煤炭技术,24(6):88,doi:10.3969/j.issn.1008-8725.2005.06.061.
王伟,高星,李松营等.2012.槽波层析成像方法在煤田勘探中的应用---以河南义马矿区为例.地球物理学报,55(3):1054-1062,doi:10.6038/j.issn.0001-5733.2012.03.036.
王宇林,赵明鹏,王国成等.1998.煤层冲刷带的分类及预测.辽宁工程技术大学学报(自然科学版),17(3):249-253.
徐果明,倪四道,王汉标.1998.瑞利型槽波的本征方程及其应用.煤炭学报,23(2):124-129.
杨小慧,李德春,于鹏飞.2010.煤层中瑞利型槽波的频散特性.物探与化探,34(6):750-752.
杨真,冯涛,Wang S G.2010.0.9m薄煤层SH型槽波频散特征及波形模式.地球物理学报,53(2):442-449,doi:10.3969/j.issn.0001-5733.2010.02.023.
尹晋平.2011.浅谈煤层冲刷带特征及预测研究.山西科技报.2011-11-10(015).
袁腊梅,凡友华,孙书荣.2009.广义反射-透射系数算法的无量纲化.地震学报,31(4):377-384.
张德亮.2015.煤层厚度变化的地质成因分析.内蒙古煤炭经济,(12):211-212,doi:10.3969/j.issn.1008-0155.2015.12.116.