多震相菲涅耳体射线走时同时反演成像
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摘要
高频假设下的地震射线理论以及相应的地震成像理论表明,在射线稀疏条件下,不可能得到较高分辨率的构造成像;而有限频射线理论更符合实际地震的传播规律,即地震波的走时不仅与中心射线(传统的几何射线)上的速度分布有关,而且与中心射线附近一定范围(称其为第一菲涅耳体)内的速度异常分布有关.鉴于此,本文提出了计算多震相地震波菲涅耳体有限频射线的方法,并定义了走时敏感核函数,同时给出了利用多震相菲涅耳体有限频射线进行速度模型和反射界面同时反演成像的公式.利用多震相走时资料,使用传统射线层析成像方法与有限频射线层析成像方法进行了速度和界面的同时反演成像.结果表明,当射线密度较小时,无论是对速度模型的重建还是对反射界面几何形状的更新,有限频射线层析成像方法均优于传统射线层析成像方法,而变频有限频射线层析成像则是实际地震层析成像的首选反演算法.
Traditional ray tomography method based on high frequency assumption is unable to obtain a high resolution tomographic picture with sparse rays.In contrast,the finite-frequency ray theory is more suitable for real seismic propagation law,that is to say that the travel time is dependent not only on the velocity distribution along a central ray(or traditional geometric ray),but also on the velocity anomaly within a region(referred as the first Fresnel volume),which embraces the central ray.In this paper we first put forward an algorithm to calculate the multi-phase Fresnel volume finite-frequency ray,and then give a inversion method to simultaneously invert both velocity and reflector geometry by using these multi-phase arrival time information.In synthetic example,both the traditional ray tomographic and finite-frequency ray tomographic methods are used to simultaneously update both velocity field and reflector geometry with multi-phase arrival times,the results show that the finite-frequency ray tomographic method is advantageous over the traditional ray tomographic method in terms of velocity reconstruction and reflector geometry updating when the ray density is relatively low.The finite-frequency ray tomographic method with varying frequency is a good choice in real seismic tomographic application.
Traditional ray tomography method based on high frequency assumption is unable to obtain a high resolution tomographic picture with sparse rays.In contrast,the finite-frequency ray theory is more suitable for real seismic propagation law,that is to say that the travel time is dependent not only on the velocity distribution along a central ray(or traditional geometric ray),but also on the velocity anomaly within a region(referred as the first Fresnel volume),which embraces the central ray.In this paper we first put forward an algorithm to calculate the multi-phase Fresnel volume finite-frequency ray,and then give a inversion method to simultaneously invert both velocity and reflector geometry by using these multi-phase arrival time information.In synthetic example,both the traditional ray tomographic and finite-frequency ray tomographic methods are used to simultaneously update both velocity field and reflector geometry with multi-phase arrival times,the results show that the finite-frequency ray tomographic method is advantageous over the traditional ray tomographic method in terms of velocity reconstruction and reflector geometry updating when the ray density is relatively low.The finite-frequency ray tomographic method with varying frequency is a good choice in real seismic tomographic application.
引文
白超英,黄国娇,李忠生.2011.三维复杂层状介质中多震相走时联合反演成像[J].地球物理学报,54(1):182--192.Bai C Y,Huang G J,Li Z S.2011.Simultaneous inversion combining multiple-phase travel times within 3Dcomplex layered media[J].Chinese Journal of Geophysics,54(1):182--192(in Chinese).
成谷,马在田,耿建华,曹景忠.2002.地震层析成像发展回顾[J].勘探地球物理进展,25(3):6--12.Cheng G,Ma Z T,Geng J H,Cao J Z.2002.A review on the growth of seismic tomography[J].Progress in Exploration Geophysics,25(3):6--12(in Chinese).
黄国娇,白超英.2010.二维复杂层状介质中地震多波走时联合反演成像[J].地球物理学报,53(12):2972--2981.Huang G J,Bai C Y.2010.Simultaneous inversion with multiple traveltimes within 2-D complex layered media[J].Chinese Journal of Geophysics,53(12):2972--2981.
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.Jiang Y,Chen X F.2011.Review on the comparative study between finite-frequency tomography and ray-theoreticaltomography[J].Progress in Geophysics,26(5):1566--1575(in Chinese).
刘玉柱,董良国,朱金平.2011.菲涅耳体地震层析成像分辨率研究[J].地球物理学报,54(9):2338--2347.Liu Y Z,Dong L G,Zhu J P.2011.Research on the seismic resolution of Fresnel volume tomography[J].Chinese Journal of Geophysics,54(9):2338--2347(in Chinese).
唐小平,白超英.2009.最短路径算法下三维层状介质中多次波追踪[J].地球物理学报,52(10):2635--2643.Tang X P,Bai C Y.2009.Multiple ray tracing within 3-D layered media with the shortest path method[J].ChineseJournal of Geophysics,52(10):2635--2643(in Chinese).
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.Xu X M,Shi D N,Li X F.2009.Research progress of the finite-frequency tomography method[J].Progress in Geophysics,24(2):432--438(in Chinese).
赵瑞,白超英.2010.复杂层状模型中多次波快速追踪:一种基于非规则网格的最短路径算法[J].地震学报,32(4):433--444.Zhao R,Bai C Y.2010.Fast multiple ray tracing within complex layered media:The shortest path method based onirregular grid cells[J].Acta Seismologica Sinica,32(4):433--444(in Chinese).
Aki K,Lee W H K.1976.Determination of three dimensional velocity anomalies under a seismic array using first P arrival times from local earthquakes[J].J Geophys Res,81(23):4381--4399.
ˇCervenV,Soares J E P.1992.Fresnel volume ray tracing[J].Geophysics,57(7):902--915.
Husen S,Kissling E.2001.Local earthquake tomography between rays and waves:Fat ray tomography[J].Phys EarthPlanet Inter,123(2):129--149.
Montelli R,Nolet G,Dahlen F A,Masters G,Engdahl E R,Hung H S.2004.Finite-frequency tomography reveals avariety of plumes in the mantle[J].Science,303(5656):338--343.
Thurber C,Eberhart-Phillips D.1999.Local earthquake tomography with flexible gridding[J].Comput Geosci,25:809--818.
Tromp J,Tape C,Liu Q Y.2005.Seismic tomography,adjoint method,time reversal and banana-doughnut kernels[J].Geophys J Int,160(1):195--216.
Vasco D W,Peterson J E,Majer E L.1995.Beyond ray tomography:Wave paths and Fresnel volumes[J].Geophysics,60(6):1790--1804.
Woodward M J.1992.Wave-equation tomography[J].Geophysics,57(1):15--26.
Zhao L,Jordan T H,Olsen K B,Chen P.2005.Fréchet kernels for imaging regional earth structure based on threedimensional reference models[J].Bull Seismol Soc Am,95(6):2066--2080.
成谷,马在田,耿建华,曹景忠.2002.地震层析成像发展回顾[J].勘探地球物理进展,25(3):6--12.Cheng G,Ma Z T,Geng J H,Cao J Z.2002.A review on the growth of seismic tomography[J].Progress in Exploration Geophysics,25(3):6--12(in Chinese).
黄国娇,白超英.2010.二维复杂层状介质中地震多波走时联合反演成像[J].地球物理学报,53(12):2972--2981.Huang G J,Bai C Y.2010.Simultaneous inversion with multiple traveltimes within 2-D complex layered media[J].Chinese Journal of Geophysics,53(12):2972--2981.
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.Jiang Y,Chen X F.2011.Review on the comparative study between finite-frequency tomography and ray-theoreticaltomography[J].Progress in Geophysics,26(5):1566--1575(in Chinese).
刘玉柱,董良国,朱金平.2011.菲涅耳体地震层析成像分辨率研究[J].地球物理学报,54(9):2338--2347.Liu Y Z,Dong L G,Zhu J P.2011.Research on the seismic resolution of Fresnel volume tomography[J].Chinese Journal of Geophysics,54(9):2338--2347(in Chinese).
唐小平,白超英.2009.最短路径算法下三维层状介质中多次波追踪[J].地球物理学报,52(10):2635--2643.Tang X P,Bai C Y.2009.Multiple ray tracing within 3-D layered media with the shortest path method[J].ChineseJournal of Geophysics,52(10):2635--2643(in Chinese).
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.Xu X M,Shi D N,Li X F.2009.Research progress of the finite-frequency tomography method[J].Progress in Geophysics,24(2):432--438(in Chinese).
赵瑞,白超英.2010.复杂层状模型中多次波快速追踪:一种基于非规则网格的最短路径算法[J].地震学报,32(4):433--444.Zhao R,Bai C Y.2010.Fast multiple ray tracing within complex layered media:The shortest path method based onirregular grid cells[J].Acta Seismologica Sinica,32(4):433--444(in Chinese).
Aki K,Lee W H K.1976.Determination of three dimensional velocity anomalies under a seismic array using first P arrival times from local earthquakes[J].J Geophys Res,81(23):4381--4399.
ˇCervenV,Soares J E P.1992.Fresnel volume ray tracing[J].Geophysics,57(7):902--915.
Husen S,Kissling E.2001.Local earthquake tomography between rays and waves:Fat ray tomography[J].Phys EarthPlanet Inter,123(2):129--149.
Montelli R,Nolet G,Dahlen F A,Masters G,Engdahl E R,Hung H S.2004.Finite-frequency tomography reveals avariety of plumes in the mantle[J].Science,303(5656):338--343.
Thurber C,Eberhart-Phillips D.1999.Local earthquake tomography with flexible gridding[J].Comput Geosci,25:809--818.
Tromp J,Tape C,Liu Q Y.2005.Seismic tomography,adjoint method,time reversal and banana-doughnut kernels[J].Geophys J Int,160(1):195--216.
Vasco D W,Peterson J E,Majer E L.1995.Beyond ray tomography:Wave paths and Fresnel volumes[J].Geophysics,60(6):1790--1804.
Woodward M J.1992.Wave-equation tomography[J].Geophysics,57(1):15--26.
Zhao L,Jordan T H,Olsen K B,Chen P.2005.Fréchet kernels for imaging regional earth structure based on threedimensional reference models[J].Bull Seismol Soc Am,95(6):2066--2080.