有限频层析成像方法研究进展
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摘要
本文详细介绍了地震学中最近发展起来的一种非常重要的层析成像方法一有限频层析成像方法,对有限频理论进行了重点阐述,并对有限频层析成像方法的有效性进行了探讨,接下来总结了有限频地震层析成像方法的研究进展,并对有限频层析成像方法在地震学中的应用进行了展望.由于在非均匀介质中考虑了地震波遇到速度异常时的散射现象和波前复原效应,有限频层析成像方法大大提高了对速度异常体的分辨能力.
This paper gives a detailed introduction to a special kind of seismic tomography method known as finitefrequency tomography put forward in the later 1990s and developed vigorously recently.It emphases on the finitefrequency theory,discusses the validation of finite-frequency tomography method,and summarizes the progress of finite-frequency tomography and looks forward to its future application in seismology.In inhomogeneous media,because of considering the scattering phenomenon and wave-front healing effects happening when seismic waves meet velocity anomalies,the finite-frequency tomography method improves the resolution to the velocity anomalies remarkably.
This paper gives a detailed introduction to a special kind of seismic tomography method known as finitefrequency tomography put forward in the later 1990s and developed vigorously recently.It emphases on the finitefrequency theory,discusses the validation of finite-frequency tomography method,and summarizes the progress of finite-frequency tomography and looks forward to its future application in seismology.In inhomogeneous media,because of considering the scattering phenomenon and wave-front healing effects happening when seismic waves meet velocity anomalies,the finite-frequency tomography method improves the resolution to the velocity anomalies remarkably.
引文
[1] Aki K,Christoffersson A,Husebye E: S.Three-dimensional seismic structure of the lithosphere under Montana lasa[J].Bull.Seism.Soc.Amer.,1976,66(2) :501-524．
[2] Aki K,Christoffersson A,Husebye E S.Determination of the three-dimensional seismic structure of the lithosphere[J].J.Geophys.Res.,1977,82(2) :277-296．
[3] Marquering H,Dahlen F A,Nolet G.Three-dimensional sensitivity kernels for finite-frequency travehimes: the banana doughnut paradox[J].Geophys.J.Int.,1999,137: 805-815．
[4] Dahlen F A,Hung Shu-huei,Nolet G.Frechet kernels for finite-frequency traveltimes-Ⅰ.Theory[J].Geophys.J.Int.,2000,141 : 157-174．
[5] Hung Shu-huei,Dahlen F A,Nolet G.Frechet kernels for finite-frequency traveltimes-Ⅱ.Examples[J].Geophys.J.Int.,2000,141,175-203．
[6] Zhao L,Jordan T H,Chapman C H.Three-dimensional Frechet differential kernels for seismic delay times [J].Geophy.J.Int.,2000,141(3) :558-576．
[7] VanDecar J,Crosson R.Determination of teleseismic relative phase arrival times using multi-channel cross-correlation and least squares[J].Bull.seism.Soc.Am.,1990,80:150-159．
[8] Woodward R L,Masters G.Global upper mantle structure from long-period di? erential traveltimes [J].J.geophys.Res.,1991,96:6351-6377．
[9] Luo Y,Schuster G T.Wave-equation traveltime inversion[J].Geophysics,1991,56(5) :645-653．
[10] Nolet G,Dahlen F A,Montelli R.Traveltimes and amplitudes of seismic waves: a re-assessment[J],in Seismic Earth : Array Analysis of Broadband Seismograms,Geophysical Monograph,2005,157: 37-47．
[11] Nolet G,Montelli R.Optimal pararnetrization of tomographic models[J].Geophys.J.Int.,2005,161:365-372．
[12] Nolet G,Dahlen F A.Wave front healing and the evolution of seismic delay times[J].J.Geophys.Res.,2000,105:19043-19054．
[13] Hung Shu-huei,Dahlen F A,Nolet G.Wavefront healing: a banana-doughnut perspective[J].Geophys.J.Int.,2001,146:289-312．
[14] Yang Hsin-ying,Hung Shu-huei.Validation of ray and wave theoretical travel times in heterogeneous random media [J].Geophys.Res.Lett.,2005,32(20) : L20302,doi:10． 1029/2005GL023501．
[15] Baig A M,Dahlen F A,Hung Shu-huei.Traveltimes of waves in three-dimension random media [J].Geophys.J.Int.,2003,153:467-482．
[16] Woodward M J.Wave-equation tomography[J].Geophysics,1992,57(1) : 15-26．
[17] Tong Jun,Dahlen F A,Nolet G,Marquering H.Diffraction effects upon finite-frequency travel times: a simple 2-D example[J].Geophys.Res.Lett.,1998,25(11) :1983-1986．
[18] Spetzler J,Snieder R.The formation of caustics in two and three-dimensional media[J].Geophys.J.Int.,2001,144 (1) :175-182．
[19] Spetzler J,Snieder R.The Fresnel volume and transmitted waves[J].Geophys,2004,69(3) :653-663．
[20] Montelli R,Notet G,Dahlen F A,Masters G,Engdahl E R,Hung Shu-huei.Finite-frequency tomography reveals a variety of plumes in the mantle[J].Science,2004,303:338-343．
[24] Montelli R,Nolet G,Masters G,Dahlen F A,Hung Shu huek Global P and PP traveltime tomography: rays versus waves[J].Geophys.J.Int.,2004,158:637-654．
[22] Baig A,Dahlen F A.Statistics of traveltimes and amplitudes in random media[J].Geophys.J.Int.,2004,158(1) :187-210．
[23] Baig A,Dahlen F A.Travehime biases in random media and the s-wave discrepancy[J].Geophys.J.Int.,2004,158(3) :922-938．
[24] de Hoop M V,van der Hilst R D.On sensitivity kernels for'waveequation' transmission tomography[J].Geophys.J. Int.,2005,160:621-633．
[25] van der Hilst R D,de Hoop M V.Banana-doughnut kernels and mantle tomography[J].Geophys.J.Int.,2005,163:956-961．
[26] Dahlen F A.,Nolet G.Comment on the paper "On sensitivity kernels for ' wave-equation ' transmission tomography" by de Hoop and van der Hilst[J].Geophys.J.Int.,2005,163(3) :949-951．
[27] Montelli R,Nolet G,Dahlen F A.Comment on 'Banana doughnut kernels and mantle tomography' by van der Hilst and de Hoop[J].Geophys.J.Int.,2006,167:1204-1210．
[28] de Hoop M V,van der Hilst RD.Reply to acomment by F A.Dahlen and G.Nolet on:On sensitivity kernels for wave equation tomography[J].Geophys.J.Int.,2005,163:952-955．
[29] van der Hilst R D,de Hoop M V.Reply to comment by R.Montelli,G.Nolet and F.A.Dahlen on 'Banana-doughnut kernels and mantle tomography' [J].Geophys.J.Int.,2006,167:1211-1214．
[30] Spetzler J,Trampert J,Snieder R.The effects of scattering in surface wave tomography[J].Geophys.J.Int.,2002,149:755-767．
[31] Zhou Y,Dahlen F A,Nolet G.Three-dimensional sensitivity kernels for surface wave ohservables[J].Geophys.J.Int.,2004,158(1) :142-168．
[32] Yoshizawa K,Kennett B L N.Sensitivity kernels for finite-frequency surface waves[J].Geophys.J.Int.,2005,162:910-926．
[33] Sieminski A,Lveeque J J,Dehayle E.Can finite-frequency effects he accounted for in ray theory surface wave tomography? [J].Geophys.Res.Lett.,2004,31(24) :L24614,doi:10． 1029/2004GL021402．
[34] Tramper J,Spetzler J.Surface wave tomography: finite-frequency effects lost in the null space[J].Geophys.J.Int.,2006,164 : 394-400．
[35] Boschi L,Becker T W,Soldati G,Dziewonski A M.On the relevance of Born theory in global seismic tomography[J].Geophys.Res.Lett.,2006,33: L06302,doi: 10． 1029/2005GL025063．
[36] Zhou Ying,Dahlen F A,Nolet G,Laske G.Finite-frequency effects in global surface wave tomography[J].Geophys.J.Int.,2005,163(3) :1087-1111．
[37] Zhou Ying,Nolet G,Dahlen F A,Laske G.Global uppermantle structure from finite-frequency surface-wave tomography[J].J.Geophys.Res.,2006,111(B4) :B04304,doi: 10． 1029/2005JB003677．
[38] Zhang Z G,Shen Y,Zhao L.Finite-frequency sensitivity kernels for head waves[J].Geophys.J.Int.,2007,171:847-856．
[39] Zhao L,Jordan T H.Structural sensitivities of finite frequency seismic waves: a full-wave approach[J].Geophys.J.Int.,2006,165:981-990．
[40] Tromp J,Tape C,Liu Q Y.Seismic tomography,adjoint methods,time reversal and banana-doughnut kernels [J].Geophys.J.Int.,2005,160(1) :195-216．
[41] Liu Q Y,Tromp J.Finite-frequency kernels based upon adjoint methods[J].Bull.seism.Soc.Am.,2006,96: 2383-2397．
[42] Tape C,Liu Q Y,Tromp J.Finite-frequency tomography using adjoint methods-Methodology and examples using membrane surface waves[J].Geophys.J.Int.,2007,168(3) :1105-1129．
[43] Liu Q Y,Tromp J.Finite-frequency sensitivity kernels for global seismic wave propagation based upon adjoint methods[J].Geophys.J.Int.,2008,174(1) :265-286．
[44] Sieminski A,Liu Q Y,Trampert J,Tromp J.Finitefrequency sensitivity of surface waves to anisotropy based upon adjoint methods[J].Geophys.J.Int.,2007,168(3) :1153-1174．
[45] Sieminski A,Liu Qin-ya,Trampert J,Tromp J.Finitefrequency sensitivity of body waves to anisotropy based upon adjoint methods[J].Geophys.J.Int.,2007,171(1) :368-389．
[46] Dahlen F A.Finite-frequency sensitivity kernels for boundary topography perturbations[J].Geophys,J.Int.,2005,162:525-540．
[47] Zhao L,Jordan T H,Olsen K B,Chen P.Frechet kernels for imaging regional earth structure based on threedimensional reference models[J].Bull Seism.Soc.Am.,2005,95(6) :2066-2080．
[48] Yang T,Shen Y.Frequency-dependent crustal correction for finite-frequency seismic tomography[J].Bull.Seism.Soc.Am.,2006,96(6) :2441-2448．
[49] Pollitz F F,Finite-frequency traveltime tomography of San Francisco Bay region crustal velocity structure[J].Geophys.J.Int.,2007,171:630-656．
[50] Gautier S,Nolet G,Virieux J.Finite-frequency tomography in a crustal environment: Application to the western part of the Gulf of Corinth[J].Geophysical Prospecting,2008,56(4) :493-503．
[51] Hung Shu-huei,Garnero EJ,Chao L Y,Kuo B Y,Thorne L.Finite frequency tomography of D" shear velocity heterogeneity beneath the Caribbean[J].J.Geophys.Res.,2005,110(BT):B07305,doi:10． 1029/2004JB003373．
[52] Chevrot S,Zhao L.Multiscale finite-frequency Rayleigh wave tomography of Kaapvaal Craton[J].Geophys.J.Int.,2007,169(1) :201-215．
[53] Chevrot S.Finite-frequency vectorial tomography: a new method for high-resolution imaging of upper mantle anisotropy[J].Geophys.J.Int.,2006,165:641-657．
[54] Favier N,Chevrot S.Sensitivity kernels for shear wave splitting in transverse isotropic media[J].Geophys.J.Int.,2003,153(1) :213-228．
[55] Calvet M,Chevrot S.Traveltime sensitivity kernels for PKP phases in the mantle[J].Physics of the Earth and Planetary Interiors,2005,15a(1-3) :21-31．
[56] Calvet M,Chevrot S,Souriau A.P-wave propagation in transversely isotropic media I.Finite-frequency theory [J].Physics of the Earth and Planetary Interiors,2006,156:12-20．
[57] Sieminski Anne,Paulssen H,Trampert J,Tromp J.FiniteFrequency SKS Splitting: Measurement and sensitivity kernels[J].Bull.Seism.Soc.Am.,2008,98(4) : 1797-1810．
[58] Nolet G,Karato S I,Montelli R.Plume fluxes from seismic tomography[J].Earth and Planetary Science Letters,2006,148:685-699．
[59] Montelli R,Nolet G,Dahlen F A,Masters G.A catalogue of deep mantle plumes: new results from finite-frequency tomography[J].Geochem.Geophys.Geosyst.(G3) ,2006,7(11) : Q11007,doi : 10． 1029/2006GC001248．
[60] Hung Shu-huei,Shen Y,Chao L Y.Imaging seismic velocity structure beneath the Iceland hot spot: a finite frequency approach[J].J.Geophys.Res.,2004,109:B08305,doi;10,1029/2003JB002889．
[61] Yang T,Shen Y,van der Lee S,Solomon S C,Hung Shu huei.Upper mantle structure beneath the Azores hotspot from finite-frequency seismic tomography [J.Earth and Planetary Science Letters,2006,250: 11-26．
[2] Aki K,Christoffersson A,Husebye E S.Determination of the three-dimensional seismic structure of the lithosphere[J].J.Geophys.Res.,1977,82(2) :277-296．
[3] Marquering H,Dahlen F A,Nolet G.Three-dimensional sensitivity kernels for finite-frequency travehimes: the banana doughnut paradox[J].Geophys.J.Int.,1999,137: 805-815．
[4] Dahlen F A,Hung Shu-huei,Nolet G.Frechet kernels for finite-frequency traveltimes-Ⅰ.Theory[J].Geophys.J.Int.,2000,141 : 157-174．
[5] Hung Shu-huei,Dahlen F A,Nolet G.Frechet kernels for finite-frequency traveltimes-Ⅱ.Examples[J].Geophys.J.Int.,2000,141,175-203．
[6] Zhao L,Jordan T H,Chapman C H.Three-dimensional Frechet differential kernels for seismic delay times [J].Geophy.J.Int.,2000,141(3) :558-576．
[7] VanDecar J,Crosson R.Determination of teleseismic relative phase arrival times using multi-channel cross-correlation and least squares[J].Bull.seism.Soc.Am.,1990,80:150-159．
[8] Woodward R L,Masters G.Global upper mantle structure from long-period di? erential traveltimes [J].J.geophys.Res.,1991,96:6351-6377．
[9] Luo Y,Schuster G T.Wave-equation traveltime inversion[J].Geophysics,1991,56(5) :645-653．
[10] Nolet G,Dahlen F A,Montelli R.Traveltimes and amplitudes of seismic waves: a re-assessment[J],in Seismic Earth : Array Analysis of Broadband Seismograms,Geophysical Monograph,2005,157: 37-47．
[11] Nolet G,Montelli R.Optimal pararnetrization of tomographic models[J].Geophys.J.Int.,2005,161:365-372．
[12] Nolet G,Dahlen F A.Wave front healing and the evolution of seismic delay times[J].J.Geophys.Res.,2000,105:19043-19054．
[13] Hung Shu-huei,Dahlen F A,Nolet G.Wavefront healing: a banana-doughnut perspective[J].Geophys.J.Int.,2001,146:289-312．
[14] Yang Hsin-ying,Hung Shu-huei.Validation of ray and wave theoretical travel times in heterogeneous random media [J].Geophys.Res.Lett.,2005,32(20) : L20302,doi:10． 1029/2005GL023501．
[15] Baig A M,Dahlen F A,Hung Shu-huei.Traveltimes of waves in three-dimension random media [J].Geophys.J.Int.,2003,153:467-482．
[16] Woodward M J.Wave-equation tomography[J].Geophysics,1992,57(1) : 15-26．
[17] Tong Jun,Dahlen F A,Nolet G,Marquering H.Diffraction effects upon finite-frequency travel times: a simple 2-D example[J].Geophys.Res.Lett.,1998,25(11) :1983-1986．
[18] Spetzler J,Snieder R.The formation of caustics in two and three-dimensional media[J].Geophys.J.Int.,2001,144 (1) :175-182．
[19] Spetzler J,Snieder R.The Fresnel volume and transmitted waves[J].Geophys,2004,69(3) :653-663．
[20] Montelli R,Notet G,Dahlen F A,Masters G,Engdahl E R,Hung Shu-huei.Finite-frequency tomography reveals a variety of plumes in the mantle[J].Science,2004,303:338-343．
[24] Montelli R,Nolet G,Masters G,Dahlen F A,Hung Shu huek Global P and PP traveltime tomography: rays versus waves[J].Geophys.J.Int.,2004,158:637-654．
[22] Baig A,Dahlen F A.Statistics of traveltimes and amplitudes in random media[J].Geophys.J.Int.,2004,158(1) :187-210．
[23] Baig A,Dahlen F A.Travehime biases in random media and the s-wave discrepancy[J].Geophys.J.Int.,2004,158(3) :922-938．
[24] de Hoop M V,van der Hilst R D.On sensitivity kernels for'waveequation' transmission tomography[J].Geophys.J. Int.,2005,160:621-633．
[25] van der Hilst R D,de Hoop M V.Banana-doughnut kernels and mantle tomography[J].Geophys.J.Int.,2005,163:956-961．
[26] Dahlen F A.,Nolet G.Comment on the paper "On sensitivity kernels for ' wave-equation ' transmission tomography" by de Hoop and van der Hilst[J].Geophys.J.Int.,2005,163(3) :949-951．
[27] Montelli R,Nolet G,Dahlen F A.Comment on 'Banana doughnut kernels and mantle tomography' by van der Hilst and de Hoop[J].Geophys.J.Int.,2006,167:1204-1210．
[28] de Hoop M V,van der Hilst RD.Reply to acomment by F A.Dahlen and G.Nolet on:On sensitivity kernels for wave equation tomography[J].Geophys.J.Int.,2005,163:952-955．
[29] van der Hilst R D,de Hoop M V.Reply to comment by R.Montelli,G.Nolet and F.A.Dahlen on 'Banana-doughnut kernels and mantle tomography' [J].Geophys.J.Int.,2006,167:1211-1214．
[30] Spetzler J,Trampert J,Snieder R.The effects of scattering in surface wave tomography[J].Geophys.J.Int.,2002,149:755-767．
[31] Zhou Y,Dahlen F A,Nolet G.Three-dimensional sensitivity kernels for surface wave ohservables[J].Geophys.J.Int.,2004,158(1) :142-168．
[32] Yoshizawa K,Kennett B L N.Sensitivity kernels for finite-frequency surface waves[J].Geophys.J.Int.,2005,162:910-926．
[33] Sieminski A,Lveeque J J,Dehayle E.Can finite-frequency effects he accounted for in ray theory surface wave tomography? [J].Geophys.Res.Lett.,2004,31(24) :L24614,doi:10． 1029/2004GL021402．
[34] Tramper J,Spetzler J.Surface wave tomography: finite-frequency effects lost in the null space[J].Geophys.J.Int.,2006,164 : 394-400．
[35] Boschi L,Becker T W,Soldati G,Dziewonski A M.On the relevance of Born theory in global seismic tomography[J].Geophys.Res.Lett.,2006,33: L06302,doi: 10． 1029/2005GL025063．
[36] Zhou Ying,Dahlen F A,Nolet G,Laske G.Finite-frequency effects in global surface wave tomography[J].Geophys.J.Int.,2005,163(3) :1087-1111．
[37] Zhou Ying,Nolet G,Dahlen F A,Laske G.Global uppermantle structure from finite-frequency surface-wave tomography[J].J.Geophys.Res.,2006,111(B4) :B04304,doi: 10． 1029/2005JB003677．
[38] Zhang Z G,Shen Y,Zhao L.Finite-frequency sensitivity kernels for head waves[J].Geophys.J.Int.,2007,171:847-856．
[39] Zhao L,Jordan T H.Structural sensitivities of finite frequency seismic waves: a full-wave approach[J].Geophys.J.Int.,2006,165:981-990．
[40] Tromp J,Tape C,Liu Q Y.Seismic tomography,adjoint methods,time reversal and banana-doughnut kernels [J].Geophys.J.Int.,2005,160(1) :195-216．
[41] Liu Q Y,Tromp J.Finite-frequency kernels based upon adjoint methods[J].Bull.seism.Soc.Am.,2006,96: 2383-2397．
[42] Tape C,Liu Q Y,Tromp J.Finite-frequency tomography using adjoint methods-Methodology and examples using membrane surface waves[J].Geophys.J.Int.,2007,168(3) :1105-1129．
[43] Liu Q Y,Tromp J.Finite-frequency sensitivity kernels for global seismic wave propagation based upon adjoint methods[J].Geophys.J.Int.,2008,174(1) :265-286．
[44] Sieminski A,Liu Q Y,Trampert J,Tromp J.Finitefrequency sensitivity of surface waves to anisotropy based upon adjoint methods[J].Geophys.J.Int.,2007,168(3) :1153-1174．
[45] Sieminski A,Liu Qin-ya,Trampert J,Tromp J.Finitefrequency sensitivity of body waves to anisotropy based upon adjoint methods[J].Geophys.J.Int.,2007,171(1) :368-389．
[46] Dahlen F A.Finite-frequency sensitivity kernels for boundary topography perturbations[J].Geophys,J.Int.,2005,162:525-540．
[47] Zhao L,Jordan T H,Olsen K B,Chen P.Frechet kernels for imaging regional earth structure based on threedimensional reference models[J].Bull Seism.Soc.Am.,2005,95(6) :2066-2080．
[48] Yang T,Shen Y.Frequency-dependent crustal correction for finite-frequency seismic tomography[J].Bull.Seism.Soc.Am.,2006,96(6) :2441-2448．
[49] Pollitz F F,Finite-frequency traveltime tomography of San Francisco Bay region crustal velocity structure[J].Geophys.J.Int.,2007,171:630-656．
[50] Gautier S,Nolet G,Virieux J.Finite-frequency tomography in a crustal environment: Application to the western part of the Gulf of Corinth[J].Geophysical Prospecting,2008,56(4) :493-503．
[51] Hung Shu-huei,Garnero EJ,Chao L Y,Kuo B Y,Thorne L.Finite frequency tomography of D" shear velocity heterogeneity beneath the Caribbean[J].J.Geophys.Res.,2005,110(BT):B07305,doi:10． 1029/2004JB003373．
[52] Chevrot S,Zhao L.Multiscale finite-frequency Rayleigh wave tomography of Kaapvaal Craton[J].Geophys.J.Int.,2007,169(1) :201-215．
[53] Chevrot S.Finite-frequency vectorial tomography: a new method for high-resolution imaging of upper mantle anisotropy[J].Geophys.J.Int.,2006,165:641-657．
[54] Favier N,Chevrot S.Sensitivity kernels for shear wave splitting in transverse isotropic media[J].Geophys.J.Int.,2003,153(1) :213-228．
[55] Calvet M,Chevrot S.Traveltime sensitivity kernels for PKP phases in the mantle[J].Physics of the Earth and Planetary Interiors,2005,15a(1-3) :21-31．
[56] Calvet M,Chevrot S,Souriau A.P-wave propagation in transversely isotropic media I.Finite-frequency theory [J].Physics of the Earth and Planetary Interiors,2006,156:12-20．
[57] Sieminski Anne,Paulssen H,Trampert J,Tromp J.FiniteFrequency SKS Splitting: Measurement and sensitivity kernels[J].Bull.Seism.Soc.Am.,2008,98(4) : 1797-1810．
[58] Nolet G,Karato S I,Montelli R.Plume fluxes from seismic tomography[J].Earth and Planetary Science Letters,2006,148:685-699．
[59] Montelli R,Nolet G,Dahlen F A,Masters G.A catalogue of deep mantle plumes: new results from finite-frequency tomography[J].Geochem.Geophys.Geosyst.(G3) ,2006,7(11) : Q11007,doi : 10． 1029/2006GC001248．
[60] Hung Shu-huei,Shen Y,Chao L Y.Imaging seismic velocity structure beneath the Iceland hot spot: a finite frequency approach[J].J.Geophys.Res.,2004,109:B08305,doi;10,1029/2003JB002889．
[61] Yang T,Shen Y,van der Lee S,Solomon S C,Hung Shu huei.Upper mantle structure beneath the Azores hotspot from finite-frequency seismic tomography [J.Earth and Planetary Science Letters,2006,250: 11-26．
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