初至波相位走时层析
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摘要
近地表速度结构通常是利用射线走时层析或菲涅尔体走时层析等反演方法得到的,但它们的目标函数仍利用射线走时残差构建,导致反演精度不高.为此,本文提出了基于散射积分算法的初至波相位走时层析成像方法.该方法的核心是:(1)提出了依赖于频率的相位走时概念;(2)利用依赖于频率的相位走时信息,而非单一的无限频率射线走时;(3)发展了一种改进的相位展开方法,即通过监测相位不连续性和2π周期判定来消除相位折叠现象;(4)考虑了地震波传播的有限频特征,即基于波动理论而非传统的射线路径或有限空间的菲涅尔体构建核函数.通过利用Overthrust模型的数值实验及与传统射线走时层析和菲涅尔体走时层析的对比表明:本文提出的方法是一种有效的初至波走时反演方法.同时,基于Overthrust模型的数值试验还证明了下列结论,即通过挖掘更多的走时信息的确可以获得更高的反演精度和分辨率.
Near-surface velocity structures are generally built by the ray-based traveltime tomography or the Fresnel-volume tomography in which,however,the objective function is usually constructed with the traveltime residual of raypaths.As a result,the inversion accuracy is not high.To obtain results with higher accuracy and resolution,we propose a first-arrival phase-traveltime tomographic method with an improved scattering-integral algorithm.The core of this method is:(1)putting forward the concept of frequency-dependent phase traveltime;(2)inverting the frequency-dependent traveltime instead of the asymptotic ray-based traveltime;(3)developing an improved phase-unwrapping method,e.g.unwrapping the phase by means of monitoring the phase discontinuity and judging the 2πjumps;(4)taking the finite-frequency effect of the seismic wave propagation into account,using the wave equation but not raypaths or Fresnel volumes as the sensitivity kernel.The numerical experiments on an Overthrust model and the comparisons between this method with the conventional raybased traveltime tomography and Fresnel-volume traveltime tomography prove that this method is an effective first-arrival traveltime inversion method.Meanwhile,the numerical experiments also prove that the inversion accuracy and resolution can be apparently improved by digging more traveltime information contained in the first-arrival waveform.
Near-surface velocity structures are generally built by the ray-based traveltime tomography or the Fresnel-volume tomography in which,however,the objective function is usually constructed with the traveltime residual of raypaths.As a result,the inversion accuracy is not high.To obtain results with higher accuracy and resolution,we propose a first-arrival phase-traveltime tomographic method with an improved scattering-integral algorithm.The core of this method is:(1)putting forward the concept of frequency-dependent phase traveltime;(2)inverting the frequency-dependent traveltime instead of the asymptotic ray-based traveltime;(3)developing an improved phase-unwrapping method,e.g.unwrapping the phase by means of monitoring the phase discontinuity and judging the 2πjumps;(4)taking the finite-frequency effect of the seismic wave propagation into account,using the wave equation but not raypaths or Fresnel volumes as the sensitivity kernel.The numerical experiments on an Overthrust model and the comparisons between this method with the conventional raybased traveltime tomography and Fresnel-volume traveltime tomography prove that this method is an effective first-arrival traveltime inversion method.Meanwhile,the numerical experiments also prove that the inversion accuracy and resolution can be apparently improved by digging more traveltime information contained in the first-arrival waveform.
引文
Bednar J B,Shin C,Pyun S.2007.Comparison of waveform inversion,Part 2:Phase approach.Geophysical Prospecting,55(4):465-475.
Bishop T N,Bube K P,Cutler R T,et al.1985.Tomographic determination of velocity and depth in laterally varying media.Geophysics,50(4):903-923.
Choi Y,Alkhalifah T.2013.Frequency-domain waveform inversion using the phase derivative.Geophysical Journal International,195(3):1904-1916.
Gélis C,Virieux J,Grandjean G.2007.Two-dimensional elastic full waveform inversion using Born and Rytov formulations in the frequency domain.Geophysical Journal International,168(2):605-633.
Liu Y Z,Dong L G,Li P M,et al.2009.Fresnel volume tomography based on the first arrival of the seismic wave.Chinese Journal of Geophysics(in Chinese),52(9):2310-2320,doi:10.3969/j.issn.0001-5733.2009.09.015.
Liu Y Z,Dong L G,Wang Y W,et al.2009.Sensitivity kernels for seismic Fresnel volume tomography.Geophysics,74(5):U35-U46.
Liu Y Z,Dong L G.2012.Influence of wave front healing on seismic tomography.Science China Earth Sciences,55(11):1891-1900.
Liu Y Z,Yang J Z,Chi B X,et al.2015.An improved scatteringintegral approach for frequency-domain full waveform inversion.Geophysical Journal International,202(3):1827-1842.
Oppenheim A V,Schafer R W.1975.Digital Signal Processing.Inglewood Gliffs,N J:Prentice Hall.
Poggiagliolmi E,Berkhout A J,Boone M M.1982.Phase unwrapping,possibilities and limitations.GeophysicalProspecting,30(3):281-291.
Sheng J M,Leed A,Buddensiek M,et al.2006.Early arrival waveform tomography on near-surface refraction data.Geophysics,71(4):47-57.
Shin C,Min D J,Marfurt K J,et al.2002.Traveltime and amplitude calculations using the damped wave solution.Geophysics,67(5):1637-1647.
Shin C,Min D J.2006.Waveform inversion using a logarithmic wavefield.Geophysics,71(3):R31-R42.
Spetzler G,Snieder R.2004.The Fresnel volume and transmitted waves.Geophysics,69(3):653-663.
Wielandt E.1987.On the validity of the ray approximation for interpreting delay times.∥Nolet G ed.Seismic Tomography.Dordrecht:Springer,85-98.
Woodward M J.1992.Wave-equation tomography.Geophysics,57(1):15-26.
Zhu X H,Sixta D P,Angstman B G.1992.Tomostatics:Turningray tomography+static corrections.∥62nd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts.
刘玉柱,董良国,李培明等.2009.初至波菲涅尔体地震层析成像.地球物理学报,52(9):2310-2320,doi:10.3969/j.issn.0001-5733.2009.09.015.
Bishop T N,Bube K P,Cutler R T,et al.1985.Tomographic determination of velocity and depth in laterally varying media.Geophysics,50(4):903-923.
Choi Y,Alkhalifah T.2013.Frequency-domain waveform inversion using the phase derivative.Geophysical Journal International,195(3):1904-1916.
Gélis C,Virieux J,Grandjean G.2007.Two-dimensional elastic full waveform inversion using Born and Rytov formulations in the frequency domain.Geophysical Journal International,168(2):605-633.
Liu Y Z,Dong L G,Li P M,et al.2009.Fresnel volume tomography based on the first arrival of the seismic wave.Chinese Journal of Geophysics(in Chinese),52(9):2310-2320,doi:10.3969/j.issn.0001-5733.2009.09.015.
Liu Y Z,Dong L G,Wang Y W,et al.2009.Sensitivity kernels for seismic Fresnel volume tomography.Geophysics,74(5):U35-U46.
Liu Y Z,Dong L G.2012.Influence of wave front healing on seismic tomography.Science China Earth Sciences,55(11):1891-1900.
Liu Y Z,Yang J Z,Chi B X,et al.2015.An improved scatteringintegral approach for frequency-domain full waveform inversion.Geophysical Journal International,202(3):1827-1842.
Oppenheim A V,Schafer R W.1975.Digital Signal Processing.Inglewood Gliffs,N J:Prentice Hall.
Poggiagliolmi E,Berkhout A J,Boone M M.1982.Phase unwrapping,possibilities and limitations.GeophysicalProspecting,30(3):281-291.
Sheng J M,Leed A,Buddensiek M,et al.2006.Early arrival waveform tomography on near-surface refraction data.Geophysics,71(4):47-57.
Shin C,Min D J,Marfurt K J,et al.2002.Traveltime and amplitude calculations using the damped wave solution.Geophysics,67(5):1637-1647.
Shin C,Min D J.2006.Waveform inversion using a logarithmic wavefield.Geophysics,71(3):R31-R42.
Spetzler G,Snieder R.2004.The Fresnel volume and transmitted waves.Geophysics,69(3):653-663.
Wielandt E.1987.On the validity of the ray approximation for interpreting delay times.∥Nolet G ed.Seismic Tomography.Dordrecht:Springer,85-98.
Woodward M J.1992.Wave-equation tomography.Geophysics,57(1):15-26.
Zhu X H,Sixta D P,Angstman B G.1992.Tomostatics:Turningray tomography+static corrections.∥62nd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts.
刘玉柱,董良国,李培明等.2009.初至波菲涅尔体地震层析成像.地球物理学报,52(9):2310-2320,doi:10.3969/j.issn.0001-5733.2009.09.015.