基于三次卷积插值的时间域多尺度全波形反演
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摘要
时间域全波形反演采用全频带地震数据时容易陷入局部极值,通过滤波器对地震数据分频段开展时间域的多尺度反演研究。从一阶导数的高阶交错网格有限差分格式出发,给出了不同差分阶数下不同频段反演时可取的空间步长;采用巴特沃斯自相关滤波器将地震数据滤波成一系列不同频段的地震数据,从低频到高频依次反演,上一个低频段反演的结果作为下一个高频段反演的初始模型。考虑到不同频段反演时采用的空间步长不是简单的倍数关系,通过引入三次卷积插值技术来实现不同频段之间的插值。理论模型试算证明:在不同的反演频带下分别选择合适的空间步长,同时相应改变时间步长,能最大程度减少反演所需时间;三次卷积插值技术可实现粗网格大小与细网格大小为任意倍数的插值,基于三次卷积插值法反演可得到与常规统一网格步长反演法精度相当的结果。
The time domain full waveform inversion using the full band data is usually unsuccessful because the misfit error is easily trapped into local minima value.This problem can be solved with filter technique to realize the time domain multiscale inversion.Starting from the high-order staggered grid finite difference scheme,the space step corresponding to different frequency bands at different difference orders is given. The seismic data is filtered into different frequency-bands by the Butterworth autocorrelation filter to realize multiscale inversion. In the inversion,the low-frequency inversion result is used as the starting model in the high-frequency inversion.Considering that the spatial step of different frequency bands is not a simple multiple relation,the interpolation between different frequency-bands is realized by using the cubic convolution interpolation.The test of theoretical model proves that it can reduce the time required for the inversion,when the appropriate space step in different inversion bands is selected and the time step is changed correspondingly.The cubic convolution interpolation technique can realize the interpolation with discretionary ratio between coarse mesh and fine mesh.This method can not only realize the multi-scale inversion quickly,but alsocan get the same accuracy inversion result as the tra-ditional fixed-spatial-step method.
The time domain full waveform inversion using the full band data is usually unsuccessful because the misfit error is easily trapped into local minima value.This problem can be solved with filter technique to realize the time domain multiscale inversion.Starting from the high-order staggered grid finite difference scheme,the space step corresponding to different frequency bands at different difference orders is given. The seismic data is filtered into different frequency-bands by the Butterworth autocorrelation filter to realize multiscale inversion. In the inversion,the low-frequency inversion result is used as the starting model in the high-frequency inversion.Considering that the spatial step of different frequency bands is not a simple multiple relation,the interpolation between different frequency-bands is realized by using the cubic convolution interpolation.The test of theoretical model proves that it can reduce the time required for the inversion,when the appropriate space step in different inversion bands is selected and the time step is changed correspondingly.The cubic convolution interpolation technique can realize the interpolation with discretionary ratio between coarse mesh and fine mesh.This method can not only realize the multi-scale inversion quickly,but alsocan get the same accuracy inversion result as the tra-ditional fixed-spatial-step method.
引文
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[20]董良国,马在田,曹景忠,等.一阶弹性波方程交错网格有限差分解法[J].地球物理学报,2000,43(3):411-418.DONG Liangguo, MA Zaitian, CAO Jingzhong, et al. A staggered-grid high-order difference method of one-order elastic wave equation[J].Chinese J.Geophys.,2000,43(3):411-418.
[21] CHU C,STOFFA P L.Determination of finite-difference weights using scaled binomial windows[J].Geophysics,2012,77(3):W17-W26.
[22]韩复兴,孙建国,杨昊.基于二维三次卷积插值算法的波前扩散构建射线追踪[J].吉林大学学报(地球科学版),2008,38(2):336-346.HAN Fuxin,SUN Jianguo,YANG Hao. Ray-tracing of wavefront construction by bicubic convolution interpolation[J]. Journal of Jilin University(Earth Science Edition),2008,38(2):336-346.
[23] VIGH D,STARR E,KAPOOR J.Developing Earth models with full waveform inversion[J].The Leading Edge,2009,28(4):432-435.
[24] ZHANG Z,LIN Y,HUANG L. Full-waveform inversion in the time domain with an energy-weighted gradient[A].81st SEG Annual International Meeting[C].San Antonio,2011:2772-2776.
[25] KOHN D,DENIL D,KURZMANN A,et al. On the influence of model parameterization in elastic full waveform tomography[J].Geophysics Journal International,2012,191(1):325-345.
[26] SHIPP R,SINGH S. Two-dimensional full wavefield inversion of wide-aperture marine seismic streamer data[J].Geophysics Journal International,2002,151(2):325-344.
[27] BOHLEN T. Parallel 3-D viscoelastic finite difference seismic modeling[J].Computers&Geosciences,2002,28:887-899.
[2]杨勤勇,胡光辉,王立歆.全波形反演研究现状及发展趋势[J].石油物探,2014,53(1):77-82.YANG Qinyong,HU Guanghui,WANG Lixin. Research status and development trend of full waveform inversion[J]. Geophysical Prospecting for Petroleum,2014,53(1):77-82.
[3] VIRIEUX J,OPERTO S.An overview of full-waveform inversion in exploration geophysics[J]. Geophysics,2009,74(6):WCC1-WCC26.
[4] TARANTOLA A.Inversion of seismic reflection data in the acoustic approximation[J].Geophysics,1984,9(8):1259-1266.
[5] PRATT R G.Seismic waveform inversion in the frequency domain,Part 1:Theory and verification in a physical scale model[J]. Geophysics,1999,64(3):888-901.
[6] SHIN C,CHA Y H. Waveform inversion in the Laplace domain[J].Geophysics,2008,173(3):922-931.
[7]成景旺,吕晓春,顾汉明,等.基于柯西分布的频率域全波形反演[J].石油地球物理勘探,2014,49(5):940-945.CHENG Jingwang,LXiaochun,GU Hanming,et al. Full waveform inversion with Cauchy distribution in the frequency domain[J].Oil Geophysical Prospecting,2014,49(5):940-945.
[8]张广智,孙昌路,盘新朋,等.快速共轭梯度法频率域全波形反演[J].石油地球物理勘探,2016,51(4):730-737.ZHANG Guangzhi,SUN Changlu,PAN Xinpeng,et al. Acoustic full waveform inversion with Cauchy in the frequency domain based on fast conjugate gradient method[J]. Oil Geophysical Prospecting,2016,51(4):730-737.
[9] HAN M,HAN L G,LIU C C,et al.Frequency-domain auto-adapting full waveform inversion with blended source and frequency-group encoding[J].Applied Geophysics,2013,10(1):41-52.
[10]曹书红,陈景波.频率域全波形反演中关于复频率的研究[J].地球物理学报,2014,57(7):2302-2313.CAO Shuhong,CHEN Jingbo. Studies on complex frequencies in frequency domain full waveform inversion[J].Chinese J.Geophys.,2014,57(7):2302-2313.
[11]高凤霞,刘财,冯暄,等.几种优化方法在频率域全波形反演中的应用效果及对比分析研究[J].地球物理学进展,2013,28(4):2060-2068.GAO Fengxia,LIU Cai,FENG Xuan,et al.Comparisons and analyses of several optimization methods in the application of frequency-domain full waveform inversion[J]. Process in Geophys.,2013,28(4):2060-2068.
[12] BEN-HADJ-ALI H,OPERTO S,VIRIEUX J.Velocity model building by 3D frequency-domain,full-waveform inversion of wide-aperture seismic data[J].Geophysics,2008,73(5):VE101-VE117.
[13]李媛媛,李振春,张凯,等.基于双级并行的弹性波频率域全波形多尺度反演方法[J].应用地球物理,2015,12(4):545-554.LI Yuanyuan,LI Zhenchun,ZHANG Kai,et al. Frequency-domain elastic full-waveform multiscale inversion method based on duallevel parallelism[J].Applied Geophysics,2015,12(4):545-554.
[14]苗永康.基于L-BFGS算法的时间域全波形反演[J].石油地球物理勘探,2015,50(3):469-474.MIAO Yongkang.Full waveform inversion in time domain based on limited-memory BFGS algorithm[J].Oil Geophysical Prospecting,2015,50(3):469-474.
[15]白璐,韩立国,张盼,等.最小平方滤波时间域全波形反演[J].石油地球物理勘探,2016,51(4):721-729.BAI Lu,HAN Liguo,ZHANG Pan,et al. Time-domain full waveform inversion based on least square filter[J]. Oil Geophysical Prospecting,2016,51(4):721-729.
[16] SIGURE L,ETGEN J T,ALBERTIN U.3D frequency-domain waveform inversion using time-domain finite-difference methods[A].70th EAGE Conference&Exhibition[C].Rome,2008,F022.
[17] BUNKS C,SCALECK F M,ZALESKI S,et al. Multiscale seismic waveform inversion[J].Geophysics,1995,60(5):1457-1473.
[18] BOONYASIRIWAT C,VAUL V,ROUTH P,et al.An efficient multiscale method for time-domain waveform tomography[J].Geophysics,2009,74(6):WCC59-WCC68.
[19] SIGURE L,PRATT R.Efficient waveform inversion and imaging:A strategy for selecting temporal frequencies[J]. Geophysics,2004,69(1):231-248.
[20]董良国,马在田,曹景忠,等.一阶弹性波方程交错网格有限差分解法[J].地球物理学报,2000,43(3):411-418.DONG Liangguo, MA Zaitian, CAO Jingzhong, et al. A staggered-grid high-order difference method of one-order elastic wave equation[J].Chinese J.Geophys.,2000,43(3):411-418.
[21] CHU C,STOFFA P L.Determination of finite-difference weights using scaled binomial windows[J].Geophysics,2012,77(3):W17-W26.
[22]韩复兴,孙建国,杨昊.基于二维三次卷积插值算法的波前扩散构建射线追踪[J].吉林大学学报(地球科学版),2008,38(2):336-346.HAN Fuxin,SUN Jianguo,YANG Hao. Ray-tracing of wavefront construction by bicubic convolution interpolation[J]. Journal of Jilin University(Earth Science Edition),2008,38(2):336-346.
[23] VIGH D,STARR E,KAPOOR J.Developing Earth models with full waveform inversion[J].The Leading Edge,2009,28(4):432-435.
[24] ZHANG Z,LIN Y,HUANG L. Full-waveform inversion in the time domain with an energy-weighted gradient[A].81st SEG Annual International Meeting[C].San Antonio,2011:2772-2776.
[25] KOHN D,DENIL D,KURZMANN A,et al. On the influence of model parameterization in elastic full waveform tomography[J].Geophysics Journal International,2012,191(1):325-345.
[26] SHIPP R,SINGH S. Two-dimensional full wavefield inversion of wide-aperture marine seismic streamer data[J].Geophysics Journal International,2002,151(2):325-344.
[27] BOHLEN T. Parallel 3-D viscoelastic finite difference seismic modeling[J].Computers&Geosciences,2002,28:887-899.