射线类偏移成像中的模型平滑处理研究
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摘要
本文从能量泛函的角度着手,基于速度梯度,采用最速下降法推导了基于偏微分方程的速度模型平滑公式,用于解决射线类偏移成像过程当中速度模型的平滑处理问题.同时针对偏微分方程速度模型平滑系数中阈值k的选取对速度模型空间结构的影响,在简单的高速体速度模型上分析了不同k值的选取对原始速度模型空间结构的改变,并通过射线路径和时间场的对比分析证明偏微分方程速度模型平滑处理相对于卷积算子平滑的优越性.最后通过在Marmousi、Sigsbee 2A原始速度模型以及平滑处理后的速度模型上的成像结果分析验证偏微分方程模型平滑的有效性.
From the perspective of energy functional theory,based on velocity gradient,the smoothing formula for a velocity model based on partial differential equations is derived by the steepest descent method(Gradient method),which can be used to solve the problem of the velocity model smoothed in ray type migration imaging.At the same time,considering the effect of the selection of threshold kin smoothness coefficient of partial differential equations on the velocity model,variations of spatial structure of the original velocity model are analyzed on a simple high-speed velocity model.By comparing the ray path and time field,it is proved that the smoothing of velocity model using partial differential equation is superior to convolution operator.Finally,the effectiveness of velocity model smoothing process using partial differential equation is verified by analyzing the migration imaging results on Marmousi and Sigsbee 2 A original and smoothed velocity models.
From the perspective of energy functional theory,based on velocity gradient,the smoothing formula for a velocity model based on partial differential equations is derived by the steepest descent method(Gradient method),which can be used to solve the problem of the velocity model smoothed in ray type migration imaging.At the same time,considering the effect of the selection of threshold kin smoothness coefficient of partial differential equations on the velocity model,variations of spatial structure of the original velocity model are analyzed on a simple high-speed velocity model.By comparing the ray path and time field,it is proved that the smoothing of velocity model using partial differential equation is superior to convolution operator.Finally,the effectiveness of velocity model smoothing process using partial differential equation is verified by analyzing the migration imaging results on Marmousi and Sigsbee 2 A original and smoothed velocity models.
引文
Chen L.2015.The application of the partial differential equations diffusion model in image de-noising[Master thesis](in Chinese).Kunming:Kunming University of Science and Technology.
Ding C,Yin Q B,Lu M Y.2013.Summary of partial differential equation(PDE)method on digital image processing.Computer Science(in Chinese),40(S2):341-346.
Gabor D.1965.Information theory in electron microscopy.Laboratory Investigation,14(6):801-807.
Gao Z H,Sun J G,Sun X,et al.2017.A fast algorithm for depth migration by the Gaussian beam summation method.Journal of Geophysics and Engineering,14(1):173-183.
Gray S H.2000.Velocity smoothing for depth migration:how much is too much?∥70th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1055-1058.
Han F X.2009.On some computational problems in wavefront construction method[Ph.D.thesis](in Chinese).Changchun:Jilin University.
Han F X,Sun J G,Wang K.2011.Analysis of velocity model smoothing.Journal of Jilin University(Earth Science Edition)(in Chinese),41(5):1610-1616,1645.
Hummel R.1987.Representations based on zero-crossings in scalespace.∥Fischler M A,Firschein O eds.Readings in Computer Vision.Los Altos,Calif:Morgan Kaufmann Publishers,Inc.
Jiang L S,Bian B J.2012.Concise Course on Equations of Mathematical Physics(in Chinese).Beijing:Higher Education Press.
Lailly P,Sinoquet D.1996.Smooth velocity models in reflection tomography for imaging complex geological structures.Geophysical Journal International,124(2):349-362.
Lopez-Molina C,Galar M,Bustince H,et al.2014.On the impact of anisotropic diffusion on edge detection.Pattern Recognition,47(1):270-281.
Pacheco C,Larner K.2005.Velocity smoothing before depth migration:Does it help or hurt?∥75th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1970.
Perona P,Malik J.1990.Scale-space and edge detection using anisotropic diffusion.IEEE Transactions on Pattern Analysis and Machine Intelligence,12(7):629-639.
Shi X L,Sun J G,Sun H,et al.2016.Depth migration in time domain using wavefront construction:delta packet approach.Journal of Jilin University(Earth Science Edition)(in Chinese),46(6):1847-1854.
Witkin A P.1983.Scale-space filtering.∥International joint conference on Artificial intelligence.Karlsruhe,West Germany,2:1019-1021.
Yang X.2003.Principles and Applications of Image Partial Differential Equations(in Chinese).Shanghai:Shanghai Jiao Tong University Press.
Yuan M L,Huang J P,Liao W Y,et al.2017.Least-squares Gaussian beam migration.Journal of Geophysics and Engineering,14(1):184-196.
陈龙.2015.偏微分方程扩散模型在图像去噪中的应用[硕士论文].昆明:昆明理工大学.
丁畅,尹清波,鲁明羽.2013.数字图像处理中的偏微分方程方法综述.计算机科学,40(S2):341-346.
韩复兴.2009.论波前构建法中的几个计算问题[博士论文].长春:吉林大学.
韩复兴,孙建国,王坤.2011.速度模型的光滑处理分析.吉林大学学报(地球科学版),41(5):1610-1616,1645.
姜礼尚,边保军.2012.数学物理方程简明教程.北京:高等教育出版社.
石秀林,孙建国,孙辉等.2016.基于波前构建法的时间域深度偏移-delta波包途径.吉林大学学报(地球科学版),46(6):1847-1854.
杨新.2003.图像偏微分方程的原理与应用.上海:上海交通大学出版社.
Ding C,Yin Q B,Lu M Y.2013.Summary of partial differential equation(PDE)method on digital image processing.Computer Science(in Chinese),40(S2):341-346.
Gabor D.1965.Information theory in electron microscopy.Laboratory Investigation,14(6):801-807.
Gao Z H,Sun J G,Sun X,et al.2017.A fast algorithm for depth migration by the Gaussian beam summation method.Journal of Geophysics and Engineering,14(1):173-183.
Gray S H.2000.Velocity smoothing for depth migration:how much is too much?∥70th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1055-1058.
Han F X.2009.On some computational problems in wavefront construction method[Ph.D.thesis](in Chinese).Changchun:Jilin University.
Han F X,Sun J G,Wang K.2011.Analysis of velocity model smoothing.Journal of Jilin University(Earth Science Edition)(in Chinese),41(5):1610-1616,1645.
Hummel R.1987.Representations based on zero-crossings in scalespace.∥Fischler M A,Firschein O eds.Readings in Computer Vision.Los Altos,Calif:Morgan Kaufmann Publishers,Inc.
Jiang L S,Bian B J.2012.Concise Course on Equations of Mathematical Physics(in Chinese).Beijing:Higher Education Press.
Lailly P,Sinoquet D.1996.Smooth velocity models in reflection tomography for imaging complex geological structures.Geophysical Journal International,124(2):349-362.
Lopez-Molina C,Galar M,Bustince H,et al.2014.On the impact of anisotropic diffusion on edge detection.Pattern Recognition,47(1):270-281.
Pacheco C,Larner K.2005.Velocity smoothing before depth migration:Does it help or hurt?∥75th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1970.
Perona P,Malik J.1990.Scale-space and edge detection using anisotropic diffusion.IEEE Transactions on Pattern Analysis and Machine Intelligence,12(7):629-639.
Shi X L,Sun J G,Sun H,et al.2016.Depth migration in time domain using wavefront construction:delta packet approach.Journal of Jilin University(Earth Science Edition)(in Chinese),46(6):1847-1854.
Witkin A P.1983.Scale-space filtering.∥International joint conference on Artificial intelligence.Karlsruhe,West Germany,2:1019-1021.
Yang X.2003.Principles and Applications of Image Partial Differential Equations(in Chinese).Shanghai:Shanghai Jiao Tong University Press.
Yuan M L,Huang J P,Liao W Y,et al.2017.Least-squares Gaussian beam migration.Journal of Geophysics and Engineering,14(1):184-196.
陈龙.2015.偏微分方程扩散模型在图像去噪中的应用[硕士论文].昆明:昆明理工大学.
丁畅,尹清波,鲁明羽.2013.数字图像处理中的偏微分方程方法综述.计算机科学,40(S2):341-346.
韩复兴.2009.论波前构建法中的几个计算问题[博士论文].长春:吉林大学.
韩复兴,孙建国,王坤.2011.速度模型的光滑处理分析.吉林大学学报(地球科学版),41(5):1610-1616,1645.
姜礼尚,边保军.2012.数学物理方程简明教程.北京:高等教育出版社.
石秀林,孙建国,孙辉等.2016.基于波前构建法的时间域深度偏移-delta波包途径.吉林大学学报(地球科学版),46(6):1847-1854.
杨新.2003.图像偏微分方程的原理与应用.上海:上海交通大学出版社.