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《Chinese Journal of Geophysics》 1995-S1

## NUMERICAL SOLUTION METHOD FOR A CLASS OF ILL-POSED PROBLEM OF HYPERBOLIC EQUATION ABOUT STRUCTURE IMAGE(Ⅱ): PROPERLY POSEDNESS OF THE APPROXIMATE PROBLEM AND CONVERGENCE OF ITS SOLUTION

FAN SHANG-WU (Institute of Computational Mathematics and Scientific/Engineering Computing,Academia Sinica,Beijing 100080)
A class of structure image problem in geophysics may be described by ill-posed problem of hyperbolic partial differential equation.In this case, the solution of this ill-posed problem represents the reflected wave field which characterizes geological structure.In the paper[1],the formulation of this ill-posed problem and its approximate problem were proposed. In this paper, the properly-posedness of the approximate problem is discussed on the basis of paper [1].It means that the solution of the approximate problem is existential,unique and continuous about the initial data.Furthermore,the convergence of the solution of the approximate problem Is also proved.It means that the solution of the approximate problem with the approximate initial data converges to the solution of the original basic problem with the exactinitial data, when the approximate initial data converges to the exact initial data.Conse quently,the numerical solution problem of ill-posed basic problem is reduced to the numerical solution problem of the properly-posed approximate problem.The latter can be implemented by use of finite difference method or finite element method.
【Fund】： 国家自然科学基金委员会、中国科学院、中国石油天然气总公司和大庆石油管理局联合资助
【CateGory Index】： P631.4
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 【Citations】
 Chinese Journal Full-text Database 2 Hits
 1 YANG WEN-CAI(Beijing Computer Center, Ministry of Geology and Mineral Resources);A GENERALIZED INVERSION TECHNIQUE FOR POTENTIAL FIELD DATA PROCESSING[J];Chinese Journal of Geophysics;1986-03 2 FAN SHANG-WU (Institute of Camputational Mathematics and Scientific/Engineering Computing,Academia Sinica,Beijing 100080);NUMERICAL SOLUTION METHOD FOR A CLASS OF ILLPOSED PROBLEM OF HYPERBOLIC EQUATION ABOUT STRUCTURE IMAGE(Ⅰ):BASIC PROBLEM AND APPROXIMATE PROBLEM[J];Chinese Journal of Geophysics;1995-S1
 【Co-citations】
 Chinese Journal Full-text Database 10 Hits
 1 ;On the reverse problem of integral geometry in computerized tomography[J];Computerized Tomography Teory and Applications;1991-02 2 Li Zhibin(Dept.of Basic Scicnce);An Iterative Algorithm and Estimation of the Convergence Rate for Inverse Problem of 1-D Wave Equation[J];JOURNAL OF DALIAN RAILWAY INSTITUTE;1994-02 3 Zheng Jiamao (Department of Mathematics and Mechanics);Inversion of the Coefficient of Wave Equation with Non-Zero Initial Conditions[J];Journal of Southeast University;1991-02 4 Li Youming(lnstitute of Geophysics, CAS, Beijing 100101)Yang Wencai(Beijing Computer Center of Geology, Beijing 100083);REVIEW ON SEISMIC INVERSION PROBLEMS[J];Progress In Geophysics;1992-03 5 Ruan Xiaoqin ;Zhao Bing(Shen Zhen University, Shen Zhen 518060 ) (Xian Petrolem Institute,Xian 710065 );ANALYTIC INVERSION FOR INDUCTION LOGGING EQUATION[J];PROGRESS IN GEOPHYSICS;1997-02 6 JING Rongzhong,BAO Guangshu,CHEN Shaoqiu (School of InfoPhysics and Geomatics Engineering, Central South University, Changsha 410083, China);A review of the researches for geophysical combinative inversion[J];Progress In Geophysics;2003-03 7 LIU Hong1,WANG Xiu-min1,ZENG Rui1,LI You-min1,GOU Yong-feng2(1.Institute of Geology & Geophysics,Chinese Academy of Sciences,Beijing 100029,China;Petroleum and Gas Resource Key Laboratory,Chinese Academy of Sciences,Beijing 100029,China;2.Daqing Geophysical Exploration Company,CNPC,Daqing 163357,China);Symbol description to integral solution of one-way wave operator[J];Progress in Geophysics;2007-02 8 LIU Hong(Institute of Geology & Geophysics,Chinese Academy of Sciences,Beijing 100029,China);In memory of first anniversary of professor LI Shi-xong's death[J];Progress in Geophysics;2008-01 9 WU Wei,LIU Hong(Institute of Geology & Geophysics,Chinese Academy of Sciences,Beijing 100029,China);Preliminary study on the phase integral method with a Large step one-way wave operator[J];Progress in Geophysics;2009-01 10 YANG WEN-CAI JIAO FU-GUANG(Beijing Computer Center, The Ministry of Geology and Mineral Resources);VELOCITY IMAGING FROM REFLECTION SEISMIC DATA BY JOINT INVERSION TECHNIQUES[J];Chinese Journal of Geophysics;1987-06
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