弹性波散射反演的一种新思路
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摘要
针对半空间界面半圆形凹陷和介质内圆孔对SH(shearing horizontal)波散射的反演问题提出一种优化求解方法。具体分析两种情况下弹性波散射反演问题的模型和特点,给出反演目标函数和反演数学模型,利用黄金分割法或对分法进行寻优求解。算例结果表明方法的可行性。文中方法对研究得比较成熟的弹性波散射正演问题对应的反演问题的求解具有应用价值和理论指导意义。
An new optimization method in solving the inverse SH(shearing horizontal)-wave scattering problems of the half circular cavity on the boundary of the half space and the circular cavity shallow-embedded in the half space was put forward.The model and characteristics of the two kinds of inverse problems of the elastic waves were analyzed concretely,the optimization objective function and the inverse mathematical model are given,the golden section method or the half-division method was used to solve the inverse problems,the results of the given examples show the feasibility of the method.This method has application value and theoretical instruction meaning to the solution of the inverse scattering problems of elastic waves which positive problems are well studied.
An new optimization method in solving the inverse SH(shearing horizontal)-wave scattering problems of the half circular cavity on the boundary of the half space and the circular cavity shallow-embedded in the half space was put forward.The model and characteristics of the two kinds of inverse problems of the elastic waves were analyzed concretely,the optimization objective function and the inverse mathematical model are given,the golden section method or the half-division method was used to solve the inverse problems,the results of the given examples show the feasibility of the method.This method has application value and theoretical instruction meaning to the solution of the inverse scattering problems of elastic waves which positive problems are well studied.
引文
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[15]张秉铭,张中杰.一种新的地层弹性参数直接反演方法[J].地震学报,2000,22(6):654-660.ZHANG BingMing,ZHANG ZhongJie.A new way of directlyelastic parameters inversion[J].Acta Seismologica Sinica,2000,22(6):654-660(In Chinese).
[16]戴辉,钟伟芳,吴国荣.半空间SH波方程的非线性反演[J].华中科技大学学报,2001,29(4):96-98.DAI Hui,ZHONG WeiFang,WU GuoRong.Nonlinear inversion ofthe SH wave equation in a half space for density[J].Journal ofHuazhong University of Science and Technology,2001,29(4):96-98(In Chinese).
[17]冯国峰,韩波,刘家琦.二维波动方程约束反演的大范围收敛广义脉冲谱方法[J].地球物理学报,2003,46(2):265-270.FENG GuoFeng,HAN Bo,LIU JiaQi.Widely convergentgeneralized pulse-spectrum methods for 2-D wave equation inversion[J].Chinese Journal of Geophysics,2003,46(2):265-270(InChinese).
[18]孙卫涛,董渊.波动方程反演的全局优化方法研究[J].地球物理学进展,2007,22(3):797-803.SUN WeiTao,DONG Yuan.Study on global optimization methodsfor wave equation inversion problems[J].Progress in Geophysics,2007,22(3):797-803(In Chinese).
[19]殷文.叠前弹性波反演非线性优化方法[J].中国石油大学学报:自然科学版,2008,32(3):45-49.YIN Wen.Nonlinear optimization method on prestack elastic waveinversion[J].Journal of China university of Petroleum:NaturalScience Edition,2008,32(3):45-49(In Chinese).
[20]王竹溪,郭敦仁.特殊函数概论[M].北京:北京大学出版社,2000:385-387.WANG ZhuXi,GUO DunRen.Introduction to special function[M].Beijing:Peking University Press,2000:385-387(InChinese).
[21]史文谱,刘迎曦,李守巨,等.对分法在多元优化问题中的推广应用[J].兰州理工大学学报,2004,30(2):116-118.SHI WenPu,LIU YingXi,LI ShouJu,et al.Application of half-division method in solving mulitivariate optimization[J].Journal ofLanzhou Universityof Technology,2004,30(2):116-118(InChinese).
[22]史文谱,刘迎曦,巩华荣,等.黄金分割法在无约束多元优化问题中的应用[J].东北师大学报:自然科学版,2003,35(2):11-14.SHI WenPu,LIU YingXi,GONG HuaRong,et al.Application ofgolden section method in solving unconstrained multiple variableoptimization[J].Journal of Northeast Normal University:NaturalScience Edition,2003,35(2):11-14(In Chinese).
[2]黎在良,刘殿魁.固体中的波[M].北京:科学出版社,1995:105-423LI ZaiLiang,LIU DianKui.Waves in solid[M].Beijing:SciencePress,1995:105-423(In Chinese).
[3]钟伟芳,聂国华.弹性波的散射理论[M].武昌:华中理工大学出版社,1997:137-189.ZHONG WeiFang,NIE GuoHua.Scattering theory of elastic waves[M].Wuchang:Huazhong University of Science and TechnologyPress,1997:137-189(In Chinese).
[4]SHI Wen-pu,LIU Dian-kui,SONG Yong-tao,et al.Scattering ofcircular cavity in right-angle planar space to steady SH-wave[J].Applied Mathematics and Mechanics,2006,27(12):1619-1626.
[5]史文谱,禇京莲,巩华荣,等.二维直角平面内偏心圆形衬砌对稳态入射平面SH波的散射[J].机械强度,2007,29(3):442-448.SHI WenPu,CHU JingLian,GONG HuaRong,et al.Scattering ofcircular eccentric lining in right angle plane space to steady incidentplane SH wave[J].Journal of Mechanical Strength,2007,29(3):442-448(In Chinese).
[6]史文谱,李莉,张春萍,等.弹性约束半空间内浅埋圆孔对SH波的散射[J].机械强度,2009,31(5):740-746.SHI WenPu,LI Li,ZHANG ChunPing,et al.Scattering of SHwave to the circular cavity in the half space with elastic constraintacting on the straight boundary[J].Journal of MechanicalStrength,2009,31(5):740-746(In Chinese).
[7]马兴瑞,陶良,黄文虎,等.弹性波反演方法及其应用[M].2版.北京:科学出版社,1999:1-306.MA XingRui,TAO Liang,HUANG WenHu,et al.Inversemethods of elastic waves and the applications[M].2nd ed.Beijing:Science Press,1999:1-306(In Chinese).
[8]杨林德.岩土工程问题的反演理论与工程实践[M].北京:科学出版社,1996:1-275.YANG LinDe.Inverse theory of the rock engineering problems andthe engineering practice[M].Beijing:Science Press,1996:1-275(In Chinese).
[9]王家映.地球物理反演理论[M].2版.北京:高等教育出版社,2002:1-179.WANG JiaYing.Inverse theory in geophysics[M].2nd ed.Beijing:High Education Press,2002:1-179(In Chinese).
[10]刘继军.不适定问题的正则化方法及应用[M].北京:科学出版社,2005:1-199.LIU JiJun.Regularization methods and applications of ill-posedproblems[M].Beijing:Science Press,2005:1-199(InChinese).
[11]王等刚,刘迎曦,李守巨.弹性力学非线性反演方法概述[J].力学进展,2003,33(2):166-174.WANG DengGang,LIU YingXi,LI ShouJu.Survey on nonlinearinversion methods in elastomechanics[J].Advances in Mechanics,2003,33(2):166-174(In Chinese).
[12]赵宪生,梁桂蓉,罗运先.子波反演与波阻抗反演[J].物探化探计算技术,1999,21(3):206-211ZHAO XianSheng,LIANG GuiRong,LUO YunXian.Waveletinversion and wave impedance inversion[J].ComputingTechniques for Geophysical and Geochemical Exploration,1999,21(3):206-211(In Chinese).
[13]杨慧珠,刁顺.非线性弹性波反演探讨[J].石油地球物理勘探,1996,31(1):8-13.YANG HuiZhu,DIAO Shun.Nonlinear elastic wave inversion[J].Oil Geophysical Prospecting,1996,31(1):8-13(In Chinese).
[14]徐俊,朱文浩.半空间SH波方程的非线性反演问题[J].江汉石油学院学报,1997,19(2):120-131.XU Jun,ZHU WenHao.Problems of nonlinear inversion of SHelastic wave equation in half space[J].Journal of JianghanPetroleum Institute,1997,19(2):120-131(In Chinese).
[15]张秉铭,张中杰.一种新的地层弹性参数直接反演方法[J].地震学报,2000,22(6):654-660.ZHANG BingMing,ZHANG ZhongJie.A new way of directlyelastic parameters inversion[J].Acta Seismologica Sinica,2000,22(6):654-660(In Chinese).
[16]戴辉,钟伟芳,吴国荣.半空间SH波方程的非线性反演[J].华中科技大学学报,2001,29(4):96-98.DAI Hui,ZHONG WeiFang,WU GuoRong.Nonlinear inversion ofthe SH wave equation in a half space for density[J].Journal ofHuazhong University of Science and Technology,2001,29(4):96-98(In Chinese).
[17]冯国峰,韩波,刘家琦.二维波动方程约束反演的大范围收敛广义脉冲谱方法[J].地球物理学报,2003,46(2):265-270.FENG GuoFeng,HAN Bo,LIU JiaQi.Widely convergentgeneralized pulse-spectrum methods for 2-D wave equation inversion[J].Chinese Journal of Geophysics,2003,46(2):265-270(InChinese).
[18]孙卫涛,董渊.波动方程反演的全局优化方法研究[J].地球物理学进展,2007,22(3):797-803.SUN WeiTao,DONG Yuan.Study on global optimization methodsfor wave equation inversion problems[J].Progress in Geophysics,2007,22(3):797-803(In Chinese).
[19]殷文.叠前弹性波反演非线性优化方法[J].中国石油大学学报:自然科学版,2008,32(3):45-49.YIN Wen.Nonlinear optimization method on prestack elastic waveinversion[J].Journal of China university of Petroleum:NaturalScience Edition,2008,32(3):45-49(In Chinese).
[20]王竹溪,郭敦仁.特殊函数概论[M].北京:北京大学出版社,2000:385-387.WANG ZhuXi,GUO DunRen.Introduction to special function[M].Beijing:Peking University Press,2000:385-387(InChinese).
[21]史文谱,刘迎曦,李守巨,等.对分法在多元优化问题中的推广应用[J].兰州理工大学学报,2004,30(2):116-118.SHI WenPu,LIU YingXi,LI ShouJu,et al.Application of half-division method in solving mulitivariate optimization[J].Journal ofLanzhou Universityof Technology,2004,30(2):116-118(InChinese).
[22]史文谱,刘迎曦,巩华荣,等.黄金分割法在无约束多元优化问题中的应用[J].东北师大学报:自然科学版,2003,35(2):11-14.SHI WenPu,LIU YingXi,GONG HuaRong,et al.Application ofgolden section method in solving unconstrained multiple variableoptimization[J].Journal of Northeast Normal University:NaturalScience Edition,2003,35(2):11-14(In Chinese).
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