垂直发育裂隙介质中PP波扰动法近似反射系数研究  

Study on Approximate Reflection Coefficient of PP Wave Disturbance Method in Vertically Developing Fractured Media

作　　者：何现启 彭凌星 朱自强[2] 鲁光银[2] HE Xian-qi;PENG Ling-xing;ZHU Zi-qiang;LU Guang-yin(Hunan Provincial Communications Planning, Survey & Design Institute Co., Ltd., Changsha 410200, China;School of Geosciences an Info-physics of Central South University, Changsha 410083, China)

机构地区：[1]湖南省交通规划勘察设计院有限公司,长沙410200 [2]中南大学地球科学与信息物理工程学院,长沙410083

出　　处：《科学技术与工程》2021年第28期11971-11980,共10页Science Technology and Engineering

基　　金：国家自然科学基金(41174061)。

摘　　要：为了实现裂隙介质中的地震AVO(amplitude variation with offset)反演,基于Christoffel方程和边界条件,推导了EDA介质中PP波、PS1波、PS2波精确反射系数表达式,并采用扰动法推导了极端弱各向异性介质中PP波的近似反射系数,通过弹性系数简化得到HTI、裂隙EDA介质中PP波的近似反射系数。模型计算结果表明:在弱各向异性条件下,HTI(horizontal transverse isotropy)介质中地震波的近似反射系数公式计算精度较高,相对误差在4%以内;当裂隙介质在弱各向异性(各向异性系数<0.1)的情况下,当入射角在40°以内时,PP波近似反射系数与精确反射系数的绝对误差在10^(-4)以内,相对误差小于4%,但随着入射角的加大其计算误差有所增加。对各向异性较强烈(各向异性系数达到0.2)的裂隙介质,当入射角相对较小时(小于45°时),裂隙介质中PP波近似反射系数计算式对于强各向异性的介质仍然成立。通过对反射系数的近似研究,可以将裂隙介质中反射系数的非线性问题转为线性问题,进而利用这些特性进行参数反演,有利于提高反演速度。In order to realize seismic AVO(amplitude variation with offset)inversion in fractured media,precise reflection coefficients of PP、PS1、PS2 wave in extensive dilatancy anisotropy(EDA)medium were first derived from the Christoffel equation and boundary conditions,and the approximate reflection coefficient of PP wave in extremely weak anisotropic media was derived by perturbation method,and the approximate reflection coefficient of PP wave in HTI and fractured media was obtained by simplifying the elastic coefficient.The results of model calculations show that the calculation accuracy of the approximate reflection coefficient formula is relatively high for HTI media under weakly anisotropic conditions,and the relative error is within 4%.For weak EDA media(anisotropic coefficient<0.1),when the incident angle is less than 40°,the absolute error of the approximate reflection coefficient of the PP wave is less than 10^(-4),and its calculation error increases as the incident angle increases.For media with strong anisotropy(anisotropic coefficient reaches 0.2),when the angle is relatively small(less than 45°),the calculation formula of approximate reflection coefficient of PP wave in EDA medium is still valid.Through the approximate study of reflection coefficient,the nonlinear problem of reflection coefficient in EDA(extensive dilatancy ani-sotropy)media can be transformed into a linear problem,and then these characteristics can be used for parameter inversion,which is conducive to improving the inversion speed.

关 键 词：HTI(horizontal transverse isotropy)介质 EDA介质 PP波 精确反射系数 近似反射系数 

分 类 号：P315[天文地球—地震学]