垂直发育裂隙介质中PP波扰动法近似反射系数研究

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。

The study of approximate reflection coefficient of PP wave in vertically developing fractured media using disturbance method

In this paper, the precise reflection coefficients of PP wave in EDA medium are first derived from the christoffel equation and boundary conditions. Based on this, an isotropic medium is used as the background medium to derive approximate reflection coefficient of PP wave in extremely weakly anisotropic medium. The approximate reflection coefficient of PP wave in HTI and EDA medium is derived by substituting the elastic coefficient of HTI and EDA medium into the reflection coefficient formula of PP wave in extreme anisotropic medium, and the calculation of the approximate reflection coefficient of PP in HTI and EDA media is studied through model calculations. The results 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 7%; for EDA media with small anisotropy parameters (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 10-3, and the relative error is less than 10 %, and its calculation error increases as the incident angle increases. For media with strong anisotropy (anisotropic coefficient reaches 0.2), the relative error reaches 35% when the angle of incidence reaches 60 °, but the relative error remains within 10% when the angle of incidence is less than 45 °. When the angle is relatively small, the calculation formula of approximate reflection coefficient of PP wave in EDA medium is still valid for the medium with strong anisotropy. The approximate study of the reflection coefficient can provide a basis for the survey line layout and offset setting of the seismic survey. It is beneficial to improve the inversion speed,By studying the reflection coefficient and linearizing the accurate reflection coefficient.