垂直发育裂隙介质中PP波扰动法近似反射系数研究
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P3

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国家自然科学基金项目(面上项目,重点项目,重大项目)


The study of approximate reflection coefficient of PP wave in vertically developing fractured media using disturbance method
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The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)

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    摘要:

    本文基于christoffel方程和边界条件,推导了垂直发育裂隙介质中PP波、PS1波、PS2波精确反射系数表达式;在此基础上采用扰动推导了极端弱各向异性介质中PP波的近似反射系数,然后将HTI、EDA介质的弹性系数带入极端各向异性介质中PP波的反射系数公式并简化得到HTI、裂隙介质中PP波的近似反射系数,并通过模型计算研究了HTI、裂隙介质中PP的近似反射系数变化规律,结果表明在弱各向异性条件下,HTI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;当裂隙介质在各向异性参数较小(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%,且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,当入射角达60°时其相对误差达25%,但入射角小于45°时其相对误差仍然保持在10%以内,即当入射角相对较小时,裂隙介质中PP波近似反射系数计算式对于各向异性较强的介质仍然成立。通过对反射系数的近似研究,可以为地震勘察的测线布置、偏移距设置提供依据,并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。

    Abstract:

    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.

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何现启,彭凌星,朱自强,等. 垂直发育裂隙介质中PP波扰动法近似反射系数研究[J]. 科学技术与工程, 2021, 21(28): 11971-11980.
He Xianqi, Peng Lingxing, Zhu Ziqiang, et al. The study of approximate reflection coefficient of PP wave in vertically developing fractured media using disturbance method[J]. Science Technology and Engineering,2021,21(28):11971-11980.

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  • 收稿日期:2021-03-23
  • 最后修改日期:2021-07-14
  • 录用日期:2021-05-20
  • 在线发布日期: 2021-09-29
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