Rock physics modeling and elastic wave forward modeling methods in a three-dimensional azimuthally anisotropic medium of orthorhombic symmetry
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摘要: 通过线性滑动理论和岩石物理等效理论， 将两组正交直立裂隙介质等效为一种正交方位各向异性介质进行三维岩石物理建模， 通过高阶交错网格有限差分求解弹性波动方程模拟地震波在该种介质中的传播过程. 在建模过程中改变物性参数， 分析不同裂隙密度条件下的炮集和波场特征， 以及正交各向异性的方位特征. 研究结果表明， 各向异性强度随裂隙密度等物性增大而增强， 而且这些特征在共炮点道集和波场中均有所体现.Abstract: In this paper， by rock physical equivalent theory and linear slip theory， two sets of orthorhombic fractures are equivalent to a new three-dimensional azimuthally anisotropic medium of orthorhombic symmetry for rock physical modeling. And then elastic wave equations are solved to simulate the propagation process in this medium by high-order staggered-grid finite-difference method. During the process of modeling， with the variation of physical parameters， we analyze CSP (common shot points) sets and the wave field characteristics on the conditions of different fracture densities， as well as azimuthal characteristics of orthorhombic anisotropy. The research results show that the anisotropic strengths enhance with fracture density increasing， which is reflected in the CSP sets and forwarding wavefield.
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图 3 加最佳匹配层条件前(a)、后(b)的三维正交各向异性介质波场
Figure 3. Wavefield forward modeling in three-dimensional orthorhombic anisotropy medium without PML (a) and with PML (b)
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图 4 裂隙密度为0.1时的三维正交各向异性介质波场
Figure 4. Wavefield forward modeling in three-dimensional orthorhombic anisotropy medium without PML (a) and with PML (b)
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图 5 正交各向异性介质波场随裂隙密度ρF变化
Figure 5. Variation of wave-field with fracture density ρF in orthorhombic anisotropy medium
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图 7 裂隙密度为0.02时层状模型u分量正交介质共炮点道集
Figure 7. u component wave field in orthorhombic anisotropy medium for layered model at 0.5 s when fracture density is taken as 0.02
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图 8 裂隙密度为0.02时层状模型正交介质0.5s时的波场
Figure 8. u component wave field in orthorhombic anisotropy medium for layered model at 0.5 s when fracture density is taken as 0.02
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图 9 裂隙密度为0.02时层状模型正交介质u分量不同方位共炮点道集
Figure 9. CSP gathers of u component in orthorhombic anisotropy medium with different azimuths in layered model when fracture density is taken as 0.02
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图 10 不同裂隙密度ρF下层状模型正交介质u分量共炮点道集
Figure 10. CSP gathers of u component in orthorhombic anisotropy medium in layered model with different fracture densities ρF
表 1 标准交错网格中弹性波场分量和弹性参数的空间位置
Table 1 Position of elastic wavefield components and elastic parameters in standard staggered grid
网格点 弹性波长分量
和弹性参数1 σxx,σyy,σzz'c11,
c12,c13,c22,c23,c332 σyz,c44 3 σxz,c55 4 σxy,c66 5 υx,ρ-1 6 υy,ρ-1 7 υz,ρ-1 
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何燕. 2008. 正交各向异性弹性波高阶有限差分正演模拟研究[D]. 东营: 中国石油大学(华东)地球资源与信息学院: 4. He Y. 2008. High-Order Finite-Difference Forward Modeling of Elastic-Wave in Orthorhombic Anisotropic Media[D]. Dongying: College of Georesources and Information, China University of Petroleum: 4 (in Chinese).
孙成禹. 2007. 地震波理论与方法[M]. 东营: 中国石油大学出版社: 211. Sun C Y.2007. Theory and Methods of Seismic Waves[M]. Dongying: China University of Petroleum Press: 211 (in Chinese).
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