任意空间取向TI介质弹性波速度特征分析

发布时间：2018-02-24 08:35

本文关键词： 任意空间取向 TI介质相速度群速度极化方位各向异性　出处：《石油地球物理勘探》2017年04期 　论文类型：期刊论文

【摘要】：相速度和群速度是表征地层介质物性特征的重要参数,在各向异性地震波传播理论研究和实际地震数据处理应用中都有重要作用。本文从本构坐标系下TI介质的弹性矩阵出发,通过Bond变换给出任意空间取向TI介质(ATI介质,Arbitrarily Transverse Isotropy)在观测坐标系下的刚度矩阵。联合弹性动力学的本构方程、柯西方程和牛顿运动微分方程,得到ATI介质的弹性波波动方程和Christoffel方程。通过本征值方法求解Christoffel频散方程,导出了ATI介质中3D相速度精确解析式;借鉴Crampin推导各向异性群速度公式的思路,推导出ATI介质中弹性波群速度公式。研究表明,本文给出的ATI介质弹性波速度解析式具有一般性,在特定条件下能退化成TTI、EDA介质,对各向异性射线追踪和偏移成像等具有重要意义。数值计算实例表明,ATI介质三维相速度和群速度曲面关于其对称轴对称,在观测坐标系下,不同类型TI介质的速度各向异性存在明显差异,据此可实现地下周期性细薄层或裂缝的走向识别。基于交错网格有限差分正演,在VTI、HTI、TTI、EDA和ATI五种TI模型介质中开展了地震波场正演模拟,对比分析了波场快照和群速度解析解,验证了ATI介质弹性波速度公式的正确性,同时明确了群速度控制着地震波场的波前形状。此外,还讨论了各向异性参数对地震体波相速度、群速度特征的影响。
[Abstract]:Phase velocity and group velocity are important parameters to characterize the physical properties of stratigraphic media and play an important role in the study of anisotropic seismic wave propagation theory and the application of practical seismic data processing. In this paper, we proceed from the elastic matrix of TI medium in constitutive coordinate system. The stiffness matrix of arbitrary spatially oriented TI medium Transverse Isotropy in observational coordinate system is given by means of Bond transformation. The constitutive equations, Cauchy equation and Newtonian differential equation of motion of elastic dynamics are combined. The elastic wave wave equation and Christoffel equation of ATI medium are obtained. The Christoffel dispersion equation is solved by eigenvalue method, and the exact analytical formula of 3D phase velocity in ATI medium is derived. The formula of elastic wave group velocity in ATI medium is derived. It is shown that the analytical formula of elastic wave velocity in ATI medium is general and can degenerate into TTI / EDA medium under certain conditions. It is of great significance for anisotropic ray tracing and migration imaging. Numerical examples show that the 3-D phase velocity and group velocity surfaces of ATI medium are symmetric and axisymmetric in the observation coordinate system. There are obvious differences in velocity anisotropy among different types of TI media, which can be used to identify the direction of underground periodic thin layers or fractures. Based on the staggered grid finite difference forward modeling, The forward modeling of seismic wave field has been carried out in five kinds of TI model media such as VTI TDI and ATI. The wave field snapshot and group velocity analytical solution have been compared and analyzed. The correctness of elastic wave velocity formula of ATI medium has been verified. In addition, the influence of anisotropic parameters on the phase velocity and group velocity of seismic body is discussed.
【作者单位】：中国石油大学(华东)地球科学与技术学院;海洋国家实验室海洋矿产资源评价与探测技术功能实验室;中石化石油工程地球物理公司华东分公司;
【基金】：国家自然科学基金项目“基于石油勘探中地震面波信息的近地表参数反演方法研究”(41374123);国家自然科学基金项目“基于微地震数据的致密油气储层裂纹演化分形特征研究”(41504097) 国家科技重大专项项目“复杂目标多尺度资料高精度处理关键技术研究”(2016ZX05006-002-03)联合资助
【分类号】：P631.4

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