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。
As important parameters for the description of media property,phase and group velocities play one of the most important roles in the seismic wave propagation research and seismic data processing.Based on the stiffness matrix of TI media under constitutive coordinates and Bond transform,the elastic matrix of arbitrarily transverse isotropy(ATI)media is derived in this paper.Using constitutive equation,Cauchy's routine and Newton's motion differential equation,the elastic wave equation and Christoffel equation of ATI media are obtained.And then the analytic expression of phase velocity is derived by solving the dispersion relation equation with eigenvalue method.On the basis of the group velocity equation derived by Crampin,we derive the group velocity expression of ATI media.It is shown that the analytic expression of phase velocity is a generalized formula and can be simplified to tilted transverse isotropy(TTI)or extensive dilatancy anisotropy(EDA)media under special case,which is very important for ray tracing and migration.In ATI media,3D surfaces of phase and group velocities are symmetric around its symmetry axis.In terms of phase and group velocities under the same observing system,there is much difference among different kinds of TI media,which can be used in the recognition of orientation for fractures or periodic thin beds.Based on staggered-mesh finite difference forward modeling,the group velocity analytic expression curves are compared with seismic wave snapshots in vertical transverse isotropy(VTI),horizontal transverse isotropy(HTI),TTI,EDA,and ATI media.The analytical solution of group velocity is verified,and it is proved that the group velocity controls wave front shape of seismic wave field.Influences of anisotropic parameter on phase and group velocities in ATI media are also discussed in this paper.
出处
《石油地球物理勘探》
EI
CSCD
北大核心
2017年第4期715-733,共19页
Oil Geophysical Prospecting
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
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
arbitrary spatial orientation
TI medium
phase velocity
group velocity
polarization azimuth anisotropy
