Velocity characteristic analysis of elastic wave for TI media with arbitrary spatial orientation
Yao Zhen'an1,2, Sun Chengyu1,2, Deng Xiaofan3, Wu Dunshi1,2
1. School of Geosciences, China University of Petroleum(East China), Qingdao, Shandong 266580, China;
2. Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao, Shandong 266071, China;
3. Huadong Branch, Geophysical Corporation, SINOPEC, Nanjing, Jiangsu 210009, China
Abstract: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.
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