Ray tracing for continuously rotated local coordinates belonging to a specified anisotropy |
| |
Authors: | E Iversen I P?en?ík |
| |
Institution: | (1) NORSAR, P.O. Box 53, 2027 Kjeller, Norway;(2) Geophysical Institute, Acad. Sci. Czech Republic, 141 31 Praha 4, Czech Republic |
| |
Abstract: | Conventional ray tracing for arbitrarily anisotropic and heterogeneous media is expressed in terms of 21 elastic moduli belonging
to a fixed, global, Cartesian coordinate system. Our principle objective is to obtain a new ray-tracing formulation, which
takes advantage of the fact that the number of independent elastic moduli is often less than 21, and that the anisotropy thus
has a simpler nature locally, as is the case for transversely isotropic and orthorhombic media. We have expressed material
properties and ray-tracing quantities (e.g., ray-velocity and slowness vectors) in a local anisotropy coordinate system with
axes changing directions continuously within the model. In this manner, ray tracing is formulated in terms of the minimum
number of required elastic parameters, e.g., four and nine parameters for P-wave propagation in transversely isotropic and
orthorhombic media, plus a number of parameters specifying the rotation matrix connecting local and global coordinates. In
particular, we parameterize this rotation matrix by one, two, or three Euler angles. In the ray-tracing equations, the slowness
vector differentiated with respect to traveltime is related explicitly to the corresponding differentiated slowness vector
for non-varying rotation and the cross product of the ray-velocity and slowness vectors. Our formulation is advantageous with
respect to user-friendliness, efficiency, and memory usage. Another important aspect is that the anisotropic symmetry properties
are conserved when material properties are determined in arbitrary points by linear interpolation, spline function evaluation,
or by other means. |
| |
Keywords: | Ray tracing rotated anisotropy transverse isotropy orthorhombic symmetry TTI medium |
本文献已被 SpringerLink 等数据库收录! |
|