The exact eikonals for the quasi-compressional ( qP ) and quasi-shear ( qSV ) modes of seismic wave propagation in a transversely isotropic (TI) medium are considered. These are compared in a travel time sense with weak anisotropic and linearized approximations. The comparisons involve ray propagation in a 2D plane layered structure where the axis of anisotropy need not necessarily be aligned with the local coordinate system. The motivation for this is to determine the accuracy of the approximate and linearized eikonals when compared to the exact eikonal for the computation of ray paths in a media displaying weak anisotropy. This exercise is an initial step in addressing an analogous but more complex problem, specifically, ray tracing in orthorhombic media. This 3D symmetry is becoming more fundamental in seismic data processing and modeling as 3D seismic acquisition methods become the norm rather than the exception. As a consequence, the development of relevant software for processing and modeling of the more complex media types should be available in a variety of forms. A single rotation angle is used here, about the x2 spatial axis, or equivalently the p2 axis in slowness space, as ray propagation is assumed to be 2D , in the ( x1 , x3 ) Cartesian plane. For higher order rotations in 3D media, it is convenient to consider the more general 2D problem as a subset of orthorhombic symmetry, which is being dealt with in ongoing works. To minimize the complexity of this discussion, the anisotropic parameters are assumed to be homogeneous within a layer. This is done to obtain an accurate comparison of travel time results using exact, approximate, and linearized methods.
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