Two dimensional ray tracing in layered elastic media is shown to be a simple procedure, whether the Iayers are isotropic or anisotropic, when certain criteria are met, those of 'mild anisotropy'. This implies not that the 'anisotropy parameters' are met, but that the medium behaves so that there is no anomalous polarization, there is no triplication, and any quasi-shear wave is slower than any quasicompressional wave. The two-point scheme uses the fact that all rays from source to receiver, including converted and reflected waves, have a common value of horizontal slowness (Snell's Law). Possible values of horizontal slowness have bounds depending on the specified layers through which the ray passes, and the specified ray type in each layer. Whenever a ray originates from the source with a horizontal slowness within these limits, it will reach the receiver depth, although in general at a point that is horizontally offset from the actual receiver position. When the conditions of mild anisotropy are met, range increases monotonically with horizontal slowness, yielding &. unique, easy to find, horizontal slowness, and its associated ray which arrives at the receiver depth at the correct range. The scheme is analysed in detail for the wave modes in the vertical plane of a transversely isotropic medium or in a plane of symmetry of an orthorhombic medium. In particular, the modes studied are those whose displacements lie in the plane of propagation, the so called qP and qS modes.


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