Ray tracing for continuously rotated local coordinates belonging to a specified anisotropy

Einar Iversen & Ivan Psencik


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 a medium possessing a transversely isotropic or orthorhombic symmetry locally. We have expressed the material properties and the ray-tracing quantities (e.g., the ray-velocity and slowness vectors) in a local anisotropy coordinate system with axes changing directions continuously within the model. In this manner, a transversely isotropic medium is described locally by five elastic moduli and two angles; an orthorhombic medium is described locally by nine elastic moduli and three angles. The new formulation is advantageous with respect to user-friendliness, efficiency, and memory usage. Concerning improved efficiency, a prominent role is played by the cross product of the ray-velocity and slowness vectors specified in the local coordinate system. 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.


Ray tracing, rotated anisotropy, transverse isotropy, orthorhombic symmetry, TTI medium.

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In: Seismic Waves in Complex 3-D Structures, Report 16, pp. 47-76, Dep. Geophys., Charles Univ., Prague, 2006.
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