Initial conditions for paraxial ray tracing in inhomogeneous anisotropic media

Vlastislav Cerveny & Tijmen Jan Moser


Paraxial ray methods have found broad applications in the seismic ray method and in numerical modelling and interpretation of high-frequency seismic wave fields propagating in inhomogeneous, isotropic or anisotropic structures. The basic procedure in paraxial ray methods consists in dynamic ray tracing. We derive the initial conditions for dynamic ray equations, for rays initiated at three types of initial manifolds given in a three-dimensional medium: 1) curved surfaces (surface source), 2) isolated points (point source), and 3) curved, planar and non-planar lines (line source). These initial conditions are very general, valid for homogeneous or inhomogeneous, isotropic or anisotropic media, and for both a constant and a variable initial travel time along the initial manifold. The results presented in the paper considerably extend the possible applications of the paraxial ray method.


Computational seismology, theoretical seismology, seismic anisotropy, wave propagation.

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In: Seismic Waves in Complex 3-D Structures, Report 18, pp. 139-161, Dep. Geophys., Charles Univ., Prague, 2008.
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