Gaussian beams in inhomogeneous anisotropic layered structures

Vlastislav Cerveny & Ivan Psencik


Gaussian beams concentrated close to rays of high-frequency seismic body waves propagating in an inhomogeneous anisotropic layered structure are studied. The amplitude profiles of the Gaussian beam along the plane perpendicular to the ray and along the plane perpendicular to the slowness vector are Gaussian. The Gaussian profile is controlled by the 2×2 complex-valued matrix M of the second derivatives of the travel-time field at any point of the ray. The matrix M can be simply determined at any point of the ray if the ray-propagator matrix along the ray is known and if the value of M is specified at a selected point of the ray. The ray-propagator matrix can be determined by dynamic ray tracing along the ray. In inhomogeneous anisotropic medium, the dynamic ray tracing can be performed alternatively in several coordinate systems: in global Cartesian coordinates, in ray-centred coordinates and in wavefront orthonormal coordinates. In addition, also simplified dynamic ray tracing in global Cartesian coordinates can be used, which reduces the number of equations of the dynamic ray tracing system. The derived expressions for the Gaussian beams are applicable to general 3-D inhomogeneous layered structures of arbitrary anisotropy (specified by upto 21 independent position-dependent elastic moduli). Possible simplification of the procedure are outlined.


Paraxial travel times, Gaussian beams, dynamic ray tracing, anisotropic heterogeneous medium.

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In: Seismic Waves in Complex 3-D Structures, Report 19, pp. 123-156, Dep. Geophys., Charles Univ., Prague, 2009.
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