First-order P-wave ray synthetic seismograms in inhomogeneous weakly anisotropic media

Ivan Psencik and Veronique Farra


We propose approximate equations for P-wave ray-theory Green function for smooth inhomogeneous weakly anisotropic media. Equations are based on perturbation theory, in which deviations of anisotropy from isotropy are considered to be the first-order quantities. For evaluation of the approximate Green function, earlier derived first-order ray-tracing equations and in this paper derived first-order dynamic-ray-tracing equations are used.

The first-order ray-theory P-wave Green function for inhomogeneous, weakly anisotro-pic media of arbitrary symmetry depends, at most, on 15 weak-anisotropy parameters. For anisotropic media of higher-symmetry than monoclinic, all equations involved differ only slightly from the corresponding equations for isotropic media. For vanishing anisotropy, the equations reduce to equations for computation of standard ray-theory Green function for isotropic media. These properties make the proposed approximate Green function an easy and natural substitute of traditional Green function for isotropic media.

Numerical tests for configuration and models used in seismic prospecting indicate negligible dependence of accuracy of the approximate Green function on inhomogeneity of the medium. Accuracy depends more strongly on strength of anisotropy in general and on angular variation of phase velocity due to anisotropy in particular. For example, for anisotropy of about 8 %, considered in the examples presented, the relative errors of the geometrical spreading are usually under 1 %; for anisotropy of about 20 %, however, they may locally reach as much as 20 %.


Inhomogeneous media, perturbation methods, P waves, seismic anisotropy, seismic ray theory, synthetic seismograms.

Whole paper

The image of the paper in GIF 150dpi (935 kB) is designed for an instant screen preview.

The paper is available in PostScript (1 085 kB!) and GZIPped PostScript (286 kB).

In: Seismic Waves in Complex 3-D Structures, Report 17, pp. 111-134, Dep. Geophys., Charles Univ., Prague, 2007.
SW3D - main page of consortium Seismic Waves in Complex 3-D Structures .