A method of synthetic seismogram calculation in arbitrary anisotropic media is developed. A solution in the frequency domain is derived in the form of a double integral with respect to horizontal slowness and azimuthal angle. Approximation of the influence of azimuthal anisotropy by Fourier series expansion makes it possible to carry out the integration over azimuthal angle analytically using series coefficients derived from simultaneous linear equations. As a result the double contour integral is reduced to a Fourier-Bessel integral over horizontal slowness which retains information about azimuthal anisotropy. Numerical evaluation of this integral enables us to compute body wave seismograms with allowance for nonogeometrical effects. This approach can be applied to reflection-transmision problems or to the calculation of individual wavelet propagation in multilayered anisotropic media.

The influence of anisotropy on point source radiation in a homogeneous medium is analyzed. Comparison of numerical results with high frequency asymptotic solution provides a reasonable physcial interpretation for wave propagation anomalies. Synthetic data for a medium of orthorhombic symmetry show that the radiation pattern and the polarization of shear waves are very sensitive to the presence of anisotropy. The most pronounced amplitude distortions are by focusing of energy near velocity maxima and by defocusing near velocity minima. Numerical modeling reveals significant nongeometrical phenomena in anisotropic media. In some cases deviations from geometrical seismics are substaintial even in the far field. ¿American Geophysical Union 1990