An approximate hybrid approach to computing high-frequency body wave synthetic seismograms in 2-D and 3-D laterally varying layered structures containing thin transition layers is suggested. It combines the ray method with the matrix (reflectivity) method. The ray method is applied to thick layers with smooth variations of velocity and the reflectivity method is applied to thin transition layers. Alternatively, the method of summation of Gaussian beams is used instead of the ray method in the hybrid code. An algorithm and the relevant program package BEAM87, designed for such hybrid computations in 2-D laterally varying layered structures containing one laterally varying thin transition layer, are briefly described. The thin transition layer may represent a region of a high velocity gradient, a laminated region, a region of a low Q, etc. It is simulated by a stack of very thin layers. The accuracy of the hybrid computations is tested on 1-D models by the comparison with reflectivity-method computations. The hybrid method yields sufficiently accurate results for transition layers, the thickness of which is smaller than one half of the prevailing wavelength of the wavefield under consideration, particularly for small angles of incidence. For reflected waves, the best accuracy is obtained for subcritical reflections, but the accuracy is lower for critical and overcritical reflections. The accuracy in the critical region is improved, if the Gaussian beam summation method is used instead of the ray method in the hybrid scheme. Numerical examples of synthetic body wave seismograms for a laterally varying model containing thin transition layers of various types are presented.
Gaussian beam summation method, ray method, reflectivity method, synthetic seismograms, thin transition layers.
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