Abstract
SUMMARY The summation of Gaussian beams in homogeneous layered media has been implemented for 3-D seismic forward modelling in this paper. The Gaussian beam method, which considers a bundle of rays in the vicinity of a central ray with a bell-shaped amplitude, is known as an extended ray method for handling caustics and diffractions. However, owing to the restriction of the paraxial assumption and the lack of a universal beam phase, this method has not been accurately applied to 3-D problems. These difficulties are overcome in this paper by providing (i) the optimal determination of the beam orientation and the beam shape by minimizing their beam widths; (ii) the ranges of validity, such as the beam conditions and the paraxial condition; and (iii) the diffractions of Gaussian beams from edges and tips. Comparisons with other solutions for caustics and diffractions demonstrate the accuracy of this extended method even in singular regions.
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