Integral superposition of paraxial Gaussian beams in inhomogeneous anisotropic layered structures is studied. It removes certain singularities of the standard ray method, like caustics. Individual quantities in the integral superposition can be calculated by ray tracing and by dynamic ray tracing in Cartesian coordinates. Instead of 3 × 3 paraxial matrices, it is sufficient to compute only two first columns of these matrices. This simplifies considerably the computations. The wave under consideration may be generated by a point source with an arbitrary radiation function, or by a surface source with the variable initial time along it. For a wave generated by a point-force source, the integral superposition of paraxial Gaussian beams yields the Green function. The receiver point may be situated arbitrarily in the model, including structural interfaces and the Earth's surface. It is customary (but not necessary) to introduce the target surface Σ passing through the receiver (or close to it), along which the data needed in the integral superposition of paraxial Gaussian beams are stored. The same target surface Σ may be used for different elementary waves. The formula for integral superposition may be applied to arbitrary reflected, converted, or multiply reflected waves, propagating in inhomogeneous anisotropic media. It may also be applied to waves propagating in inhomogeneous weakly anisotropic media. For S waves propagating in weakly anisotropic media, the coupling ray theory may be used, in which one coupled, frequency-dependent S wave is considered instead of two separate S1 and S2 waves. The derived integral superposition of paraxial Gaussian beams is valid even for the coupled S wave and removes the unpleasant shear-wave singularities of anisotropic media.
integral superposition of paraxial Gaussian beams, inhomogeneous anisotropic media, inhomogeneous weakly anisotropic media, S waves in weakly anisotropic media.
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