Ray Expansion Theory
Ray series are power series, the coefficients of which are the discontinuities in arbitrary order partial time derivatives of the desired functions, while the time of arrival of the wave front is the independent variable; in so doing the order of the partial time derivative coincides with the power exponent of the independent variable.
In solving problems of the propagation and attenuation of transient waves carrying the jumps in the field parameters on the wave front, the methods utilizing ray expansions are most efficient. A zeroth term of a ray series exactly describes the changes in the field parameter discontinuity along the ray, but the rest of the terms within the radius of the series convergence reveal the changes in the field behind the wave front.
The questions of the ray series application to transient wave problems have been considered by many investigators, and...