Y. L. Li
US Army Construction Eng. Res. Lab., P.O. Box 9005, Champaign, IL 61826-9005
Three exact analytic solutions of the Helmholtz equation are obtained in closed form for the case of a point source in range-dependent inhomogeneous media. The solutions are obtained by starting with a onefold integral representation for the solution that is derived from the path integral. For a point source in such media above either a soft or hard ground, the exact analytic solutions are also derived. These solutions are particularly useful for testing the validity of approximate or numerical solutions for cases with a range-dependent background medium. They also facilitate construction of more general solutions for problems with scattering in a range-dependent background medium, through the use of integral equation techniques.