Exact and Asymptotic Solutions for the Field of a Point Source in a Transversely Isotropic Medium

Exact and asymptotic solutions are obtained for the acoustic field generated by an isotropic pulsed point source in an infinite transversely isotropic elastic medium. The exact solution for the displacement field is obtained in the form of a double integral over the horizontal slowness and the frequency by using the method of integral transforms. The calculation of the integral over the horizontal slowness by the method of stationary phase reduces the exact solution to an asymptotic solution that is convenient for numerical calculations. Formulas are given for calculating the spreading factors and the wave fronts of quasi-longitudinal qP-waves and quasi-transverse qSV-waves. With the formulas obtained, the displacement field of a point source is investigated for a particular transversely isotropic medium.