Frequency- and time-domain asymptotic fields near the critical cone in fluid-fluid configuration

Abstract

Near the critical cone of a point source placed at the interface between two half-space fluid media, investigation is made of the asymptotic fields in the frequency domain and their synthetic wave forms in the time domain. While the leading-order (and the head-wave) components give a good description of the true fields well off the critical cone, the uniform asymptotic (UA) analysis has to be made for the approximation near the critical cone. The UA analysis splits into two cases, depending on the medium densities and wave speeds. For Case 1, the UA1 approximation is employed that takes into account the proximity of the stationary-phase point to the branch point. In Case 2, the UA2 approximation is employed in which consideration is also given to the proximity of the stationary point to the pole and to the combined effect of the stationary point, the branch point, and the pole. The validities of the asymptotic fields are checked in the time domain by comparing the asymptotic field wave forms against the wave-number-synthetic wave forms. The UA fields show good accuracy and causal behaviors, with the causality of the UA2 fields previously unreported in the literature.