Transient analytic point-source response of a layered acoustic medium; Part II

In part I (this issue) analytic methods are described for propagating directly in the time domain the full wave field of transient plane waves at arbitrary incidence angles through parallel acoustic homogeneous layers. The theory of part I is used here to compute transient point-source responses by way of integrating the transient plane-wave responses over various (real and nonreal) incidence angles. At first the complete transient point-source reflection (transmission) responses are formulated with the help of the transient Sommerfeld-Weyl integral that was developed previously by us. This leads to a transient solution in form of an infinite integral over incidence angles involving an (angle-dependent) integrand that is a time-convolution between a transient reflectivity (transmissivity) function and an inverse transient analytic square root operator. The transient Sommerfeld-Weyl integral solution is then proven to be causal. This causality provides the starting point for formulating exact transient point-source responses in terms of integrals over a finite range of incidence angles only.