Point‐Source Excitation of the Density Contrast Wedge: Perturbation for Nearly Equal Sound Speeds
Abstract
The extension of the Biot–Tolstoy exact time‐domain solution to the density contrast wedge is used to develop an iterative procedure that facilitates construction of the first‐order perturbation of the exterior field with respect to distinct wave speed for a point source, which is either smoothly switched on and off within a finite time or is oscillatory for all time. In both cases, this perturbation field is symmetric with respect to the source and field points and appears as an integral over the wedge involving the isovelocity solution for the interior region. The ‘geometrical acoustics’ components are simplified for ‘rational’ wedge angles in the switch‐on/off case and estimated in the far field in the oscillatory case to be generated by a ray passing through the wedge, possibly with internal reflection.