Range of validity of seismic ray and beam methods in general inhomogeneous media – II. A canonical problem

Summary. The Green's function, in a constant gradient medium, is derived for an explosive point source, in the frequency and the time domains. The analytical dynamic ray tracing (DRT) solution is rederived with conditions stated in Part I. The Gaussian beam (GB) solution is investigated. New beam parameters and conditions are defined. Comparisons between exact and approximate solutions are undertaken.
For both methods, DRT and GB, conditions of validity are explicit and quantitative. An accuracy criterion is defined in the time domain, and measures a global relative error. The range of validity is expressed in the form of two inequalities for the dynamic ray tracing method and of five inequalities for the Gaussian beam method. Results remain accurate at ray turning points. For the types of medium considered, the breakdown of the dynamic ray tracing method is smoother and better behaved than that of Gaussian beams. As examples, a vertical seismic profiling configuration, and a shallow earthquake are modelled, using Gaussian beams.