With the aid of the above parameters, simple conditions are obtained for the decoupled far field, the decoupled near field, two point dynamic ray tracing, paraxial wave fields and Gaussian beams. Chapter III deals with a canonical problem. The Green s function, in a constant gradient medium, is presented, for an explosive point source, in frequency and time domains. 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 type of medium considered, the breakdown of the dynamic ray tracing method is smoother and better behaved than that of the Gaussian beams. As examples, a vertical seismic profiling configuration and a shallow earthquake are modeled using Gaussian beams. Chapter IV describes the paraxial ray method and its uses in modeling seismic waves. It is a flexible and fast method for computing asymptotic Green s functions. The method is an extension of the standard ray method and a degenerate case of Gaussian beams.