Elastic Gaussian wave packets in isotropic media

The theory of Gaussian wave packet (GWP) propagation in elastic materials is developed. The GWP solutions are in the form of localized disturbances with Gaussian spatial envelopes at any instant in time. The method is explicitly time dependent, but is conceptually no more difficult than time harmonic ray theory. The equations of propagation and evolution are very similar to those of standard, elastodynamic ray theory, but include an extra degree of freedom not considered previously: the temporal width of the pulse. The theory is valid if the carrier wavelength is short in comparison with typical length scales in the medium. Interfaces of discontinuity in material properties give rise to reflected and transmitted GWPs. Explicit expressions are presented that relate the incident GWP to the reflected and transmitted GWPs. These results are illustrated by numerical simulations of a pulse incident upon a spherical interface.