Three-dimensional source field modeling by self-consistent Gaussian beam superposition

Abstract

A self-consistent superposition of Gaussians on a discretized (configuration)-(wave number) phase space lattice has recently been applied to two-dimensional wave propagation into an elastic solid [Felsen et al., J. Acoust. Soc. Am. 89, 63 (1991)]. It is here generalized to three dimensions by modeling the radiation from planar finitely extended two-dimensional source distributions into an elastic solid. A distribution of forces over the source aperture is expanded self-consistently into Gaussian basis elements, which are then propagated into the unbounded medium. Numerical results are presented for simple smoothly tapered and abruptly truncated source profiles. As for the two-dimensional case, the validity of complex-source-point modeling of the Gaussians is explored by comparing the fields obtained from them with those generated by an independent numerical reference solution. Moreover, it is demonstrated how different self-consistent choices of beams affect the convergence of the Gaussian series expansion.