Source field modeling by self-consistent Gaussian beam superposition (two-dimensional)

Gaussians are useful models for high-frequency source field inputs into complex environments because they approximate the outputs of certain transducers, have favorable spectral and filtering properties, and can be propagated similar to ray fields. By recent analytic developments, any source field can be expressed exactly as a self-consistent superposition of Gaussians on a discretized (configuration)-(wave number) phase space lattice. This extends the use of Gaussians systematically to realistic transducer outputs. The method is already being applied to electromagnetic and acoustic propagation. It is here extended to modeling the radiation from transducers into an elastic solid. Restricting to the two-dimensional case, a distribution of forces over a finite, one-dimensional planar aperture is expanded self-consistently into Gaussian basis elements, which are then propagated into the unbounded medium. Numerical results reveal how successive addition of Gaussians for the compressional and shear potentials, as well as the displacements, homes in systematically on the assumed aperture profile, and on an independently generated numerical reference solution for the radiated near and far fields. Moreover, it is demonstrated how different self-consistent choices of beams affect the convergence. Furthermore, the validity of complex-source-point modeling of the Gaussians is explored for later applications where the input will be required to propagate across interfaces, as in a layered medium.