  Solar oscillations can be modeled by Galbrun's equation which describes
Lagrangian wave displacement in a self-gravitating stratified medium. For
spherically symmetric backgrounds, we construct an algorithm to compute
efficiently and accurately the coefficients of the Green's tensor of the
time-harmonic equation in vector spherical harmonic basis. With only two
resolutions, our algorithm provides values of the kernels for all heights of
source and receiver, and prescribes analytically the singularities of the
kernels. We also derive absorbing boundary conditions (ABC) to model wave
propagation in the atmosphere above the cut-off frequency. The construction of
ABC, which contains varying gravity terms, is rendered difficult by the complex
behavior of the solar potential in low atmosphere and for frequencies below the
Lamb frequency. We carry out extensive numerical investigations to compare and
evaluate the efficiency of the ABCs in capturing outgoing solutions. Finally,
as an application towards helioseismology, we compute synthetic solar power
spectra that contain pressure modes as well as internal-gravity (g-) and
surface-gravity (f-) ridges which are missing in simpler approximations of the
wave equation. For purpose of validation, the location of the ridges in the
synthetic power spectra are compared with observed solar modes.
