A spectral model is presented to describe the acoustic-gravity wave response in a multiconstituent thermosphere on a spherical earth with realistic vertical temperature distribution. The waves are treated as perturbations in a globally uniform atmosphere without background winds. For periods much less than one day, the effects of planetary rotation (Coriolis force) are relatively small, and Legendre polynomials (zonal spherical harmonics) are then the appropriate eigenfunctions to describe the horizontal variations. Through numerical integration in height, the transfer function is constructed for some vertical source distribution in the thermosphere. In the horizontal wave number space (order of polynomials), the transfer-function reveals four components: (1) The trapped component which is confined to the source region. (2) The quasi-horizontally propagating wave which is represented by the lower cut-off and the first resonance maximum in the transfer function. In the thermosphere it is also the dominant maximum. The horizontal wave length and propagation velocity (about 700 m/s) are large. (3) The obliquely propagating waves, generated primarily through partial reflection from the base of the thermosphere or total reflection from the earth's surface. These waves appear as broad secondary maxima in the transfer function; their horizontal wave lengths and propagation velocities are relatively small; they are important near the source but cannot propagate very far horizontally. (4) The ducted waves which are produced in the lower atmosphere by the total reflection from the earth's surface and partial reflection from the mesopause temperature minimum. Leaking back into the thermosphere where they originate, these waves have relatively short wavelengths but can travel large horizontal distances away from the source (pole to equator). The important first and second harmonic modes have propagation velocities of 250 and 170 m/s respectively and appear in the transfer function as narrow resonance maxima. Such waves may explain the medium scale traveling ionospheric disturbances at low latitudes which are associated with magnetic activity.