Excitation of f- and p- modes by Reynolds stresses and entropy fluctuations is reviewed. Approximations made to allow semi-analytic analysis are discussed. The spectrum of solar convection is presented and shown to NOT be separable into independent spatial and temporal factors. An appropriate fitting formula is presented.

Time-distance local helioseismology has been analyzed using numerical simulations. One approach is simulation of solar surface convection on supergranule scales (48 Mm wide by 20 Mm deep). A surface shear layer develops. There is a continuous increase in the horizontal scale of the convective motions with increasing depth. Some small granular scale downflows at the surface are swept sideways by diverging larger scale upflows from below to merge into stronger downdrafts in these larger downflow boundaries. Elsewhere, some granular downflows have to beat their way against the upflows from below are halted. These simulations have a rich spectrum of f- and p- modes that turn within the computational domain. Cross-correlations between each surface location and each location below the surface reveals the wave propagation pattern from the surface. Waves at the surface that propagate into the interior, spread horizontally and are refracted back toward the surface. Time-distance diagrams have been constructed and inverted to determine the subsurface flows, which can then be compared with the average flows in the simulation.

A second approach calculates the propagation of linearized waves through a fixed, but non-uniform, background state. Some examples of such analysis are presented.