Inversions for local helioseismology are an important and necessary step for obtaining
three-dimensional maps of various physical quantities in the solar interior. Frequently,
the full inverse problems that one would like to solve prove intractable because of
computational constraints. Due to the enormous seismic data sets that already exist
and those forthcoming, this is a problem that needs to be addressed. To this end,
we present a very efficient linear inversion algorithm for local helioseismology.
It is based on a subtractive optimally localized averaging (SOLA) scheme in the Fourier
domain, utilizing the horizontal-translation invariance of the sensitivity kernels.
In Fourier space the problem decouples into many small problems, one for each horizontal
wave vector. This multi-channel SOLA method is demonstrated for an example problem
in time-distance helioseismology that is small enough to be solved both in real and
Fourier space. We find that both approaches are successful in solving the inverse
problem. However, the multi-channel SOLA algorithm is much faster and can easily be