  To recover the flow information encoded in travel-time data of time-distance
helioseismology, accurate forward modeling and a robust inversion of the travel
times are required. We accomplish this using three-dimensional finite-frequency
travel-time sensitivity kernels for flows along with a 2+1 dimensional (2+1D)
optimally localized averaging (OLA) inversion scheme. Travel times are measured
by ridge filtering MDI full-disk Doppler data and the corresponding Born
sensitivity kernels are computed for these particular travel times. We also
utilize the full noise covariance properties of the travel times which allow us
to accurately estimate the errors for all inversions. The whole procedure is
thus fully consistent. Due to ridge filtering, the kernel functions separate in
the horizontal and vertical directions, motivating our choice of a 2+1D
inversion implementation. The inversion procedure also minimizes cross-talk
effects among the three flow components, and the averaging kernels resulting
from the inversion show very small amounts of cross-talk. We obtain
three-dimensional maps of vector solar flows in the quiet Sun at spatial
resolutions of 7-10 Mm using generally 24 h of data. For all of the flow maps
we provide averaging kernels and the noise estimates. We present examples to
test the inferred flows, such as a comparison with Doppler data, in which we
find a correlation of 0.9. We also present results for quiet-Sun supergranular
flows at different depths in the upper convection zone.
