  The purpose of deep-focusing time--distance helioseismology is to construct
seismic measurements that have a high sensitivity to the physical conditions at
a desired target point in the solar interior. With this technique, pairs of
points on the solar surface are chosen such that acoustic ray paths intersect
at this target (focus) point. Considering acoustic waves in a homogeneous
medium, we compare travel-time and amplitude measurements extracted from the
deep-focusing cross-covariance functions. Using a single-scattering
approximation, we find that the spatial sensitivity of deep-focusing travel
times to sound-speed perturbations is zero at the target location and maximum
in a surrounding shell. This is unlike the deep-focusing amplitude
measurements, which have maximum sensitivity at the target point. We compare
the signal-to-noise ratio for travel-time and amplitude measurements for
different types of sound-speed perturbations, under the assumption that noise
is solely due to the random excitation of the waves. We find that, for highly
localized perturbations in sound speed, the signal-to-noise ratio is higher for
amplitude measurements than for travel-time measurements. We conclude that
amplitude measurements are a useful complement to travel-time measurements in
time--distance helioseismology.
