  Wave travel-time shifts in the vicinity of sunspots are typically interpreted
as arising predominantly from magnetic fields, flows, and local changes in
sound speed. We show here that the suppression of granulation related wave
sources in a sunspot can also contribute significantly to these travel-time
shifts, and in some cases, an asymmetry between in and outgoing wave travel
times. The tight connection between the physical interpretation of travel times
and source-distribution homogeneity is confirmed. Statistically significant
travel-time shifts are recovered upon numerically simulating wave propagation
in the presence of a localized decrease in source strength. We also demonstrate
that these time shifts are relatively sensitive to the modal damping rates;
thus we are only able to place bounds on the magnitude of this effect. We see a
systematic reduction of 10-15 seconds in $p$-mode mean travel times at short
distances ($\sim 6.2$ Mm) that could be misinterpreted as arising from a
shallow (thickness of 1.5 Mm) increase ($\sim$ 4%) in the sound speed. At
larger travel distances ($\sim 24$ Mm) a 6-13 s difference between the ingoing
and outgoing wave travel times is observed; this could mistakenly be
interpreted as being caused by flows.
