  The recent increasing interest in detecting gravitational waves (GWs) by
lunar seismic measurement urges us to have a clear understanding of the
response of the moon to passing GWs. In this paper, we clarify the relationship
between two seemly different response functions which have been derived
previously using two different methods, one taking the field-theory approach
and the other using the tidal force induced by GWs. We revisit their derivation
and prove, by both analytical arguments and numerical calculations, that the
two response functions are equivalent. Their apparent difference can be
attributed to the choice of different coordinates. Using the correct response
function, we calculate the sensitivities (to GWs) of several designed lunar
seismometers, and find that the sensitivity curves between $10^{-3}$ and $0.1$
Hz are much flatter than the previous calculations based on normal-mode model.
Our results will help clarifying the scientific objectives of lunar GW
observation, as well as provide important constraints on the design of lunar GW
detectors.
