  The response of the Moon to gravitational waves (GWs) is used by some of the
proposed lunar GW detectors like the Lunar Gravitational-wave Antenna (LGWA) to
turn the Moon into an antenna for GWs. The deep connection between the lunar
internal structure, its geophysical environment and the study of the Universe
is intriguing, but given our limited understanding of the Moon today, it also
makes it very difficult to predict the science potential of lunar GW detectors
accurately. Lunar response models have been developed since the Apollo program,
but there is evidence coming from seismic measurements during the Apollo
missions that the models are not good enough and possibly underestimating the
lunar GW response especially in the decihertz frequency band. In this paper, we
will provide an extension of Freeman Dyson's half-space model to include
horizontally layered geologies, which allows us to carry out computationally
efficient calculations of the lunar GW response above 0.1\,Hz compared to the
normal-mode simulations used in the past. We analyze how the results depend on
the values of geometric and elastic parameters of the layered geological model,
and we find that modifications of the geological model as required to explain
Apollo seismic observations can boost the lunar GW response.
