Lunar response to gravitational waves

It has been suggested to use seismic detectors on the Moon as a tool to search for gravitational waves in an intermediate frequency range between mHz and Hz. Employing three different spherically symmetric models for the lunar interior, we investigate the response of the Moon to gravitational waves in Einstein and Jordan-Brans-Dicke gravity. We find that the first eigenfrequencies of the different models depend only weakly on the model details, with the fundamental frequency ${\ensuremath{\nu}}_{1}$ close to 1 ms both for spheroidal and toroidal oscillations. In contrast, the resulting displacement varies up to a factor 5, being in the range $(3.6\ifmmode\times\else\texttimes\fi{}{10}^{12}--1.9\ifmmode\times\else\texttimes\fi{}{10}^{13})/{h}_{0}\text{ }\text{ }\mathrm{cm}$ for spheroidal oscillations with amplitude ${h}_{0}$ and assuming a quality factor ${Q}_{n}=3300$. Toroidal oscillations are suppressed by a factor $2\ensuremath{\pi}\ensuremath{\nu}R/c$, both in Einstein gravity and in general scalar-tensor theories.