The Laser Interferometer Lunar Antenna (LILA), a concept for measuring sub-Hz gravitational waves on the Moon, would use laser strainmeters to obtain extremely sensitive strain measurements from 1 mHz to 1 Hz. With proposed strain sensitivities, LILA would also be able to measure the normal modes of the Moon from 1-10 mHz at high signal-to-noise ratio. Such measurements would enable significant advances in our understanding of both the spherically symmetric and even 3D deep internal structure of the Moon. Strainmeter measurements may even be able to detect the translational mode of the solid inner core of the Moon at frequencies below 0. 1 mHz. Inertial seismometers, on the other hand, are unlikely to reach the performance of 10^-16 m/s²/Hz required to reliably detect normal modes below 5-10 mHz, even with optimistic assumptions on future projected performance.
Panning et al. (Thu,) studied this question.