Numerical simulation of lunar response to gravitational waves and its 3D topographic effect using the spectral-element method

The Moon has been regarded as a natural Weber bar capable of amplifying gravitational waves (GWs) for detecting events across a wide range of frequencies. However, accurately determining the amplification effects remains challenging due to the absence of 3D numerical simulation methods. In this study, we develop a high-order 3D finite element method (spectral-element method, SEM) to numerically simulate the lunar response to GWs below 20 mHz. We verify the accuracy of our method by comparing the resonant peaks of our results with those from semianalytical solutions and find that the frequency deviation is less than 3% for the first peak at about 1 mHz and less than 0.8% for the subsequent peaks up to 10 mHz. Using this method, we evaluate the amplification of GW signals due to 3D topographic effects of the Moon, and we find enhancements at a series of specific frequency components. These results highlight the non-negligible effect of surface topography on the lunar response to GWs, as a fundamental factor that holds significant implications across both global and regional analyses. Our work paves the way for a comprehensive evaluation of the Moon’s resonant response to GWs, helpful for the strategic planning of lunar GW detections.