Thick Lunar Crust Amplifies Gravitational-Wave Signal

TL;DR

This work demonstrates that the Moon’s rugged surface and heterogeneous crust significantly shape the seismic imprint of mid-band gravitational waves. By marrying high-resolution 2D spectral-element simulations with a normal-mode perturbation framework grounded in Woodhouse kernels, the authors resolve both local topographic effects and global mode-mixing-driven energy redistribution from quadrupole ($l=2$) GW forcing into higher-order spheroidal modes. They find an average amplification of $M_E \approx 1.1$–$1.2$ in thick-crust regions, with localized boosts up to about tenfold near eigen-frequencies, arising from mode coupling across the Moon’s heterogeneous interior. These results establish the Moon as a calibratable resonant GW detector and provide spatial amplification maps to guide landing-site selection, while offering a pathway to constrain the Moon’s 3D interior through GW seismology.

Abstract

Gravitational waves (GWs) in the $10^{-3}-0.1$ Hz band encode unique signatures of the early universe and merging compact objects, but they are beyond the reach of existing observatories. Theoretical models suggest that the Moon could act as a resonant detector, but the unknown influence of its rugged surface and heterogeneous interior has cast doubt on this prospect. Here, we resolve this long-standing uncertainty by constructing the first high-resolution, structurally realistic model of the lunar GW response. We achieve this by combining high-fidelity spectral-element simulations with the analytical power of normal-mode perturbation theory, thereby resolving topographical effects down to $3.7$ km grid spacing while maintaining the capacity to discern global free-oscillation patterns. This dual-methodology approach not only recovers the expected predominant quadrupole ($l=2$) oscillation mode, but also exposes a systematic signal amplification of $(10-20)\%$ in thick-crust regions. This enhancement is traced by our normal-mode analysis to a mode-coupling process, in which the original quadrupolar oscillation induced by the passing GWs distributes energy into a series of higher-order modes, the hybridized eigenmodes of the laterally heterogeneous Moon. Near certain eigen-frequencies and at specific locations, we observe up to tenfold amplification, highlighting the power of numerical simulations in resolving these structurally fine-tuned features. Our work establishes the Moon as an accurately calibrated resonant GW detector, and the resulting amplification maps provide quantitative guide for the optimal landing site selection.

Figures (6)

• Figure 1: Lunar model with topography and crustal-thickness variations. (a) Lunar crustal thickness model. The yellow triangles mark the locations of Apollo seismographs. The black line indicates the great circle passing through Mare Humboldtianum, Mare Imbrium, and the SPA basin. The potential landing sites of Chang’e-7 and FFS are marked as stars around the south pole. (b) Crustal thickness model truncated at $l=4$. Solid lines represent crustal thickness contours in km. (c) The topography and crustal thickness along the great circle shown in (a), magnified by 30 and 5 times, respectively, to reveal details.
• Figure 2: Comparison between layered and heterogeneous models and the simulated location-frequency distribution of amplification ratios. (a) The snapshot of lunar response to GWs for a spherically layered model at t = 100 s. (b) The same as (a) but for the model with varying topography and crustal thickness shown in Figure 1c. In a and b, the topography and crustal thickness are magnified by 30 and 5 times in the outside annulus, respectively. (c) The same as (a) but at t = 3000 s. (d) The same as (b) but at t = 3000 s. More snapshots can be found in webs. (e) The averaged amplification ratio $M_E$ (red line). The black line is the crustal thickness for reference. (f) The amplification ratio $m_E (\omega)$ of the vertical component in the frequency band 0–40 mHz, where the black contour lines indicate the amplification ratio of 5.
• Figure 3: Amplification according to the normal-mode perturbation theory. (a) Total energy magnification $M_E$, integrated over frequency and averaged over polarization. Here, all the free-oscillation modes up to $l=6$ are included. (b) Contribution from the $l=2$ free-oscillation mode alone. For comparison, the crustal thickness contours from Fig. 1(b) are overlaid.
• Figure A1: The SEM grids and the GW-source model. (a) Global lunar model featuring crustal thickness variation, with a surface element size of about $3.7$ km. (b) Enlarged regional crust grids around the azimuth of $0^{\circ}$. (c) Enlarged regional crust grids around the south pole. (d) Spatial distribution of the force density. (e) The source time function with a duration of $5,000$ s. (f) The normalized amplitude spectrum.
• Figure A2: The distribution of the force density vector with an azimuthal resolution of $1^{\circ}$. Subfigures correspond to different polarization angles ($\theta=10^{\circ}, 20^{\circ}, \ldots, 80^{\circ}$) for the GW source.