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Thick Lunar Crust Amplifies Deci-Hertz Gravitational-Wave Signals

Lei Zhang1,*, Han Yan2,3,*, Xian Chen2,3,†, and Jinhai Zhang1,‡

  • *These authors contributed equally to this work.
  • †Contact author: xian.chen@pku.edu.cn
  • ‡Contact author: zjh@mail.iggcas.ac.cn
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Phys. Rev. Lett. 137, 021408 – Published 9 July, 2026

DOI: https://doi.org/10.1103/d9jf-gxk5

Abstract

Gravitational waves (GWs) in the 0.01∼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 poses a challenge to the accurate modeling of its response. Here, we address this long-standing uncertainty by constructing the first high-resolution, two-dimensional model of the lunar GW response, more realistic than previous ones. 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 2 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 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 GW distributes energy into a series of higher-order modes, the hybridized eigenmodes of a laterally heterogeneous Moon. In certain narrow frequency ranges, we observe up to tenfold amplification spanning into the deci-hertz band, highlighting the power of numerical simulations in resolving these structurally fine-tuned features for designing future detectors. Our Letter establishes the Moon as a resonant GW detector albeit its complex topographical structures, and the resulting amplification maps provide a quantitative guide for the optimal landing site selection.

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synopsis

Plans for Moon-Based Gravitational-Wave Detectors Get a Lift from Geology

Published 9 July, 2026

A proposed gravitational-wave observatory on the Moon might gather more information than previously thought, thanks to geology.

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References (59)

  1. B. P. Abbott, R. Abbott, T. D. Abbott et al., Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102 (2016).
  2. A. Abramovici, W. E. Althouse et al., LIGO: The laser interferometer gravitational-wave observatory, Science 256, 325 (1992).
  3. F. Acernese, M. Agathos et al., Advanced Virgo: A second-generation interferometric gravitational wave detector, Classical Quantum Gravity 32, 024001 (2015).
  4. T. Akutsu, M. Ando et al. (KAGRA Collaboration), KAGRA: 2.5 generation interferometric gravitational wave detector, Nat. Astron. 3, 35 (2019).
  5. H. Xu, S. Chen, Y. Guo et al., Searching for the nano-hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array data release I, Res. Astron. Astrophys. 23, 075024 (2023).
  6. EPTA and InPTA Collaborations, The second data release from the European Pulsar Timing Array. III. Search for gravitational wave signals, Astron. Astrophys. 678, A50 (2023).
  7. G. Agazie, M. F. Alam, A. Anumarlapudi et al., The NANOGrav 15 yr data set: Observations and timing of 68 millisecond pulsars, Astrophys. J. Lett. 951, L9 (2023).
  8. D. J. Reardon, A. Zic, R. M. Shannon et al., Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array, Astrophys. J. Lett. 951, L6 (2023).
  9. M. Arca Sedda, C. P. L. Berry, K. Jani et al., The missing link in gravitational-wave astronomy: Discoveries waiting in the decihertz range, Classical Quantum Gravity 37, 215011 (2020).
  10. M. Colpi, K. Danzmann et al., LISA definition study report, arXiv:2402.07571.
  11. J. Luo, L.-S. Chen, H.-Z. Duan et al., TianQin: A space-borne gravitational wave detector, Classical Quantum Gravity 33, 035010 (2016).
  12. Z. Luo, Y. Wang, Y. Wu, W. Hu, and G. Jin, The Taiji program: A concise overview, Prog. Theor. Exp. Phys. 2021, 05A108 (2021).
  13. S. Kawamura, M. Ando, N. Seto et al., The Japanese space gravitational wave antenna: DECIGO, Classical Quantum Gravity 28, 094011 (2011).
  14. W.-T. Ni, Core noise and GW sensitivities of AMIGO, Int. J. Mod. Phys. D 31, 2250039 (2022).
  15. J. Weber, Detection and generation of gravitational waves, Phys. Rev. 117, 306 (1960).
  16. J. Weber, Gravitational waves, Phys. Today 21, No. 4, 34 (1968).
  17. F. J. Dyson, Seismic response of the Earth to a gravitational wave in the 1-Hz band, Astrophys. J. 156, 529 (1969).
  18. P. Lognonné, M. Le Feuvre, C. L. Johnson, and R. C. Weber, Moon meteoritic seismic hum: Steady state prediction, J. Geophys. Res. (Planets) 114, E12003 (2009).
  19. A. Ben-Menahem, Excitation of the Earth’s eigenvibrations by gravitational radiation from astrophysical sources, Nuovo Cimento C 6, 49 (1983).
  20. M. Bianchi, E. Coccia, C. N. Colacino, V. Fafone, and F. Fucito, Testing theories of gravity with a spherical gravitational wave detector, Classical Quantum Gravity 13, 2865 (1996).
  21. J. Majstorović, S. Rosat, and Y. Rogister, Earth’s spheroidal motion induced by a gravitational wave in flat spacetime, Phys. Rev. D 100, 044048 (2019).
  22. H. Yan, X. Chen, J. Zhang, F. Zhang, M. Wang, and L. Shao, Toward a consistent calculation of the lunar response to gravitational waves, Phys. Rev. D 109, 064092 (2024).
  23. J. Majstorović, L. Vidal, and P. Lognonné, Modeling lunar response to gravitational waves using normal-mode approach and tidal forcing, Phys. Rev. D 111, 044061 (2025).
  24. X. Bi and J. Harms, Response of the Moon to gravitational waves, Phys. Rev. D 110, 064025 (2024).
  25. D. E. Smith, M. T. Zuber et al., Initial observations from the Lunar Orbiter Laser Altimeter (LOLA), Geophys. Res. Lett. 37, L18204 (2010).
  26. M. A. Wieczorek, G. A. Neumann, F. Nimmo et al., The crust of the moon as seen by GRAIL, Science 339, 671 (2013).
  27. Y. H. Huang, J. M. Soderblom, D. A. Minton, M. Hirabayashi, and H. J. Melosh, Bombardment history of the moon constrained by crustal porosity, Nat. Geosci. 15, 531 (2022).
  28. M. A. Wieczorek and R. J. Phillips, Potential anomalies on a sphere: Applications to the thickness of the lunar crust, J. Geophys. Res. 103, 1715 (1998).
  29. J. H. Woodhouse, The coupling and attenuation of nearly resonant multiplets in the Earth’s free oscillation spectrum, Geophys. J. (Oxford) 61, 261 (1980).
  30. F. A. Dahlen and J. Tromp, Theoretical Global Seismology (Princeton University Press, Princeton, NJ, 1999).
  31. J. H. Woodhouse and F. A. Dahlen, The effect of a general aspherical perturbation on the free oscillations of the Earth, Geophys. J. Int. 53, 335 (1978).
  32. G. Masters, J. Park, and F. Gilbert, Observations of coupled spheroidal and toroidal modes, J. Geophys. Res. 88, 10285 (1983).
  33. A. Deuss and J. H. Woodhouse, Theoretical free-oscillation spectra: The importance of wide band coupling, Geophys. J. Int. 146, 833 (2001).
  34. X. Chen, The Moon as a gateway to discovery: How lunar gravitational-wave detection advances science across disciplines, npj Space Explor. 2, 1 (2026).
  35. J. Harms, F. Ambrosino, L. Angelini et al., Lunar gravitational-wave antenna, Astrophys. J. 910, 1 (2021).
  36. M. Branchesi, M. Falanga, J. Harms et al., Lunar gravitational-wave detection, Space Sci. Rev. 219, 67 (2023).
  37. K. Jani, M. Abernathy, E. Berti et al., Laser Interferometer Lunar Antenna (LILA): Advancing the U.S. priorities in gravitational-wave and lunar science, arXiv:2508.11631.
  38. H. J. Paik and K. Y. Venkateswara, Gravitational wave detection on the Moon and the Moons of Mars, Adv. Space Res. 43, 167 (2009).
  39. P. Amaro-Seoane, L. Bischof, J. J. Carter, M.-S. Hartig, and D. Wilken, LION: Laser interferometer on the Moon, Classical Quantum Gravity 38, 125008 (2021).
  40. J. Li, F. Liu, Y. Pan, Z. Wang, M. Cao, M. Wang, F. Zhang, J. Zhang, and Z.-H. Zhu, Detecting gravitational wave with an interferometric seismometer array on lunar nearside, Sci. China Phys. Mech. Astron. 66, 109513 (2023).
  41. L. Zhang, H. Yan, X. Chen, and J. Zhang, 2D numerical simulation of lunar response to gravitational waves using finite element method, Phys. Rev. D 111, 063014 (2025).
  42. L. Zhang, H. Yan, J. Zhang, and X. Chen, Numerical simulation of lunar response to gravitational waves and its 3D topographic effect using the spectral-element method, Phys. Rev. D 113, 023031 (2026).
  43. D. Komatitsch, S. Tsuboi, J. Tromp, A. Levander, and G. Nolet, The spectral-element method in seismology, Geophys. Monogr.-Am. Geophys. Union 157, 205 (2005).
  44. L. Zhang, J. Wang, Y. Xu, C. He, and C. Zhang, A procedure for 3D seismic simulation from rupture to structures by coupling SEM and FEM, Bull. Seismol. Soc. Am. 110, 1134 (2020).
  45. See Supplemental Material at http://link.aps.org/supplemental/10.1103/d9jf-gxk5 for the details of the numerical calculation and theoretical formalism, which includes Refs. [46,47].
  46. D. Komatitsch and J. Tromp, Spectral-element simulations of global seismic wave propagation—I. Validation, Geophys. J. Int. 149, 390 (2002).
  47. D. Komatitsch, J. Ritsema, and J. Tromp, The spectral-element method, Beowulf computing, and global seismology, Science 298, 1737 (2002).
  48. H. Yan and L. Zhang, See CrustalAmplify folder in 10.5281/zenodo.20309657 (2026).

  49. Note that ω=2πf. The frequency units “mHz” or “Hz” in this Letter refer to f rather than the angular frequency ω.

  50. G. Masters, J. H. Woodhouse, and G. Freeman, mineosv1.0.2 [software], Computational infrastructure for geodynamics, https://geodynamics.org/cig (2011).

  51. Mode-perturbation approach calculations are done within 2 h on a personal desktop computer without a dedicated GPU, showing its advantage on narrow-band, low-frequency global (full-Moon) analysis.

  52. H. Yan, X. Chen, J. Zhang, F. Zhang, L. Shao, and M. Wang, Constraining the stochastic gravitational wave background using the future lunar seismometers, Phys. Rev. D 110, 043009 (2024).
  53. L. Zhang, J. Zhang, and R. N. Mitchell, Dichotomy in crustal melting on early Mars inferred from antipodal effect, Innovation 3 (2022).
  54. X. Zhang, L. Zhang, J. Zhang, R. N. Mitchell, Strong heterogeneity in shallow lunar subsurface detected by Apollo seismic data, J. Geophys. Res. 127, e2022JE007222 (2022).
  55. K. Onodera, T. Kawamura, S. Tanaka, Y. Ishihara, and T. Maeda, Quantitative evaluation of the lunar seismic scattering and comparison between the Earth, Mars, and the Moon, J. Geophys. Res. 127, e2022JE007558 (2022).
  56. S. E. Wiggins, B. C. Johnson, T. J. Bowling, H. J. Melosh, and E. A. Silber, Impact fragmentation and the development of the deep lunar megaregolith, J. Geophys. Res. 124, 941 (2019).
  57. G. V. Latham, M. Ewing, F. Press, G. Sutton, J. Dorman, Y. Nakamura, N. Toksöz, R. Wiggins, J. Derr, and F. Duennebier, Passive seismic experiment, Science 167, 455 (1970).
  58. Y. Nakamura, Seismic velocity structure of the lunar mantle, J. Geophys. Res. 88, 677 (1983).
  59. M. P. Panning, P. Lognonné, T. Creighton, J. Trippe, V. Quetschke, J. Majstrorović, and K. Jani, Potential for lunar interior science by the gravitational-wave detector LILA, arXiv:2509.15452.

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Phys. Rev. Lett. 137, 021408– Published 9 July, 2026
  • Received 23 January 2026
  • Revised 13 May 2026
  • Accepted 18 May 2026
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