Porosity beneath the lunar polar regions as revealed by GRAIL gravity data.

Impact cratering is one of the most important geological processes that has affected the evolution of the Moon’s crust. Impact cratering fractures the crust and generates porosity, which in turn affects physical properties such as the bulk density, thermal conductivity, and seismic velocity. As a result of NASA’s GRAIL mission, the lunar gravity field has been resolved to an unprecedented spatial resolution of up to 3 km in places, making it possible to estimate not only how the density of the upper crust varies laterally (e.g., Wieczorek et al. 2013, Wahl et al. 2020), but also how density varies with depth (e.g., Besserer et al. 2014, Gong et al. 2016, Šprlák et al. 2020). Estimating the 3D density structure of the crust is a non-unique problem, and in order to make this problem tractable, previous studies needed to impose the form of the density profile, which was assumed to be either constant, linear, exponential, or layered.

 

In the pioneering work of Besserer et al. (2014), a localized spectral admittance approach (Wieczorek & Simons, 2005; 2007) was used to derive the so-called effective density spectrum, and this was compared to predictions from models with a prescribed density profile. This study made use of an early gravity model GRGM900B that had a maximum spherical harmonic degree of 900 (Lemoine et al., 2014), which was the state of the art at the time. However, their analysis only made use of degrees up to 550, which was their estimate of the global resolution of the model. This study tested two simple parameterizations of the density profile, linear and exponential, but these are in all likelihood an over simplification of reality. Though this study provided many valuable insights, there are still many questions concerning how sensitive the Moon’s gravity is to depth variations in density.

 

Over the past decade, several advances have made a reanalysis of the Besserer et al. (2014) results pertinent. First, new gravity models have been constructed that utilize all data from the GRAIL extended mission phase, with the most recent being developed up to degree 1800 (GL1800F, Park et al., 2025). Šprlák et al. (2018) have shown that the degree 550 cutoff used by Besserer et al. (2014) is problematic, given that it was based on an estimate of the gravity field below the Brillouin sphere (the maximum radius of the planet). Furthermore, Besserer et al. (2014) used the same maximum spherical harmonic degree for all of their localized analyses, but the spatial resolution of the gravity model is known to be better at the poles where the spacecraft orbits overlap and in places where the spacecraft altitude was lower than average.

 

In this study, we improve upon previous work by applying localized spectral analyses combined with a Bayesian inversion method. In comparison to Besserer et al., we use a smaller spherical cap size of 9° with a smaller spectral bandwidth of 87. By using all localization windows with concentration factors greater than 0.99, we have 23 windows in comparison to 30 used by Besserer et al. We make use of the gravity model GL1800F, which has a resolution that is twice greater than the previously employed GRGM900B model. Furthermore, we better quantify the maximum permissible degree of our localized analyses by use of a degree-strength map and by use of the correlation between gravity and topography. Lastly, we use a multi-layer depth-dependent density model where the density and depth of each layer are sampled using a Markov Chain Monte Carlo (MCMC) method.

 

We focus our analysis on the lunar pole regions, where dense orbital coverage by the GRAIL mission provides particularly high-resolution gravity data. In particular, based on the correlation between gravity and topography, we estimate that the spatial resolution of these regions is close to spherical harmonic degree of 900, which is comparable to what is given by the degree strength map of GRGM1200 RM1. For the polar regions, we test density models that are constrained to increase with depth, as well as models that have no constraints. We also investigate models with different numbers of layers. From our numerical inversions, we expect to be able to determine the form of the density profile with depth in the crust, and also to determine the maximum depth that is sensitive to the GRAIL data.

 

Reference：

Besserer, J., Nimmo, F., Wieczorek, M. A., et al. (2014). GRAIL gravity constraints on the vertical and lateral density structure of the lunar crust. Geophysical Research Letters, 41(16), 5771–5777.

Gong, S., Wieczorek, M. A., Nimmo, F., et al. (2016). Thicknesses of mare basalts on the Moon from gravity and topography. Journal of Geophysical Research: Planets, 121(5), 854–870.

Lemoine, F. G., Goossens, S., Sabaka, T. J., et al. (2014). GRGM900C: A degree 900 lunar gravity model from GRAIL primary and extended mission data. Geophysical Research Letters, 41(10), 3382–3389.

Park, R. S., Berne, A., Konopliv, A. S., et al. (2025). Thermal asymmetry in the Moon's mantle inferred from monthly tidal response. Nature. (in press)

Šprlák, M., Han, S.-C., & Featherstone, W. E. (2018). Forward modelling of global gravity fields with 3D density structures and an application to the high-resolution (~ 2 km) gravity fields of the Moon. Journal of Geodesy, 92(8), 847–862.

Šprlák, M., Han, S.-C., & Featherstone, W. E. (2020). Crustal density and global gravitational field estimation of the Moon from GRAIL and LOLA satellite data. Planetary and Space Science, 192, 105032.

Wahl, D., Wieczorek, M. A., Wünnemann, K., et al. (2020). Crustal Porosity of Lunar Impact Basins. Journal of Geophysical Research: Planets, 125(4), e2019JE006335.

Wieczorek, M. A., & Simons, F. J. (2005). Localized spectral analysis on the sphere. Geophysical Journal International, 162(3), 655–675.

Wieczorek, M. A., & Simons, F. J. (2007). Minimum-variance multitaper spectral estimation on the sphere. Journal of Fourier Analysis and Applications, 13(6), 665–692. 

Wieczorek, M. A., Neumann, G. A., Nimmo, F., et al. (2013). The Crust of the Moon as Seen by GRAIL. Science, 339(6120), 671–675.