NASA’s Planetary Geology, Geophysics and Geochemistry Laboratory

Probing Lateral Density Variations in the Crust from Gravity and Topography: Applications to the Moon and Mars

Sander Goossens

We have developed a new constraint to be used for the determination of gravity field models from satellite tracking data that allows for a direct estimation of lateral variations in the density of the crust. Following our earlier work (Goossens et al. 2017) where we used a constraint based on topography to directly estimate the average bulk density of the crust, we have now developed an extended constraint based on the Bouguer correction with lateral density variations (e.g., Wieczorek 2015). We called this constraint RM-S, rank-minus-S, because it has S degrees of freedom, which are the coefficients of a spherical harmonic expansion of crustal density. The details of this constraint can be found in Goossens & Sabaka (2025). To test this constraint, we have applied it to a pre-GRAIL lunar data set (Goossens et al. 2011), and to the data set of the Mars gravity field model GMM-3 (Genova et al. 2016).

Here, we present several data sets that are presented in our paper. These data sets consist of text files of spherical harmonic coefficients of derived crustal densities, or gravity field models. We refer to the paper for details on the models. The format of these files is as follows:

• The first line contains the GM (m³/s²), reference radius (m), and maximum degree and order of the model. If the model describes density, the GM and reference radius are set to 1.
• The following lines contain: degree l, order m, the coefficients C_lm, S_lm, and their formal errors. The coefficients are 4π-normalized.

Data

Results for the Moon

Spherical harmonics expansion of the density of the lunar crust from localization and the effective density method, degree and order 50: download

Spherical harmonics expansion of the density of the lunar crust from the matrix method, degree and order 12: download

Spherical harmonics expansion of the density of the lunar crust from the matrix method, degree and order 50, using the constraint D = 5×10¹¹ (see the paper for more information): download

Spherical harmonics expansion of the lunar gravity field based on pre-GRAIL data with the RM-S constraint λ=10¹⁵: download

Spherical harmonics expansion of the lunar gravity field based on pre-GRAIL data with the RM-S constraint λ=10¹⁶: download

Spherical harmonics expansion of the lunar gravity field based on pre-GRAIL data with the RM-S constraint λ=10¹⁷: download

Results for Mars

Spherical harmonics expansion of the density of the martian crust from an RM-S constrained model using λ=10²⁰, the matrix method and a constraint of D =10⁹: download

Spherical harmonics expansion of the martian gravity field based on the GMM-3 data matrix with the RM-S constraint λ=10¹⁶: download

Spherical harmonics expansion of the martian gravity field based on the GMM-3 data matrix with the RM-S constraint λ=10¹⁸: download

Spherical harmonics expansion of the martian gravity field based on the GMM-3 data matrix with the RM-S constraint λ=10²⁰: download

Spherical harmonics expansion of the martian gravity field based on the GMM-3 data matrix with the RM-S constraint λ=10²⁷: download

Data Usage Policy

Please cite the following reference when using any of the products described above:

Manuscript: Goossens, S. and Sabaka, T.J. (2025), Probing lateral density variations in the crust from gravity and topography: applications to the Moon and Mars, The Planetary Science Journal, doi:10.3847/PSJ/adbaf0.

Dataset: Goossens, S. and Sabaka, T.J. (2025), Probing lateral density variations in the crust from gravity and topography: applications to the Moon and Mars [Data set]. NASA Goddard Space Flight Center Planetary Geodesy Data Archive. doi:10.60903/GSFCPGDA-GRAIL-RMS.

Funding

Support for this research was provided by NASA's Planetary Science Division Research Program, through ISFM work package Planetary Geodesy at Goddard Space Flight Center.

References

Genova, A., Goossens, S., Lemoine, F.G., Mazarico, E., Neumann, G.A., Smith, D.E., Zuber, M.T. (2016), Seasonal and static gravity field of Mars from MGS, Mars Odyssey and MRO radio science, Icarus, Vol. 272, pp. 228-245, doi:10.1016/j.icarus.2016.02.050.

Goossens, S., Matsumoto, K., Liu, Q., Kikuchi, F., Hanada, H., Lemoine, F.G., Rowlands, D.D., Ishihara, Y., Noda, H., Namiki, N., Iwata, T., Sasaki, S. (2011), Improved high-resolution lunar gravity field model from SELENE and historical tracking data, American Geophysical Union Fall Meeting, abstract P44B-05.

Goossens, S., T. J. Sabaka, A. Genova, E. Mazarico, J. B. Nicholas, and G. A. Neumann (2017), Evidence for a low bulk crustal density for Mars from gravity and topography, Geophys. Res. Lett., 44, 7686–7694, doi:10.1002/2017GL074172.

Wieczorek, M.A., Gravity and Topography of the Terrestrial Planets (2015), in: Treatise on Geophysics (Second Edition), Editor: Gerald Schubert, Elsevier, ISBN 9780444538031, doi:10.1016/B978-0-444-53802-4.00169-X.