<p>The shape and location of density anomalies inside the Moon provide insights into processes that produced them and their subsequent evolution. Gravity measurements provide the most complete data set to infer these anomalies on the Moon [1]. However, gravity inversions suffer from inherent non-uniqueness. To circumvent this issue, it is often assumed that the Bouguer gravity anomalies are produced by the relief of the crust-mantle or other internal interface [2]. This approach limits the recovery of 3D density anomalies or any anomaly at different depths. In this work, we develop an algorithm that provides a set of likely three-dimensional models consistent with the observed gravity data with no need to constrain the depth of anomalies a priori.</p><p>The volume of a sphere is divided in 6480 tesseroids and n Voronoi regions. The algorithm first assigns a density value to each Voronoi region, which can encompass one or more tesseroids. At each iteration, it can add or delete a region, or change its location [2, 3]. The optimal density of each region is then obtained by linear inversion of the gravity field and the likelihood of the solution is calculated using Bayes&#8217; theorem. After convergence, the algorithm then outputs an ensemble of models with good fit to the observed data and high posterior probability. The ensemble might contain essentially similar interior density distribution models or many different ones, providing a view of the non-uniqueness of the inversion results.</p><p>We use the lunar radial gravity acceleration obtained by the GRAIL mission [4] up to spherical harmonic degree 400 as input data in the algorithm. The gravity acceleration data of the resulting models match the input gravity very well, only missing the gravity signature of smaller craters. A group of models show a deep positive density anomaly in the general area of the Clavius basin. The anomaly is centered at approximately 50&#176;S and 10&#176;E, at about 800 km depth. Density anomalies in this group of models remain relatively small and could be explained by mineralogical differences in the mantle. Major variations in crustal structure, such as the near side / far side dichotomy and the South Pole Aitken basin are also apparent, giving geological credence to these models. A different group of models points towards two high density regions with a much higher mass than the one described by the other group of models. It may be regarded as an unrealistic model. Our method embraces the non-uniqueness of gravity inversions and does not impose a single view of the interior although geological knowledge and geodynamic analyses are of course important to evaluate the realism of each solution.</p><p>References: [1] Wieczorek, M. A. (2006), Treatise on Geophysics 153-193. doi: 10.1016/B978-0-444-53802-4.00169-X. [2] Izquierdo, K et al. (2019) Geophys. J. Int. 220, 1687-1699, doi: 10.1093/gji/ggz544, [3]&#160; Izquierdo, K. et al., (2019) LPSC 50, abstr. 2157. [4] Lemoine, F. G., et al. ( 2013), J. Geophys. Res. 118, 1676&#8211;1698 doi: 10.1002/jgre.20118.</p><p>&#160;</p>
Methods for estimating uncertainty in factor analytic solutions
