Small-scale density variations in the lunar crust revealed by GRAIL

Abstract

Data from the Gravity Recovery and Interior Laboratory (GRAIL) mission have revealed that ~98% of the power of the gravity signal of the Moon at high spherical harmonic degrees correlates with the topography. The remaining 2% of the signal, which cannot be explained by topography, contains information about density variations within the crust. These high-degree Bouguer gravity anomalies are likely caused by small-scale (10's of km) shallow density variations. Here we use gravity inversions to model the small-scale three-dimensional variations in the density of the lunar crust. Inversion results from three non-descript areas yield shallow density variations in the range of 100-200 kg/m³. Three end-member scenarios of variations in porosity, intrusions into the crust, and variations in bulk crustal composition were tested as possible sources of the density variations. We find that the density anomalies can be caused entirely by changes in porosity. Characteristics of density anomalies in the South Pole-Aitken basin also support porosity as a primary source of these variations. Mafic intrusions into the crust could explain many, but not all of the anomalies. Additionally, variations in crustal composition revealed by spectral data could only explain a small fraction of the density anomalies. Nevertheless, all three sources of density variations likely contribute. Collectively, results from this study of GRAIL gravity data, combined with other studies of remote sensing data and lunar samples, show that the lunar crust exhibits variations in density by ±10% over scales ranging from centimeters to 100's of kilometers.

Figure 1:

Global Lunar Maps. A) Topography, expanded to spherical harmonic degree 1800. B) Bouguer gravity filtered using the complementary minimum amplitude filter (see text). C) Gravity Gradient map, with a high-pass filter applied at degree 50 and a low-pass cosine filter applied from degree 350 to degree 400. The outlined boxes refer to the three study areas of figure 6.

Figure 2:

A) Root mean square power spectrum of GRAIL gravity model (GRGM900B_Bouguer). Red dotted line indicates the degree at which the minimum amplitude filter has a magnitude one half. B) Minimum amplitude (black; Wieczorek et al., 2013) and complementary minimum amplitude (red) filters applied to the gravity data. The complementary minimum amplitude filter was used in all analyses in this work. A low-pass filter from degree 550 to degree 600 was added to the complementary filter (not shown here) to prevent ringing.

Figure 3:

A) Bouguer corrected gravity anomaly of the Freundlich-Sharonov basin. B) Tikhonov curve (L-curve) with the data misfit on the y-axis and the model norm on the x-axis. The β values vary from left to right on the curve in increments of a factor of 10. C) Cross-section of the optimal density model indicated by the black circle in B). D) Cross-section through the crustal thickness model of the same location in C).

Figure 4:

A) Bouguer corrected gravity anomaly of linear feature 1 from Andrews-Hanna et al. (2013). B) Tikhonov curve (or L-curve). The β values vary from left to right on the curve in increments of a factor of 10. C) Horizontal cross-section through the optimal density model solution indicated by the black circle in B), at 10 km depth. D) Vertical cross-section through the density model in C) at the location of the black line.

Figure 5:

Inversion results of gravity data derived from a synthetic density model. Panels A and B are horizontal planar sections of the synthetic and recovered density model, respectively, at depths of 10 km. Bottom panels C and D are vertical cross-sections located at the black lines in A and B of the synthetic and recovered density model, respectively.

Figure 6:

Topography (A-C) and Bouguer gravity (D-F) maps of non-descript areas (locations indicated in Fig. 1). Gravity data was filtered with the complementary minimum amplitude filter.

Figure 7:

Optimal inversion result for non-descript Area 1. The horizontal cross-section (A) is taken at 2 km depth, and the vertical cross-section (B) is taken at the location of the black line in A. The color bars each refer to a different analysis of the solution. FVN indicates the change in composition of the bulk lunar crust as represented by the fractional volume of noritic anorthosite, FVB indicates the fractional volume of a basaltic intrusion into the crust.

Figure 8:

Optimal inversion result for non-descript Area 2 (details are the same as Fig. 7).

Figure 9:

Optimal inversion model for non-descript Area 3 (details are the same as Fig. 7).

Figure 10:

Tikhonov/L-curve for area 3. The optimal β for this area is the knee point where β=10⁻² and the two extremes are also indicated.

Figure 11:

(A-E) Mineral abundance maps derived from remote sensing data for Area 2 of pyroxene, plagioclase, olivine, iron oxide, and a (olivine+pyroxene)/plagioclase ratio, respectively. (F-J) The corresponding scatter plots, showing the best-fit line along with the associated the p-values and R² values.

Figure 12:

Same as Fig. 11, but for Area 3.

Figure 13:

Histograms of the density inversions derived from the continuous density anomaly forward model (A), the discrete density anomaly forward model (B), and the GRAIL data over the non-descript area (C).

Figure 14:

Normal probability quantile-quantile (QQ) plots of the density inversions of the synthetic gravity from the continuous (A) and discrete (B) density models, and of the true gravity data (C). The thin line in each panel represents a normal distribution.