3‐D inversion of gravity data in spherical coordinates with application to the GRAIL data

Abstract

inversion of gravity data has been widely used to reconstruct the density distributions of ore bodies, basins, crust, lithosphere, and upper mantle. For global model of 3-D density structures of planetary interior, such as the Earth, the Moon, or Mars, it is necessary to use an inversion algorithm that operates in the spherical coordinates. We develop a 3-D inversion algorithm formulated with specially designed model objective function and radial weighting function in the spherical coordinates. We present regional and global synthetic examples to illustrate the capability of the algorithm. The inverted results show density distribution features consistent with the true models. We also apply the algorithm to a set of lunar Bouguer gravity anomaly derived from the Gravity Recovery and Interior Laboratory (GRAIL) gravity field and obtain a lunar 3-D density distribution. High-density anomalies are clearly identified underlying lunar basins, a wide region of the lateral density heterogeneities that exist beneath the South Pole-Aitken basin are found, and low-density anomalies are distributed beneath the Feldspathic Highlands Terrane on the lunar far-side. The consistency of these results with those obtained independently from other existing methods verifies the newly developed algorithm.

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

“…The density anomaly extends from the base of the model domain up to ~16 km depth, based on the average depth beneath the basin at which the density anomaly is at 50% of its maximum value, which is consistent with the expected depth of the crust-mantle interface obtained from crustal thickness modeling. These results are also consistent with the global continuous density inversions of the GRAIL data (Liang et al, 2014), indicating that the Cartesian geometry assumed in this study (rather than the global spherical inversion of Liang et al (2014) is adequate for local studies.…”

“…3) in order to test the model against a large-scale Bouguer anomaly arising from deep mantle uplift that is well-resolved Moho uplift models. A recent study used a similar continuous density inversion to obtain a global model for density variations, including all spherical harmonic degrees (Liang et al, 2014). That study showed that the predicted density anomalies beneath the lunar basins are consistent with the expected density anomalies arising from an uplifted mantle plug.…”

“…However, for globally stable models of crustal thickness and crustal density anomalies, some pair of filters resembling the minimum amplitude filter used by Wieczorek et al (2013), and the complementary minimum amplitude filter used here, is required. Although it is possible to attribute Bouguer gravity anomalies of all wavelengths to continuous subsurface density variations (e.g., Liang et al, 2014), it is not possible to attribute anomalies of all wavelengths to variations in relief of along the crust-mantle interface. Since our focus is on the small-scale density variations in the crust that cannot be ascribed to relief along the crust-mantle interface, our results are not sensitive to the choice of filter, provided that it is complementary to a stable crustal thickness model.…”

“…We use continuous density inversions (Li and Oldenburg, 1996;Liang et al, 2014) to model small-scale density variations in the lunar crust. We first test the model by applying it to the mantle uplift beneath the Freundlich-Sharonov impact basin.…”

3D joint inversion of gravity gradiometry and magnetic data in spherical coordinates with the cross-gradient constraint

“…There have been many efforts in this area by formulating the modelling and inversion in the spherical coordinates. In particular, Liang et al (2014) develop a method for 3D inversion of gravity data in spherical framework by extending the work of Li and Oldenburg (1996) in the Cartesian coordinates. Du et al (2013) develop a spherical magnetic inversion algorithm using a similar formulation.…”