Preferential Filtering and Gravity Anomaly Seperation Using Gravity

Introduction: Understanding the lunar gravity field can provide fundamental information about lunar internal structure, bulk composition, heat flow, and the duration of volcanism and tectonism. We aim to utilize the gravity field from the Gravity Recovery and Interior Laboratory (GRAIL) mission to reconstruct the history of lunar volcanic history. The high-resolution GRAIL gravity maps show that over 98% of the Moon’s gravity anomalies are associated with topography, and only 2% of the gravity anomalies represent subsurface structures [1]. The subsurface of the Moon has been highly affected by impacts that have not only changed the topography but have also produced impact melts that altered subsurface densities and porosities [1]. For this reason, even after the free-air correction, the Moon’s free-air anomaly map still mostly reflects high-frequency gravitational anomalies due to impacts [1]. In order to retrieve gravity anomalies that represent interior structure rather than surficial features, we performed a preferential filtering on the free-air anomaly map derived from GRAIL lunar gravity model GL0660A. We then constructed a 2D inversion model to visualize potential intrusive bodies in the lunar crust. Gravity Data: High-resolution measurements of the lunar gravity field were recently made by the GRAIL mission [1]. The available Radio Science Digital Map Product (RSDMAP) data products are derived from the GL0660A GRAIL lunar gravity model [1]. GL0660A is a degree and order 660 spherical harmonic model (truncated to degree and order 320) [1], and it is available from the Planetary Data System (PDS) LGRS RDR archive. The free-air gravity anomaly map has a resolution of 4 pixel/degree (~7.6 km/pixel on a reference sphere with semi-major-axis radius of 1,738.0 km) [1]. Each pixel gives free-air gravity anomaly in milligals (mGal). Preferential Filtering and Gravity Anomaly Separation: In the spatial domain, the total free-air gravity anomaly, gfa(x,y), is the sum of gravitational anomalies originating from the deep subsurface, gd(x,y), and gravitational anomalies originating from the shallow subsurface, gs(x,y) [2,3]: gfa(x,y) = gd(x,y) + gs(x,y) (1). Similarly, in the frequency domain, the Fourier power spectrum (P) of the total free-air gravity signal is the sum of the radially averaged power spectra of subsurface (Pi) components [4]: P = Pd1 + Pd2+...+ Pdi+Ps1+Ps2+...+Psi (2). The power spectrum of the gravity signal due to a subsurface layer is an exponential function [5,6]: P = se!!!! (3), where h is the depth to the subsurface layer, k is the angular, or radial, frequency of its power spectrum, and the constant s is the strength, or intensity, of the gravitational signal associated with that layer [5,6]. Combining Eqs. (2) and (3) yields [4]: P = s!e!! + s!e!! +⋯+ s!e!! (4). We use a preferential filtering method to eliminate high-frequency anomalies associated with surficial features. The preferential filtering method is similar to frequency‐domain Wiener filtering [7,9]. We use this method to filter the free-air gravity anomaly data at a specific bandwidth in order to selectively retrieve the gravity signal associated with a specific depth [7,8,9]. The Wiener preferential filtering operator we use is of the form [7,8]: W!"# = !! !!,!"# (5),