Efficient 3‐D Large‐Scale Forward Modeling and Inversion of Gravitational Fields in Spherical Coordinates With Application to Lunar Mascons

Abstract

An efficient forward modeling algorithm for calculation of gravitational fields in spherical coordinates is developed for 3-D large-scale gravity inversion problems. The 3-D Gauss-Legendre quadrature (GLQ) is used to calculate the gravitational fields of mass distributions discretized into tesseroids. Equivalence relations in the kernel matrix of the forward modeling are exploited to decrease storage and computation time. The numerical tests demonstrate that the computation time of the proposed algorithm is reduced by approximately 2 orders of magnitude, and the memory requirement is reduced by N′ λ times compared with the traditional GLQ method, where N′ λ is the number of the model elements in the longitudinal direction. These significant improvements in computational efficiency and storage make it possible to calculate and store the dense Jacobian matrix in 3-D large-scale gravity inversions. The equivalence relations can be applied to the Taylor series method or combined with the adaptive discretization to ensure high accuracy. To further illustrate the capability of the algorithm, we present a regional synthetic example. The inverted results show density distributions consistent with the actual model. The computation took about 6.3 hr and 0.88 GB of memory compared with about a dozen days and 245.86 GB for the traditional 3-D GLQ method. Finally, the proposed algorithm is applied to the gravity field derived from the latest lunar gravity model GL1500E. Three-dimensional density distributions of the Imbrium and Serenitatis basins are obtained, and high-density bodies are found at the depths 10-60 km, likely indicating a significant uplift of the high-density mantle beneath the two mascon basins.

3‐D Density Structure of the Lunar Mascon Basins Revealed by a High‐Efficient Gravity Inversion of the GRAIL Data

“…In Table 1, the absolute computation time for calculating the kernel and the product between the kernel and the density vector is demonstrated separately. Comparing the proposed method with the method of Zhao et al (2019), the time for kernel computing is almost equal with a negligible difference. The computational efficiency in the kernel-vector product is increased by about 20 times in this model compared with Zhao et al (2019).…”

“…Furthermore, the computational efficiency of the 3-D GLQ method with adaptive discretization is relatively low, especially for a high-resolution (fine) large-scale 3-D gravity inversion. Zhao et al (2019) proposed an equivalent storage strategy that increases the computational efficiency by approximately two orders of magnitude and largely decreases the memory requirement, which also provides an elegant solution to storing a dense Jacobian matrix in fine 3D gravity inversions.…”

Moho Beneath Tibet Based on a Joint Analysis of Gravity and Seismic Data

“…The EIGEN-6C4 model (Förste et al, 2014, http://icgem.gfz-potsdam.de/tom_longtime) to degree and order 720 is used to compute the free-air gravity disturbances at the elevation 10 km refer to the GRS80 reference ellipsoid (Figure 5b). The gravity effects (Figure 5c) of the topography (Figure 5a) derived from ETOPO1 (Amante & Eakins, 2009) are calculated globally (Zhao et al, 2019) with the correction density of 2,670 kg/m 3 . The Bouguer gravity disturbances (Figure 5d) are obtained by removing the gravity effect of the topography from the free-air gravity disturbances.…”

Usporedba različitih pristupa Bouguer-ove redukcije na temelju satelitskih gravimetrijskih podataka

“…According to the above introduction to the development of the Bouguer reduction method, the reduction approach can be divided into two categories based on the coordinate system, namely, the Cartesian coordinate system (comprising two cases, that is, whether the Earth's curvature is considered) and the spherical coordinate system. The Bouguer gravity reduction methods described above are widely used in the correction of satellite gravity data (Vaish and Pal, 2015;Pal and Majumdar, 2015;Tamay et al, 2018;Almalki and Mahmud, 2018;Maurya et al, 2017;Mahatsente et al, 2018;Peters et al, 2018;Zhu and Li, 2018;Chen et al, 2018;Sobh et al, 2018;Deng and Shen, 2019;Zhao et al, 2019). Most relevant satellite gravity data studies select one of these two reduction approaches for practical applications.…”