Abstract
AbstractAn 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.
Highlights
A fast and accurate forward modeling algorithm for computation of the gravity responses at a set of observation points for a given subsurface density distribution is required for many geophysical applications
An efficient forward modeling algorithm for calculation of gravitational fields in spherical coordinates is developed for 3D large-scale gravity inversion problems. 3D Gauss-Legendre quadrature (GLQ) is used to calculate the gravitational fields of mass distributions discretized into tesseroids
The numerical tests demonstrate that the computation time of the proposed algorithm is reduced by approximately two orders of magnitude, and the memory requirement is reduced by N' times compared with the traditional GLQ method, where N' is the number of the model elements in the longitudinal direction
Summary
A fast and accurate forward modeling algorithm for computation of the gravity responses at a set of observation points for a given subsurface density distribution is required for many geophysical applications. For computation of the gravity effect in a Cartesian coordinate system, subsurface mass distributions are typically discretized into right rectangular prisms since they provide a relatively simple and useful way to approximate complicated density sources without “holes” [Caratori Tontini et al, 2009]. Numerical integration methods have been used to solve this problem, including the 2D, 3D Gauss-Legendre quadrature (GLQ) [Asgharzadeh et al, 2007; Wild-Pfeiffer, 2008], the Taylor-series expansion [Deng et al, 2016; Grombein et al, 2013; Heck and Seitz, 2007] and approximation of tesseroids by other forms, which induce nearly the same gravity field, but which effect can be computed (e.g., Kaban et al, 2004, 2016a). We apply the algorithm to a 3D gravity inversion of the latest lunar gravity model GL1500E [Konopliv et al, 2014]
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