Tesseroids: Forward-modeling gravitational fields in spherical coordinates

Uieda, Leonardo; Barbosa, Valéria C. F.; Braitenberg, Carla

doi:10.1190/geo2015-0204.1

Cited by 161 publications

(171 citation statements)

References 22 publications

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“…The commonly used Gaussian weights and nodes for the GLQ formulae up to 5 orders are given by Wild‐Pfeiffer (). As we can see from equation , the GLQ method approximates the 3‐D volume integrals by a weighted sum of the point mass effects

f ((),,, {\overset{truê}{r}}_{i}^{'}, {\overset{truê}{φ}}_{k}^{'}, {\overset{truê}{λ}}_{j}^{'})

(Uieda et al, ). In this paper, we employ two Gaussian nodes in each direction.…”

Section: Methodsmentioning

confidence: 99%

“…Li et al () designed an algorithm to enforce the criterion proposed by Ku (). Recently, Uieda et al () published an open‐source software package Tesseroids and a modified version of the adaptive discretization of Li et al (), providing a sufficiently accurate way to evaluate the Newton's integral by the 3‐D GLQ method. However, the computational efficiency of the forward modeling algorithm is still a severe issue in large‐scale 3‐D gravity inversion.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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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.

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f ((),,, {\overset{truê}{r}}_{i}^{'}, {\overset{truê}{φ}}_{k}^{'}, {\overset{truê}{λ}}_{j}^{'})

(Uieda et al, ). In this paper, we employ two Gaussian nodes in each direction.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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“…The VGG were computed in spherical coordinates, at a calculation height of 1 meter above the topography or sea level, on a regular grid of 0.05°, using the software Tesseroids (Uieda et al, ). This spherical approximation is valid in regions close to the equator, where the radius of the sphere (6,378,137 m) approximates the semimajor axis of the WGS84 reference ellipsoid (Li & Götze, ).…”

Section: Methodsmentioning

confidence: 99%

3‐D Modeling of Vertical Gravity Gradients and the Delimitation of Tectonic Boundaries: The Caribbean Oceanic Domain as a Case Study

Gómez-García

Meeßen

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et al. 2019

Geochem Geophys Geosyst

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Geophysical data acquisition in oceanic domains is challenging, implying measurements with low and/or nonhomogeneous spatial resolution. The evolution of satellite gravimetry and altimetry techniques allows testing 3‐D density models of the lithosphere, taking advantage of the high spatial resolution and homogeneous coverage of satellites. However, it is not trivial to discretise the source of the gravity field at different depths. Here, we propose a new method for inferring tectonic boundaries at the crustal level. As a novelty, instead of modeling the gravity anomalies and assuming a flat Earth approximation, we model the vertical gravity gradients (VGG) in spherical coordinates, which are especially sensitive to density contrasts in the upper layers of the Earth. To validate the methodology, the complex oceanic domain of the Caribbean region is studied, which includes different crustal domains with a tectonic history since Late Jurassic time. After defining a lithospheric starting model constrained by up‐to‐date geophysical data sets, we tested several a‐priory density distributions and selected the model with the minimum misfits with respect to the VGG calculated from the EIGEN‐6C4 data set. Additionally, the density of the crystalline crust was inferred by inverting the VGG field. Our methodology enabled us not only to refine, confirm, and/or propose tectonic boundaries in the study area but also to identify a new anomalous buoyant body, located in the South Lesser Antilles subduction zone, and high‐density bodies along the Greater, Lesser, and Leeward Antilles forearcs.

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“…Tesseroids software (Uieda et al, 2010) is used to compute the vertical gravity anomaly of our model in the same points, in which the free-air gravity values have been observed, using formulas from Nagy et al (2000). To compare modeled and observed fields, we must accomplish some elaborations: First of all, we have to integrate Figure 13.…”

Section: Forward Modeling and Comparison With Observed Datamentioning

confidence: 99%

Laser-scan and gravity joint investigation for subsurface cavity exploration — The Grotta Gigante benchmark

Pivetta

Braitenberg

2015

GEOPHYSICS

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We have studied a big karstic cave (Grotta Gigante) in northern Italy using an innovative combination of laser-scan and gravity data. We aimed to forward model the gravity anomaly due to the cavity, verify its compatibility with the Bouguer field, and identify the eventual presence of other sources of gravity anomalies. A sensitivity study was performed preliminarily to assess the minimum size of bodies that could be detected by the gravity surveys. The 3D density model of the Grotta Gigante was constructed using as a geometric constraint the laser-scan data set, which mapped the internal morphologies of the cave, and density measurements on collected rock samples. The laser point cloud was reduced in data density, filtered from the outliers, and subdivided into two surfaces representing the vault and the floor of the cave, to correctly define the prism model. Then, a mean density value, obtained from laboratory measurements, was assigned to the prisms. We computed the gravity effect of the model in the same points at which the gravity field had been measured. Excellent correlation was found for the cavity; some gravity anomalies were revealed in the surrounding area of the Grotta Gigante that could be effected by other underground karstic morphologies. We attempted to estimate the probable size and depth of the causative bodies, compatible with the geologic environment. This site testified to the goodness of gravity methods for the exploration of such structures, that is, particularly important for risk assessment in a karstic area. The cave itself, the biggest tourist cave worldwide, represents an upper limit for expected gravity signals. The combination of exact knowledge of the causative body and the related gravity anomalies composed a unique data set (that we released to the public, as a benchmark), useful for testing inversion and forward model gravity algorithms.

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Tesseroids: Forward-modeling gravitational fields in spherical coordinates

Cited by 161 publications

References 22 publications

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

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

3‐D Modeling of Vertical Gravity Gradients and the Delimitation of Tectonic Boundaries: The Caribbean Oceanic Domain as a Case Study

Laser-scan and gravity joint investigation for subsurface cavity exploration — The Grotta Gigante benchmark

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