Benchmark forward gravity schemes: the gravity field of a realistic lithosphere model WINTERC-G

Root, Bart; Sebera, Josef; Szwillus, Wolfgang; Thieulot, Cédric; Martinec, Zdenĕk; Fullea, Javier

doi:10.5194/se-13-849-2022

“…ASPECT is a code to model convection processes in the Earth's mantle and is used for studies on, for example, subduction zone dynamics, dynamic topography, gravity field anomalies, and mantle plume dynamics (e.g., Austermann et al., 2017; Dannberg & Gassmöller, 2018; Glerum et al., 2018; Root et al., 2022). In the following sections, we describe the constitutive equations used in ASPECT and how they are modified for the purpose of modeling solid Earth deformation.…”

Section: Numerical Modelmentioning

confidence: 99%

Modeling Viscoelastic Solid Earth Deformation Due To Ice Age and Contemporary Glacial Mass Changes in ASPECT

Weerdesteijn

¹

,

Naliboff

²

,

Conrad

³

et al. 2023

Geochem Geophys Geosyst

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Glacial isostatic adjustment (GIA) is the ongoing response of the solid Earth and the geoid to past and present changes in ice and ocean loading and produces solid Earth ground motion and mass redistributions. The solid Earth ground motion can be measured using GNSS (Global Navigation Satellite Systems) and the solid Earth mass displacements using ground-based gravimetry and satellite gravimetry, such as GRACE (Gravity Recovery and Climate Experiment). These geodetic measurements capture the ongoing response of the solid Earth to changes from both past (i.e., ice age) and contemporary ice load changes. Near areas of past and current ice cover, it is commonly thought that solid Earth ground motion results from a combination of (a) a viscous response to past ice load changes, and (b) an elastic response to contemporary ice load changes. Consequently, these

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3D large-scale forward modeling of gravitational fields using triangular spherical prisms with polynomial densities in depth

Ouyang,

Chen,

Wu

2024

J Geod

0

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To take the sphericity of the Earth into account, tesseroids are often utilized as grid elements in large-scale gravitational forward modeling. However, such elements in a latitude–longitude mesh suffer from degenerating into poorly shaped triangles near poles. Moreover, tesseroids have limited flexibility in describing laterally variable density distributions with irregular boundaries and also face difficulties in achieving completely equivalent division over a spherical surface that may be desired in a gravity inversion. We develop a new method based on triangular spherical prisms (TSPs) for 3D gravitational modeling in spherical coordinates. A TSP is defined by two spherical surfaces of triangular shape, with one of which being the radial projection of the other. Due to the spherical triangular shapes of the upper and lower surfaces, TSPs enjoy more advantages over tesseroids in describing mass density with different lateral resolutions. In addition, such an element also allows subdivisions with nearly equal weights in spherical coordinates. To calculate the gravitational effects of a TSP, we assume the density in each element to be polynomial along radial direction so as to accommodate a complex density environment. Then, we solve the Newton’s volume integral using a mixed Gaussian quadrature method, in which the surface integral over the spherical triangle is calculated using a triangle-based Gaussian quadrature rule via a radial projection that transforms the spherical triangles into linear ones. A 2D adaptive discretization strategy and an extension technique are also combined to improve the accuracy at observation points near the mass sources. The numerical experiments based on spherical shell models show that the proposed method achieves good accuracy from near surface to a satellite height in the case of TSPs with various dimensions and density variations. In comparison with the classical tesseroid-based method, the proposed algorithm enjoys better accuracy and much higher flexibility for density models with laterally irregular shapes. It shows that to achieve the same accuracy, the number of elements required by the proposed method is much less than that of the tesseroid-based method, which substantially speeds up the calculation by more than 2 orders. The application to the tessellated LITHO1.0 model further demonstrates its capability and practicability in realistic situations. The new method offers an attractive tool for gravity forward and inverse problems where the irregular grids are involved.

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Analytical Solutions for Gravitational Potential up to Its Third-order Derivatives of a Tesseroid, Spherical Zonal Band, and Spherical Shell

Deng

¹

,

Sneeuw

²

2023

Surv Geophys

3

0

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The spherical shell and spherical zonal band are two elemental geometries that are often used as benchmarks for gravity field modeling. When applying the spherical shell and spherical zonal band discretized into tesseroids, the errors may be reduced or cancelled for the superposition of the tesseroids due to the spherical symmetry of the spherical shell and spherical zonal band. In previous studies, this superposition error elimination effect (SEEE) of the spherical shell and spherical zonal band has not been taken seriously, and it needs to be investigated carefully. In this contribution, the analytical formulas of the signal of derivatives of the gravitational potential up to third order (e.g., V, $$V_{z}$$ V z , $$V_{zz}$$ V zz , $$V_{xx}$$ V xx , $$V_{yy}$$ V yy , $$V_{zzz}$$ V zzz , $$V_{xxz}$$ V xxz , and $$V_{yyz}$$ V yyz ) of a tesseroid are derived when the computation point is situated on the polar axis. In comparison with prior research, simpler analytical expressions of the gravitational effects of a spherical zonal band are derived from these novel expressions of a tesseroid. In the numerical experiments, the relative errors of the gravitational effects of the individual tesseroid are compared to those of the spherical zonal band and spherical shell not only with different 3D Gauss–Legendre quadrature orders ranging from (1,1,1) to (7,7,7) but also with different grid sizes (i.e., $$5^{\circ }\times 5^{\circ }$$ 5 ∘ × 5 ∘ , $$2^{\circ }\times 2^{\circ }$$ 2 ∘ × 2 ∘ , $$1^{\circ }\times 1^{\circ }$$ 1 ∘ × 1 ∘ , $$30^{\prime }\times 30^{\prime }$$ 30 ′ × 30 ′ , and $$15^{\prime }\times 15^{\prime }$$ 15 ′ × 15 ′ ) at a satellite altitude of 260 km. Numerical results reveal that the SEEE does not occur for the gravitational components V, $$V_{z}$$ V z , $$V_{zz}$$ V zz , and $$V_{zzz}$$ V zzz of a spherical zonal band discretized into tesseroids. The SEEE can be found for the $$V_{xx}$$ V xx and $$V_{yy}$$ V yy , whereas the superposition error effect exists for the $$V_{xxz}$$ V xxz and $$V_{yyz}$$ V yyz of a spherical zonal band discretized into tesseroids on the overall average. In most instances, the SEEE occurs for a spherical shell discretized into tesseroids. In summary, numerical experiments demonstrate the existence of the SEEE of a spherical zonal band and a spherical shell, and the analytical solutions for a tesseroid can benefit the investigation of the SEEE. The single tesseroid benchmark can be proposed in comparison to the spherical shell and spherical zonal band benchmarks in gravity field modeling based on these new analytical formulas of a tesseroid.

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Benchmark forward gravity schemes: the gravity field of a realistic lithosphere model WINTERC-G

Cited by 7 publications

References 51 publications

Modeling Viscoelastic Solid Earth Deformation Due To Ice Age and Contemporary Glacial Mass Changes in ASPECT

Modeling Viscoelastic Solid Earth Deformation Due To Ice Age and Contemporary Glacial Mass Changes in ASPECT

3D large-scale forward modeling of gravitational fields using triangular spherical prisms with polynomial densities in depth

Analytical Solutions for Gravitational Potential up to Its Third-order Derivatives of a Tesseroid, Spherical Zonal Band, and Spherical Shell

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