Gravity Field Modeling Using Tesseroids with Variable Density in the Vertical Direction

Lin, Miao; Denker, Heiner; Müller, Jürgen

doi:10.1007/s10712-020-09585-6

Cited by 20 publications

(25 citation statements)

References 56 publications

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“…This method subdivides a tesseroid into numerous smaller tesseroids, effectively minimizing the distance between adjacent GLQ nodes and hence improving accuracy (Z. Li et al, 2011;Lin et al, 2020;Uieda et al, 2016).…”

Section: Forward Methodsmentioning

confidence: 99%

“…When the distance between the computation point and the tesseroid is small, the integration is unstable, and adaptive subdivision is employed (Lin & Denker, 2019). This method subdivides a tesseroid into numerous smaller tesseroids, effectively minimizing the distance between adjacent GLQ nodes and hence improving accuracy (Z. Li et al., 2011; Lin et al., 2020; Uieda et al., 2016).…”

Section: Methodsmentioning

confidence: 99%

“…The gravitational attraction of marine sediments was calculated using tesseroids (Equations 1–5) with polynomial variable density in the vertical direction (Lin et al., 2020). Sediment thickness data were derived from the

{5}^{\prime }\times {5}^{\prime }

global marine sediment thickness data set GlobSedv3 (Straume et al., 2019), as shown in Figure 9d.…”

Section: The Scs Casesmentioning

confidence: 99%

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An Improved Method to Moho Depth Recovery From Gravity Disturbance and Its Application in the South China Sea

Chen

2022

JGR Solid Earth

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The Mohorovĩcíc discontinuity (Moho) is the boundary between the Earth's crust and upper mantle. It is critical to determine accurate Moho depth for gaining insight into the deep structure of the Earth, material and energy exchange processes, and geodynamic problems (Ebbing et al., 2018;Gozzard et al., 2019;Xu et al., 2017). Currently, the seismic and gravimetric methods are the primary geophysical methods for determining the depth of Moho. Seismic methods are quite expensive, and seismic stations are sparse in many regions with extreme conditions (e.g., ocean, plateau, and polar). In addition, seismic methods could be ineffective for recovering three-dimensional (3D) Moho topography across vast regions. Along with seismic surveys, gravity observations can also be used to estimate the Moho depth. In recent decades, as satellite-gravity missions, the Gravity Recovery and Climate Experiment (GRACE) (Tapley et al., 2004), the Gravity field and steady-state Ocean Circulation Explorer (GOCE) (Floberghagen et al., 2011), GRACE Follow-On (GRACE-FO) (Kornfeld et al., 2019), and satellite altimetry (Sandwell et al., 2014) have advanced, it is now possible to obtain high resolution and accurate gravity data with almost global and homogeneous coverage. At the moment, several global gravity field models (GGMs) have been constructed with high accuracy and resolution by combining terrestrial, altimetric, and satellite gravity data, such as EGM2008 (Pavlis et al., 2012), EIGEN-6C4 (Förste et al., 2014), and XGM2019e_2159 (Zingerle et al., 2020. These GGMs with maximum degree/order of 2190 (Spatial resolution ∼10 km) have been

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Section: Forward Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

{5}^{\prime }\times {5}^{\prime }

global marine sediment thickness data set GlobSedv3 (Straume et al., 2019), as shown in Figure 9d.…”

Section: The Scs Casesmentioning

confidence: 99%

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An Improved Method to Moho Depth Recovery From Gravity Disturbance and Its Application in the South China Sea

Chen

2022

JGR Solid Earth

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“…Only five components of the gravity gradient tensor are independent since the tensor components are symmetric and T rr + T θθ + T φφ = 0. As analytical solutions are unavailable, we use Gauss‐Legendre quadrature to evaluate the integrals in Equations 1–3 in the forward modeling (Asgharzadeh et al., 2007; Li et al., 2011; Lin et al., 2020; Uieda et al., 2016; Zhong et al., 2019).…”

Section: Methodsmentioning

confidence: 99%

Constrained Gravity Inversion With Adaptive Inversion Grid Refinement in Spherical Coordinates and Its Application to Mantle Structure Beneath Tibetan Plateau

et al. 2022

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We develop a novel gravity inversion algorithm in spherical coordinates based on adaptive inversion mesh refinement and multiphysical parameter constraints. The inversion mesh is discretized into tesseroids (spherical prisms) to take the curvature of the Earth into account. To reduce the number of unknowns and computational cost, the inversion mesh is adaptively refined according to the spatial variation of parameters at each iteration. Wavelet compression is used to further reduce the computational requirement. Besides, to alleviate the nonuniqueness of inversion, the algorithm is capable of incorporating a priori models from other geophysical methods via cross‐gradient coupling and/or direct parameter coupling. For cross‐gradient coupling, the vector product of spatial gradients of two model parameters is included in the objective function. For direct parameter coupling, an a priori model is converted to a density model using the relation between two physical properties, which is then used as the initial and reference model in the inversion. A synthetic example is presented to demonstrate the effectiveness of our inversion method. Finally, we invert the gravity data over the Tibetan Plateau to obtain the density variations in the upper mantle, with a global S wave tomographic model used as a constraint. The inversion model shows that the mantle lithosphere beneath the Himalayan collision zone varies from west to east. Low‐density anomalies are observed beneath the southern and the northern Tibetan Plateau, which are consistent with published low‐velocity anomalies and magmatism distributions, possibly indicating two asthenospheric upwellings.

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“…The density hypothesis and digital models (e.g., CRUST1.0 (Laske et al 2013) and UNB_TopoDens (Sheng et al 2019)) arbitrary-order polynomial density (Zhang and Jiang 2017), GV and GGT in the Fourier domain with the depth-dependent polynomial density (Wu and Chen 2016;Wu 2018), GGT with the depth-dependent density (Jiang et al 2018), and GP, GV, and GGT with the depth-dependent nth-order polynomial density (Karcol 2018;Fukushima 2018b). Similarly, the gravitational effects of a spherical shell were derived in the form of the polynomial density, i.e., the GP and GV with the radial fifth-order polynomial density (Karcol 2011) and the GP, GV, and GGT with the linear, quadratic, and cubic order polynomial density (Lin et al 2020). Regarding a tesseroid (Anderson 1976;Heck and Seitz 2007), its gravitational effects up to the GGT were derived in the form of the linear density in Fukushima (2018a), Lin and Denker (2019), and Soler et al (2019).…”

Section: Introductionmentioning

confidence: 99%

Evaluation of gravitational curvatures for a tesseroid and spherical shell with arbitrary-order polynomial density

Deng

2023

J Geod

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In recent years, there are research trends from constant to variable density and low-order to high-order gravitational potential gradients in gravity field modeling. Under the research circumstances, this paper focuses on the variable density model for gravitational curvatures (or gravity curvatures, third-order derivatives of gravitational potential) of a tesseroid and spherical shell in the spatial domain of gravity field modeling. In this contribution, the general formula of the gravitational curvatures of a tesseroid with arbitrary-order polynomial density is derived. The general expressions for gravitational effects up to the gravitational curvatures of a spherical shell with arbitrary-order polynomial density are derived when the computation point is located above, inside, and below the spherical shell. When the computation point is located above the spherical shell, the general expressions for the mass of a spherical shell and the relation between the radial gravitational effects up to arbitrary-order and the mass of a spherical shell with arbitrary-order polynomial density are derived. The influence of the computation point’s height and latitude on gravitational curvatures with the polynomial density up to fourth-order is numerically investigated using tesseroids to discretize a spherical shell. Numerical results reveal that the near-zone problem exists for the fourth-order polynomial density of the gravitational curvatures, i.e., relative errors in $$\log _{10}$$ log 10 scale of gravitational curvatures are large than 0 below the height of about 50 km by a grid size of $$15'\times 15'$$ 15 ′ × 15 ′ . The polar-singularity problem does not occur for the gravitational curvatures with polynomial density up to fourth-order because of the Cartesian integral kernels of the tesseroid. The density variation can be revealed in the absolute errors as the superposition effects of Laplace parameters of gravitational curvatures other than the relative errors. The derived expressions are examples of the high-order gravitational potential gradients of the mass body with variable density in the spatial domain, which will provide the theoretical basis for future applications of gravity field modeling in geodesy and geophysics.

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Gravity Field Modeling Using Tesseroids with Variable Density in the Vertical Direction

Cited by 20 publications

References 56 publications

An Improved Method to Moho Depth Recovery From Gravity Disturbance and Its Application in the South China Sea

An Improved Method to Moho Depth Recovery From Gravity Disturbance and Its Application in the South China Sea

Constrained Gravity Inversion With Adaptive Inversion Grid Refinement in Spherical Coordinates and Its Application to Mantle Structure Beneath Tibetan Plateau

Evaluation of gravitational curvatures for a tesseroid and spherical shell with arbitrary-order polynomial density

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