Downward continuation of gravitational field quantities to an irregular surface by spectral weighting

Pitoňák, Martin; Novák, Pavel; Eshagh, Mehdi; Tenzer, Robert; Šprlák, Michal

doi:10.1007/s00190-020-01384-6

Cited by 6 publications

(4 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…which is obtained from spherical harmonics T i;n derived by spherical analysis of the gradient group T i . Spectral weights a i;n are defined as follows (Eshagh 2012;Pitoňák et al 2020):…”

Section: Spectral Combinationmentioning

confidence: 99%

Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method

Pitoňák

Šprlák

Novák

2023

International Association of Geodesy Symposia

Self Cite

View full text Add to dashboard Cite

In this study, we apply a spectral combination method for estimation of height anomalies from gradients of the gravitational potential measured by satellites. The spectral combination method is used for solving over-determined problems within gravity field modelling when multiple types of gravity data are collected and used for recovery of unobservable quantities (typically the gravitational potential). The method applies solutions to geodetic boundary-value problems formulated in spherical approximation for gradients of the gravitational potential of up to the third order. Spectral forms of the solutions are combined using spectral weights defined under the condition of minimizing the global mean-square error of the estimators. Mathematical models are implemented and tested using gradients synthesized from a global geopotential model which allows for closed-loop testing of the estimators. The tests reveal among others that horizontal derivatives of the gravitational potential influence recovered values more than their vertical counterparts.

show abstract

Section: Spectral Combinationmentioning

confidence: 99%

Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method

Pitoňák

Šprlák

Novák

2023

International Association of Geodesy Symposia

Self Cite

View full text Add to dashboard Cite

show abstract

“…Applying the same optimization technique for calculating the convolution of functions on a uniform grid, which was used in [20], for a fast algorithm for solving the forward gravity problem, we can write (7) in the form:…”

Section: Definition Of the Operation Up(•)mentioning

confidence: 99%

“…In [7], the authors formulate a functional model for a spectral downward continuation of selected gravitational field quantities to an irregular topographic surface. This functional model is further generalized to allow for transformation between different types of gravitational field quantities.…”

Section: Introductionmentioning

confidence: 99%

Parallel Algorithms for Solving Inverse Gravimetry Problems: Application for Earth’s Crust Density Models Creation

2021

View full text Add to dashboard Cite

The paper describes a method of gravity data inversion, which is based on parallel algorithms. The choice of the density model of the initial approximation and the set on which the solution is sought guarantees the stability of the algorithms. We offer a new upward and downward continuation algorithm for separating the effects of shallow and deep sources. Using separated field of layers, the density distribution is restored in a form of 3D grid. We use the iterative parallel algorithms for the downward continuation and restoration of the density values (by solving the inverse linear gravity problem). The algorithms are based on the ideas of local minimization; they do not require a nonlinear minimization; they are easier to implement and have better stability. We also suggest an optimization of the gravity field calculation, which speeds up the inversion. A practical example of interpretation is presented for the gravity data of the Urals region, Russia.

show abstract

“…With the first measurement of radial gravitational curvatures (or gravity curvatures, GC, third-order derivatives of the gravitational potential) using the atom interferometry sensors in the laboratory condition (Rosi et al 2015), the subsequent study of the GC was focused on their theory and simulation applications in geodesy and geophysics (Šprlák and Novák 2015(Šprlák and Novák , 2017Hamáčková et al 2016;Sharifi et al 2017;Novák et al 2017;Pitoňák et al 2017Pitoňák et al , 2018Pitoňák et al , 2020Shen 2018a, b, 2019;Novák et al 2019;Du and Qiu 2019;Romeshkani et al 2020Romeshkani et al , 2021. The GC were more sensitive to field sources than the loworder gravitational effects (i.e., GP, GV, and GGT) (Heck 1984;Du and Qiu 2019).…”

Section: Introductionmentioning

confidence: 99%

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

Deng

2023

J Geod

View full text Add to dashboard Cite

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.

show abstract

Downward continuation of gravitational field quantities to an irregular surface by spectral weighting

Cited by 6 publications

References 52 publications

Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method

Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method

Parallel Algorithms for Solving Inverse Gravimetry Problems: Application for Earth’s Crust Density Models Creation

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

Contact Info

Product

Resources

About