On Solving the Forward Problem of Gravimetry in Curvilinear and Cartesian Coordinates: Krasovskii’s Ellipsoid and Plane Modeling

Мартышко, П. С.; Ladovskij, I. V.; Бызов, Д. Д.; Chernoskutov, A. I.

doi:10.1134/s1069351318040079

Cited by 8 publications

(6 citation statements)

References 6 publications

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“…Let us choose some discretization of D = N i=1 D i and approximate the volume of an element of the partition D i by a polyhedron Di , obtaining an approximated model. Now, we can apply the previously proposed [10] algorithm to solve the forward gravity problem. Let us represent the basic steps of the algorithm and for the first time present the derivation of the closed-form formula for the gravitational field of a polyhedron.…”

Section: The Forward Gravity Problemmentioning

confidence: 99%

“…The source codes of the program, distribution kit, test model, and user instructions are publicly available at https://github.com/AlexIII/GRAFEN (accessed on 10 March 2024) under a free MIT license. The convergence, speed, and errors of computing the gravity field by using the proposed method were tested by comparison with the five-point Gauss-Legendre (GL) numerical integration method [10] for various configurations of partitions of the "ellipsoidal" model of the Earth's crust. The testing showed that the increase in computation speed by the proposed method is tens of times (compared to the Gauss-Legendre method), with an equivalent error rate.…”

Section: The Forward Gravity Problemmentioning

confidence: 99%

“…It allows one to search for a solution to the inverse problem for high-resolution density models (with the number of partition elements of the order of 10 8 ) within an acceptable time. Previously, the authors developed such a software implementation based on the original algorithm [10] for an ellipsoidal model of a section of the Earth's crust and demonstrated its speed and accuracy in comparison to Gauss-Legendre cubature formulas. Then, the algorithm was generalized to solve a forward problem on the topography (given by a height map) [2].…”

Section: Inverse Problem Of Gravimetrymentioning

confidence: 99%

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Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study

Byzov,

Martyshko

2024

Mathematics

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In this paper, the derivation of a concise closed form for the gravitational field of a polyhedron is presented. This formula forms the basis of the algorithm for calculating the gravitational field of an arbitrary shape body with high accuracy. Based on this algorithm, a method for gravity data inversion (creating density models of the Earth’s crust) has been developed. The algorithm can accept either regular or irregular polyhedron discretization for density model creation. The models are approximated with dense irregular grids, elements of which are polyhedrons. When performing gravity data inversion, we face three problems: topography with large amplitude, the sphericity of the planet, and a long computation time because of the large amount of data. In our previous works, we have already considered those problems separately but without explaining the details of the computation of the closed-form solution for a polyhedron. In this paper, we present for the first time a performance-effective numerical method for the inversion of gravity data based on topography. The method is based on closed-form expression for the gravity field of a spherical density model of the Earth’s crust with the upper topography layer, and provides great accuracy and speed of calculation. There are no restrictions on the model's geometry or gravity data grid. As a case study, a spherical density model of the Earth’s crust of the Urals is created.

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Section: The Forward Gravity Problemmentioning

confidence: 99%

Section: The Forward Gravity Problemmentioning

confidence: 99%

Section: Inverse Problem Of Gravimetrymentioning

confidence: 99%

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Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study

Byzov,

Martyshko

2024

Mathematics

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“…Let us choose some discretization of D = N i=1 D i . Now we can approximate the volume of an element of the partition D i by a polyhedron Di , obtaining an approximated model, to which we can apply the previously proposed [Martyshko et al, 2018b] algorithm for solving the direct gravity problem. Here we will reproduce the basic steps of the algorithm.…”

Section: Direct Gravity Calculation For a Spherical Density Model Wit...mentioning

confidence: 99%

“…When a satisfactory solution in the "flat" framework is found, it can be used as an initial approximation for the original inverse problem (taking into account the topography and sphericity). This step can be performed with transformation of the "flat" geometry into spherical [Martyshko et al, 2018b]. Thus, we will consider the problem of refinement of the already existing model, which includes all the necessary a priori data, to fit the target field.…”

Section: Inverse Linear Problem For the Gravity Fieldmentioning

confidence: 99%

Computationally Effective Gravity Inversion Allows for High-Resolution Regional Density Modeling of Earth's Crust with the Inclusion of the Topography Layer

Martyshko

Бызов

Chernoskutov

2022

Russian Journal of Earth Sciences

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The problem of inverting measured gravity data for large regions is of a great importance for planetary structure studies. Unfortunately, the usual methods of local gravity field inversion do not scale up well. There are three primary factors that start to play significant role: topography or terrain surface with large height differences, spherical geometry of the planet, and high computational complexity. In our previous work we were separately considering each of those problems in detail. In this paper however, we will address those issues simultaneously, offering a complete and computationally effective method of recovering spherical density model of Earth's crust with the upper topography layer. The method utilizes a closed form expression for the discretized model's gravity field which allows for great accuracy and speed without enforcing restrictions on model geometry or gravity field data grid. Inversion process is based on the conjugate gradient method. An example of inversion for a synthetic regional model is presented.

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Numerical solution of the forward magnetic field problem for models with irregular polyhedron discretization taking into account the "demagnetization effect"

Мартышко

Бызов

Chernoskutov

2020

International Conference of Numerical Analysis and Applied Mathematics Icnaam 2019

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On Solving the Forward Problem of Gravimetry in Curvilinear and Cartesian Coordinates: Krasovskii’s Ellipsoid and Plane Modeling

Cited by 8 publications

References 6 publications

Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study

Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study

Computationally Effective Gravity Inversion Allows for High-Resolution Regional Density Modeling of Earth's Crust with the Inclusion of the Topography Layer

Numerical solution of the forward magnetic field problem for models with irregular polyhedron discretization taking into account the "demagnetization effect"

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