What is it about?
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.
Featured Image
Why is it important?
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.
Perspectives
The conducted tests show that it is now possible to interpret observed gravity data without first calculating corrections for the topography, using anomalies in free air to create the spherical density models. This paper provides an example of such an interpretation based on parallel algorithms developed by the authors and implemented using distributed computing on graphic accelerators of personal computers. A solution to a practical three-dimensional inverse problem of gravimetry for the Urals region has been obtained, taking the topography into account; a digital density model of the Earth’s crust has been created using the observed gravity data. The effectiveness of the interpretation method developed by the authors does not depend on the regularity of either the density model grids or the calculated field. In this case, the parameters of the density model, limited by surface topography, are determined. This approach will significantly improve the accuracy of determining model parameters.
Prof Petr Sergeyevich Martyshko
Institute of Geophysics UB RAS
Read the Original
This page is a summary of: Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study, Mathematics, March 2024, MDPI AG,
DOI: 10.3390/math12060837.
You can read the full text:
Contributors
The following have contributed to this page
