A numerical study on the integration radius separating convergent and divergent spherical harmonic series of topography-implied gravity

Bucha, Blažej; Kühn, Michael

doi:10.1007/s00190-020-01442-z

J Geod

2020

DOI: 10.1007/s00190-020-01442-z

|View full text |Cite

A numerical study on the integration radius separating convergent and divergent spherical harmonic series of topography-implied gravity

Blažej Bucha

Michael Kühn

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

2024

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Fast Computation of Terrain-Induced Gravitational and Magnetic Effects on Arbitrary Undulating Surfaces

Chen

2023

Surv Geophys

View full text Add to dashboard Cite

Based on a brief review of forward algorithms for the computation of topographic gravitational and magnetic effects, including spatial, spectral and hybrid-domain algorithms working in either Cartesian or spherical coordinate systems, we introduce a new algorithm, namely the CP-FFT algorithm, for fast computation of terrain-induced gravitational and magnetic effects on arbitrary undulating surfaces. The CP-FFT algorithm, working in the hybrid spatial-spectral domain, is based on a combination of CANDECOMP/PARAFAC (CP) tensor decomposition of gravitational integral kernels and 2D Fast Fourier Transform (FFT) evaluation of discrete convolutions. By replacing the binomial expansion in classical FFT-based terrain correction algorithms using CP decomposition, convergence of the outer-zone computation can be achieved with significantly reduced inner-zone radius. Additionally, a Gaussian quadrature mass line model is introduced to accelerate the computation of the inner zone effect. We validate our algorithm by computing the gravitational potential, the gravitational vector, the gravity gradient tensor, and magnetic fields caused by densely-sampled topographic and bathymetric digital elevation models of selected mountainous areas around the globe. Both constant and variable density/magnetization models, with computation surfaces on, above and below the topography are considered. Comparisons between our new method and space-domain rigorous solutions show that with modeling errors well below existing instrumentation error levels, the calculation speed is accelerated thousands of times in all numerical tests. We release a set of open-source code written in MATLAB language to meet the needs of geodesists and geophysicists in related fields to carry out more efficiently topographic modeling in Cartesian coordinates under planar approximation.

show abstract

Fast Computation of Terrain-Induced Gravitational and Magnetic Effects on Arbitrary Undulating Surfaces

Chen

2023

Surv Geophys

View full text Add to dashboard Cite

show abstract

On the topographic bias by harmonic continuation of the geopotential for a spherical sea-level approximation

Sjöberg

2024

Journal of Geodetic Science

View full text Add to dashboard Cite

Topography is a problem in geoid determination by the Stokes formula, a high degree Earth Gravitational Model (EGM), or for a combination thereof. Herein, we consider this problem in analytical/harmonic downward continuation of the external potential at point P to a geocentric spherical sea level approximation in geoid determination as well as to a sphere through the footpoint at the topography of the normal through P. Decomposing the topographic bias into a Bouguer shell component and a terrain component, we derive these components. It is shown that there is no terrain bias outside a spherical dome of base radius equal to the height H P of P above the sphere, and the height of the dome is about 0.4 × H P . In the case of dealing with an EGM, utilizing Molodensky truncation coefficients is one way to cope with the bias.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

A numerical study on the integration radius separating convergent and divergent spherical harmonic series of topography-implied gravity

Cited by 2 publications

References 49 publications

Fast Computation of Terrain-Induced Gravitational and Magnetic Effects on Arbitrary Undulating Surfaces

Fast Computation of Terrain-Induced Gravitational and Magnetic Effects on Arbitrary Undulating Surfaces

On the topographic bias by harmonic continuation of the geopotential for a spherical sea-level approximation

Contact Info

Product

Resources

About