Deterministic, stochastic, hybrid and band-limited modifications of Hotine’s integral

Featherstone, Will

doi:10.1007/s00190-013-0612-9

Cited by 28 publications

(7 citation statements)

References 64 publications

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“…In theory, if Dg n max ð Þ has no errors, then the residual Dg À Dg n max ð Þ excludes all harmonics of degree n n max , and orthogonality would also allow the exclusion of these harmonics from S. Once the integration is limited to a neighborhood of (y,l,R), as it must be in practice, there are a number of ways to modify the kernel so as to minimize the resulting truncation error (Sjö berg, 1991, and references therein); for a review, see also Featherstone (2013). Even though the integral is a global integral, it can be truncated to a neighborhood of the computation point since Stokes' kernel attenuates rapidly with distance from its origin.…”

Section: Modelsmentioning

confidence: 99%

Potential Theory and the Static Gravity Field of the Earth

Jekeli

2015

Treatise on Geophysics

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Section: Modelsmentioning

confidence: 99%

Potential Theory and the Static Gravity Field of the Earth

Jekeli

2015

Treatise on Geophysics

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“…near here It is acknowledged that there exist other methods for the determination of spectral weights, relies on the stochastic properties of measurements or using deterministic weighting approaches. The interested reader should consult Featherstone (2013) for a comprehensive and complete overview of the various weighting approaches and the resulted kernel modifications using Hotine integral.…”

Section: Combination Of Egm and Terrestrial Measurementsmentioning

confidence: 99%

A study of different wavelength spectral components of the gravity field derived from various terrestrial data sets

2014

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In the general scheme of gravity field modelling long , medium and short wavelength constituents of the gravity field derived from e.g. geopotential model, terrestrial data and digital terrain model respectively, are routinely combined. In this study, spectral characteristics of terrestrial data sets are investigated. The estimation of spectral sensitivity of gravity related quantities such as gravity anomaly, vertical deflections and gravity gradients was accomplished through Fourier PSD and covariance analysis depending on the spatial distribution of data points. The information content of the estimated spectra were validated on global and local levels to access their further utilization. The spectra were compared to the 1D spectrum of the gravitational field derived from spherical harmonic coefficients using a high resolution global gravitational model as well as to an analytical approximation. Besides the frequency domain investigations the information content regarding the different wavelength structure comprised in terrestrial and EGM2008 model is investigated in the space domain based on covariance analysis. As a combined validation process the gravity degree variances were transformed to the necessary auto and cross covariance functions to predict geoid height from gravity anomaly, which ensures an independent validation process of the computed spectrum. Based on the spectral characteristics of terrestrial measurement spectral weights for spectral combination were derived involving global gravity field model, gravity and gravity gradient data in gravity field modelling. To determine the geoid in the whole spectral band the specific integral kernels in the spectral domain should be modified using the suggested spectral weights.

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“…Earth's total mass; a is the radius to which the harmonic coefficients, nm C , of a reference field refer; 3) and ( 4) , the integral in equation ( 2) may be truncated to a region, like South Korea. This also offers the ability to modify Stokes's function in order to further reduce the error committed in the truncation of the integral (Jekeli, 1981;Featherstone, 2013).…”

Section: Geoid Determinationmentioning

confidence: 99%

Geoid Determination in South Korea from a Combination of Terrestrial and Airborne Gravity Anomaly Data

Jekeli

Yang

Kwon

2013

Journal of the Korean Society of Surveying, Geodesy, Photogramm

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The determination of the geoid in South Korea is a national imperative for the modernization of height datums, specifically the orthometric height and the dynamic height, that are used to monitor hydrological systems and environments with accuracy and easy revision, if necessary. The geometric heights above a reference ellipsoid, routinely obtained by GPS, lead immediately to vertical control with respect to the geoid for hydrological purposes if the geoid height above the ellipsoid is known accurately. The geoid height is determined from gravimetric data, traditionally ground data, but in recent times also from airborne data. This paper illustrates the basic concepts for combining these two types of data and gives a preliminary performance assessment of either set or their combination for the determination of the geoid in South Korea. It is shown that the most critical aspect of the combination is the gravitational effect of the topographic masses above the geoid, which, if not properly taken into account, introduces a significant bias of about 8 mgal in the gravity anomalies, and which can lead to geoid height bias errors of up to 10 cm. It is further confirmed and concluded that achieving better than 5 cm precision in geoid heights from gravimetry remains a challenge that can be surmounted only with the proper combination of terrestrial and airborne data, thus realizing higher data resolution over most of South Korea than currently available solely from the airborne data.

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Deterministic, stochastic, hybrid and band-limited modifications of Hotine’s integral

Cited by 28 publications

References 64 publications

Potential Theory and the Static Gravity Field of the Earth

Potential Theory and the Static Gravity Field of the Earth

A study of different wavelength spectral components of the gravity field derived from various terrestrial data sets

Geoid Determination in South Korea from a Combination of Terrestrial and Airborne Gravity Anomaly Data

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