Least-Squares Collocation

Tscherning, C. C.

doi:10.1007/978-3-319-02370-0_51-1

Cited by 8 publications

(7 citation statements)

References 6 publications

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“…where R is mean radius of the Earth, 𝜓 is spherical distance between points P and Q, 𝑟 and 𝑟 are spherical coordinates of points P and Q respectively, 𝑃 are Legendre polynomials, 𝑘 are expansion coefficients. To determine the coefficients 𝑘 the well-known Cherning-Rapp model was used (Tscherning, 2015):…”

Section: Methodsmentioning

confidence: 99%

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Gravimetric geoid model determination of Central Ukraine area using combination of LSC and truncated SHA methods

Dzhuman¹

2023

Acta Geodynamica Et Geomaterialia

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In this paper we investigate the possibility of combining least squares collocation (LSC) and spherical functions (spherical harmonic analysis SHA) with real eigenvalues methods for calculating the geoid model. A comparison of local analytical covariance functions calculated on the basis of Legendre polynomials and polynomials with real eigenvalues is carried out. We computed geoid model for the region of Central Ukraine using the proposed method and assessed its accuracy. The input data for the computation of model are gravity anomalies, obtained after filtering the results of digitization of gravimetric maps by the 3σ criterion, functionals of the Earth's gravity field from the global gravity model EGM2008 and GNSS leveling data. The standard deviation was found between the model values of the geoid height and the values, obtained from GNSS leveling at the points of the state geodetic network. The accuracy of the geoid model obtained using the proposed method is approximately 2 cm. Such accuracy is primarily conditioned by the quality of initial data. To increase the accuracy of the model it is necessary to carry out a complex of gravimetric works in the studied region.

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Section: Methodsmentioning

confidence: 99%

“…On a regional scale other methods are used to solve similar problems based on model and operational approaches of physical geodesy. Such methods include least square collocation (LSC) (Tscherning, 2015), calculation of geoid heights based on the Stokes formula (Sideris, 2005), use of radial basis functions (Marchenko et al, 2015) etc.…”

Section: Introductionmentioning

confidence: 99%

Gravimetric geoid model determination of Central Ukraine area using combination of LSC and truncated SHA methods

Dzhuman¹

2023

Acta Geodynamica Et Geomaterialia

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“…The comparison was performed by first removing the long-wavelength gravity anomaly component in terrestrial gravity measurements using the GGM. Subsequently, a residual surface was computed by applying a leastsquares collocation (LSC; Tscherning, 2015) on the residual gravity anomaly data. The residual surface was then upward continued to the mean flight altitude using 2D-FFT as (Klingel et al, 2003;Hwang et al, 2007):…”

Section: Comparison With Terrestrial Gravity Datamentioning

confidence: 99%

“…Using this approach, we first removed the longwavelength and short-wavelength part from the gravity data observation using predicted gravity model from global/satellite gravity model and topography variation, respectively. Afterwards, the residual gravity anomalies were used to estimate the residual geoid model using proper Stokes' integration methods, e.g., Fast Fourier Transform (FFT;Schwarz et al, 1990) or Least Square Collocation (LSC; Tscherning, 2015). Completing the RCR technique, both long and shortwavelength geoid signals were restored to the geoid model.…”

Section: Introductionmentioning

confidence: 99%

Determination of gravity anomalies in Java, Indonesia, from airborne gravity survey

Bramanto¹,

Prijatna²,

Pahlevi³

et al. 2021

Terr. Atmos. Ocean. Sci.

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The Geospatial Information Agency of Indonesia (BIG) recently carried out an airborne gravity survey mission to support a reliable Indonesian geoid model. The gravity observations covered all the main islands of Indonesia. This paper presents a state-of-the-art for gravity anomalies derivation using airborne gravity mission in Java, Indonesia. The common gravity corrections for deriving the scalar free-air gravity anomalies along the flight trajectory had been estimated using GNSS-derived positions. The corrected data were then filtered using the FIR method in which the cut-off frequency had been predetermined by considering aircraft altitude, geological setting, and instrument's accuracy.To assess the airborne gravity results, we compared them with the upward continued terrestrial gravity measurements. In addition, we performed crossover analysis and adjusted the estimated biases to the airborne gravity measurements. The accuracy of adjusted airborne gravity anomaly was estimated to 3.37 mGal. In conclusion, the airborne gravity mission provided valuable data needed for further geodesy and geophysics applications.

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“…This approach has been used in the determination of the regional geoid models in many studies so far, and it has yield accurate results in these studies (see [3,7,). In addition to the KTH method, there are also different gravimetric geoid determination algorithms used for regional gravimetric geoid modeling in the literature (see [32][33][34][35][36][37]).…”

Section: Introductionmentioning

confidence: 99%

Assessments of Gravity Data Gridding Using Various Interpolation Approaches for High-Resolution Geoid Computations

Karaca,

Erol,

Erol

2024

Geosciences

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This article investigates the role of different approaches and interpolation methods in gridding terrestrial gravity anomalies. In this regard, first of all, simple and complete Bouguer anomalies are considered in gravity data gridding. In the comparison results of gridding these two Bouguer anomaly datasets, the effect of the high-frequency contribution of topographic gravitation (by means of the terrain correction) is clarified. After that, the role of the used interpolation algorithm on the resulting grid of mean gravity anomalies and hence on the geoid modeling accuracy is inspected. For this purpose, four different interpolation methods including geostatistical Kriging, nearest neighbor, inverse distance to a power (IDP), and artificial neural networks (ANNs) are applied. Here, the IDP and nearest neighbor methods represent simple-structured algorithms among the interpolation methods tested in this study. The ANN method, on the other hand, is preferred as a complex, optimization-based soft computing method that has been applied in recent years. In addition, the geostatistical Kriging method is one of the conventional methods that is mostly applied for gridding gravity data in geodesy and geophysics. The calculated gravity anomalies in grids are employed in high-resolution geoid model computations using the least squares modifications of Stokes formula with additive corrections (LSMSA) technique. The investigations are carried out using the test datasets of Auvergne, France that are provided by the International Service for the Geoid for scientific research. It is concluded that the interpolation algorithms affect the gravity gridding results and hence the geoid model determination. The ANN method does not provide superior results compared to the conventional algorithms in gravity gridding. The geoid model with 4.1 cm accuracy is computed in the test area.

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Least-Squares Collocation

Cited by 8 publications

References 6 publications

Gravimetric geoid model determination of Central Ukraine area using combination of LSC and truncated SHA methods

Gravimetric geoid model determination of Central Ukraine area using combination of LSC and truncated SHA methods

Determination of gravity anomalies in Java, Indonesia, from airborne gravity survey

Assessments of Gravity Data Gridding Using Various Interpolation Approaches for High-Resolution Geoid Computations

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