Geoid modeling with least squares modification of Hotine’s integral using gravity disturbances in Turkey

Mustafa Serkan Isik; Bihter Erol; Muhammed Raşit Çevikalp; Serdar Erol

doi:10.1007/s12145-022-00843-2

Geoid modeling with least squares modification of Hotine’s integral using gravity disturbances in Turkey

Mustafa Serkan Isik^*, Bihter Erol, Muhammed Raşit Çevikalp, Serdar Erol

^*Corresponding author for this work

Department of Geomatics Engineering

Istanbul Technical University

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

This study aims to investigate the regional gravimetric geoid modeling accuracy performance using least squares modification of Hotine’s integral with additive corrections (LSMHA) method in Turkey. The gravimetric geoid model is computed using 1' × 1' resolution gravity disturbances calculated from the complete Bouguer anomaly grid. It is validated in absolute and relative manners using the countrywide and locally distributed precise GNSS/leveling dataset having 100 and 301 benchmarks, respectively. The validation statistics are generated before and after removing the systematic differences between the geoid model and the local vertical datum. The obtained accuracy of the calculated geoid model with LSMHA is compared with the best-fitting geoid model computed via commonly used least squares modification of Stokes’s integral (LSMSA) method. The results reveal that the accuracy of the Hotine’s solution is 8.8 cm, compared to the 8.6 cm achieved from the Stokes counterpart in the whole country. Based on the local assessment in the western part of Turkey, the models show much better fitting performance at the local 301 GNSS/leveling benchmarks than the countrywide validation results. The accuracies of the Hotine’s and Stokes’s solutions at the local GNSS/leveling dataset are 4.4 and 4.3 cm, respectively. As a result, it is revealed that the LSMHA method using gravity disturbance gives a competitive result to the LSMSA method in regional gravimetric geoid modeling.

Original language	English
Pages (from-to)	1889-1904
Number of pages	16
Journal	Earth Science Informatics
Volume	15
Issue number	3
DOIs	https://doi.org/10.1007/s12145-022-00843-2
Publication status	Published - Sept 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Funding

The research presented in this article constitutes a part of the first author’s Ph.D. thesis study at the Graduate School of Istanbul Technical University (ITU). ITU General Research Project with Protocol No. MGA-2018-41592 is acknowledged for the TUTGA GNSS/leveling dataset. The IzJRS GNSS/leveling dataset was provided by ITU Geodesy Division. The gravity anomaly dataset was used from the ITU Gravity Research Group database (Erol et al. 2020 ; Işık et al. 2022). The figures in the article were drawn using Generic Mapping Tools (GMT) software (Wessel et al. 2019) and Python 3 programming language.

Funders	Funder number
ITU Geodesy Division	2019, 2022
Istanbul Teknik Üniversitesi	MGA-2018-41592

Keywords

Geoid model validation
GNSS/leveling data
Gravimetric geoid modeling
Gravity disturbance
Hotine’s integral
Least Squares Modification of Hotine’s Integral

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.1007/s12145-022-00843-2

Cite this

@article{142bd80c189b4f50bd657475a1d2c80d,

title = "Geoid modeling with least squares modification of Hotine{\textquoteright}s integral using gravity disturbances in Turkey",

abstract = "This study aims to investigate the regional gravimetric geoid modeling accuracy performance using least squares modification of Hotine{\textquoteright}s integral with additive corrections (LSMHA) method in Turkey. The gravimetric geoid model is computed using 1' × 1' resolution gravity disturbances calculated from the complete Bouguer anomaly grid. It is validated in absolute and relative manners using the countrywide and locally distributed precise GNSS/leveling dataset having 100 and 301 benchmarks, respectively. The validation statistics are generated before and after removing the systematic differences between the geoid model and the local vertical datum. The obtained accuracy of the calculated geoid model with LSMHA is compared with the best-fitting geoid model computed via commonly used least squares modification of Stokes{\textquoteright}s integral (LSMSA) method. The results reveal that the accuracy of the Hotine{\textquoteright}s solution is 8.8 cm, compared to the 8.6 cm achieved from the Stokes counterpart in the whole country. Based on the local assessment in the western part of Turkey, the models show much better fitting performance at the local 301 GNSS/leveling benchmarks than the countrywide validation results. The accuracies of the Hotine{\textquoteright}s and Stokes{\textquoteright}s solutions at the local GNSS/leveling dataset are 4.4 and 4.3 cm, respectively. As a result, it is revealed that the LSMHA method using gravity disturbance gives a competitive result to the LSMSA method in regional gravimetric geoid modeling.",

keywords = "Geoid model validation, GNSS/leveling data, Gravimetric geoid modeling, Gravity disturbance, Hotine{\textquoteright}s integral, Least Squares Modification of Hotine{\textquoteright}s Integral",

author = "Isik, {Mustafa Serkan} and Bihter Erol and {\c C}evikalp, {Muhammed Ra{\c s}it} and Serdar Erol",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2022",

month = sep,

doi = "10.1007/s12145-022-00843-2",

language = "English",

volume = "15",

pages = "1889--1904",

journal = "Earth Science Informatics",

issn = "1865-0473",

publisher = "Springer Verlag",

number = "3",

}

TY - JOUR

T1 - Geoid modeling with least squares modification of Hotine’s integral using gravity disturbances in Turkey

AU - Isik, Mustafa Serkan

AU - Erol, Bihter

AU - Çevikalp, Muhammed Raşit

AU - Erol, Serdar

PY - 2022/9

Y1 - 2022/9

N2 - This study aims to investigate the regional gravimetric geoid modeling accuracy performance using least squares modification of Hotine’s integral with additive corrections (LSMHA) method in Turkey. The gravimetric geoid model is computed using 1' × 1' resolution gravity disturbances calculated from the complete Bouguer anomaly grid. It is validated in absolute and relative manners using the countrywide and locally distributed precise GNSS/leveling dataset having 100 and 301 benchmarks, respectively. The validation statistics are generated before and after removing the systematic differences between the geoid model and the local vertical datum. The obtained accuracy of the calculated geoid model with LSMHA is compared with the best-fitting geoid model computed via commonly used least squares modification of Stokes’s integral (LSMSA) method. The results reveal that the accuracy of the Hotine’s solution is 8.8 cm, compared to the 8.6 cm achieved from the Stokes counterpart in the whole country. Based on the local assessment in the western part of Turkey, the models show much better fitting performance at the local 301 GNSS/leveling benchmarks than the countrywide validation results. The accuracies of the Hotine’s and Stokes’s solutions at the local GNSS/leveling dataset are 4.4 and 4.3 cm, respectively. As a result, it is revealed that the LSMHA method using gravity disturbance gives a competitive result to the LSMSA method in regional gravimetric geoid modeling.

AB - This study aims to investigate the regional gravimetric geoid modeling accuracy performance using least squares modification of Hotine’s integral with additive corrections (LSMHA) method in Turkey. The gravimetric geoid model is computed using 1' × 1' resolution gravity disturbances calculated from the complete Bouguer anomaly grid. It is validated in absolute and relative manners using the countrywide and locally distributed precise GNSS/leveling dataset having 100 and 301 benchmarks, respectively. The validation statistics are generated before and after removing the systematic differences between the geoid model and the local vertical datum. The obtained accuracy of the calculated geoid model with LSMHA is compared with the best-fitting geoid model computed via commonly used least squares modification of Stokes’s integral (LSMSA) method. The results reveal that the accuracy of the Hotine’s solution is 8.8 cm, compared to the 8.6 cm achieved from the Stokes counterpart in the whole country. Based on the local assessment in the western part of Turkey, the models show much better fitting performance at the local 301 GNSS/leveling benchmarks than the countrywide validation results. The accuracies of the Hotine’s and Stokes’s solutions at the local GNSS/leveling dataset are 4.4 and 4.3 cm, respectively. As a result, it is revealed that the LSMHA method using gravity disturbance gives a competitive result to the LSMSA method in regional gravimetric geoid modeling.

KW - Geoid model validation

KW - GNSS/leveling data

KW - Gravimetric geoid modeling

KW - Gravity disturbance

KW - Hotine’s integral

KW - Least Squares Modification of Hotine’s Integral

UR - http://www.scopus.com/inward/record.url?scp=85136233507&partnerID=8YFLogxK

U2 - 10.1007/s12145-022-00843-2

DO - 10.1007/s12145-022-00843-2

M3 - Article

AN - SCOPUS:85136233507

SN - 1865-0473

VL - 15

SP - 1889

EP - 1904

JO - Earth Science Informatics

JF - Earth Science Informatics

IS - 3

ER -

Geoid modeling with least squares modification of Hotine’s integral using gravity disturbances in Turkey

Abstract

Bibliographical note

Funding

Keywords

UN SDGs

Access to Document

Other files and links

Fingerprint

Cite this