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An optimal approach for the development of precise regional geoid in Pakistan through a comparative study with least square collocation and FFT techniques

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Abstract

This study attempts to develop a strategy of data management, processing, evaluation, and analysis that best suits for the regional gravimetric geoid in Pakistan where gravimetric data is sparse. A high-precision gravimetric geoid has been developed covering the Salt Range and Kohat-Potowar Plateau along with Punjab and KPK plain area south of it bounded by latitude 30–33N and longitude 70–73E and with random data distribution. The study also covers the analysis and comparison of observed gravity data with GETECH Bouguer anomalies. The gravity prediction error study was carried out using least square collocation (LSC) at the data gaps and at GETECH locations for data quality analysis. Covariance analysis of both datasets using LSC was made for error study and compared with covariance function by FFT technique. Variety of datasets, e.g., observed gravity; GETECH Bouguer anomalies, SRTM30 digital elevation model, and observed leveling data were combined with global geopotential model through LSC and FFT techniques. The geoid model was computed by applying high-frequency corrections from observed gravity and topography to the Earth Gravity Model 1996 global geopotential model in a remove-restore procedure. The elevation grids with 30″ 5′ and 18′ resolutions gave a best possible statistics in combination with the EGM96 reference field to order and degree 360. The results of bias parameter N o estimation and adjustment were compared with draping of GPS/leveling height anomalies for final fitting of the geoid; LSC- and FFT-derived height anomalies were found to be comparable after the N o adjustment and draping with respect to GPS/leveling.

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References

  • Arabelos D, Tscherning CC (2007) On a strategy for the use of GOCE gradiometer data for the development of a geopotential model. Proceedings of “The 3rd International GOCE User Workshop”, ESA-ESRIN, Frascati, Italy, 6–8 November 2006 (ESA SP-627, January 2007)

  • Colombo OL (1979) Optimal estimation from data regularly sampled on a sphere with applications in geodesy. Reports of the Department of Geodetic Science, Report No. 291, The Ohio State University, Columbus, Ohio, USA

  • Forsberg R (1984) Local covariance functions and density distributions. Report no.356, Deptt. of Geodetic Science. Ohio State University, Columbus, Ohio

    Google Scholar 

  • Forsberg R, Tscherning C (1997) Topographic effects in gravity field modeling for bvp. In Sanso, F. and Rummel, R., Editors, geodetic Boundary value Problems in view of the cm geoid, vol. 65, pages 241–272. Springer, lecture Notes in Earth Sciences

  • GETECH (1995) South East Asia Gravity Project report, 1995

  • Goad CC, Tscherning CC, Chin MM (1984) Gravity empirical covariance values for the continental United States. J Geophys Res 89(B9):7962–7968

    Article  Google Scholar 

  • Gravsoft (2005) A system for geodetic gravity field modelling. C.C. Tscherning, Department of Geophysics, Juliane Maries Vej 30, DK-2100 Copenhagen N. R. Forsberg and P. Knudsen, Kort og Matrikelstyrelsen, Rentemestervej-8, DK-2400 Copenhagen NV

  • Heiskanen WA, Moritz H (1967) Physical geodesy. Freeman, San Francisco

    Google Scholar 

  • Heitz S, Tscherning CC (1972) Comparison of two Methods of Astro-Gravimetric Geoid Determination based on Least Squares Prediction and Collocation. Tellus, 24:271–276

  • Howe E, Stenseng LCC, Tscherning CC (2003) Analysis of one month of CHAMP state vector and accelerometer data for the recovery of the gravity potential. Adv Geosci 1:1–4

  • Kearsley AHW (1986) Data requirements for determining precise relative geoid heights from gravimetry. J Geophys Res 91:9193–9201

  • Kiamehr R (2006) A strategy for determining the regional geoid by combining limited ground data with satellite-based global geopotential and topographical models: a case study of Iran. J Geod 79(10/11):602–612

    Article  Google Scholar 

  • Lemoine FG, Smith DE, Smith R, Kunz L, Pavlis NK, Klosko SM, Chinn DS, Torrence MH, Williamson RG, Cox CM, Rachlin KE, Wang YM, Pavlis EC, Kenyon SC, Salman R, Trimmer R, Rapp RH, Nerem RS (1997) The development of the NASA, GSFC and NIMA joint geopotential model. In: Segawa, Fugimoto, Okubo (eds) IAG Synzposza 117: Gravzly, Geozd, and Marzne Geodesy. Springer, Berlin, pp 461–470

    Google Scholar 

  • Molodensky MS, Eremeev VF, Yurkina MI (1962) Methods for the study of the external gravitational field and figure of the Earth. Israeli Program for Scientific Translations, Jerusalem

    Google Scholar 

  • Moritz H (1973) Stepwise and sequential collocation. Department of Geodetic Science, Reports of the No. 203, The Ohio State University, Columbus, USA

  • Moritz H (1980) Advance Physical Geodesy. H Whichman Verlag Karlsruhe

  • Nash RA, Jordan SK (1978) Statistical geodesy: an engineering perspective. Proc. IEEE 66 vol.5 pp. 532–550

  • Omang OCD, Forsberg R (2000) How to handle topography in practical geoid determination: three examples. J Geod 74:458–466

    Article  Google Scholar 

  • Rapp RH (1997) Use of potential coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly/geoid undulation difference. J Geod 71:282–289

    Article  Google Scholar 

  • Rapp RH, Rummel R (1975) Methods for the computation of detailed geoids and their accuracy. Report No. 233. Department of Geodetic Science and Surveying, Ohio State University, Columbus, Ohio

    Google Scholar 

  • Sadiq M, Tscherning CC, Ahmad Z (2009b) An estimation of the height system bias parameter No using least squares colloca-tion from observed gravity and GPS/leveling data. Stud Geophys Geodaet

  • Sadiq M, Ahamad Z, Akhter G (2009b) A study on the evaluation of the geoid-quasigeoid separation term over Pakistan with solution of 1st and 2nd order height terms. Earth Planets Space 61:1–9

    Article  Google Scholar 

  • Sansό F, Tscherning CC (2003) Fast spherical collocation: theory and examples. J Geodesy 77:101–112. doi:10.1007/s00190-002-0310-5

  • Sideris MG, Forsberg R (1990) Review of geoid prediction methods in mountainous regions. Determination of the geoid, present and future. Symposium No. 106 Milan June 11–13 1990

  • Sideris MG, She BB (1995) A new high resolution geoids of Canada and part of the US by the 1D-FFT method. B Geod 69(2):92–108

  • Sjoberg LE (1995) On the quasigeoid to geoid separation, manuscripta geodaetica 20:182–192

  • Strang van Hees G (1990) Stoke’s formula using fast Fourier techniques. Manuscripta Geodaetica, vol. 15, pp. 235–239

  • Surfer-7-03 (2000) Surface mapping system, Golden Software Inc, 809 14th Street Golden Colorado, 80401–1866. Sr # GS-99999

  • Tscherning CC (1994) Geoid determination by least square collocation using GRAVSOFT. Lecture notes “Int. School of the determination and use of the geoid”, Milano, Oct., 1994, pp. 135–164, published by International Geoid Service, 1994

  • Tscherning, C., & Rapp, R. H. (1974). Closed covariance expressions for gravity anomalies, geoid undulations, and deflections of the vertical implied by anomaly degree variance models, Department of Geodetic Science, OSU, Report No. 208, 1974

  • USGS, EROS, SRTM30 (2008) Digital Elevation Model DATA Center, SIOUX Fall, SD 57198–0001, http://srtm.usgs.gov/data/obtainingdata.htmal

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Acknowledgments

Higher Education Commission of Pakistan is highly acknowledged for sponsoring this study under the indigenous Ph.D. program at the Department of Earth Sciences Quaid-i-Azam University (QAU) Islamabad, Pakistan. The Directorate General of Petroleum Concessions (DGPC), Ministry of Petroleum and Natural Resources, and Survey of Pakistan Islamabad, Pakistan, are also acknowledged for providing the gravity, elevation, and GPS/leveling data of the study area to the Department of Earth Sciences, QAU, Islamabad. We thank, for constructive remarks, Rene Forsberg, Neils Bohr Institute Copenhagen University Denmark.

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Authors and Affiliations

  1. National Engineering and Scientific Commission (NESCOM), Islamabad, Pakistan

    Sadiq Muhammad

  2. Department of Earth Sciences, Quaid-i-Azam University, Islamabad, 45320, Pakistan

    Ahmad Zulfiqar

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  1. Sadiq Muhammad
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  2. Ahmad Zulfiqar
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Correspondence to Sadiq Muhammad.

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Muhammad, S., Zulfiqar, A. An optimal approach for the development of precise regional geoid in Pakistan through a comparative study with least square collocation and FFT techniques. Arab J Geosci 8, 7481–7498 (2015). https://doi.org/10.1007/s12517-014-1693-3

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  • DOI: https://doi.org/10.1007/s12517-014-1693-3

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