Skip to main content
Log in

Towards the measurement of zero vertical gradient of gravity on the Earth’s surface

  • Published:
Studia Geophysica et Geodaetica Aims and scope Submit manuscript

Abstract

It is well known that the vertical gradient of gravity measured on the Earth’s surface depends strongly on nearby topographical shapes. We simply inverted the problem and posed the question whether a zero vertical gradient can be observed using relative gravity meters and the classical tower method of measurement in appropriate terrain conditions. Extensively using the model of a vertical cone to simulate the real in-field conditions, we have found that reversed-cone-shaped topographic depressions represent the most perspective forms, which can contribute to extremely small values of the resulting vertical gradient. In one such form, namely a karstic sinkhole, we measured the value of −0.071 mGal/m (10−5 s−2). In addition, we successfully modeled this value using a detailed local digital elevation model. We thus conclude that zero vertical gradient of gravity should be observable by common means, also on the Earth’s surface, and not only underground within very dense rocks as some ores can be. Once this is verified it could represent a contribution to the theory of the Earth’s gravity field and its geophysical as well as geodetic applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ager C.A. and Liard J.O., 1982. Vertical gravity gradient surveys: Field results and interpretations in British Columbia, Canada. Geophysics, 47, 919–925.

    Article  Google Scholar 

  • Antonov Yu.V., Zhavoronkin V.I. and Slyusarev S.V., 1996. Measurement of vertical increments of gravity above bodies of regular shape. Vestnik Voronezhskogo Universiteta, Seriya Geologitscheskaya, 2, 177–182 (in Russian).

    Google Scholar 

  • Bodemüller H., 1960. Measurement and evaluation of the vertical gradient of gravity. Z. Vermess., 4, 101–112 (in German).

    Google Scholar 

  • Breili K. and Rolstad C., 2009. Ground-based gravimetry for measuring small spatial-scale mass changes on glaciers. Ann. Glaciol., 50, 141–147.

    Article  Google Scholar 

  • Butler D.K., 1984a. Interval gravity-gradient determination concepts. Geophysics, 49, 828–832.

    Article  Google Scholar 

  • Butler D.K., 1984b. Microgravimetric and gravity gradient techniques for detection of subsurface cavities. Geophysics, 49, 1084–1096.

    Article  Google Scholar 

  • Casten U. and Gram C., 1989. Recent developments in underground gravity surveys. Geophys. Prospect., 37, 73–90.

    Article  Google Scholar 

  • Csapó G. and Völgyesi L., 2002. Determination and reliability estimation of vertical gradients based on test measurements. Reports on Geodesy, 69, Warsaw University of Technology, Warsaw, Poland, 303–308.

    Google Scholar 

  • Fajklewicz Z., 1976. Gravity vertical gradient measurements for the detection of small geologic and anthropogenic forms. Geophysics, 41, 1016–1030.

    Article  Google Scholar 

  • Fajklewicz Z., 2007. Applied Gravimetry. AGH University of Science and Technology Press, Cracow, Poland, 433 pp (in Polish).

    Google Scholar 

  • Gumert W.R., 1985. Advantages of continuous profiling airborne gravity surveys. Proceedings of the International Meeting on Potential Fields in Rugged Topography. Bulletin No. 7. Institute of Geophysics, University of Lausanne, Lausanne, Switzerland, 16–18.

    Google Scholar 

  • Hammer S., 1938. Investigations of the vertical gradient of gravity. Eos Trans. AGU, 19, 72–82, DOI: 10.1029/TR019i001p00072.

    Article  Google Scholar 

  • Hammer S., 1950. Density determinations by underground gravity measurements. Geophysics, 15, 637–652.

    Article  Google Scholar 

  • Hammer S., 1970. The anomalous vertical gradient of gravity. Geophysics, 35, 153–157.

    Article  Google Scholar 

  • Hammer S., 1981. Short Note: Magnitude of anomalies in the vertical gradient of gravity. Geophysics, 46, 1609–1610.

    Article  Google Scholar 

  • Hinze W.J., Aiken C., Brozena J., Coakley B., Dater D., Flanagan G., Forsberg R., Hildenbrand T., Keller G.R., Kellogg J., Kucks R., Li X., Mainville A., Morin R., Pilkington M., Plouff D., Ravat D., Roman D., Urrutia-Fucugauchi J., Véronneau M., Webring M. and Winester D., 2005. New standards for reducing gravity data: The North American gravity database. Geophysics, 70, J25–J32.

    Article  Google Scholar 

  • Hofmann-Wellenhof B. and Moritz H., 2005. Physical Geodesy. Springer-Verlag, Berlin, Germany, 403 pp.

    Google Scholar 

  • Hunt T.M., Sato T., Nakao T. and Takemura T., 1999. Improvements to microgravity monitoring — determinantion of the vertical gravity gradient. Geothermal Resources Council Transactions, 23, 419–423 (http://pubs.geothermal-library.org/lib/grc/1016506.pdf).

    Google Scholar 

  • Hunt T., Sugihara M., Sato T. and Takemura T., 2002. Measurement and use of the vertical gravity gradient in correcting repeat microgravity measurements for the effects of ground subsidence in geothermal systems. Geothermics, 31, 525–543.

    Article  Google Scholar 

  • Jacoby W. and Smilde P.L., 2009. Gravity Interpretation. Springer-Verlag, Berlin, Germany, 395 pp.

    Google Scholar 

  • Janle P., Makris J. and Menzel H., 1971. Experimental investigations of the vertical gradient of gravity. Bolletino di Geofisica Teorica ed Applicata, 13, 51–52, 254–263.

    Google Scholar 

  • Jiang Z., Pálinkáš V., Francis O., Jousset P., Mäkinen J., Merlet S., Becker M., Coulomb A., Kessler-Schulz K., Schulz H., Rothleitner Ch., Tisserand L. and Lequin D, 2012. Relative Gravity measurements during the 8th International Comparison of Absolute Gravimeters (2009). Metrologia, 49, 95–107.

    Article  Google Scholar 

  • Kumagai N., Abe E. and Yoshimura Y., 1960. Measurement of vertical gradient of gravity and its significance. Bolletino di Geofisica Teorica ed Applicata, 2, 607–630.

    Google Scholar 

  • Kuo J.T., Ottaviani M. and Singh S.K., 1969. Variations of vertical gravity gradient in New York City and Alpine, New Jersey. Geophysics, 34, 235–248.

    Article  Google Scholar 

  • LaFehr T. R. and Chan K., 1986. Discussion on “The normal vertical gradient of gravity” by J. H. Karl (Geophysics, 48, 1011–1013, July 1983). Geophysics, 51, 1505–1508.

    Article  Google Scholar 

  • Marušiak I. and Mikuška J., 2013. Pohanka_Cylinder/Cone, Program for Calculation of the Gravitational Effect of the Homogenous Vertical Cylinder, Cone or Frustum of Cone. G-Trend s.r.o., Bratislava, Slovakia (in Slovak).

    Google Scholar 

  • Marušiak I., Zahorec P., Papčo J., Pašteka R. and Mikuška J., 2013. Toposk, Program for the Terrain Correction Calculation. G-Trend s.r.o., Bratislava, Slovakia (in Slovak).

    Google Scholar 

  • Meurers B., 2001. Remarks on the discontinuity of the gravity gradient at the apex of a cone. Proceedings of the 8th International Meeting on Alpine Gravimetry, Leoben 2000. Österreichische Beiträge zu Meteorologie und Geophysik, 26, 181–186.

    Google Scholar 

  • Pohánka V., 1988. Optimum expression for computation of the gravity field of a homogenous polyhedral body. Geophys. Prospect., 36, 733–751.

    Article  Google Scholar 

  • Swain C.J., 1984. Discussion on “The normal vertical gradient of gravity” by J. H. Karl (Geophysics, 48, 1011–1013). Geophysics, 49, 1563.

    Article  Google Scholar 

  • Thyssen-Bornemisza S. and Stackler F.W., 1956. Observation of the vertical gradient of gravity in the field. Geophysics, 21, 771–779.

    Article  Google Scholar 

  • Zahorec, P., Papčo J., Mikolaj M., Pašteka R. and Szalaiová V, 2014. The role of near topography and building effects in vertical gravity gradients approximation. First Break, 32, 65–71.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pavol Zahorec.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zahorec, P., Mikuška, J., Papčo, J. et al. Towards the measurement of zero vertical gradient of gravity on the Earth’s surface. Stud Geophys Geod 59, 524–537 (2015). https://doi.org/10.1007/s11200-015-0837-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11200-015-0837-6

Keywords

Navigation