Modeling Gravity Gradients from Surface Gravity Anomaly Data

Year 2024, Volume: 26 Issue: 78, 470 - 480

Sibel Uzun

Abstract

Gravity gradients are useful to characterize near mass anomalies since they are much more sensitive to short wavelength anomalies than gravitational accelerations. Estimating gravity gradients from surface gravity data is based on numerical implementations of solutions to geodetic boundary value problem for determination of disturbing potential. One of methods to solve this problem is least-squares collocation which is basically based on data and a defined covariance function. This study deals with estimating gravity gradient tensor components from along track surface gravity anomaly data. The Least-Squares Collocation solution is based on a stationary local covariance function defined for the disturbing potential which allows upward continuation of the observations to a desired altitude. The modeling method is evaluated in using Earth Gravitational Model 2008(EGM2008) and real airborne gravity gradiometry data collected over Southern Texas, Oklahoma region. The results show that modeled gravity gradients estimated in both on the ground and at a certain altitude have basically good agreement with EGM08 gradients. Modeled gradients including horizontal components in the east-west direction exhibit some discrepancies in comparison to the airborne gradiometry data, which may be attributed to some measurement errors in the gradient data.

Keywords

Least-squares collocation, Covariance matrix, Gravity gradient tensor

Yüzey Gravite Anomali Verilerinden Gravite Gradyentlerin Modellenmesi

Abstract

Gravite gradyentleri kısa dalga boylu anomalilere yerçekimi ivmelerinden daha fazla duyarlı oldukları için yüzeye yakın kütle anomalilerini belirlemede faydalıdırlar. Gravite Gradyentlerinin yüzey gravite anomalilerinden kestirimi bozucu potansiyelin belirlenmesinde jeodezik sınır değer problemi çözümlerinin sayısal uygulamalarına dayanmaktadır. Bu problemi çözmenin yöntemlerinden birisi temel olarak veriye ve tanımlanan bir kovaryans fonksiyonuna dayanan En Küçük Kareler Kollokasyonudur. Bu çalışma bir profil boyunca verilen yüzey gravite anomali verilerinden gravite gradyent tensör elemanlarının kestirimi ile ilgilidir. En küçük kareler kollokasyon çözümü gözlemlerin istenen bir yüksekliğe yukarı uzanımına imkan veren bozucu potansiyel için tanımlanmış bir durağan yerel kovaryans fonksiyonuna dayanır. Modelleme yöntemi Yer Gravite Modeli 2008 ve Güney Teksas Oklahoma bölgesi üzerinde toplanmış gerçek havadan gravite gradyometri verileri kullanılarak değerlendirilmiştir. Sonuçlar, hem yeryüzü üzerinde hem de belirli bir yükseklikte kestirilen modellenmiş gravite gradyentlerinin EGM08 gradyentleri ile uyumlu olduğunu göstermektedir. Doğu-batı yönündeki yatay bileşenleri içeren modellenmiş gradyentler, havadan gradyometre verilerine kıyasla bazı uyumsuzluklar göstermektedir; bu durum gradyent verilerindeki bazı ölçüm hatalarına bağlı olabilir.

Keywords

Ek küçük kareler kollokasyon, Kovaryans matris, Gravite gradyent tensor

References

• [1] Jekeli, C. 2003. Statistical Analysis of Moving-Base Gravimetry and Gravity Gradiometry, Report No.466, Ohio State University
• [2] Jekeli, C. 2006. Airborne Gradiometry Error Analysis: Surveys in Geophysics, V.27, pp. 257-275. DOI:10.1007/s10712-005-3826-4
• [3] Kohrn, B. S., Bonet, C., DiFrancesco, D. and Gibson, H. 2011. Geothermal Exploration Using Gravity Gradiometry - a Salton Sea Example: GRC transactions. V.35, pp.1699-1702
• [4] Represas P., Monteiro Santos F.A., Ribeiro. J., Ribeiro J.A., Almeida E.P., Gonçalves R., Moreira M. and Mendes-Victor L.A., 2013. Interpretation of gravity data to delineate structural features connected to low-temperature geothermal resources at Northeastern Portugal: Journal of applied geophysics, V.92, pp. 30-38. DOI: 10.1016/j.jappgeo.2013.02.011
• [5] Shoffner J.D., Li Y., Sabin A. and Lazaro M., 2011. Understanding the utility of gravity and gravity gradiometry for geothermal exploration in the Southern Walker Lake Basin, Nevada: GRC Transactions, V.35, pp.1747-1751
• [6] Martinez, C., Li, Y., Krahenbuhl, R. and Braga, M. A. 2013. 3D inversion of airborne gravity gradiometry data in mineral exploration: A case study in the Quadrilatero Ferrifero, Brazil, V.78, no.1, pp. B1-B11. DOI: 10.1190/GEO2012-0106.1
• [7] Mataragio, J. 2012. Exploring for Gold and Geothermal Systems in the Great Basin Using Full Tensor Gravity Gradiometry: GRC Transactions, V. 36, pp. 1009-1012
• [8] Pappa, F., Ebbing, J., Ferraccioli, F. and van der Wal, W. 2019. Modelling Satellite Gravity Gradient Data to Derive Density, Temperature and Viscosity Structure of the Antarctic Lithosphere: Journal of Geophysical Research: Solid Earth, V.124, pp. 12053-12076. DOI: 10.1029/2019JB017997
• [9] Mickus, K.L. and Hinojosa, J.H. 2001. The complete gravity gradient tensor derived from the vertical component of gravity: a Fourier transform technique: Journal of applied Geophysics, V.46, pp.159-174. DOI:10.1016/S0926-9851(01)00031-3
• [10] Wan, X., Annan, R.F. and Ziggah, Y.Y. 2023. Altimetry-Derived Gravity Gradients Using Spectral Method and Their Performance in Bathymetry Inversion Using Back-Propagation Neural Network: Journal of Geophysical Research: Solid Earth, V.128. DOI:10.1029/2022JB025785
• [11] Jekeli, C. and Zhu, L. 2006. Comparison of methods to model the gravitational gradients from topographic data bases: Geophysical Journal International, V.166, pp.999-1014. DOI: 10.1111/j.1365-246X.2006.03063.x
• [12] Jekeli, C. and Zhu, L. 2009. Gravity gradient modeling using gravity and DEM: Journal of Geodesy, V.83, pp. 557-567. DOI: 10.1007/s00190-008-0273-2
• [13] Hofmann-Wellenhof, B., Moritz, H. 2005. Physical Geodesy. Springer Verlag, Berlin, 403 p.
• [14] Jekeli, C. 2017. Spectral Methods in Geodesy and Geophysics: Taylor and Francis, 415 p.
• [15] Jekeli, C. 2010. Least-squares Collocation, Lecture notes, School of Earth Sciences, Ohio State University.
• [16] Moritz, H. 1980. Advanced Physical Geodesy, Herbert Wichmann Verlag, Karlsruhe (reprint 2008 by Division of Geodesy and Geospatial Science, School of Earth Sciences, Ohio State University), 500 p.
• [17] Erkan, K. 2015. Geophysical Investigations on Gravity Gradiometry and Magnetic Data over the Wichita Uplift Region, Southwestern Oklahoma, Report No. 509, Ohio State University
• [18] Ham, W.E., Denison, R.E. and Meritt, C.A. 1964. Basement rocks and structural evolution of Southern Oklahoma: Oklahoma Geological Survey Bulletin, 95, 302 p. plate I.
• [19] Jekeli, C. 1993. A review of gravity gradiometer survey system data analyses: Geophysics, V.58, No:4, pp.508-514. DOI:10.1190/1.1443433
• [20] Robbins, S.L. and Keller, G.R. 1992. Complete Bouguer and Isostatic residual maps of the Anadarko Basin, Wichita Mountains and surrounding areas, Oklahoma, Kansas, Texas and Colorado, US Geological Survey Bulletin, No:1866G, 11 p. [21] Pavlis, N.K., Holmes, S.A., Kenyon, S.C., Factor, J.F. 2012. The development and evaluation of Earth Gravitational Model (EGM2008): Journal of Geophysical Research, V.117, B04406. DOI: 10.1029/2011JB008916