Improving the Accuracy of Analytical Downward Continuation of Terrestrial Gravity Anomalies

نوع مقاله : مقاله پژوهشی

نویسنده

Department of Geotechnical and Transport Engineering, Faculty of Civil Engineering, Shahrood University of Technology, Shahrood, Iran.

چکیده

The determination of the geoid using the Stokes integral involves transforming gravity data from their measurement altitude to the geoid/ellipsoid surface. This study focuses on improving the accuracy of analytical downward continuation (ADC) for reducing terrestrial gravity anomalies to the geoid. The ADC method uses the Taylor series and successive vertical gradients of the gravity anomalies. The Moritz integral formula, which is based on Poisson's integral, is used to derive the vertical gravity gradient. To enhance its accuracy, a mean vertical gradient is proposed by introducing an analytical formula based on planar approximation. This formula improves accuracy by 50%. Numerical analysis, using simulated free air anomalies up to harmonic degree/order 5540/5540, reveals that the difference between mean and point ADC results in geoidal height can be several decimeters. The study also finds that the ADC of 2'×2' anomalies remains stable even with different levels of noise, while the Taylor series of 1'×1' gravity anomalies diverges.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Improving the Accuracy of Analytical Downward Continuation of Terrestrial Gravity Anomalies

نویسنده [English]

  • Mehdi Goli
Department of Geotechnical and Transport Engineering, Faculty of Civil Engineering, Shahrood University of Technology, Shahrood, Iran.
چکیده [English]

The determination of the geoid using the Stokes integral involves transforming gravity data from their measurement altitude to the geoid/ellipsoid surface. This study focuses on improving the accuracy of analytical downward continuation (ADC) for reducing terrestrial gravity anomalies to the geoid. The ADC method uses the Taylor series and successive vertical gradients of the gravity anomalies. The Moritz integral formula, which is based on Poisson's integral, is used to derive the vertical gravity gradient. To enhance its accuracy, a mean vertical gradient is proposed by introducing an analytical formula based on planar approximation. This formula improves accuracy by 50%. Numerical analysis, using simulated free air anomalies up to harmonic degree/order 5540/5540, reveals that the difference between mean and point ADC results in geoidal height can be several decimeters. The study also finds that the ADC of 2'×2' anomalies remains stable even with different levels of noise, while the Taylor series of 1'×1' gravity anomalies diverges.

کلیدواژه‌ها [English]

  • Analytical Downward Continuation
  • Mean Vertical Gradient
  • Gravity Anomaly
  • Taylor Series

مراجع

Bjerhammar, A. (1969). On the boundary value problem of physical geodesy. Tellus, 21(4), 451-516, doi: 10.1111/j.2153-3490.1969.tb00460.x.
Cooper, G. (2004). The stable downward continuation of potential field data. Exploration Geophysics, 35(3), 260-265. doi: 10.1071/EG04260.
Fedi, M., & Florio, G. (2002). A stable downward continuation by using the ISVD method. Geophysical Journal International, 151(1), 146-156. doi: 10.1190/1.1450821.
Foroughi, I., Vaníček, P., Kingdon, R.W., Goli, M., Sheng, M., Afrashte, Y., Novak, P., & Santos, C.M. (2018). Sub-centimetre geoid. Journal of Geodesy, 92(2), 111-123. doi: 10.1007/s00190-017-1075-5.
Forsberg, R. (1987). A new covariance model for inertial gravimetry and gradiometry. Journal of Geophysical Research: Solid Earth, 92(B2), 1305–1310.
Goli, M., Foroughi, I., & Novak, P. (2018). On estimation of stopping criteria for iterative solutions of gravity downward continuation. Canadian Journal of Earth Sciences, 55(4), 397-405. doi: 10.1139/cjes-2017-0208.
Goli, M., Najafi-Alamdari, M., & Vaníček, P. (2011). Numerical behaviour of the downward continuation of gravity anomalies. Studia Geophysica et Geodaetica, 55(2), 191-202. doi: 10.1007/s11200-011-0011-8.
Li, X., Huang J., Klees, R., Forsberg, R., Willberg, M., Slobbe, D.C., Hwang, C., & Pail, R. (2022). Characterization and stabilization of the downward continuation problem for airborne gravity data. Journal of Geodesy, 96(18), doi: 10.1007/s00190-022-01607-y.
Hirt, C., Featherstone, W.E., & Claessens, S.J. (2011). On the accurate numerical evaluation of geodetic convolution integrals. Journal of Geodesy, 85(8), 519-538. doi: 10.1007/s00190-011-0451-5.
Heiskanen, W.A., & Moritz, H. (1967). Physical Geodesy. W.H. Freeman and Company, San Francisco, 364 p.
Huang, J., Sideris, M.G., Vaníček, P., & Tziavos, I.N. (2003). Numerical investigation of downward continuation techniques for gravity anomalies. Bollettino di Geodesia e Scienze Affini, 62(1), 33-48.
Huang, J., Vaníček, P., & Novák, P. (2000). An alternative algorithm to FFT for the numerical evaluation of Stokes's integral. Studia Geophysica et Geodaetica, 44(4), 374-380. doi: 10.1023/A:1022160504156.
Long, L.T., & Kaufmann, R.D. (2013). Acquisition and analysis of terrestrial gravity data. Cambridge University Press.
Martinec, Z. (1996). Stability investigations of a discrete downward continuation problem for geoid determination in the Canadian Rocky Mountains. Journal of Geodesy, 70(12), 805-828. doi: 10.1007/s001900050069.
Molodenskij, M.S., Eremeev, V.F., & M.I., Yurkina. (1962). Method for Study of the External Gravitation Field and Figure of the Earth. Translated from Russian, Israel Program for Scientific Translations, Jerusalem.
Moritz, H. (1980). Advanced physical geodesy. Herbert Wichmann Verlag.
Pašteka, R., Kušnírák, D., & Karcol, R. (2018). Matlab tool REGCONT2: effective source depth estimation by means of Tikhonov’s regularized downwards continuation of potential fields. Contributions to Geophysics and Geodesy, 48(3), 205-222. doi: 10.2478/congeo-2018-0010.
Pavlis, N.K., Holmes, S.A., Kenyon, S.C., & Factor, J.K. (2012). The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research: Solid Earth, 117(B4). doi: 10.1029/2011JB008916.
Sajjadi, S., Martinec, Z., Prendergast, P., Hagedoorn, J., & Šachl, L. (2021). The stability criterion for downward continuation of surface gravity data with various spatial resolutions over Ireland. Studia Geophysica et Geodaetica, 65(1), 59-76. doi: 10.1007/s11200-020-0769-7.
Sebera, J., Šprlák, M., Novák, P., Bezděk, A., & Vaľko, M. (2014). Iterative Spherical Downward Continuation Applied to Magnetic and Gravitational Data from Satellite. Surveys in Geophysics, 35(4), 941-958. doi: 10.1007/s10712-014-9285-z.
Sideris, M.G. (1987). Spectral methods for the numerical solution of Molodensky's problem. University of Calgary, Ph.D. thesis.
Sun, W., & Vaníček, P. (1998). On some problems of the downward continuation of the 5' × 5' mean Helmert gravity disturbance. Journal of Geodesy, 72(7), 411-420. doi: 10.1007/s001900050216.
Vaníček, P., Sun, W., Ong, P., Martinec, Z., Najafi, M., Vajda, P., & ter Horst, B. (1996). Downward continuation of Helmert's gravity. Journal of Geodesy, 71(1), 21-34. https://doi.org/10.1007/s001900050072.
Vaníček, P., Novák, P., Sheng, M., Kingdon, R., Janák, J., Foroughi, I., Martinec, Z., & Santos, M. (2017). Does Poisson’s downward continuation give physically meaningful results?. Studia Geophysica et Geodaetica, 61(3), 412-428. doi: 10.1007/s11200-016-1167-z.
Xu, S.-z., Yang, J., Yang, C., Xiao, P., Chen, S., & Guo, Z. (2007). The iteration method for downward continuation of a potential field from a horizontal plane. Geophysical Prospecting, 55(6), 883-889. doi: 10.1111/j.1365-2478.2007.00634.x.
Zeng, X., Liu, D., Li, X., Chen, D., & Niu, C. (2015). An improved regularized downward continuation of potential field data. Journal of Applied Geophysics, 106, 114-118. Doi: 10.1016/j.jappgeo.2015.02.011.
Zeng, X., Li, X., Su, J., Liu, D., & Zou, H. (2013). An adaptive iterative method for downward continuation of potential-field data from a horizontal plane. Geophysics, 78(4), J43-J52. doi: 10.1190/1.3237432.
Zhang, C., Lü, Q., Yan, J., & Qi, G. (2018). Numerical solutions of the mean-value theorem: new methods for downward continuation of potential fields. Geophysical Research Letters, 45(8), 3461-3470. doi: 10.1002/2018GL076995.
Zhang, H., Ravat, D., & Hu, X. (2013). An improved and stable downward continuation of potential field data: The truncated Taylor series iterative downward continuation method. Geophysics, 78(2), J75-J86. 10.1190/geo2012-0145.1.
Zhang, Y., Wong, Y.S., & Lin, Y. (2016). BTTB–RRCG method for downward continuation of potential field data. Journal of Applied Geophysics, 126, 74-86, doi: 10.1016/j.jappgeo.2015.12.001.
Zhao, Q., Xu, X., Forsberg, R., & Strykowski, G. (2018). Improvement of Downward Continuation Values of Airborne Gravity Data in Taiwan. Remote Sensing, 10, 12.
Zingerle, P., Pail, R., Gruber, T., & Oikonomidou, X. (2020). The combined global gravity field model XGM2019e. Journal of Geodesy, 94(7), 66. doi: 10.1007/s00190-020-01398-0.
فیزیک زمین و فضا
دوره 49، شماره 4
تاریخ انتشار الکترونیکی: 1 اسفند 1402
اسفند 1402
صفحه 27-35

فایل ها

هم رسانی

ارجاع به این مقاله

آمار