employee from 01.01.2002 until now
Center of Geodesy, Cartography and SDI
employee
Russian Federation
from 01.01.1975 to 01.01.2022
Russian Federation
GRNTI 37.15 Геомагнетизм и высокие слои атмосферы
GRNTI 37.25 Океанология
GRNTI 37.31 Физика Земли
GRNTI 38.01 Общие вопросы геологии
The problem of downward continuation of airborne gravimetry data is discussed. Use of spherical radial basis functions (SRBF) to solve this ill-posed problem is proposed. Gravity disturbances observed at flight high are continued downward to disturbing potential. The SRBF method is numerically tested using synthesised data for flight heights 2000 m, 4600 m and 6000 m and grid steps 1 arcmin and 2.5 arcmin in area bounded by colatitudes 40°, 43° and longitudes 153°, 157° (spherical coordinates). The experiments prove that the SRBF method can provide stable and accurate results. Moreover, as a result of this procedure one have an approximator in the form of a linear combination of SRBF which allows to determine the values of different transforms of potential by applying the corresponding operators to this expression.
airborne gravimetry, disturbing potential, downward continuation, gravity disturbance, spherical radial basis functions
1. Alberts, B., & Klees, R. (2004). A comparison of methods for the inversion of airborne gravity data. Journal of Geodesy, 78(1-2), 55-65. https://doi.org/10.1007/s00190-003-0366-x
2. Försberg, R. (2003). Downward continuation of airborne gravity data. In I. N. Tziavos (Ed.), Gravity and Geoid 2002, 3rd Meeting of the International Gravity and Geoid Commission (IGGC) (pp. 51-56). ZITI Editions.
3. Försberg, R., Olesen, A., Bastos, L., Gidskehaug, A., Meyer, U., & Timmen, L. (2000). Airborne geoid determination. Earth, Planets and Space, 52(10), 863-866. https://doi.org/10.1186/bf03352296
4. Kingdon, R., & Vanı́ček, P. (2011). Poisson downward continuation solution by the Jacobi method. Journal of Geodetic Science, 1(1), 74-81. https://doi.org/10.2478/v10156-010-0009-0
5. Li, X., Huang, J., Klees, R., & others. (2022). Characterization and stabilization of the downward continuation problem for airborne gravity data. J. Geod. 96, 96(4). https://doi.org/10.1007/s00190-022-01607-y
6. Liu, X., Sun, Z., Xu, K., & Ouyang, M. (2017). Downward continuation of airborne gravimetry data based on Poisson integral iteration method. Geodesy and Geodynamics, 8(4), 273-277. https://doi.org/10.1016/j.geog.2017.03.009
7. Martinec, Z. (1996). Stability investigations of a discrete downward continuation problem for geoid determination in the Canadian Rocky Mountains. Journal of Geodesy, 70(11), 805-828. https://doi.org/10.1007/bf00867158
8. Michel, V. (2013). Lectures on Constructive Approximation. Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball. In A. Aldroubi, J. Kovačević, & others (Eds.), Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball (p. 324). Springer Science, New York. https://doi.org/10.1007/978-0-8176-8403-7
9. Müller, F., Mayer-Gürr, T., & Makhloof, A. (2008). Downward Continuation of Airborne Gravimetry and Gradiometry Data Using Space Localizing Spline Functions. In M. G. Sideris (Ed.), Observing our Changing Earth (Vol. 133, pp. 143-153). Springer. https://doi.org/10.1007/978-3-540-85426-5_17
10. Neyman, Yu. M., & Sugaipova, L. S. (2016). Basics of myltiscale approximation of geopotential. MIIGAiK, Moscow, 218.
11. Neyman, Yu. M., Sugaipova, L. S., & Patalov, S. (2021). From Hotine-Koch integral to approximation by means of spherical radial basis functions. Geodesy and Aerophotosurveying, 65(1), 5-12. https://doi.org/10.30533/0536-101x-2021-65-1-5-12
12. Novák, P., & Heck, B. (2002). Downward continuation and geoid determination based on band-limited airborne gravity data. Journal of Geodesy, 76(5), 269-278. https://doi.org/10.1007/s00190-002-0252-y
13. Novák, P., Kern, M., Schwarz, K.-P., & others. (2003). On geoid determination from airborne gravity. Journal of Geodesy, 76(9-10), 510-522. https://doi.org/10.1007/s00190-002-0284-3
14. Reuter, R. (1982). Über Integralformeln der Einheitssphäre und harmonische Splinefunktionen (Vol. 33, p. VIII, 197 S. : graph. Darst.) [RWTH, Geodät. Inst. d. Rhein.-Westfäl. Techn. Hochsch.]. https://publications.rwth-aachen.de/record/68605
15. Rexer, M., & Hirt, C. (2015). Spectral analysis of the Earth’s topographic potential via 2D-DFT: a new data-based degree variance model to degree 90,000. Journal of Geodesy, 89(9), 887-909. https://doi.org/10.1007/s00190-015-0822-4
16. Sansò, F. (1995). The long road from measurements to boundary value problems in physical geodesy. Manuscripta Geodaetica, 20(5), 326-344.
17. Sansò, Fernando, & Sideris, M. G. (2013). The Local Modelling of the Gravity Field by Collocation. In Fernando Sansò & M. G. Sideris (Eds.), Geoid Determination: Theory and Methods (pp. 203-258). Springer. https://doi.org/10.1007/978-3-540-74700-0_5
18. Sugaipova, L. S. (2018). Development and study of methods for myltiscale modelling of geopotential [Phdthesis]. In Doctor Thesis. MIIGAiK (p. 325).
19. Zingerle, P., Pail, R., Gruber, T., & Oikonomidou, X. (2020). The combined global gravity field model XGM2019e. Journal of Geodesy, 94(7), 66. https://doi.org/10.1007/s00190-020-01398-0
