Vol. 337 No. 5 (2026)
DOI https://doi.org/10.18799/24131830/2026/5/5186
Technology of 3D density modeling of the upper crust of the Voronezh crystalline massif
Relevance. Construction of three-dimensional models of the lithosphere structure based on interpretation of geophysical data is an urgent task at the present stage of development of geophysics. Aim. Development of technology for three-dimensional density modeling of the upper part of the earth crust based on inversion of the gravity field. Methods. The technology consists of a stage of preliminary regional constructions of a generalized geological and geophysical model of the earth crust for the study area. These data made it possible to exclude the gravitational effect of the sedimentary cover, estimate the thickness of the "gravity-active" layer of the crystalline basement and calculate a regional density model of the lithosphere based on solving the inverse problem in a spherical formulation. At the stage of detailed modeling, the regional density model and the corresponding regional gravity field serve as the basis for constructing a density model of the upper part of the earth crust of the studied region. The inverse problem for local gravity field anomalies caused by density heterogeneities in the upper crust is solved in Cartesian coordinates using the approximation operator of the normal solution for the horizontal layer. The iterative solution scheme is developed for the data on the real relief of field observations and uses a modified method of local corrections. The final detailed density model of the upper part of the earth crust is presented in absolute values of density on a regular plan grid with a step of 2 km and a discrete grid of layers, the thickness of which regularly increases with depth from 0.05 to 4 km. The choice of the grid for solving the inverse gravimetry problem is consistent with the adopted accuracy of the solution and the characteristic sizes of the sought geological heterogeneities. The depth of the lower boundary of the model layer is 16 km. Results. The developed technology is applied to create a detailed density model of the upper crust of the eastern part of the Voronezh crystalline massif. Conclusions. The proposed method of constructing three-dimensional density models of platform territories, based on the density measurements of sedimentary and surface parts of crystalline rocks, as well as assessments of their predicted distribution at depth, allows us to form a fundamentally new multi-stage approach to interpreting gravimetry data. The data on three-dimensional density distribution obtained on the basis of the technology, fully consistent with a large volume of a priori geological and geophysical information, allow us to obtain fundamentally new knowledge about the deep geological structure of the study area.
For citation: Voronova T.A., Muravina O.M., Glaznev V.N., Antonova I.Yu. Technology of 3D density modeling of the upper crust of the Voronezh crystalline massif. Bulletin of the Tomsk Polytechnic University. Geo Assets Engineering, 2026, vol. 337, no. 5, pp. 160-175. https://doi.org/10.18799/24131830/2026/5/5186
Keywords:
three-dimensional density modeling, gravitational field, inverse problem, earth crust, Voronezh crystalline massif, geological structures of the crystalline basement
References:
1. White D.J., Forsyth D.A., Asudeh I., Carr S.D., Wu H., Easton R.M., Mereu R.F. A seismic-based cross-section of the Grenville Orogen in southern Ontario and western Quebec. Canadian Journal of Earth Sciences, 2000, vol. 37, no. 2–3. pp. 183–192. DOI: 10.1139/e99-094
2. Glaznev V.N. Complex geophysical models of the lithosphere of Fennoscandia. Apatity, KaeM Publ., 2003. 252 p. (In Russ.)
3. Janik T., Grad M., Guterch A., Dadlez R., Yliniemi J., Tiira T., Keller G.R., Gaczynski E. Lithospheric structure of the Trans-European Suture Zone along the TTZ and CEL03 seismic profiles (from NW to SE Poland). Tectonophysics, 2005, vol. 411, pp. 129–156. DOI: 10.1016/j.tecto.2005.09.005
4. Kukkonen I.T., Lahtinen R. Finnish reflection experiment FIRE 2001-2005. Geological Survey of Finland Special Paper, 2006, vol. 43, 247 p.
5. Maystrenko Y.P., Scheck-Wenderoth M., Hartwig A., Anka Z., Watts A.B., Hirsch K.K., Fishwick S. Structural features of the Southwest African continental margin according to results of lithosphere-scale 3D gravity and thermal modelling. Tectonophysics, 2013, vol. 604, pp. 104–121. DOI: 10.1016/j.tecto.2013.04.014
6. Mints M.V., Dokukina K.A., Konilov A.N., Philippova I.B., Zlobin V.L., Babayants P.S., Belousova E.A., Blokh Yu.I., Bogina M.M., Bush W.A., Dokukin P.A., Kaulina T.V., Natapov L.M., Piip V.B., Stupak V.M., Suleimanov A.K., Trusov A.A., Van K.V., Zamozhniaya N.G. East European Craton: Early Precambrian history and 3D models of deep crustal structure. The Geological Society of America Special Paper, 2015, vol. 510, 433 p. DOI: 10.1130/2015.2510(12)
7. Mintz M.V., Sokolova E.Yu., Vardanyants I.L., Smirnov M.Yu., Uspensky N.I., Golubtsova N.S., Kulikov V.A., Pushkarev P.Yu., Taran Ya.V., Zolotaya L.A., Kosnyreva M.A., Yakovlev Ya.G., Rokityansky I.I., Ryazantsev P.Yu., Nilov M.Yu., Glaznev V.N., Muravina O.M. 3D model of the deep structure of the Svecofennian accretionary orogen based on data from CDP seismic reflection method, MT sounding and density modeling. Proceedings of the Karelian Scientific Center of the Russian Academy of Sciences, 2018, no. 2, pp. 34–61. (In Russ.) DOI: 10.17076/geo656
8. Abbott D.H., Mooney W.D., VanTongeren J.A. The character of the Moho and lower crust within Archean cratons and the tectonic implications. Tectonophysics, 2013, vol. 609, pp. 690–705. DOI: 10.1016/j.tecto.2013.09.014
9. Barton P.J. The relationship between seismic velocity and density in the continental crust – a useful constraint. Geophysical Journal of the Royal Astronomical Society, 1986, vol. 87, no. 1, pp. 195–208. DOI: 10.1111/j.1365-246X.1986.tb04553.x
10. Sobolev S.V., Babeyko A.Y. Modelling of mineralogical composition, density and elastic wave velocities in anhydrous magmatic rocks. Surveys in Geophysics, 1994, vol. 15, pp. 515–544. DOI: 10.1007/BF00690173
11. Mintz M.V. Deep crustal structure, evolution and mineral deposits of the Early Precambrian basement of the East European Craton: interpretation of the data along the 1-EU Geotraverse, the 4B and TATSEIS Profiles. Eds. G.S. Gusev, N.V. Mezhelovsky, V.P. Fedorchuk. Moscow, GEOKART, GEOS Publ., 2010. Vol. 1, 408 p. (In Russ.)
12. Muravina O.M. Density model of the Earth's crust of the Voronezh crystalline massif, Vestnik Voronezh State University. Ser. Geology, 2016, no. 1, pp. 108–114. (In Russ.)
13. Glaznev V.N., Minc M.V, Muravina O.M. Density modeling of the earth crust for the central part of the East-European Platform. Vestnik KRAUNC. Ser. Nauki o Zemle, 2016, no. 1 (29), pp. 53–63. (In Russ.)
14. Ladovskii I.V., Martyshko P.S., Tsidaev A.G., Kolmogorova V.V., Byzov D.D. Lithosphere density model of the middle Urals segment. Physics of the Earth, 2023, no. 2, pp. 62–77. (In Russ.) DOI: 10.31857/S0002333723020084
15. Byzov D.D, Martyshko P.S, Fedorova N.V, Rublev A.L. Deep structure of the Middle Urals according to magnetic and gravitational data. Russian Journal of Earth Sciences, 2024, vol. 24, ES3006. (In Russ.) DOI: 10.2205/2024es000924
16. Shirokova T.P., Lygin I.V., Sokolova T.B. Features of the seismic-gravity modeling in di erent physical-geological situations. Bulletin of Moscow University. Series 4: Geology, 2022, no. 1, pp. 42–53. (In Russ.) DOI: 10.33623/0579-9406-2022-1-42-53
17. Li Y., Oldenburg D.W. 3-D inversion of gravity data. Geophysics, 1998, vol. 63, pp. 109–119. DOI: 10.1190/1.1444302
18. Commer M. Three-dimensional gravity modelling and focusing inversion using rectangular meshes. Geophysical Prospecting, 2011, vol. 59, pp. 966–979. DOI: 10.1111/j.1365-2478.2011.00969.x
19. Gallardo L.A., Fontes S.L., Meju M.A., Buonora M.P., De Lugao P.P. Robust geophysical integration through structure-coupled joint inversion and multispectral fusion of seismic reflection, magnetotelluric, magnetic, and gravity images: Example from Santos Basin, offshore Brazil. Geophysics, 2012, vol. 77. pp. B237–B251. DOI: 10.1190/geo2011-0394.1
20. Kamm J., Lundin I.A., Bastani M., Sadeghi M., Pedersen L.B. Joint inversion of gravity, magnetic, and petrophysical data – a case study from a gabbro intrusion in Boden, Sweden. Geophysics, 2015, vol. 80. pp. B131–B152. DOI: 10.1190/geo2014-0122.1
21. Lygin I.V., Chepigo L.S., Sokolova T.B., Kuznetsov K.M., Bulychev A.A. Technique of interactive gravity and magnetic modeling accounting of a priori geological and geophysical data. Geophysics, 2022, no. 3, pp. 74–83. (In Russ.) DOI: 10.34926/geo.2022.95.89.008
22. Glaznev V.N., Zhavoronkin V.I., Muravina O.M., Antonova I.Yu., Voronova T.A., Kholin P.V. The construction of the upper crust of the Yeletskiy section of Losevskiy terrane (Voronezh crystalline massif) according to the density modeling data. Vestnik Voronezh state university. Ser. Geology, 2019, no. 1, pp. 97–105. (In Russ.)
23. Marakova I.A., Veltistova O.M., Sabelnikov M.Yu., Nurtazaeva M.A. Modeling of complex tectonic zones of the preduralsky foothill through on solving inverse problems of geophysics. Geophysics, 2024, no. 4, pp. 61–65. (In Russ.) DOI: 10.34926/geo.2024.31.15.008
24. Glaznev V.N., Muravina O.M., Il’in V.V., Voronova T.A. Three-dimensional model for the deep structure of the Pavlovsk batholith from the Don terrane (East-Don Orogen). Doklady Earth Sciences, 2024, vol. 519, suppl. 2, pp. S317–S324. DOI: 10.1134/S1028334X24605789
25. Vogel C.R. Computational methods for inverse problems. Frontiers in Applied Mathematics SIAM, 2002, vol. 183 p. DOI: 10.1137/1.9780898717570
26. Kobrunov A.I. Mathematical foundations of the theory of interpretation of geophysical data. Moscow, CenterLitNefteGaz Publ., 2008. 286 p. (In Russ.)
27. Fullagar P.K., Pears G.A., McMonnies B. Constrained inversion of geologic surfaces – pushing the boundaries. The Leading Edge, 2008, vol. 27, no. 1, pp. 98–105. DOI: 10.1190/1.2831686
28. Akimova E.N., Misilov V.E., Martyshko P.S. Algorithms for solving the structural gravity problem in a multilayer medium. Doklady Earth Sciences, 2013, vol. 453, no. 2, pp. 1278–1281. DOI: 10.7868/S0869565213360164
29. Martyshko P., Ladovskii I., Byzov D. Parallel algorithms for solving inverse gravimetry problems: application for earth’s crust density models creation. Mathematics, 2021, vol. 9, no. 2966. DOI: 10.3390/math9222966
30. Vitale A., Fedi M. Self-constrained inversion of potential fields through a 3D depth weighting. Geophysics, 2020, vol. 85, pp. G143–G156. DOI: 10.1190/geo2019-0812.1
31. Xu Z., Zou G., Wei Q., Tian J., Yuan H. Focusing joint inversion of gravity and magnetic data using a clustering stabilizer in a space of weighted parameters. Geophysical Journal International, 2021, vol. 224. pp. 1344–1359. DOI: 10.1093/gji/ggaa518
32. Liu B., Bian S., Ji B., Wu S., Xian P., Chen C., Zhang R. Application of the Fourier series expansion method for the inversion of gravity gradients using gravity anomalies. Remote Sensing, 2022, vol. 15, pp. 230. DOI: 10.3390/rs15010230
33. Glaznev V.N., Muravina O.M., Rayevsky A.B. Approximation operator of the inverse gravimetry problem for a horizontal layer. Vestnik Voronezh state university. Ser. Geology, 2023, no. 1, pp. 97–105. (In Russ.) DOI: 10.17308/geology/1609-0691/2023/1/97-105
34. Ma G., Niu Y., Li L., Li Z., Meng Q. Adaptive space–location-weighting function method for high-precision density inversion of gravity data. Remote Sensing, 2023, vol. 15, pp. 5737. DOI: 10.3390/rs15245737
35. Xian M., Xu Z., Zhdanov M.S., Ding Y., Wang R., Wang X., Li J., Zhao G. Recovering 3D salt dome by gravity data inversion using ResU-Net++. Geophysics, 2024, vol. 89. pp. G93–G108. DOI: 10.1190/geo2023-0551.1
36. Bai Z., Wang Y., Wang C., Yu C., Lukyanenko D., Stepanova I., Yagola A.G. Joint gravity and magnetic inversion using CNNs’ deep learning. Remote Sensing, 2024, vol. 16, p. 1115. DOI: 10.3390/rs16071115
37. Qu Z., Min G., Xu Z., Xian M., Zhang Y., She A., Li J. A novel depth-weighting approach based on regularized downward continuation for enhanced gravity inversion. Remote Sensing, 2025, vol. 17, pp. 1184. DOI: 10.3390/rs17071184
38. Balk P.I., Dolgal A.S. Generalized solutions of the inverse problem and new technologies for the quantitative interpretation of gravity anomalies. Izvestiya, Physics of the Solid Earth, 2018, vol. 54, no. 2, pp. 372–387. DOI: 10.7868/S0002333718020151
39. Martyshko P.S., Ladovskii I.V., Byzov D.D. Tsidaev A.G. Gravity data inversion with method of local corrections for finite elements models. Geosciences (Switzerland), 2018, vol. 8. pp. 373. DOI: 10.3390/geosciences8100373
40. Dolgal A.S., Khristenko L.A. Improvement of computer technology for separating gravity anomalies using equivalent sources. Geophysical research, 2023, vol. 24, no. 1, pp. 31–43. (In Russ.) DOI: 10.21455/gr2023.1-2
41. Lithosphere of the Voronezh crystalline massif based on geophysical and petrophysical data. Ed. by N.M. Chernyshov. Voronezh, Nauchnaya kniga Publ., 2012. 330 p. (In Russ.)
42. Muravina O.M., Zhavoronkin V.I., Glaznev V.N. Petrophysical characteristics of the sedimentary cover of the Voronezh anteclise. Vestnik Voronezh state university. Ser. Geology, 2013, no. 1, pp. 189–196. (In Russ.)
43. Bogdanova S.V., Gorbatschev R., Garetsky R.G. Europe/East European Craton. Reference Module in Earth Systems and Environmental Sciences. Amsterdam, The Netherlands, Elsevier, 2016. pp. 1–16. DOI: 10.1016/B978-0-12-409548-9.10020-X
44. Strakhov V.N. The theory of linear inverse gravimetric problems. Dokl. Academy of Sciences of the USSR, 1990, vol. 311, no. 5, pp. 1093–1096. (In Russ.)
45. Glaznev V.N., Muravina O.M. Zhavoronkin V.I., Lebedev I.P., Voronova T.A. Petrodensity map of the Precambrian basement of the Voronezh crystalline massif. Scale 1:1000000: explanatory note. Voronezh, Nauchnaya kniga Publ., 2020. 101 p. (In Russ.)
46. Glaznev V.N., Muravina O.M., Voronova T.A., Kholin V.M. Estimation of the thickness of the gravity layer of the earth's crust of the Voronezh crystalline massif. Vestnik Voronezh state university. Ser. Geology, 2014, no. 4, pp. 78–84. (In Russ.)
47. Grad M., Tiira T. The Moho depth map of the European Plate. Geophysical Journal International, 2009, vol. 176, pp. 279–292. DOI: 10.1111/j.1365-246X.2008.03919.x
48. Isaev V.I., Lobova G., Merenkova A.S., Osipova E.N., Kuzmenkov S.G., Fomin A.N. Heat flow density distribution map of the foundation roof in the eastern part of the Tomsk region. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2022, vol. 333, no. 4, pp. 37–52. (In Russ.) DOI: 10.18799/24131830/2022/4/3653
49. Dolgal A.S., Kostitsyn V.I., Novikova P.N., Ryzhov N.V., Khokhlova V.V. Suppression of geological interference during the transformation of regional gravity anomalies. Geophysics, 2024, no. 5, pp. 24–29. (In Russ.) DOI: 10.34926/geo.2024.53.11.006
50. Pavlis N.K., Holmes S.A., Kenyon S.C., Factor J.K. The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research, 2012, vol. 117, B4. DOI: 10.1029/2011JB008916
51. Martyshko P.S., Prutkin I.L. Technology of separation of sources of gravitational field by depth. Geophysical Journal, 2003, vol. 25, no. 3, pp. 159–169. (In Russ.)
52. Kartvelishvili K.M. Planetary density model and the normal gravitational field of the Earth. Moscow, Nauka Publ., 1983. 93 p. (In Russ.)
53. Ladovskii I.V., Martyshko P.S., Byzov D.D., Kolmogorova V.V. On selecting the excess density in gravity modeling of inhomogeneous media. Izvestiya, Physics of the Solid Earth, 2017, vol. 53, no. 1, pp. 130–139. DOI: 10.7868/S0002333716060053
54. Martyshko P.S., Byzov D.D., Chernoskutov A.I. Interpretation of gravity data measured by topography. Doklady Earth Sciences, 2020, vol. 495, no. 2, pp. 914–917. DOI: 10.31857/S2686739720120075
55. Dolgal A.S., Kostitsyn V.I., Novikova P.N., Ryzhov N.V., KhokhlovaV.V. Selection of the Earth model for the transformation of gravity anomalies in the process of regional studies. Geophysics, 2022, no. 5, pp. 6–12. (In Russ.) DOI: 10.34926/geo.2022.55.36.001
56. Muravina O.M., Glaznev V.N., Voronova T.A., Terentiev R.A. A three-dimensional density model of the upper crust at the junction of the Losevo and Vorontsovka terranes (Voronezh crystalline massif). Russian Journal of Pacific Geology, 2024, vol. 17, suppl. 2, pp. S182–S192. DOI: 10.1134/S1819714023080183
57. Terentiev R.A., Voronova T.A., Muravina O.M., Glaznev V.N. Deciphering of the tectonic elements and internal structureof the Paleoproterozoic Losevo terrane (Volga-Don orogen) using density modeling data. Vestnik Voronezh state university. Ser. Geology, 2024, no. 3, pp. 79–95. (In Russ.) DOI: 10.17308/geology/1609-0691/2024/3/79–95
58. Terentiev R.A., Savko K.A., Santosh M. Paleoproterozoic evolution of the arc-back-arc system in the east Sarmatian orogen (East European Craton): zircon shrimp geochronology and geochemistry of the Losevo volcanic suite. American Journal of Science, 2017, vol. 317, pp. 707–753. DOI: 10.2475/06.2017.03
59. Savko K.A., Kholin V.M., Bazikov N.S., Samsonov A.V. The Sarmatia megablock as a fragment of the Vaalbara supercontinent: correlation of geological events at the Archean Paleoproterozoic transition. Stratigraphy and Geological Correlation, 2017, vol. 25, no. 2, pp. 123–145. DOI: 10.7868/S0869592X17020065
60. Molotkov S.P., Kostyukov V.I., Lositsky V.I., Krivtsov I.I., Zolototrubova E.I., Ponomareva R.N. Geological map of the Voronezh crystalline massif at a scale of 1:500000. Voronezh, Ministry of Natural Resources of the Russian Federation, State Enterprise «Voronezhgeologiya», OJSC «Belgorodgeologiya», VSU, NKPR «Khors» Publ., 1999. (In Russ.)
61. Gerya T. Precambrian geodynamics: concepts and models. Gondwana Research, 2014, vol. 25, pp. 442‒463. DOI: 10.1016/j.gr.2012.11.008
62. Gerya T. Introduction to numerical geodynamic modelling. 2nd ed. Cambridge, Cambridge University Press, 2019. 471 p.
63. Gerya T.V., Stern R.J., Baes M., Sobolev S.V., Whattam S.A. Plate tectonics on the Earth triggered by plume‐induced subduction initiation. Nature, 2015, vol. 527, no. 7577, pp. 221–225. DOI: 10.1038/nature15752
64. Stern R.J., Gerya T. Subduction initiation in nature and models: A review. Tectonophysics, 2018, vol. 746, pp. 173–198. DOI: 10.1016/j. tecto.2017.10.014
65. Sternai P. Surface processes forcing on extensional rock melting. Scientific Reports, 2020, vol. 10, no. 1, pp. 7711. DOI: 10.1038/s41598-020-63920-w
