{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T07:39:06Z","timestamp":1747208346876,"version":"3.40.5"},"reference-count":11,"publisher":"FSBI Center of Geodesy, Cartography, and SDI","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["G&amp;C"],"published-print":{"date-parts":[[2018,11,20]]},"abstract":"<jats:p>\nGeodetic measurements provide important and statistically estimated information about the coordinates of geodetic points and their changes over time. This geodesic information can be used to study geodynamic processes and their manifestations, primarily on the earth\u2019s surface. Particularly intense such geodynamic phenomena occur in areas of active development of minerals due to the intense man-made effects on the near-surface layer of the Earth. It is logical to perform the description of surface motions using mathematical field theory. According to the changes of geodetic elements (coordinates, heights, directions) after repeated measurements it is possible to imagine the field of displacement vector of geodetic points. When studying the stress-strain state of the earth\u2019s surface, the vectors obtained can be used not only to calculate the earth\u2019s deformation tensor in the area under study, but also the differential characteristics of the vector field. One of them is called divergence. The authors of the article propose to determine the divergence of the vector field of surface displacements by discrete geodesic observations of displacement vectors made only on the surface of the study area. The model of the vector displacement field can be chosen taking into account the set of source data and the density of placement of geodetic points, the carriers of spatial coordinates.\n<\/jats:p>","DOI":"10.22389\/0016-7126-2018-940-10-46-53","type":"journal-article","created":{"date-parts":[[2018,11,20]],"date-time":"2018-11-20T14:37:31Z","timestamp":1542724651000},"page":"46-53","source":"Crossref","is-referenced-by-count":6,"title":["An algorithm for estimating the divergence of vector fields of the earth\u2019s surface motion from geodetic data"],"prefix":"10.22389","volume":"940","author":[{"given":"V.G.","family":"Kolmogorov","sequence":"first","affiliation":[{"name":"Siberian State University of Geosystems and Technologies"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3379-4770","authenticated-orcid":true,"given":"B.T.","family":"Mazurov","sequence":"additional","affiliation":[{"name":"Siberian State University of Geosystems and Technologies"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7766-2668","authenticated-orcid":true,"given":"A.A.","family":"Panzhin","sequence":"additional","affiliation":[{"name":"RAS Ural Branch Institute of Mining (IM U\u0412 RAS)"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9687","published-online":{"date-parts":[[2018,11,20]]},"reference":[{"key":"ref0","unstructured":"Akivis M. A., Gol'dberg V. V. Tenzornoe ischislenie. Moskva: Nauka, Glavnaya redaktsiya fiziko-matematicheskoj literatury, 1972, 352 p."},{"key":"ref1","unstructured":"Gzovskij M. V. Matematika v geotektonike. Moskva: Nedra, 1971, 240 p."},{"key":"ref2","unstructured":"Kolmogorov V. G., Kaljuzhin V. A. Pripoverhnostnye deformatsii v rajone Tashtagol'skogo geodinamicheskogo poligona. Izv. vuzov. Geodeziya i ajerofotos#jomka, 2015, no. \u0421\/5, pp. 15\u201319."},{"key":"ref3","unstructured":"Mazurov B.T. Model' sistemy nablyudenij za vertikal'nymi dvizheniyami zemnoj poverhnosti i izmeneniyami gravitacionnogo polya v rajone dejstvuyushchego vulkana. Izv. vuzov. Geodeziya i aehrofotos\"emka, 2007, no. 3, pp. 93\u2013102."},{"key":"ref4","unstructured":"Mejz Dzh. Teoriya i zadachi mehaniki sploshnyh sred. Moskva: Mir, 1974, 319 p."},{"key":"ref5","unstructured":"Panzhin A. A., Sashurin A. D., Panzhina N. A. Geodinamicheskij monitoring na Uzel'ginskom mestorozhdenii. Markshejderiya i nedropol'zovanie, 2016, Vol. 1, no. 3 (83), pp. 30\u201335."},{"key":"ref6","unstructured":"Sedov L. I. Mehanika sploshnoj sredy. Moskva: Nauka, Glavnaya redaktsiya fiziko-matematicheskoj literatury, 1973, Vol. 1, 536 p."},{"key":"ref7","doi-asserted-by":"crossref","unstructured":"Kodama J., Miyamoto T., Kawasaki S., Fujii Y., Kaneko K., Haganc P. (2013) Estimation of regional stress state and Young\u2019s modulus by back analysis of mining-induced deformation. Intern. Journ. of Rock Mechanics and Mining Sciences, no. 63, pp. 1\u201311.","DOI":"10.1016\/j.ijrmms.2013.05.007"},{"key":"ref8","doi-asserted-by":"crossref","unstructured":"Figueiredo B., Cornet F. H., Lamas L., Muralha J. (2014) Determination of the stress field in a mountainous granite rock mass. Intern. Journ. of Rock Mechanics and Mining Sciences, no. 72, pp. 37\u201348.","DOI":"10.1016\/j.ijrmms.2014.07.017"},{"key":"ref9","doi-asserted-by":"crossref","unstructured":"Liu C., Gao J. X., Yu X. X., Zhang J. X., Zhang A.B. (2015) Mine surface deformation monitoring using modified GPS RTK with surveying rod: initial results. Survey Review, no. 47, pp. 79\u201386.","DOI":"10.1179\/1752270614Y.0000000092"},{"key":"ref10","doi-asserted-by":"crossref","unstructured":"Yan Bao, Wen Guo, Guoquan Wang, Weijun Gan, Mingju Zhang, Jack S. Shen (2018) Millimeter-Accuracy Structural Deformation Monitoring Using Stand-Alone GPS: Case Study in Beijing, China. Journ. of Surveying Engineering, Volume 144, no. 1, pp. 27\u201332.","DOI":"10.1061\/(ASCE)SU.1943-5428.0000242"}],"container-title":["Geodesy and Cartography"],"original-title":["\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043e\u0446\u0435\u043d\u043a\u0438 \u0434\u0438\u0432\u0435\u0440\u0433\u0435\u043d\u0446\u0438\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u044b\u0445 \u043f\u043e\u043b\u0435\u0439 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u0439 \u0437\u0435\u043c\u043d\u043e\u0439 \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u0438 \u043f\u043e \u0433\u0435\u043e\u0434\u0435\u0437\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u0434\u0430\u043d\u043d\u044b\u043c"],"deposited":{"date-parts":[[2020,10,12]],"date-time":"2020-10-12T13:27:23Z","timestamp":1602509243000},"score":1,"resource":{"primary":{"URL":"https:\/\/geocartography.ru\/en\/scientific_article\/2018_10_46-53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,20]]},"references-count":11,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,11,20]]},"published-print":{"date-parts":[[2018,11,20]]}},"URL":"https:\/\/doi.org\/10.22389\/0016-7126-2018-940-10-46-53","relation":{},"ISSN":["0016-7126","2587-8492"],"issn-type":[{"type":"print","value":"0016-7126"},{"type":"electronic","value":"2587-8492"}],"subject":[],"published":{"date-parts":[[2018,11,20]]}}}