Model for storing spatial data of tensor geophysical fields

It is known that geophysical fields (geomagnetic, gravitational and electromagnetic), when recorded or modeled, represent a set of several vector components characterizing the change in the corresponding parameters in space and time. Geophysical field data is currently stored based on known data models which usually have a relational structure. Analysis of known studies has shown the redundancy and inefficiency of this approach. This is reflected in the low speed of obtaining the desired data when using complex multi-predicate queries. The continuously growing volume and complexity of the data under consideration require new approaches to organizing their storage to improve the performance of information systems used to support decision-making based on geophysical field data. This paper proposes and examines a model for representing and storing geophysical field data that ensures increased performance of information systems. An analysis of specific features of geophysical fields due to their tensor nature is presented. The main data components are considered, promising options for combining known data models are determined to obtain the best result to improve the performance of the corresponding databases. A multi-axis model of geophysical field data is proposed that takes into account the tensor multi-component structure of the fields and combines the features of the hierarchical organization of data and element-centric information markup. A distinctive feature of the proposed model is the introduction of static and dynamic axes. This approach ensures the presentation of metadata, operational and archived data, and the interaction between them at the level of background processes with the participation of software triggers with temporal predicates. Using the example of geomagnetic field data and its variations, an increase in the speed of executing single- and multi-predicate queries for data selection and insertion of new records into the storage is demonstrated. Computational experiments comparing the proposed and known approaches to the organization and storage of geophysical field data on various sets and volumes of data showed that the implementation of the multiaxis data model allows increasing the speed of executing single-predicate queries by 25.7 %, multi-predicate queries by 20.1 %, and queries for inserting new records by 21.3 %. This allows us to conclude that the proposed solution is appropriate.

1. Reay S.J., Herzog D.C., Alex S., Kharin E.P., McLean S., Nosé M., Sergeyeva N.A. Magnetic observatory data and metadata: types and availability. Geomagnetic Observations and Models, 2011, vol. 5, pp. 149–181. https://doi.org/10.1007/978-90-481-9858-0_7

2. St-Louis B. Intermagnet Technical Reference Manual. Version 4.6. Edinburgh: INTERMAGNET, BGS, 2012, 100 p.

3. Califf S., Alken P., Chulliat A., Anderson B., Rock K., Vines S., Barnes R., Liou K. Investigation of geomagnetic reference models based on the Iridium® constellation. Earth, Planets and Space, 2022, vol. 74, no. 1, pp. 37. https://doi.org/10.1186/s40623-022-01574-w

4. Lazzeri C., Samsonov A., Forsyth C., Branduardi-Raymont G., Bogdanova Y. A statistical study of the properties of, and geomagnetic responses to, large, rapid southward turnings of the interplanetary magnetic field. Journal of Geophysical Research: Space Physics, 2024, vol. 129, no. 9, pp. e2023JA032160. https://doi.org/10.1029/2023JA032160

5. Gjerloev J.W. The SuperMAG data processing technique. Journal of Geophysical Research: Space Physics, 2012, vol. 117, no. 9, pp. A09213. https://doi.org/10.1029/2012JA017683

6. Janzhura A.S., Troshichev O.A. Determination of the running quiet daily geomagnetic variation. Journal of Atmospheric and Solar Terrestrial Physics, 2008, vol. 70, no. 7, pp. 962–972. https://doi.org/10.1016/j.jastp.2007.11.004

7. Peng Z., Laramee S. Higher dimensional vector field visualization. a survey. Proc. of the Theory and Practice of Computer Graphics (TPCG ‘09), 2009, pp. 149–163.

8. Hergl C., Blecha C., Kretzschmar V., Raith F., Gunther F., Stommel M., Jankowai J., Hotz I., Nagel T., Scheuermann G. Visualization of tensor fields in mechanics. Computer Graphics Forum, 2021, vol. 40, no. 6, pp. 135–161. https://doi.org/10.1111/cgf.14209

9. Jilesh V., Pournami A. On a generalization of Laplace distribution with applications. International Journal of Data Science and Analytics, 2025. in press. https://doi.org/10.1007/s41060-024-00706-7

10. He Z., Hu X., Teng Y., Zhang X., Shen X. Data agreement analysis and correction of comparative geomagnetic vector observations. Earth, Planets and Space, 2022, vol. 74, no. 1, pp. 29. https://doi.org/10.1186/s40623-022-01583-9

11. Huang Y., Wu L., Li D. Theoretical research on full attitude determination using geomagnetic gradient tensor. The Journal of Navigation, 2015, vol. 68, no. 5, pp. 951– 961. https://doi.org/10.1017/S0373463315000259

12. Oliva P., Xu C. On the Herbrand functional interpretation. Mathematical Logic Quarterly, 2020, vol. 66, no. 1, pp. 91–98. https://doi.org/10.1002/malq.201900067

13. Vorobev, A., Vorobeva, G. Inductive method of geomagnetic data time series recovering. SPIIRAS Proceedings, 2018, vol. 2, no. 57, pp. 104-133. (in Russian). https://doi.org/10.15622/sp.57.5

14. Vorob’ev, A.V., Vorob’eva, G.R. Evaluation of the influence of geomagnetic activity on metrological characteristics of inclinometric information measuring systems. Measurement Techniques, 2017, vol. 60, no. 6, pp. 546–551. https://doi.org/10.1007/s11018-017-1232-1

15. Vorobev A., Vorobeva G., Yusupova N. Conception of geomagnetic data integrated space. SPIIRAS Proceedings, 2019, vol. 18, no. 2, pp. 390–415. (in Russian). https://doi.org/10.15622/sp.18.2.390-415

16. Muhammad A., Minhaj K. Enhancing XML data parsing and querying performance on multi-core architectures. Journal of Statistics, Computing and Interdisciplinary Research, 2024, vol. 6, no. 1, pp. 75–89. https://doi.org/10.52700/scir.v6i1.158

17. Vorobev A.V., Vorobeva G.R. An approach to detecting and eliminating spatial contour artifacts in Web GIS applications. Computer Optics, 2023, vol. 47, no. 1, pp. 126–136. (in Russian). https://doi.org/10.18287/2412-6179-co-1127

18. Vorobev A.V., Vorobeva G.R. An approach to dynamic visualization of heterogeneous geospatial vector images. Computer Optics, 2024, vol. 48, no. 1, pp. 123–138. (in Russian). https://doi.org/10.18287/2412-6179-CO-1279

19. Shene J., Chnoor R., Mzhda A. XML schema validation using Java API for XML processing. UKH Journal of Science and Engineering, 2022, vol. 6, no. 1, pp. 33–41. https://doi.org/10.25079/ukhjse.v6n1y2022

20. Chen R., Wang Z., Su H., Xie S., Wang Z. Parallel XPath query based on cost optimization. The Journal of Supercomputing, 2022, vol. 78, no. 4, pp. 5420–5449. https://doi.org/10.1007/s11227-021-04074-y

21. Areces C., Fervari R. Axiomatizing Hybrid XPath with data. Logical Methods in Computer Science, 2021, vol. 17, no. 3, pp. 5. https://doi.org/10.46298/lmcs-17(3:5)2021

22. Chernenkiy V.M., Gapanyuk Y.E., Kaganov Y.T., Dunin I.V., Lyaskovsky M.A., Larionov V.S. Storing metagraph model in relational, document-oriented, and graph databases. CEUR Workshop Proceedings, 2018, vol. 2277, pp. 82–89.

23. Terekhov V., Gapanyuk Y., Kanev A. Metagraph representation for overcoming limitations of existing knowledge bases. Proc. of the 28th Conference of Open Innovations Association (FRUCT), 2021, pp. 458–464. https://doi.org/10.23919/fruct50888.2021.9347601

24. Zichar M. Geovisualization based upon KML. Journal of Agricultural Informatics, 2012, vol. 3, no. 1, pp. 19–26. https://doi.org/10.17700/jai.2012.3.1.49

25. Ortínez-Alvarez A., Ruiz-Suárez L.G., Luis G., Ortega E., GarcíaReynoso A., Peralta O., López-Gaona A., Castro, T., MartínezArroyo A. Emission inventory point source visualization on Google Earth and integrated with HYSPLIT model. Atmósfera, 2021, vol. 34, no. 2, P. 143–156. https://doi.org/10.20937/ATM.52834