Determination of coordinates of the earthquake hypocenter by the method of circles

Objective. The aim of the study is to develop a method for determining the coordinates of the earthquake hypocenter using various combinations of second and fourth order figures as a geo-locus of the hypocenter position points.

Method. It is known that the line of intersection of figures of the second and fourth orders, in the case of coincidence of focuses, is a circle. To determine the coordinates of the earthquake source, data from seismographs are used, which are used to construct figures of the second and fourth order, the intersection point of which is the hypocenter. When using data from two seismic sensors, there are two figures, the intersection line of which is a circle. A sphere with a radius equal to the radius of the circle is constructed through the center of this circle. For the other two pairs of seismic sensors, two more spheres are also formed, The intersection point of the three spheres obtained is the sought-for hypocenter of the earthquake.

Result. A method has been developed for determining the coordinates of an earthquake source using different shapes of the second and fourth orders for different pairs of seismic sensors.

Conclusion. The method allows one to select one of the second or fourth order figures for different pairs of seismic sensors, which makes it possible to reduce the error in determining the source coordinates.

1. Aslanov T.G., Davudova D.D., Mirzakhanova L.S. Determination of the coordinates of the earthquake hypocenter using the combined method of spheres and hyperboloid // Svid. about the state. reg. prog. Computer No. 2017616673 Ros. Federation / applicant and copyright holder VSUY (RPA of the Ministry of Justice of Russia). No. 2017611151; app. 02/13/17; publ. 09.06.17. (In Russ)

2. Aslanov T.G,. Determination of the coordinates of the earthquake hypocenter using the combined method of a sphere, hyperboloid and ellipsoid // Svid. about the state. reg. prog. Computer No. 2017660545 Ros. Federation / applicant and copyright holder VSUY (RPA of the Ministry of Justice of Russia). No. 2017615709; app. 06/13/17; publ. 09/22/17. (In Russ)

3. Shakhtarin B.I., Aslanov T.G., Tetakaev U.R. Determination of the coordinates of the earthquake source using figures of the fourth and second order - the Cassini oval and hyperbola. [Vestnik Dagestanskogo gosudarstvennogo tekhnicheskogo universiteta. Tekhnicheskiye nauki] Herald of Daghestan State Technical University. Technical Sciences. 2019; 46 (4): 134-142. https://doi.org/10.21822/2073-6185- 2019-46-4-134-142 (In Russ)

4. Aslanov T.G. Determination of the coordinates of the earthquake source using the combined method. [Vestnik Dagestanskogo gosudarstvennogo tekhnicheskogo universiteta. Tekhnicheskiye nauki] Herald of Daghestan State Technical University. Technical Sciences. 2017; 44 (2): 118-125. https://doi.org/10.21822/2073-6185-2017-44-2-118-125 (In Russ)

5. Aslanov T.G., Shakhtarin B.I., Aslanov G.K. Determination of the coordinates of the earthquake source using figures of the second order - ellipse and hyperbola . Automation. Modern technologies. 2018; 11(72): 503-509 (In Russ)

6. Aslanov T.G., Aslanov G.K., Kurbanmagomedov K.D., Shakhtarin B.I. Dependence of errors in determining the coordinates of an earthquake source on calculation methods (spheres and hyperboids). [Vestnik Dagestanskogo gosudarstvennogo tekhnicheskogo universiteta. Tekhnicheskiye nauki] Herald of Daghestan State Technical University. Technical Sciences. 2017; 4 (44): 87-98 (In Russ)

7. Aslanov T.G., Musaeva U.A. Analysis of the distribution density of errors in determining the coordinates of the earthquake source by the methods of spheres and ellipsoids. [Vestnik Dagestanskogo gosudarstvennogo tekhnicheskogo universiteta. Tekhnicheskiye nauki] Herald of Daghestan State Technical University. Technical Sciences. 2019; 46 (2): 61-70. https://doi.org/10.21822/2073-6185-2019-46-2-61-70 (In Russ)

8. Aslanov T.G. Development of an algorithm for determining the coordinates of the earthquake source, with the simultaneous determination of the velocities of seismic waves // Scientific works of young researchers of the "Step into the future" program. Volume 8. "Professional". Moscow. 2005; 32-34 (In Russ)

9. Aslanov T.G., Aslanov G.K., Kudaev D.A. Determination of the velocities of seismic waves from the occurred earthquake // XXXVI final scientific and technical conference of DSTU: abstracts. Makhachkala, RIO DSTU, 2005; 72-73(In Russ)

10. Aslanov GK, Daniyalov MG, Aslanov TG, Magomedov Kh.D. On one method for determining the source of an earthquake with simultaneous determination of the velocities of seismic waves. [Trudy Instituta geologii DNTS RAN] Proceedings of the Institute of Geology, Dagestan Scientific Center of the Russian Academy of Sciences. 2010. No. 56. C. 54-59. (In Russ)

11. Aslanov T.G., Tagirov H.Yu., Magomedov G.B. Determination of coordinates of an earthquake source with simultaneous determination of seismic wave velocities using data from four or more seismic sensors // Svid. about the state. reg. prog. Computer No. 2016662097 Ros. Federation / applicant and copyright holder VSUY (RPA of the Ministry of Justice of Russia). No. 2016619293; app. 09/02/16; publ. 10/31/16.

12. Konev V.V. Linear algebra. Tutorial. Tomsk. Ed. TPU. 2008; 65 (In Russ)

13. Analytical geometry and linear algebra: textbook. allowance / A. E. Umnov. - 3rd ed., Rev. and add. -. M.: MIPT, 2011; 544. ISBN 978-5-7417-0378 (In Russ)

14. Robert Garotta. Shear waves: from registration to interpretation. Short course of lectures for higher educational institutions, 2000 Series No. 3

15. Schuster G.T. Basics of Seismic Wave Theory / G.T. Schuster - University of Utah, 2007; 154.

16. Kasahara K. Earthquake mechanics / K. Kasahara - Cambridge University Press, 1981; 272.

17. Kennett B. Seismic Wave Propagation in Stratified Media / B. Kennett. Australian National University Press, 2009; 298.

18. D'Amico S. (Ed.) Engineering Seismology, Geotechnical and Structural Earthquake Engineering. InTech; 2013; 300.

19. Blas E. A., Sereda A.-V. I. Determination of P-and S-wave reflection coefficients from P-wave seismograms. [Vestnik Murmanskogo gosudarstvennogo tekhnicheskogo universiteta] Bulletin of the Murmansk State Technical University. 2006; 9(3): 389-402. (In Russ)

20. Yetirmishli G.D., Kazymova S.E., Kazymov I.E. Studying the change in the velocities of longitudinal waves with depth from digital seismological data. Modern methods of processing and interpretation of seismological data. Materials of the III International Seismological School. Obninsk: GS RAS, 2008; 54-57. (In Russ)