ANALYSIS OF ERROR DISTRIBUTION DENSITY IN DETERMINING THE COORDINATES OF EARTHING EARTH IN THE METHODS OF SPHERES AND ELLIPSOIDS

Abstract

Objectives The purpose of the study is to obtain an expression for determining the coordinates of the earthquake focus using the ellipsoid method, as well as testing the possibility of using the method using the figures of the second order of the ellipsoid during the initial determination of the coordinates of the earthquake hypocenter.Method A comparative analysis of the probability density of errors in the hypocentral zone of the earth's surface, in combination with various spheres, ellipsoid and hyperboloid and ellipsoids, is carried out.Result Obtained an expression for determining the coordinates of the earthquake focus by the method of ellipsoids, as well as the density of the distribution of error probabilities in the determination of the earthquake hypocenter the in calculations by the method of spheres, by the combined method of spheres, hyperboloid and ellipsoid, and also by the method of ellipsoids.Conclusion Methods used to determine the coordinates of the hypocenter ellipsoid, have large errors in comparison with the method of areas. This can explained by the fact that in determining the coordinates of the hypocenter in the sphere method, three errors are used in determining the difference in the travel times of seismic waves, while in the ellipsoid method and the combined method of the sphere of the ellipsoid and hyperboloid have four errors, which introduces final errors in the distribution. All the obtained dependences of the error distribution have the form close to the Cauchy distribution.