DEFINITION OF EARTHQUAKE FOCUS COORDINATES USING A COMBINED METHOD

Objectives. The aim of the study is to determine earthquake hypocentres with the simultaneous use of both the sphere and hyperboloid methods of calculation, providing minimal possible error due to the appropriate choice of seismic sensors.

Method. A method for determining the hypocentre of earthquakes is proposed that uses methods of spheres and hyperboloids for calculations making it possible to minimise error due to the appropriate choice of seismic sensors. In this case, we proceed from the fact that the circumference is the geometric position of the intersection points of the hyperboloid and the sphere, provided that the focus of the hyperboloid and the centre of the sphere are located on one straight line.

Results. In order to find the coordinates of the earthquake focus, it is necessary to use the data of the third seismic sensor, which should not lie on the same line with the first two. If the third seismic sensor determines the distance to the earthquake focus according to the difference in travel times of the longitudinal and transverse seismic waves, then the geometric location of the earthquake focus will be the sphere. The point of intersection of this sphere with the abovementioned circumference is the earthquake focus. When locating the dependency of the earthquake hypocentre determination error in the relative location of the two seismic sensors, the values of the longitudinal and transverse seismic wave velocities, the difference in the travel times of these waves to the seismic sensors and the difference in the travel times of the longitudinal seismic wave to the two spaced seismic sensors are proposed for use in the calculations. Using the two methods listed above, it is possible to determine the error direction in determining the distance from the earthquake focus to the seismic sensor. For this purpose, the distance  is retrieved between the epicentres of earthquakes, calculated using the combined method (spheres and hyperboloids) and the sphere method. The same distance  is determined after the addition of the deliberate error t to the run time differences of the seismic waves Δt + t. The value of the  -  difference leads to a conclusion concerning the direction of the error.

Conclusion. The determination of the direction of errors is possible using the methods of spheres as well as the method of spheres and hyperboloids. The method having multidirectional errors in measuring the distances to the focus has fewer errors in determining its coordinates as compared to the method of spheres described in the work, while with co-directional errors, conversely, the errors arising when using the combined method are higher. 

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