INVESTIGATION OF THE DEPENDENCE OF EARTHQUAKE FOCUS COORDINATE DETERMINATION ERRORS ON CALCULATION METHODS (SPHERES AND HYPERBOLOIDS)

Abstract. Objectives This work is a continuation of a series of articles devoted to an analysis of the effect of the utilised second-order surface types on the accuracy of determining earthquake epicentre and hypocentre coordinates. Methods  In order to find the density of error probability distribution during the determination of earthquake hypocentres, approaches using spheres, hyperboloids, as well as combined spheres and hyperboloids, are used.The hyperboloid-based methods used for determining hypocentre coordinates have fewer errors as compared to the sphere-based method. This is explained by the fact that when determining the travel times of seismic waves, it is assumed that the error increase is the same for the difference in the seismic wave arrival times to two seismic sensors (for methods using hyperboloid), and for the difference in the arrival times of the two seismic waves to the one seismic sensor (for methods using spheres). Results  The expression for determining the earthquake focus coordinates by the hyperboloid method, as well as the density of error probability distribution during the earthquake hypocentre determination, is obtained for calculations using the sphere method, the hyperboloid method, as well as the combined sphere and hyperboloid method. A graph for the error distribution when determining the earthquake hypocentre is obtained for different locations of seismic sensors and for various error values concerning differences in the travel times of seismic waves. Conclusion  The obtained dependencies have the form of an error distribution close to the Cauchy distribution. A wavelet in the zero regions for all distributions was obtained as a result of calculations of the earthquake focus coordinates in the absence of errors in the determination of the time difference. The combined method of the hyperboloid and the sphere has a distribution form close to the hyperboloid method, while the distribution curve in the region close to zero is similar to the sphere method.

earthquake, seismic sensor, error, equation, hyperboloid, sphere, probability distribution density

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