Generalization of the analytical form of Wadati’s method for earthquake hypocentre determination

(in Croatian)

Abstract

The original Wadati’s graphical method for the earthquake hypocentre location is already presented in analytical form (Allegretti et al. 1984). However, the described method was restricted to the use of the data of four seismological stations. In this paper the equations (Eq. 1.) of seismic wave propagation are solved for the hypocentre coordinates x, y, z and the constant c = V_p V_s/(V_p-V_s) by the use of the least squares method. Providing that approximate values of x, y, z and c are known (usually it is sufficient to approximate the starting epicentre coordinates x’, y’, with the coordinates of the station with the minimal t_s-t_p time) the least squares method is applied to the error equations (Eqs. 4.). Due to the high rate of convergence it is sufficient to perform only a few iterations. This enables the use of the greater number of seismological stations and, as a consequence, the greater precision of the results. The error estimation is also possible giving the quantitative measure of the precision of the results obtained. It is also, shown, that Wadati’s method could be extended to include the seismic station height differences. This may be applied in the rock bursts investigations too.