Determination of the structure of the earth's crust by changing the velocity of seismic waves from the earthquake data

Abstract

Objective. A study of the structure of the earth's crust by determining the velocities of seismic waves from previously broken sections of the earth's crust.Methods. Two mathematical methods are proposed for determining the seismic wave velocities. The first is based on the weighted average method, and the second is based on the matrix method for solving systems of linear algebraic equations. The initial parameters used in the calculations are data from earthquakes that occurred – the coordinates of earthquake centers of origin and seismic sensors, as well as the travel times of seismic waves from the earthquake center of origin to the seismic sensors.Results. The problem of determining the propagation velocity of seismic waves in different parts of the earth's crust is solved by two different methods. The distribution densities of errors in determining the seismic wave velocities are obtained for the weighted average method, in six different situations, for the distribution of seismic wave velocities on the ground, and the matrix method, in the case of distribution of seismic wave velocities on the ground in staggered order.Conclusion. The proposed methods allow refining the coordinates of the centers of the occurred earthquakes while using the iteration method can significantly improve the accuracy of determining the coordinates of the earthquake center of origin and the speeds of seismic waves in various areas. The presence of seismic wave velocities in various parts of the earth's crust during calculations allows determining the coordinates of the earthquake source using new methods based on the use of second-order hyperboloid figures, which were not previously used by seismologists.