Predictive models for identification of parameters of seismic vibrations by applying the theory of covariance functions

Abstract

The paper analyses an opportunity to develop predictive models for identification of parameters of seismic vibrations by applying statistical processing of measurement data. The calculations used measurement data arrays according to vectors E, N and Z obtained from four seismic stations (India EVBH, Indonesia LUWIBH, Italy CERABN and Turkey BNHBH). The Doppler method and the theory of covariance functions were applied for analysing the measurement data arrays. The trend of seismic vibration intensity vectors was estimated by applying the least-squares method. In addition, the said procedure partially eliminates random errors of the measurement data from the stations. Using the intensity variation of seismic vibration vectors E, N and Z on the timescale, the estimates of autocovariance and cross-covariance functions of seismic vibration vectors were calculated by changing the quantised interval on the time scale. The average values of parameter z in the Doppler formula were calculated according to the created formula by applying the expressions of cross-covariance functions of the algebraic addition of the relevant vectors and a single vector. By applying the values of parameter z from the Doppler formula, the approximate value of the velocity of reciprocal movement of seismic vectors was calculated. In the calculations, the software developed on the basis of the MATLAB program package operators was applied.