Abstract
Abstract. Objectives The statistical analysis of real accelerograms is considered. For this purpose, graphs of real accelerograms are enlarged in abscissa and ordinate, allowing the appropriate measurements to be made and the accelerograph records to be presented in the form of numerical tables. To process these tables, a mathematical model is constructed that allows statistical studies of actual accelerograms to be carried out. Methods The acceleration of the Earth's surface during an earthquake is represented as a non-stationary random Gaussian process. The non-stationary process describing the acceleration of the Earth's surface is modelled as a function of three random parameters. In this case, the real accelerogram, which is presented in a single copy, is modelled by a random ergodic function. Results Accelerograms of strong real earthquakes and corresponding fragments of tables are given. An algorithm that allows all parameters of correlation functions and spectral densities to be determined corresponding to real earthquakes is described in detail. A constructed algorithm that allows the statistical parameters of an earthquake to be calculated, including the dominant frequency, the standard deviation, the correlation coefficient and a coefficient that takes into account the non-stationary nature of the earthquake process, is discussed. The parameters of the correlation functions of accelerograms of strong earthquakes that occurred in the cities of Taft (USA) and Gazli (Uzbekistan) are calculated. The results of the study are presented in the form of graphs and tables. Conclusion The algorithm constructed by the authors allows the statistical study of strong earthquakes, whose accelerograms are presented in a single copy, to be carried out and the corresponding correlation function parameters to be calculated. The proposed algorithm can be used for the statistical analysis of accelerograms of strong earthquakes.The parameters of correlation functions can find application in the investigation of seismic resistance of buildings, both with passive and active seismic protection.
Highlights
An algorithm that allows all parameters of correlation functions and spectral densities to be determined corresponding to real earthquakes is described in detail
The parameters of the correlation functions of accelerograms of strong earthquakes that occurred in the cities of Taft (USA) and Gazli (Uzbekistan) are calculated
The algorithm constructed by the authors allows the statistical study of strong earthquakes, whose accelerograms are presented in a single copy, to be carried out and the corresponding correlation function parameters to be calculated
Summary
The acceleration of the Earth's surface during an earthquake is represented as a non-stationary random Gaussian process. The non-stationary process describing the acceleration of the Earth's surface is modelled as a function of three random parameters. In this case, the real accelerogram, which is presented in a single copy, is modelled by a random ergodic function
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