Frequency Modeling of Earthquake Occurrences by utilizing the Fourier Transform Method

Finding a suitable method for the accurate and reliable estimation of earthquake return periods is an important challenge for research in the field of earthquake engineering. Usually, the Gutenberg-Richter recurrence law is used to determine the average frequency of earthquakes with a magnitude greater than or equal to the specific value. The Gutenberg-Richter recurrence law can provide the value of the average return period, and cannot be used to determine the full details of return periods including the short, medium and long periods. Therefore, we considered the possibility of utilizing the discrete Fourier transform method to develop the frequency model for earthquake magnitudes. For this purpose, we used a series of sine functions with different values of amplitude, frequency, and phase as a prediction frequency model. To implement the proposed method, we used a catalog of earthquakes with magnitudes greater than 3.8 occurred within a radius of 50 kilometers around the Bojnord since 1990 to 2019. In addition to having the overall consistency with the frequencies of the Gothenburg-Richter recurrence law, the developed model provides more details of earthquake frequencies for different magnitudes. Additionally, there is a high correlation between the frequencies obtained by the frequency model and the tidal frequencies of the moon and sun. The correlation coefficient between the earthquake and tidal frequencies was obtained to be 93.7%. Considering the frequencies of the developed model reveals that the main return periods of the earthquakes in this region are 2, 6 and 10 months and 1 and 25 years.