A comparison of alternative curve fitting techniques for different earthquake fault parameters of Iranian earthquakes

In this study, we tried to estimate the optimum linear equations among the parameters associated with different earthquake fault mechanisms for Iranian earthquakes. For this purpose, we tested different curve fitting methods in order to present the most proper empirical relationships between several seismic parameters for different fault systems. In the present paper, 46 large and destructive Iranian earthquakes whose magnitudes change between 5.8 and 7.8 from 1900 to 2014 were used for the analyses. A comparison was made by using four types of curve fitting techniques. The estimation procedures are considered as (1) L2 or Least Squares Regression, (2) L1 or Least Sum of Absolute Deviations Regression, (3) Robust Regression and, (4) Orthogonal Regression. Confidence intervals were selected as 95% for all types of regression relationships. In the selection of the best probability distribution, we considered the correlation coefficients of the linear regressions as a powerful and conceptually simple method. Correlation coefficients of all relationships change between 0.299 and 0.986 with Orthogonal regression, between 0.168 and 0.792 with L1 regression, between 0.059 and 0.829 with Robust regression. For Iranian earthquakes, the most suitable and reliable empirical relationships between moment magnitude (Mw) and surface wave magnitude (Ms), Mw and surface rupture length (SRL), Mw and maximum displacement (MD), and SRL and MD were obtained by Orthogonal regression since it supplies stronger correlation coefficients than those of the other regression techniques in most estimates. The results show that estimated empirical relationships among the different fault parameters by using the Orthogonal regression method can be accepted as more up-to-date and more appropriate in comparison with the other regression norms. Consequently, these equations were suggested as more reliable in the estimation of the maximum surface displacement, maximum surface rupture length and associated with the maximum credible earthquakes for different areas of Iran. Furthermore, obtained relationships can be statistically significant for the assessment of seismic, tectonic and geologic activities, and they can be used to evaluate the rupture hazard of the Iranian Plateau.