Empirical relationships between magnitude and some faulting parameters for earthquakes in Iran and adjacent regions

To assess seismic hazard, it is essential to estimate the potential seismicity, particularly estimation of size of the largest earthquake that can be identified by a distinct fault or earthquake source. One of the methods applied to estimate magnitude of earthquake is use of empirical relationships between magnitude and fault parameters. Fault parameters for the earthquakes from early instrumental period to 2014 are compiled to develop a series of empirical relationships among M_w and M_s with surface rupture length, horizontal and vertical displacements. The objective of this study is provision of an accurate piece of information about previous earthquakes through studies and investigations as well as a comprehensive and through catalog of the recent earthquakes so as to represent precise empirical relationships between the magnitude and earthquake fault parameters. Moreover, the information about earthquakes with magnitudes greater than M_w and M_s ≥5.5 were selected. In the beginning, the relationships between magnitudes and fault parameters were acquired, then the database on the basis of three slip types, consisting of strike-slip, normal and thrust, were manipulated and eventually relations were obtained. One also should not overlook the fact that three regression models, including SR, ISR and OR, were employed in this study. In SR and ISR methods, no error are considered for independent variables, whereas the mentioned error is taken into account in OR method. The OR method is obtained by minimization of the squares of the orthogonal distances to the best-fit line, whereas SR is derived by minimizing the squares of the vertical offset and also inverted standard least-squares regression (ISR) is derived by minimizing the squares of the horizontal offsets. However, roughly equal uncertainties for the two variables are regarded in the SR and OR methods. According to the obtained results, the best relationship between M_w and M_s with surface rupture length was established with correlation coefficients of 0.87 and 0.86, respectively. Also the relationships between M_s with maximum horizontal and vertical displacements with correlation coefficient of 0.63 and 0.62 in a respect way, are far better than the relationships between M_w with maximum horizontal and vertical displacements with correlation coefficient of 0.59 and 0.59. In addition, the relationships between magnitudes (M_w or M_s) and maximum horizontal displacements indicate a better fit than the relationships between the magnitudes and maximum vertical displacements. It is also worth mentioning that the best fit between M_w or M_s and surface rupture length was acquired with correlation coefficients of 0.87 and 0.86, respectively, by separating the database based on slip type. Whatever was mentioned about relationships between magnitudes and maximum horizontal and vertical displacements, is still valid by separating the database on the basis of slip type. According to the results of the direct relations, the SR and OR regression methods are far better than the ISR regression method with less error than ISR regression method. What’s more, in inverse relations, the ISR regression method estimates the coefficients with the lowest error rate in comparison with other methods. As an outcome, the findings were established from the current study are better than the global relationships for Iran and its adjacent regions. For example, in the light of the relationship between M_s and surface rupture length, the utilized global relation has been overestimated and then underestimated up to M=7.2 with respect to OR regression. The obtained relations have been simultaneously compared to two global relations within relationship between MS and surface rupture length. The results would seem to suggest that both global relations are overestimated and then underestimated up to M=6.5 in comparison with other regression methods.