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A comparison of alternative curve fitting techniques for different earthquake fault parameters of Iranian earthquakes
Comparación de técnicas de ajuste de curvas para diferentes parámetros de fallas en terremotos en Irán
DOI:
https://doi.org/10.15446/esrj.v24n4.72068Keywords:
Iranian earthquakes, L1 norm, L2 norm, Orthogonal Regression, Robust Regression, Correlation coefficient (en)Coeficiente de correlación, terremotos en Irán, norma L1, norma L2, regresión ortogonal, regresión robusta (es)
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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.
En este estudio, los autores se enfocaron en estimar las ecuaciones lineales óptimas para los parámetros asociados con diferentes mecanismos de fallas de terremotos en Irán. Con este propósito se evaluaron diferentes métodos de ajuste de curvas para presentar la relación empírica más apropiada entre varios parámetros sísmicos para diferentes sistemas de fallas. En el presente artículo se analizaron 46 terremotos ocurridos en Irán y con magnitudes entre 5.8 y 7.8, entre 1900 y el 2014. Se realizó una comparación al usar cuatro tipos de técnicas de ajuste de curvas. La estimación de los procedimientos se consideraron así (1) L2 o Regresión de Mínimos Cuadrados, (2) L1 o Suma de Mínimos en Regresión de Desviaciones Absolutas, (3) Regresión Robusta y (4) Regresión Ortogonal. Se seleccionaron intervalos de confianza del 95 por ciento para todos los tipos de relaciones de regresión. En la selección de la mejor distribución de probabilidades se consideraron los coeficientes de correlación de las regresiones lineales como un método fuerte y conceptualmente simple. Los coeficientes de correlación de todas las relaciones cambian entre 0.299 y 0.986 con regresión ortogonal; entre 0.168 y 0.792, con regresión L1 ; y entre 0.059 y 0.829, con regresión robusta. Para los terremotos en Irán, las relaciones empíricas que más se ajustan y que son más confiables entre la magnitud de momento (Mw) y la magnitud de onda superficial (Ms), entre la magnitud de momento y la longitud de ruptura superficial (SRL), entre la magnitud del momento y el desplazamiento máximo (MD), y entre la longitud de ruptura superficial y el desplazamiento máximo se obtuvieron por la regresión ortogonal, ya que esta provee coeficientes de relación más fuertes que aquellos estimados por medio de otras técnicas de regresión. Los resultados muestran que las relaciones empíricas estimadas entre los diferentes parámetros de falla al usar el método de regresión ortogonal podría ser aceptado como el más actualizado y más apropiado con respecto a otras normas de regresión. Además, estas ecuaciones se sugieren como las más confiables en la estimación del desplazamiento máximo de superficie, de la máxima longitud de ruptura superficial y asociada con la fiabilidad máxima en terremotos para diferentes zonas de Irán. Adicionalmente, las relaciones obtenidas pueden ser estadísticamente significativas para la evaluación de las actividades sísmicas, tectónicas y geológicas, y pueden ser utilizadas para medir el riesgo de ruptura en el altiplano iraní.
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