Magnitude–intensity and intensity–attenuation relationships for atlas region and Algerian earthquakes

This paper presents the results of an investigation of the magnitude–intensity and intensity–attenuation relationships for earthquakes in the Atlas block and Algeria using macroseismic data. This work is based on a selected sample of isoseismal maps from 32 events which were recently revised. Surface‐wave magnitudes, M s , are recalculated using the Prague formula and range from 4·2 to 7·45. Because the Atlas mountains block is in a collision zone, earthquakes occur in general within a layer 15 km deep. Expressions of general form for the magnitude–intensity and intensity–attenuation correlations are adopted and are, respectively,\documentclass{article}\pagestyle{empty}\begin{document}$$ M_{sc} \; = \;A_1 \; + \;A_2 (I_i)\; + \;A{}_3(R_i)\; + \;A_4 \;\log \;R_i \; + \;\sigma P $$\end{document}and\documentclass{article}\pagestyle{empty}\begin{document}$$ I\; = \;B_1 \; + \;B_2 (M_3)\; + \;B_3 (R)\; + \;B_4 \;\log \;R\; + \;\sigma P $$\end{document}where R 2 = d 2 + h 2 , d the source distance in km, h the focal depth in km, M s the revised surface‐wave magnitude, M sc the predicted surface‐wave magnitude, I i the intensity at isoseismal i , I the predicted intensity, σ the standard deviation and P is zero for 50‐percentile values and one for 84‐percentile, and the coefficients A's and B's are determined by regression analysis. The results of this study show that the intensity–attenuation models are adequate to predict quite well the die‐out of intensity with distance in the Atlas zone and coastal Algeria; it is also found that magnitude can be predicted accurately by calibrating isoseismal radii against revised instrumental surface‐wave magnitude. Such magnitude–intensity relationships may be used to evaluate the magnitude of historical earthquakes in the region under survey, with no instrumental data, for which isoseismal radii and intensities are available.