The M_D Scale in Northern Morocco: A Comparative Study of Two Empirical Approaches

Abstract

We have derived, evaluated, and compared two empirical methods for computing duration magnitude M _D from 25 short-period vertical component stations of the Northern Morocco Seismic Network (NMSN). M _D has been scaled to IGN (Insituto Geograpfico National, Spain) body-wave magnitude (mb^IGN), using a set of 479 shallow (less than 30 km) earthquakes recorded from March 1992 to February 2001, with 2.5 ≤ mb^IGN ≤ 5.4. In the first approach: Individual Network Calibration, we determined an individual M _D formula for each station. In the second approach: Global Network Calibration, we used a single relationship to compute M _Dij (from the jth observation for the i-th earthquake) magnitudes at 25 selected stations as: M _Dij = − 0.14 +1.63 log₁₀ (τ _ij )+0.031(Δij)+cSta _j . Residuals (M _Dij − mb^IGN) for both techniques were thereafter deduced. Comparison between the two approaches provided the principal results: (1) The mean correlation between estimated magnitude; M _Dij and reference magnitude; mb^IGN is about 89.9% for the individual calibration method, and near 95% for global calibration method in which station corrections cSta _j were introduced, (2) Residuals (M _Dij − mb^IGN) are relatively large, and are ranging between − 0.60 and 0.60 magnitude units, for the individual calibration method, whereas they vary in the range − 0.38 to 0.40, for the global calibration method with corrections; cSta _j . (3) A random distribution of residuals (M _Dij − mb^IGN) is observed for each station in the case of the individual approach. Thus, the resulting average of these residuals is almost equal to zero. Using a global calibration without corrections results in negative residuals for a group stations and positive residuals for another an group indicating respectively that sites corresponding to these groups have a tendency to underestimate, or overestimate observed magnitude values.