Relationships to Estimate the Magnitude Ms of Historical Earthquakes in Europe from Macroseismic Observations

We develop empirical relationships between the surface wave magnitude MS and macroseismic data, i.e. the epicentral intensity I0, isoseismal radii R(I) of different intensities I and the focal depth h. The basis of this study is formed by carefully selected instrumental parts (since 1900) of 2 earthquake catalogues: Kárník 1996 (Europe and the Mediterranean), and Shebalin et al. 1998 (Central and Eastern Europe). We use the orthogonal regression because we presume that all parameters are in error and because it has the advantage to provide a reversible regression equation. From Shebalin et al.1998 catalogue we obtain MS = 0.65 I0 + 1.90 log(h) – 1.62 with equivalent error δMS = ±0.21. In order to establish a relationship between MS and isoseismal radii we apply a theoretically based model which takes into account both exponential decay and geometrical spreading. From Shebalin et al. 1998catalogue we find MS = 0.673 I + 2.44 log (S(I)) + 0.00163 S(I) – 2.48 with δMS = ±0.28. Here I is the macroseismic intensity (I = 3…9) of the isoseismal in the focal distance S(I) [km]. Kárník 1996 gives isoseismal radii for I = 3 and 5. We obtain: MS = 0.808 I + 2.84 log (S(I)) + 0.00190 S(I) – 3.71 with δMS = ±0.65. These equations make possible reliably estimates of MS . We recommend them for application. The use of high quality data only as input in the regression analysis provides reliable relationships to estimate magnitudes. The magnitude estimation of a historical earthquake from the epicentral intensity gives reliable results only if the focal depth is known well enough. The relationship using isoseismal radii is of greater practical importance as it allows more reliable magnitude estimations of historical earthquakes. We observe regional variations in the relationships which need further investigation.poste