ESTIMATION OF EARTHQUAKE MAGNITUDES FROM EPICENTRAL INTENSITIES AND OTHER FOCAL PARAMETERS IN CENTRAL AND SOUTHERN EUROPE

Abstract

The publication of an earthquake catalogue by Karnik in 1996 (a continuation and revision of an earlier one (1969)) makes important data available covering one century of the seismic history of Central and Southern Europe. It allows us to study in detail empirical relations between the magnitude and other focal parameters. In this study well-known relations combining two or three focal parameters, $M =A +BI 0 +C log(H ), M s =D +EI 0 +F log(H ), M L =G +OI 0 +P log(H ), M L =Q +RM s +S log(H )$, are investigated (M, Karnik's magnitude; $M L $, local magnitude; $Ms $, surface wave magnitude; $I 0 $, epicentral intensity; H, focal depth in kilometres). The data show a considerable scatter with respect to the relations above. The relations are considered useful, if the following significance criteria are fulfilled. (1) The data sets comprise a minimum of 20 entries.(2) The partial correlation between the two most important parameters is greater than 70 per cent. (3) The parameter of least importance still influences the correlation of the others by more than 5 per cent. The partial correlation coefficients help to decide whether the data are to be rejected as insufficient for the regression analysis or to determine the level beyond which it is useful to perform a regression analysis excluding the parameter of lowest importance. Two kinds of regression are carried out: (1) standard linear regression assumes that only M or $M L $, respectively, are in error, while the remaining two parameters are error-free. (2) Orthogonal regression assumes that all three parameters have errors. This is the case for the data in the catalogue used here. The orthogonal regression $M =-1.682 + 0.654 I 0 + 1.868 log (H )$, with a standard deviation of $±0.284$, differs considerably from Karnik's empirical relation $M = 0.5 I 0 + log (H ) + 0.35$ for shallow foci, but agrees well with the results of earlier studies by the authors for earthquakes in SE Europe. The data set $M, I 0, H $ (for $H < 50 km$) fails criterion (3). The orthogonal least-squares fit without $log (H )$ has been found as follows: $Ms = 0.550 I 0 + 1.260$, with a standard deviation of $±0.412$. We observe systematic regional deviations from this relationship, which need further investigation. The correlation analysis shows that $M L $ and $Ms $ are weakly linked with $log (H )$, but the correlation between $M L $ and $Ms $ is very high (93 per cent). Therefore, the orthogonal relation between $M L $ and $Ms $ without the $log (H )$ term was chosen: $M L = 0.664 + 0.893 Ms $, with a standard deviation of $±0.163$. The correlations between $M L, I 0 $ and $log (H )$ do not fulfil the significance criteria. For the purpose of earthquake hazard analysis the orthogonal regression visualizes simultaneously the errors of all input data, i.e. $δM Li , δMi $ and $δ log (Hi )$. Our new relationships result from orthogonal regression analysis using a large high-quality data set. They should be applicable in Central and Southern Europe unless there are regional relationships available that fit the data better.