1. M. Herak, S. Markušić, D. Herak Department of Geophysics, Faculty of Science University of Zagreb, Zagreb

2. History and motivation... The first magnitude calibration in Croatia was done by D. Skoko in his Ph. D. dissertation in 1969. Two calibrating functions for recordings on 1000 kg Wiechert horizontal seismograph were derived – for distances of 2.2˚–20˚, and 20˚–170˚. In the ‘Balkan project’ (1974), a new formula was derived. It was retained even after introduction of electromagnetic and digital seismographs: After a significant enlargement of the network in the few first years of the 21st century, Futač (2007) checked its appropriatness, and concluded that data do not indicate the need for change. As digital high-quality data accumulated, it became clear that the formula does not work well for short distances, significantly underestimating the magnitude. This prompted recalibration of the M L -scale. The need to use moment magnitudes in hazard analyses, motivated efforts to routinely observe also M w thus initiating this work.

3. Goals and earthquakes Goals: Calibration of M L and M WA using recent digital data from the Croatian Seismographic Network, and Introduction of an automatic routine procedure for determination of M W using spectral analyses of local and regional earthquakes recorded by the Croatian Seismographic Network Selection of earthquakes: Events from the Croatian Earthquake Catalogue satisfying any of the following: Year > 2002 M > 2.5 & D < 200 km (for any station) M > 3.0 & D < 300 km (for any station) M > 3.5 & D < 400 km (for any station) M > 4.0 & D < 500 km (for any station) M > 5.0 & D < 700 km (for any station) 11900 3-component BB seimograms found!

4. Goals and earthquakes 1. Determination of seismic moment (M 0 ) and moment magnitude (M w ) The source displacement spectrum looks like: v – velocity of seismic waves f – frequency f 0 – corner frequency  – density frequency amplitude corner frequency, f 0 low frequency spectral level

5. M 0 and M w 1. Determination of seismic moment (M 0 ) and moment magnitude (M w ) Displacement spectrum at receiver at the epicentral distance  : If we know (or invert for!) attenuation ( , Q), and assume reasonable values representing the effects caused by the radiation pattern, free surface amplification and geometrical spreading, we can fit the formula to the observed spectrum and get the scalar seismic moment (M 0 ), and then compute the moment magnitude: M w = 2/3 log(M 0 ) – 6.07  – near surface attenuation Q – quality factor (for P or S-waves) R P – average radiation pattern coefficient (  0.6) F S – free surface amplification (  2 for SH) G = 1/g d – geometrical spreading function, g d – geodistance

6. M 0 and M w 1. Determination of seismic moment (M 0 ) and moment magnitude (M w ) 1.Determine theoretical onset times of Pg, Pn, Sg, Sn. 2.LP-filter, read max. S-wave amplitudes. 3.Wood-Anderson filter, read max. S-wave amplitudes 4.Determine the windows for: noise, P-waves, S-waves. 5.Compute spectra, smooth, correct for the instrument and noise. 6.Fitting theoretical curve to spectra for P- and S-waves yields estimates for: Q(f), , f 0, M 0, both for P- and S- waves 7.Compute M W as average of M W (P) and M W (S) 8.Save everything, next earthquake S-waves P-waves

7. M 0 and M w ; M L and M WA 2. Calibration of M L and the Wood-Anderson magnitude M WA 1.Compute M L and M WA for every recording (all stations) using the best calibrating function so far, in the form: 2.Compute representative earthquake magnitude for all events for which at least three magnitude estimates exist as the median of the station magnitudes. 3.Check if there is any distance dependence – if yes adjust coefficients observing all possible constraints (e.g. anchoring of M WA at 100 km). 4.Compute station corrections (SC) and start again... The best estimates are: A max is the trace amplitude in nm on the simulated Wood-Anderson seismograph (magnification 2080). This is the same M WA formula as obtained for Central Europe by Stange (2006).

8.  M = (Station magnitude) – (Earthquake magnitude) vs. time  M W  M L  M WA

9.  M = (Station magnitude) – (Earthquake mgnitude) vs. time

10. M 0 and M w – results M WS vs M WP Individual (station) magnitudes Earthquake magnitudes Corner frequency vs M W S-waves P-waves

11. M 0 and M w ; M L and M WA (Event magnitude) – (Station magnitude) (with added station corrections)

12. Relationships... Individual (station) magnitudes Earthquake magnitudes M W vs. M WA M W vs. M L M L vs. M WA

13. Station corrections Sta M L M WA M wS M wP ---------------------------- KIJV 0.02 0.06 -0.03 -0.03 CACV 0.04 0.06 -0.12 -0.08 PTJ 0.09 0.06 -0.05 -0.00 DBR 0.06 0.15 0.01 0.06 STON 0.05 0.08 0.01 0.06 STA 0.10 0.14 -0.01 -0.04 NVLJ 0.05 0.05 -0.05 -0.08 RIY -0.06 -0.12 -0.13 0.02 ZAG -0.27 -0.32 -0.21 -0.16 SLUN 0.06 0.07 -0.05 -0.04 UDBI -0.06 -0.11 -0.12 -0.05 BRJN 0.04 0.04 -0.03 -0.10 SISC -0.40 -0.41 -0.20 -0.24 HVAR 0.04 0.00 -0.02 0.12 MORI -0.04 -0.01 -0.07 -0.08 ZIRJ -0.03 -0.01 -0.03 -0.04 OZLJ 0.15 0.16 -0.13 -0.01 KALN 0.07 0.01 -0.05 -0.03 RIC -0.04 -0.11 -0.18 -0.01 KSY -0.10 -0.11 -0.17 -0.10 SLNJ 0.14 0.04 -0.01 0.14 ---------------------------- The largest (negative) station corrections are found on thick alluvium, in river valleys close to the Pannonian basin. Corrections for the moment magnitudes are smaller than for local magnitudes (  !) M L station corrections

14. Conclusions 1.Regression of M w vs. M L using both magnitudes determined independently on the same set of stations and earthquakes is far better than regressions of locally determined M L vs. M w determined (mostly for large and distant earthquakes!) by other agencies. 2.Proposed inversion of observed spectral shapes of local and regional earthquakes results in consistent M w estimation using data collected by the Croatian Seismographic Network. 3.New calibrating functions for local magnitudes (M L and M WA ) yield distance- independent estimates. 4.The correspondence between the three magnitudes is close to 1:1 relationship. This is encouraging, promising an easy conversion from M L to M W for older events. 5.Results obtained in studies done so far using M L as proxy for M W will most probably not significantly change after proper conversion.