Historical Seismograms - Evidence from the AD 2000 Izu Islands ...

204 G. E. Fiedler B.Figure 3. The San Francisco earthquake of April 18,1906, H = 13:lZ:OO GMT, recordedby the same Milne horizontal seismometer as in Figure 2, EW component, at the KewObservatory, England. Copy taken from Lawson et a!. (1908). Scale 1:l.If one compares the seismogranis shown in Figures 2 and 3, one finds that theamplitudes of the P-waves of the Caracas earthquake recorded in Kew at 911 21.5mare larger and clearer than that of the San Francisco event recorded in Kew at1311 24..5m and 13h 25.6m, even if the azirnutlial effect of tlie orientation of theinstrument vs. the direction of propagation of waves is considered. The mine isvalid for the S-waves, having the San Francisco record a clearer arid sharper onsetand only where the Rayleigh waves with periods from 30 to 20 sec appear, the tracefor the San Francisco event is much larger and strongly over-recorded for four tosix minutes.From Figure 2 we get a zero-to-peak amplitude for the first visible P-arrival of0.1 mm and this yields with a Q-value of 6.7 and the relation rnb = &, +log,,(A x103/2vT), rnb = 7.4 to 7.5, including the correction for azimuth of this east-westseismograph component and assuming a period of 3 sec for the P-wave, recordedby the relative long period Milne seismograph. This result from a horizontal componentis questionable, but one should not forget that, for example, for the recentCaracas earthquake of July 29, 1907, the USCGS/NEIS, based on worldwide moderninstrurnentsl data, published rnh magnitude values between 4.5 and 7.2, with amean of 5.6.Richter (1958) published a magnitude of 8.4 for the Caracas earthquake of 1900.Using information from B. Gutenberg’s worksheets, Ksnamori and Abe (1979) obtainedMs = 8.2, and corrected Ms = 8.1. Abe and Koguchi (1983) recomputedmagnitudes of historical earthquakes and obtained for the Caracas event Ms = 7.7.But they applied the abnormally high damping ratio of 1.55 to get the “averageresponse curve of Milne seismographs” shown on page 6 of their paper.From the mentioned damping ratio 6 = 1.55, we define tlie logarithmic decrementof damping as D = log,, II = 0.190, and with this we get the damping constant p2by the relations from B. Galitzin and E. Wiechert (see Sieberg, 1923):7r2p2 = = 0.981.7rz + (D/ log,, e)zFrom this we get the damping number h = d m = 0.137. This is equal to thedamping factor 5, which is used in this paper, because we can write ln E = 0.438 isthe logarithmic decrement “d” for half period and