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

114 Deli Cheng, Yushou Xie, and Zhifeng Ding2. Magnitude ScaleThe Gutenberg surface-wave magnitude formula (Gutenberg, 1945a) and Gutenberg-Richterbody-wave magnitude formula (Gutenberg and Richter, 1956) wereused:Ms = log A + 1.656 log A + 1.818 + S (1)mg = log($)+ Q(A,h) + C.In formula (1): A is the vector sum of maximum horizontal displacements in pmof surface waves with period of 20 f 3 sec for earthquakes with epicentral distancebetween 15" and 130" (a factor of 4 is multiplied when only one component isavailable); A is the epicentral distance, in degrees; and the station correction (S)is taken from Gutenberg (1945a). In using formula (l), Gutenberg also consideredthe influence of focal depth, radiation pattern and wave path. He pointed out thatformula (1) was obtained from earthquakes with focal depth (h) from 20 to 30km; and that for h 5 40 km, the correction does not exceed 0.2. Thus, in thispaper, formula (1) is ordinarily used for shallow shocks with h 5 40 km; and for40 < h 5 100 km, a magnitude correction, AMs, according to BZth (1977) is used:h (km) 40 50 60 70 80 90 100AM, +0.15 +0.20 +0.30 +0.35 +0.45 $0.50 +0.55When the average value of many stations was used, the influence of azimuth andwave path were not considered. Nevertheless, it is necessary to point out thataccording to Gutenberg's investigation, for seismic waves passing through the PacificBasin and that outside of it, the difference of magnitude may attain 0.5.For the years 1900 to 1948, no strict specification could be given for the amplitudeA in formula (1). Generally, one half of the wave crest-to-trough value of the surfacewavemaximum was taken, which is slightly larger than the weighted average ofthe three consecutive amplitudes around the maximum taken by Gutenberg (Bgth,1981).The body-wave magnitude formula (2) was given by Gutenberg for unified magnitude.The Q-value resulted from the modification of the shallow and deep focusbody-wave magnitude scales (Gutenberg, 194513, 1945c) by using more observationaldata. Thus, the rnB-value calculated by using formula (2) differs slightlyfrom that given in Gutenberg and Richter (1954), indicated by MB in this paper.The 1945 values of Gutenberg (1945b, 1945c) were used for the station correctionC. The maximum amplitude of the body wave was taken as amplitude A, usually10 see after the first impulse on seismograms of broad-band intermediate-periodseismographs.For earthquakes with focal depth h 5 40 km, both Ms and rng were determined.For 40 < h 5 100 km, rng was usually given and Ms with depth correction wheneverpossible. For medium and deep focus earthquakes, only rng is given.