On Magnitude Determination by Using Macroseismic Data

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On Magnitude Determination by Using Macroseismic Data (Second Paper) A. G.

On this assumption the magnitude formula: was derived from the empiri cai equation: M = Oi log I 0 r 2 C 2 [1] a r a R 2 = GE [2] found by Gutenberg and Ricliter (1942).

By using the basic relation: I = p log a q [3] applied in ali macroseismic computations, the magnitude formula: M = K x log r 2 ~ K 3 [4] -/t 2 is derived from the equation [2] on the sanie

1 On Magnitude Determination by Using Macroseismic Data (Second Paper) A. G. GALANOPOULOS(*) Ricevuto il 27 Novembre 1961 In the first paper (Galanopoulos, 1961), it was assumed that there is a linear relation of the earthquake intensity to the acceleratimi at the epicenter. On this assumption the magnitude formula: was derived from the empiri cai equation: M = Oi log I 0 r 2 C 2 [1] a r a R 2 = GE [2] found by Gutenberg and Ricliter (1942). The formula [1] was proved to be appropriate for M-determination from macroseismic data. By using the basic relation: I = p log a q [3] applied in ali macroseismic computations, the magnitude formula: M = K x log r 2 ~ K 3 [4] -/t 2 is derived from the equation [2] on the sanie assumptions. The results obtained from the equations [1] and [4] with the proper parameters derived from shocks in Greece (N = 124) and from Californian shocks (A T = 36) by the least-square method are presented in the table below. For reasons of comparison the results obtained from the corresponding equations set up by Gutenberg and Richter (1956) are given in the same table. Data used are tliose contained in the tables (4) and (5) of the first paper. Notation is the same. (*) ACKNOWLEDGMENT. The autlior is much indebted to Dr. V. Karnik for suggesting this investigation.

402 A. G. GALANOPOULOS The comparison shows that there is no difference in the Jf-determination if a linear or logarithmie relation of the intensity to the aeeeleration at the epieenter is assumed.

Table 1 - DIFFERENCES BETWEEN MACROSEISMIC MAGNITUDES COMPUTED FROM THE CORRESPONDING EQUATIONS AND IN STRUMENTAI. MAGNITUDES M* ASSIGNED BY GUTENBERG AND RLCIITER (GR), M. BATH (B) AND V. KARNIK (K).

2 402 A. G. GALANOPOULOS The comparison shows that there is no difference in the Jf-determination if a linear or logarithmie relation of the intensity to the aeeeleration at the epieenter is assumed. The same is true if a linear or logarithmie relation of the earthquake magnitude to the epicentral intensity is applied for determining the magnitude. Table 1 - DIFFERENCES BETWEEN MACROSEISMIC MAGNITUDES COMPUTED FROM THE CORRESPONDING EQUATIONS AND IN STRUMENTAI. MAGNITUDES M* ASSIGNED BY GUTENBERG AND RLCIITER (GR), M. BATH (B) AND V. KARNIK (K). Magnitude li N S S. E. S. D. M = 1.38 log I r n, (n), >n ±0.04 ± M = 0.83 log r 0.14 n, (n), >n ±0.04 ± M = 1.58 log r , (11), > ±0.04 ±0.48 M = 1.79 log I 0 r n ±0.05 ±0.28 M log r 2 Io 1.45 n ±0.05 ± M = 2.12 log r n ±0.05 ±0.32 M = logr (GR) n ±0.05 ±0.29 M = 1 fi» (GR) n ±0.08 ±0.50 M = 0.7 I n ±0.09 ±0.52 M = logt n ±0.09 ±0.57 li = depth of foci of earthquakes used (n = normal, (n) = slightly below normal, > n deep); N.= numbers of earthquakes used; = mean difference; s. E. = standard error of the mean; s. D. = standard deviation of a single observation. More important is the faet that in either relationship the epicentral intensity in itself alone is rather unreliable for determining earthquake magnitudes. This is due to the fact that the relation of the intensity to the aeeeleration at the epieenter is neither logarithmie nor linear. Moreover, in estimating the earthquake intensity the personal faotor of the field investigator is inevitably involved.

ON MAGNITUDE DETERMINATION BY USING MACROSEISMIC DATA 403 M - M* ( GR.B.K ) M - 1.38logl0r 2 _1 63 1 - M*(GR j 1 - M* ( B ) -M* ( K ) 1.38 log lo r>.

$0 o - a o O O a ao OO* A_-ff A ODO OO O O OO O «A o 0 O A a a O O O O * * OO M-M'(GR) M -M* ( B ) M-M* (K) \ -12 -IO -08 -Q6-0.«-02 1Q0»02»0«*Q6 *0.8 *1.0 M-M* (GR.B.K) M = 1 58logr 2-1.$

3 ON MAGNITUDE DETERMINATION BY USING MACROSEISMIC DATA 403 M - M* ( GR.B.K ) M logl0r 2 _ M*(GR j 1 - M* ( B ) -M* ( K ) 1.38 log lo r>.1 63 a OO O (SD & * eoo -il-o * -0-* 04 O O 0 -H- - O OO O 0 4fO OO O * '2eoo O Q A Q A & o o o OO * -03 ioo *02»04*06 *08 « O O a O * 0 * O O 0 O * o - a o O O a ao OO* A_-ff A ODO OO O O OO O «A o 0 O A a a O O O O * * OO M-M'(GR) M -M* ( B ) M-M* (K) \ -12 -IO -08 -Q6-0.«-02 1Q0»02»0«*Q6 *0.8 *1.0 M-M* (GR.B.K) M = 1 58logr M-M*(GR) O M - M' (B) A M -M* (K) M = 1 SOIogr'.l 38 O (JD * O a O» OD O «W t * _O OO oo - * _ 0 Offi O 4 * -OO b O O o O OCJD 0 ù. a aqu a o ao * O O «. / oob Fig. 1 - Variations witli M* of differences between macroseismic maguitudes computed from the correspondig equations valid for shocks in Greece and instrumentai magnitudes M* (GR, B, K). Insert, frequency distributions of differences between M and 31* (Gli, B, K).

4 0 4 A. G. GALANOPOULOS M-M' (GR > I o e - 0 6-04 0.2 - t 0.0 : - 0 2 - - 0.4 - - 0.0-0 6 M- 1.79logrI r2-3 97 M.1 79logl0r> -3 97 > -06-04 -02 100 '0.2 *0.4.06 6.0» M" M - 1.02logr'.

4-4- 4f 4-5 - -H- 4 4 44 4 4 4 4-20 M = 2.12 logr 3-3.98 T R - T -Ofl -05-0.4-02 too *02 «-0.4 *0J6 0B i I I I 45 50 55 60 65 70 75 «0 85 M' Fig.

4 4 0 4 A. G. GALANOPOULOS M-M' (GR > I o e t 0.0 : M- 1.79logrI r M.1 79logl0r> > '0.2 * » M" M logr'. Jo V M =1 02loqr I J t 4 S to.o * J I 1 I I S 5X M» 2.12 logr 2 _3.98 IO f H M = 2.12 logr T R - T -Ofl too *02 «-0.4 *0J6 0B i I I I «0 85 M' Fig. 2 - Variations with 31* of differences between macroseismic magnitudes computed from the corresponding equations valid for California shocka and instrumentai magnitudes M* (GR). Insert, frequency distributions of differences between M and 31* (GR). I

ON MAGNITUDE DETERMINATION BY USING MACROSEISMIC DATA 405 On the other hand, the relationsliip of the magnitude to the radius of perceptibility appears to be most reliable for the determination of

-J L- «6 6 0 6.6 6.0 6.5 7.0 7.6 60 8 5» M" M M" (GR ) f M«121 0 -I? -IO -oa -06-0.4-02 100-0.2 *0.4»0.6 *0.a -1.0-12 Fig.

5 ON MAGNITUDE DETERMINATION BY USING MACROSEISMIC DATA 405 On the other hand, the relationsliip of the magnitude to the radius of perceptibility appears to be most reliable for the determination of magnitudes with the same focal depth. The determination of the radius M-M'(GR) t M» logr M-_3.o 3.8 logp «0.2 ± # «ffl -08 -Q * o a J _ -I 1 1 L. -J L- « » M" M M" (GR ) f M« I? -IO -oa *0.4»0.6 *0.a Fig. 3 - Variations with ìli* of differences between macroseismic magnitudes computed from the corresponding equations valid for California shocks and instrumentai magnitudes M* (GR). Insert, frequency distri - butions of differences between M and M* (GR). of perceptibility is not influenced appreciably by personal factors, and the errors involved are negligeable. Variations in differences between macroseismic and instrumentai magnitudes and percentage frequency distributions of the various ma-

406 A. G. GALANOPOULOS gnitude differences versus instrumentai magnitude, M*. presented in Figures 1 to 4, show clearly the relative superiority of the M -M'(SR) t M-O.7I0 O.7 * 0.4 0.2 1 0.

0 4.5 5.0 55 6.0 65 7.0 7.5 80 8.5»--M* Fig.

6 406 A. G. GALANOPOULOS gnitude differences versus instrumentai magnitude, M*. presented in Figures 1 to 4, show clearly the relative superiority of the M -M'(SR) t M-O.7I0 O.7 * M lo 0.7.ìllllEIhJ^L OS Q2 ± _J 1 I I I M log I M = 12 53logl E OS too ' »--M* Fig. 4 - Variations with M* of differences between maoroseismic magnitudes computed from the corresponding equations valid for California shocks and instrumentai magnitudes M* (GR). Insert, frequency distributions of differences between M and M* (GR). formula [1] for Jlf-determmation of earthquakes originating at any focal depth. The differences in coeffìcients C and K for the two sets of data are due primarily to the difference in r used. It was stated in the first

ON MAGNITUDE DETERMINATION BY USING MACROSEISMIC DATA 407 paper that r denotes the maximum radius of perceptibility for the shocks in Greece and the mean radius for the California shocks.

7 ON MAGNITUDE DETERMINATION BY USING MACROSEISMIC DATA 407 paper that r denotes the maximum radius of perceptibility for the shocks in Greece and the mean radius for the California shocks. Owing to the existing differences in the building-civilization in the two countries, the same picture of damages does not correspond to the same earthquakeforce. As another reason we might mention the fact that the California data are generally the result of a more detailed investigation than in the case of data for shocks occurred in Greece. Most of the epicenters of shocks in Greece are offshore and the part of the shaken area corresponding to the open sea is unknown. Ali the California shocks are of nearly the same focal depth. The list of shocks in Greece includes shocks of normal and intermediate focal depth. The difference in number of observations and in the range of magnitudes must also be allowed for the differences in coefficients G and K for the two sets of data. SU M MARY This is a supplementary to paper 1 (Galanopoulos, 1961). It is shown that tliere is no difference in the M-determination if a linear or logarithmic relation of the intensity to the acceleration at the epicenter is assumed, and that the relation of the earthquake magnitude to the radius of perceptibility is much more appropriate for the M-determination of earthquakes with the same focal depth than that of the earthquake magnitude to the epicentral intensity used tlius far. Z USAMMENFASS UNG Es wird gezeigt, dass keine merkliche Differenz in der Magnitudenbestimmung existiert, falls eine lineare oder logarithmische Beziehung zwischen der Intensitàt und der Beschleunigung angenommen wird, und dass die Beziehung der Bebenmagnitude zu der makroseismischen Reichweite viel melir geeignet ist fior die Magnitudenbestimmung von Erdbeben derselben Herdtiefe als diejenige zwischen der Bebenmagnitude und der gróssten Stàrke im ScJiiittergebiet, die bisher dafilr benutzt wird. RIASSUNTO Questa nota fa seguito alla prima pubblicata nella Rivista «Annali di Geofìsica» Voi. XIV, Fase. 3 (Anno 1961).

8 408 A. G. GALANOPOULOS L'Autore dimostra che nella determinazione della Magnitudo dei terremoti, non esiste alcuna differenza se, anziché usare una relazione lineare fra intensità e accelerazione all' epicentro, ci si serve di una relazione logaritmica. E inóltre molto più appropriato, sempre per la determinazione della Magnitudo di terremoti con la stessa profondità ipocentrale, servirsi della relazione fra la Magnitudo del terremoto ed il raggio di percettibilità macrosismica dello stesso, che usare la relazione fra Magnitudo del terremoto e la sua massima intensità epicentrale, finora applicata. REFERENCES GALANOPOULOS, A., On Magnitude Determination by Using Macroseismic data, in " Ann. di Geof. ", 14, 3, (1961). GUTENBERG B. - RICHTER C., Earthquake Magnitude, Intensity Energy and Aeeeleration, in " Bull. Seism. Soc. Am. 32, 3, , (1942). Earthquake Magnitude, Intensity, Energy, and Aeeeleration, in " Bull. Seism. Soc. Am. ", 46, 2, , (1956).

Investigations of the Aftershocks of July 4, Earthquake in Epidavros (*)

Investigations of the Aftershocks of July 4, 1968 Earthquake in Epidavros (*) J. C. DRAKOPOULOS (**) - H. X. SRIVASTAVA (***) Ricevuto il 25 Febbraio 1970 SUMMARY. The spatial and tlie time distribution