On Magnitude D e t e r m i n a t i o n by Using Macroseismic Data (Second Paper) A . G . G A L A N O P O U L O S ( * ) R i c e v u t o il 27 N o v e m b r e 1 9 6 1 I n t h e first paper (Galanopoulos, 1961), it was assumed t h a t t h e r e is a linear relation of t h e earthquake intensity to t h e acceleratimi a t t h e epicenter. On this assumption t h e magnitude formula: M = Oi log I0r2 + C2 [1] was derived f r o m t h e empiri cai equation: ara„ R2 = GE [2] found b y Gutenberg a n d Ricliter (1942). The formula [1] was proved to be appropriate for M-determination from macroseismic d a t a . B y using t h e basic relation: I = p log a + q [3] applied in ali macroseismic computations, t h e magnitude formula: M = Kx log r2 + ~ + K3 [4] -/t2 is derived f r o m t h e equation [2] on t h e sanie assumptions. The results obtained f r o m t h e equations [1] and [4] with t h e proper parameters derived from shocks in Greece (N = 124) and from Californian shocks (AT = 36) b y the least-square method are presented in t h e table below. F o r reasons of comparison the results obtained from t h e cor- responding equations set up by Gutenberg and Richter (1956) are given in t h e same table. D a t a used are tliose contained in the tables (4) and (5) of t h e first paper. Notation is t h e same. (*) ACKNOWLEDGMENT. T h e a u t l i o r is m u c h i n d e b t e d t o D r . V . K a r n i k f o r s u g g e s t i n g t h i s i n v e s t i g a t i o n . 4 0 2 A . G . G A L A N O P O U L O S The comparison shows t h a t there is no difference in t h e J f - d e t e r m i - nation if a linear or logarithmie relation of t h e intensity to t h e aeeeleration a t t h e epieenter is assumed. The same is t r u e if a linear or logarithmie relation of the e a r t h q u a k e m a g n i t u d e to the epicentral intensity is applied for determining t h e magnitude. T a b l e 1 - D I F F E R E N C E S B E T W E E N M A C R O S E I S M I C M A G N I T U D E S C O M P U T E D F R O M T H E C O R R E S P O N D I N G E Q U A T I O N S A N D I N S T R U M E N T A I . M A G N I T U D E S M* A S S I G N E D B Y G U T E N B E R G A N D R L C I I T E R ( G R ) , M . B A T H ( B ) A N D V . K A R N I K ( K ) . M a g n i t u d e li N S S. E . S. D . M = 1.38 l o g I„ r 2 — 1.63 n, (n), > n 124 — 0 . 0 1 ± 0 . 0 4 ± 0 . 4 0 M = = 0 . 8 3 l o g r 2 + — + 0.14 n, (n), >n 124 — 0 . 0 2 ± 0 . 0 4 ± 0 . 4 2 3.62 n, (n), >n ± 0 . 0 4 M = 1.58 log r 2 — 1.38 11, (11), >11 124 — 0 . 0 1 ± 0 . 0 4 ± 0 . 4 8 M = 1.79 log I 0 r 2 — 3.97 n 36 — 0 . 0 2 ± 0 . 0 5 ± 0 . 2 8 M - 1.02 log r 2 + I o 1.45 n 36 — 0 . 0 3 ± 0 . 0 5 ± 0 . 3 1 2.92 ± 0 . 0 5 M = 2.12 log r 2 — 3.98 n 36 — 0 . 0 3 ± 0 . 0 5 ± 0 . 3 2 M = — 3.0 + 3.8 l o g r ( G R ) n 36 — 0 . 0 5 ± 0 . 0 5 ± 0 . 2 9 M = 1 + f i » ( G R ) n 36 + 0.05 ± 0 . 0 8 ± 0 . 5 0 M = 0.7 I 0 + 0.7 n 36 + 0.01 ± 0 . 0 9 ± 0 . 5 2 M = 12.53 l o g T 0 — 4 . 8 9 n 36 + 0 . 0 3 ± 0 . 0 9 ± 0 . 5 7 li = d e p t h of f o c i of e a r t h q u a k e s u s e d ( n = n o r m a l , (n) = s l i g h t l y b e l o w n o r m a l , > n — d e e p ) ; N . = n u m b e r s of e a r t h q u a k e s u s e d ; = m e a n d i f f e r e n c e ; s. E . = s t a n d a r d e r r o r of t h e m e a n ; s. D . = s t a n d a r d d e v i a t i o n of a s i n g l e o b s e r v a t i o n . More i m p o r t a n t is t h e f a e t t h a t in either relationship t h e epicentral intensity in itself alone is r a t h e r unreliable for determining earthquake magnitudes. This is due to t h e f a c t t h a t t h e relation of t h e intensity to t h e aeeeleration a t t h e epieenter is neither logarithmie nor linear. Moreover, in estimating t h e e a r t h q u a k e intensity t h e personal faotor of t h e field investigator is inevitably involved. ON M A G N I T U D E D E T E R M I N A T I O N B Y U S I N G M A C R O S E I S M I C D A T A 4 0 3 M - M* ( G R . B . K ) M - 1 . 3 8 l o g l 0 r 2 _ 1 6 3 •1 - M * ( G R j 1 - M * ( B ) - M * ( K ) a OO O + + (SD & + + + * ©eoo -il-O * 04 O O 0 + -H-—©-0-* + +- O OO O® + 0 4fO + OO O * + '2eoo + O + Q A Q A & o o o OO + • 1 . 3 8 l o g lo r> . 1 6 3 -10 - 0 8 -06 - 0 * -03 iOO * 0 2 » 0 4 * 0 6 * 0 8 «1.0 • 0 8 + 0.6 * 0 * • 0.2 1 0.0 -0.2 -0* -0.6 -0.8 - 1.0 o + M - M ' ( G R ) M - M * ( B ) M-M* (K) O O a O + O® O O ©0 - a o + O O + a + + a o O O * + A _ - f f A ODO O O O O OO© O + O + + «A o©0 O A a a O O O O * * O O \ -12 -IO -08 -Q6 -0.« -02 1Q0 »02 »0« *Q6 *0.8 *1.0 M - M * (GR.B.K) M = 1 5 8 l o g r 2 - 1 . 3 8 + M - M * ( G R ) O M - M ' ( B ) A M - M * (K) 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 © a o + © * O O «. + M = 1 SOIogr'.l 38 / oob F i g . 1 - V a r i a t i o n s w i t l i M * of d i f f e r e n c e s b e t w e e n m a c r o s e i s m i c m a g u i t u d e s c o m p u t e d f r o m t h e c o r r e s p o n d i g e q u a t i o n s v a l i d f o r s h o c k s i n G r e e c e a n d i n s t r u m e n t a i m a g n i t u d e s M* ( G R , B , K ) . I n s e r t , f r e q u e n c y d i s t r i b u t i o n s of d i f f e r e n c e s b e t w e e n M a n d 31* ( G l i , B , K ) . 4 0 4 A . G . G A L A N O P O U L O S M - M ' ( G R > 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 7 9 l o g l 0 r > - 3 9 7 > - 0 6 - 0 4 - 0 2 1 0 0 '0.2 *0.4 . 0 6 .0.6 • 0 4 .0 2 - 0 . 4 -0.6 M - 1 . 0 2 l o g r ' . J o _ _ V 4 5 2 9 2 + ++-+ 6 . 0 — » M " M = 1 0 2 l o q r I + J 2 t 4 S 2 . 9 2 - 0 8 - 0 6 - 0 4 -02 tO.O *0.2 +04 + 0 6 J I 1 I I 1 1— 4.S 5X1 56 6 0 6 5 7.0 7.5 M » 2 . 1 2 l o g r 2 _ 3 . 9 8 20 M = 2.12 logr3-3.98 + + + IO 44 .4- + + 5 4- 4f 4- T R - T -+ + + -H- 4 4 44 + 4 + + 4 4 + 4- + i I I I -Ofl -05 -0.4 + I -02 tOO *02 «-0.4 *0J6 +0B 4 5 5 0 5 5 6 0 6 5 7 0 7 5 « 0 8 5 — M ' F i g . 2 - V a r i a t i o n s w i t h 31* of d i f f e r e n c e s b e t w e e n m a c r o s e i s m i c m a g n i t u d e s c o m p u t e d f r o m t h e c o r r e s p o n d i n g e q u a t i o n s v a l i d f o r C a l i f o r n i a s h o c k a a n d i n s t r u m e n t a i m a g n i t u d e s M * ( G R ) . I n s e r t , f r e q u e n c y d i s t r i - b u t i o n s of d i f f e r e n c e s b e t w e e n M a n d 31* ( G R ) . O N M A G N I T U D E D E T E R M I N A T I O N B Y U S I N G M A C R O S E I S M I C D A T A 4 0 5 On t h e other hand, t h e relationsliip of the m a g n i t u d e to the radius of perceptibility appears to be most reliable for the determination of magnitudes with t h e same focal depth. The determination of the radius M-M'(GR) t « 0 . 2 ± 0 . 0 - 0 . 2 - 0 . 4 - 0 . 6 - o a M » - 3 - 0 + 3.8 logr M-_3.o +3.8 logp •#• + « ffl J |_ - I 1 1 L . - 0 8 - Q 6 - 0 4 - 0 2 1 0 0 +02 + 0 * - 0 6 - 0 6 -J L- « 6 6 0 6.6 6.0 6.5 7.0 7.6 6 0 8 5 — » M " M—M" ( GR ) f M « 1 + 2 1 0 -I? -IO -oa -06 -0.4 -02 100 -0.2 *0.4 »0.6 *0.a -1.0 -12 F i g . 3 - V a r i a t i o n s w i t h ì l i * of d i f f e r e n c e s b e t w e e n m a c r o s e i s m i c m a g n i t u d e s c o m p u t e d f r o m t h e c o r r e s p o n d i n g e q u a t i o n s v a l i d f o r C a l i f o r n i a s h o c k s a n d i n s t r u m e n t a i m a g n i t u d e s M * ( G R ) . I n s e r t , f r e q u e n c y d i s t r i - b u t i o n s of d i f f e r e n c e s b e t w e e n M a n d M* ( G R ) . of perceptibility is not influenced appreciably by personal factors, and t h e errors involved are negligeable. Variations in differences between macroseismic and instrumentai magnitudes and percentage frequency distributions of t h e various ma- 4 0 6 A . G . G A L A N O P O U L O S gnitude differences versus instrumentai magnitude, M*. presented in Figures 1 to 4, show clearly the relative superiority of the M - M ' ( S R ) t * 0 . 4 + 0 . 2 1 0 . 0 - 0 2 - 0 4 M - O . 7 I 0 + O.7 M - 0.7 lo +0.7 . ì l l l l E I h J ^ L - 1 . 4 - 1 2 - 1 0 -OS - 0 . 6 - 0 4 - Q 2 ±00 + 0 2 + 0 4 + 0 . 6 + 0 . 8 - 1 . 0 +12 _ J 1 I I I M - 12.53log I 0 - 4 8 9 + -+ + 4+ M = 12 53logl0- 4.89 . E 3 - - 1 6 - 1 4 . 1 2 1.0 - O S - 0 . 6 - 0 4 - 0 2 tOO '02 - 0 . 4 - 0 . 6 + 0 . 8 + 1 . 0 4 . 5 5 . 0 5 5 6 . 0 6 5 7 . 0 7.5 8 0 8.5 — » - - M * F i g . 4 - V a r i a t i o n s w i t h M * of d i f f e r e n c e s b e t w e e n m a o r o s e i s m i c m a g n i t u d e s c o m p u t e d f r o m t h e c o r r e s p o n d i n g e q u a t i o n s v a l i d f o r C a l i f o r n i a s h o c k s a n d i n s t r u m e n t a i m a g n i t u d e s M* ( G R ) . I n s e r t , f r e q u e n c y d i s t r i - b u t i o n s of d i f f e r e n c e s b e t w e e n M a n d M* ( G R ) . formula [1] for Jlf-determmation of earthquakes originating a t any focal depth. The differences in coeffìcients C and K for the two sets of data are due primarily to t h e difference in r used. I t was stated in the first ON M A G N I T U D E D E T E R M I N A T I O N B Y U S I N G M A C R O S E I S M I C D A T A 4 0 7 paper t h a t r denotes t h e m a x i m u m radius of perceptibility for t h e shocks in Greece and t h e mean radius for t h e California shocks. Owing to t h e existing differences in t h e building-civilization in t h e two countries, t h e same picture of damages does not correspond to the same earthquake- force. As another reason we might mention t h e f a c t t h a t t h e California d a t a are generally the result of a more detailed investigation t h a n in the case of d a t a for shocks occurred in Greece. Most of t h e epicenters of shocks in Greece are offshore and the p a r t of t h e shaken area correspond- ing to t h e open sea is unknown. Ali t h e 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 t h e range of magnitudes must also be allowed for the differences in coefficients G and K for the two sets of d a t a . 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 Magnituden- bestimmung 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). 4 0 8 A. G. G A L A N O P O U L O S L'Autore dimostra che nella determinazione della Magnitudo dei ter- remoti, non esiste alcuna differenza se, anziché usare una relazione lineare fra intensità e accelerazione all' epicentro, ci si serve di una relazione lo- garitmica. 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. R E F E R E N C E S G A L A N O P O U L O S , A . , On Magnitude Determination by Using Macroseismic data, i n " A n n . d i G e o f . " , 1 4 , 3 , ( 1 9 6 1 ) . G U T E N B E R G B . - R I C H T E R C . , Earthquake Magnitude, Intensity Energy and Aeeeleration, i n " B u l l . S e i s m . S o c . A m . 3 2 , 3 , 1 6 3 - 1 9 1 , ( 1 9 4 2 ) . — — Earthquake Magnitude, Intensity, Energy, and Aeeeleration, i n " B u l l . S e i s m . S o c . A m . " , 4 6 , 2 , 1 0 5 - 1 4 5 , ( 1 9 5 6 ) .