Tectonophysics, 93 (1983) 295-306

Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

295

NORMAL, BLUE AND RED EARTHQUAKES-A NEW WAY OF EARTHQUAKE CLASSIFICATION ON THE BASIS OF BODY-WAVE MAGNITUDES

S.J. DUDA and R. NORTMANN

Instilut jiir Geophysik, Universitiit Hamburg, Hamburg (Federal Republic of Germany)

(Received September 23. 1982)

ABSTRACT

Duda, S.J. and Nortmann, R., 1983. Normal, blue and red earthquakes-a new way of earthquake

classification on the basis of body-wave magnitudes. In: S.J. Duda and K. Aki (Editors), Quantifica-

tion of Earthquakes. Tectonophysics, 93: 295-306

Mon~hromatic magnitudes, based on P- and on S-waves, provide a means to recognize differences in

the spectral contents of body-waves radiated from earthquake foci. New, synthetic magnitude calibration

functions taking into account periods of waves recorded, improve the consistency of magnitude figures

assigned routinely to earthquakes.

First results of a world-wide regionalization of earthquakes according to their spectral character are

presented. Preponderance of short-period radiation in one class of earthquakes, and of long-period

radiation in another is seen. if the radiation is compared with that of normal earthquakes.

INTRODUCTION

The earthquake magnitude was intended to be a single number, fully expressing the strength of an earthquake. Thereby, a unique relation was postulated between the magnitude and the total seismic energy radiated from the source. However, doubts are mounting as to the possibility of determining the seismic energy with an accuracy sufficient to verify the postulate. Moreover, it becomes apparent that the strength of an earthquake cannot be adequately expressed in a single magnitude scale. By now several, independently determined magnitudes are being already reported routinely (see, e.g., NEIS and ISC).

The differences between the magnitude scales in use lie primarily in the period ranges utilized, even though the periods usually are not published with the magni- tudes. While the body-wave magnitude mB is being determined from P-waves ranging in period from about 0.1 s to 10 s, the body-wave magnitude mb from WWSSN-stations is based on P-waves with a period of about 1 s (short-period Benioff seismometers). The local magnitude M, emphasizes periods around 0.8 s,

0040- 195 1,83,$03.00 0 1983 Elsevier Science Publishers B.V.

dnd the surface-wave magnitude for sl,allol\ rurtiiquakts M, i,, bated hit L\AL~\ t:,

the period rauge 17 23 s. The mantle wave lllagnit~de M, IS fvund frt,m w;1%~h ranging in period frs)m 30 6 t5: 250 s. and finally. the moment magnitude ,%I, V,

supposed 10 be based on waves with infinite period. The bituatli.rn is aggravated.

however, by the fact that no consistency exists as to the have type underlying the

scales While for the de~erminat~or1 of rhc: loyal magnitude u~uail~ the Sg- 01

&phase is employed, the bk>dy-wave ITlliigtl~tUd~ is iYsliictcd tii P-\vhb,c\. arKi f of the

focal process on one side, and the radiated signal in the time or frequency domain

on the other. The physical parameters of special importance are thereby the fault

length and width, the dislocation. the fracture velocity. the rise tmte. the stress drop

and the seismic moment. Based on the similarity principle, the authors postulate

relations between two or more of the parameters. The spectra of the signals radiated

though prove to be dependent on the model, and no unanimous opinion exists as to

the optimum model. applicable to ail earthquakes. For a given model. however. the

shape of the spectrum radiated is fixed, as is the relation betueen the InagnItud~s

obtained as result of sampling the spectrum in the respective penod ranges.

It is seen that the seismic moment of an earthquake--- if measurable--reflects

only the strength of long-periodic radiation, and that the radiation at other periods,

together with the physical parameters controlling it, is in need of being expressed by

additional quantities.

It has been proposed (Nortmann and Duda, 1983) to sample the seismic energy

radiated in specific period bands. and to express the strength of radiation by way of

SO called spectral magnitudes. Evidently, a set of spectral magnitudes will corre- spend to a given earthquake, the spectral magnitudes being determined indepen-

dently for P- and S-waves. Digital broad-band recordings of seismic waves are preferable for the determina-

tion of a complete set of spectral magnitudes. Also, the period bands have to be

specified as to their mid-band and band-edge periods. The magnitudes obtained in

this way are called monochromatic, as they permit to measure the strength of the

earthquake in relatively narrow, non-overlapping period ranges of the seismic waves

radiated.

291

In this paper monochromatic magnitudes for a choice of earthquakes are pre-

sented. Assuming an earthquake model, the question is investigated, whether the

monochromatic magnitudes empirically determined, satisfy the predictions of the

model, or whether significant, measurable deviations of the monochromatic magni-

tudes from the predictions are present.

MONOCHROMATIC MAGNITUDES

Digital broad-band seismograms, obtained at the Central Seismological Observs-

tory of the Federal Republic of Germany at Erlangen, were analysed. Twenty-three

earthquakes, as given in Tab!e I. were selected for the investigation. The epicenters

are shown in Fig. 1.

Band-pass filters were defined, with mid-band and band-edge periods as given in

Fig. 2. .4s can be seen immediately, the bandwidth of each of the 5 filters amounts to

2 octaves,

As example, the broad-band record (BB), as well as 5 band-pass filtered selsmo-

grams. are shown for the vertical component of the P-wave, and the two horizontal

components of the S-wave (Fig. 3) of a particular earthquake. The seismogram traces

are proportional to the ground velocity at the recording site in the respective period range.

From the figures, it is seen that for the given earthquake the maximum ground

velocity at the station occurred a! filter position 3 (mid-band period: 4 s) for the

___~.__ _-__._._..__-..-.-~ _ .-__--__~-~.--- .--. -

I , I / I

1w 150 135 12r 105 90 75 60 150 w 15 C 15 3C 5 60 X 9) 051 120Q 115 150 165 180

Fig. 1. Epicenters of the earthquakes investigated (cp. Table I). The epicenters lie in three rpginnc. Kllr;l Islands. South-West Asia and Central America.

TA

BLE

I

List

of

eart

hquake

s stu

die

d

Eart

h-

quake

No.

=

Date

Kur

ii Is

lund

s

1401B

1978 Ja

n.

14

0902

197X

Feb. 0

9

2303A

1978 M

ar.

23

2303E

lY8O

Mar.

23

2403B

1978 M

ar.

24

O612B

I9

78 D

ec.

06

2302A

1980 F

eb. 23

2302B

1980 Feb.

23

3112

1980 D

ec.

3 I

Sout

h M

~P

rr A

sia

0406

19

7X J

un.

04

0411

1978 N

ov.

04

2805A

1979 M

ay

ZR

1411

1979 N

ov.

14

3112B

1979 D

ec.

31

0205

1980 M

ay

02

0405

19X

0 M

ay0

4

Cen

trui

A

mtw

cu

1903

1978 M

ar.

19

2308

1978 A

ug. 2

3

29118

1978 N

ov.

29

1403

I979 M

ar.

14

2710

1979 O

ct.

21

0908

1980 A

ug09

2410

1980 O

ct.

24

Orl

gm

ti

me

h

m

09

OX

00

03

I9

I4

05

22

10

I9

I5

09

02

06

05

1X

01

00

I9

Ii

14

05

14

03

02

31

I5

47

02

51

3X

32

30

22

27

21

21

30

35

39

38

52

07

35

45

53

s I6

02

02

20

50

01

03

53

I?

23

19

32

22

34

5X

20

I4

30

47

16

57

09

35

EpIc

ente

r D

epth

Epic

entr

al

(km

) dis

tance

(deg. 1

__

__~

id

egr.

) nlh

44.5

N

149.7

E

51

79.5

44.4

3\3

149.9

E

45

79.6

44.2

N

149.O

E

46

79.5

44.9

N

148.4

E

33

78.7

44.2

N

148.Y

k 33

79.4

44.6

N

146.6

E

91

7x.

3

43.5

N

146.8

E

44

79.3

43.2

N

146.9

E

45

79.7

46.O

N

151.5

E

53

78.6

40.4

N

63.6

E

33

37.5

37.7

N

4X

.9E

34

29.5

36.4

N

3i.a

E 98

20.0

33.9

N

5Y.7

E

33

3X

.7

36.2

N

31.5

E

79

0.0

35.7

5

29.8

E

31

19.5

3R

.lN

49.O

E

46

29.3

I7.O

N

99.7

w

36

YO

. 1

10.2

N

X5.2

W

56

86.4

l6.O

N

96.6

W

1X

89.U

17.8

N

101.3

w

49

90.3

13.8

N

90.9

w

5P

87.2

l5.9

N

88.5

W

22

84.2

l8.2

N

98.2

W

72

88.3

-

Magnit

ude

5.4

57

_.

6. I

6.4

6.5

6.7

63

5.)

6.7

6.0

6.1

5.9

6.0

5.3

5 I 5.3

5.K

5.7

6.4

6.5

5.7

h.1

6.4

MS7

5.3

5.7

6.8

7.5

7.6

7.0

5.X

6.5

5.1

h.U

6.6

5.

A.

6.4

7.0

7.7

1.6

6.X

6.4

Rcg

inn

No.

h

221

221

221

221

221

721

-21

221

221

330

345

366

34x

366

371

338

59

7x

60

5X

71

73

523

I S

ee F

ig.

I. h

Geogra

phic

al

regio

n n

um

ber

(Flm

n er

al..

1974)

299

0 - .l .izs .5

.is I i

i 16 $2

$4

123 Band-Edpe Period. s Mid-Band Period. 9

Fig. 2. 2-octave band-pass filters employed for the computation of monochromatic magnitudes

I

I 2

Fig. 3. Kuril Island earthquake, 78 Dec. 06, 14:02:01.0, 91 km, 44.6N. 146.6E (see Table 1). BB is a broad-band record with cut-off periods at 0.2 s and 200 s. I - 5 are band-pass seismograms obtained from

the broad-band record BE after the application of filters as shown in Fig. 2.

(a) shows the P-wave (vertical component), and (b) and (c) show the N-S- and E-W-component of the

S-wave, respectively. The bars at right correspond to a velocity amplitude of 100 pm/s.

P-wave. and at filter position 4 (mid-hanci perwd: 16 5) for the S u;L\s. f-he

seismogram traces feature small amplltlldes ilt the rxtrcme filter ~VG~IOII~. \h~hile tlw

minimum for the P-wave a+ filter psittcm 5 14 due to fht; f3c.t th,,t nc ~~.~fficient

P-wa\-e energy was radiated at periodc arouncj h4 < in thts rurthquske. the rnir~irnllrn

for the S-wave at filter position 1 points 11 the fact thaf the wrth> m:mtle i\ not

sufficiently pervious for S-Lvaves with perIoda 31nvnd 0.25 \ tz! he wr.~~r.~blcl a1

teleseismic distances.

It is the primary role of any rnsgnit(lde wale to I-ompencate the ~+ser\:ed ground

motion for the attenuation of the \xa\e alony the ray path, and trl .irrivb,t: al CT-K (>I-

more numbers characteristic of the source f.>f wismic waws only.

From the P-wave and S-wave grnund yelncity amphtudes. its thr\ can be

measured from the band-pass seismograms in Fig. ?. monochromatic magnitudes

were determined. For this purpose. th e a!,gorithm as given bv Nnr!m;lnn anti Dudn

(1983) w:as employed.

Figure 4 shows the monochromatic magnitudes for each of the filter plktions

I--S. as far as measurable, for both types of body-waves. It ii wen from the

monochromatic magnitudes In Fig. 4. that---;tt variance with the tr,Lc-e rmpiitudes In

Fig. 3 ~.- the spectra of hnth types of bodv-wales radiated from I hr focus h:\\e ,j

1976 Dec. 06 IL.02 010 Kurii Wan

'A

Fig. 4. Monochromatic magnitudes m(r) for P-wave and S-wave (vectorially added horizontal compo-

nents). corresponding to the seismograms in Fig. 3. The magnitudes are plotted at the respective

arithmetic average of band-edge frequencies: T, = (T- t 7, )/2, where 7; and 7-, are the band-edge ,, periods of the filter (see Fig. 2)

301

maximum at filter position 3 (mid-band period: 4 s). The shift of the spectral maximum for S-waves towards shorter periods is due to a stronger compensation of S-waves with decreasing period, in course of the magnitude determination, if compared with that of P-waves.

The spectrum of the ground motion at teleseismic distances is biased relatively to t.he spectrum of the waves radiated from the focus. The bias is caused by the different attenuation for P- and S-waves. due to the different perviousness of the intervening medium for both types of body-waves. As a rule, the attenuation iq higher for S-waves. For a given wave type, the perviousness increases with the period of the wave. The period-dependent calibration function of Nortmann and Duda (1983) compensates the bias, and yields magnitude figures believed to reflect the strength of the radiation of P- and S-waves from the focus. Thereby. the monochro- matic magnitudes m(T) are related to the energy spectral density of either wave type by the relation:

E(T) _ 1()Zrn(?l~k in J/Hz

The constant k was chosen as - 1.4, in order to assure maximum consistency with magnitude figures obtained earlier on the basis of the calibration functions of Gutenberg and Richter (1956) (cp. Nortmann and Duda, 1983).

From Fig. 4, it can be seen that for the given earthquake the monochromatic magnitudes for the S-wave are about 1.6 units larger than those for the P-wave. From the observation at a single station, as in the present case, and without knowing the position of the station with respect to the nodal lines of the fault-plane solution. it cannot be excluded that the difference is simply due to the geometric radiation pattern of the earthquake. Should the difference be genuine, however, it would signify that the total seismic energy radiated from the focus in the form of S-waves is 3.2 orders of magnitude larger than that of P-waves. i.e. that the P-wave radiation is negligible energywise with respect to that of the S-wave.

NORMAL. BLUE AND RED EARTHQUAKES

Haskell (1964, 1966) has investigated the theoretical energy density spectrum of the far field radiation from a dislocation source in an elastic medium. The maximum of the spectrum occurs at a period depending on the fault length and the rise time of the earthquake (deterministic model). or the correlation length and the correlation time of the earthquake process (statistical model). The spectrum decays with increasing periods in proportion to the square of the period, and with decreasing period in proportion to the 2nd to 4th power of the period. The width of the spectrum depends on the physical parameters characterising the process at the focus.

On the basis of the similarity principle of Aki (1967), the period of the maximum is simply proportional to the fault length. Also, the displacement amplitude spectral density at the period of the maximum is proportional to the 3rd power of the fault

length. Consequently. the maximum of the energy density spectrum radiated from

the focus is proportional to the 4th power of the period of the maximum.

The proportionality constants. however. cannot be obtained from the similarity

principle. The uncertainties with respect to the interdependence of the physical

parameters. in particular with respect to the proportionality constants. eventually

lead to a multitude of theoretical earthquake models. The question arises whether

one model can be found at all which would describe all natural earthquakes. or

whether earthquakes in different parts of the earth occur in accordance with

basically different focal process, so that more than one model is necessary for the

description.

Before the answer can be found. it seems that natural earthquakes need to be

analysed on the background of a model earthquake assumed to reflect normal

conditions during the focal process. Accepting the similarity principle and a corre-

sponding set of interrelations between the focal parameters, normal earthquakes

can be defined, and their spectral characteristic used as basis for the analysis of

natural earthquakes. Earthquakes deviating significantly from the model have been

labeled as blue and red. in order to express a relative preponderance of

short-period and long-period radiation of seismic waves (Duda and Nuttli, 1974).

REGIONALIZATION AND EMPIRICAL MODEL

The following discussion is limited to the monochromatic P-wave magnitudes,

and the analysis of monochromatic S-wave magnitudes is left for another investiga-

tion.

Figure 5 displays monochromatic P-wave magnitudes for the earthquakes in

Fig. 1 (Table I). The earthquakes are grouped in three regions, as indicated. The

magnitudes are shown as function of the respective filter position (cp. Fig. 2). All

earthquakes exhibit a maximum of their monochromatic magnitudes in the period

range under consideration. Thus, the energy spectral density of the P-wave, radiated

from the focus of each of the earthquakes, has its maximum near the period

corresponding to that of the maximum monochromatic magnitude.

The maximum monochromatic magnitude occurs, with one exception, either at

filter position 3 or 4. Thereby, the mid-band periods are 4 s and 16 s. and the

arithmetic averages of the band-edge frequencies correspond to periods of 3.2 s and

12.8 s, resp. While for the Kuril (Fig. Sa) and South-West Asia (Fig. 5b) earthquakes the

maximum lies mainly at filter position 3. it lies for the Central American earth-

quakes (Fig. 5c) at filter position 4 (in one case at 5). Moreover, it is seen that the spectra of the Kuril and South-West Asia earth-

quakes are clearly broader than those of the Central American earthquakes.

The slope of the energy density spectra at short-periods, as seen from the

monochromatic magnitudes in Fig. 5. is proportional to about the 4th power of the

303

Kurll Islands

0 1978 ILOIB

0 1976 0902 0 19 06128 A 1978 2303A l 1960 2302A

A 1978 2303E 0 1960 23028

, 1976 2LO3B V 1980 3112

rlll Period s

lb) South-West Aslo

6-

5-

f .I

5-

-l L 1

0 1978 OLO6 I 0 1978 Ull n 1979 2805A A 1979 IL11 0 1979 31128

l 1980 0205 A 1980 0405 ! I , I I I IO

Period. s 100

ICI Central America

.-

0 1978 1903 o 1978 2308

A 1978 29118

A 1979 IL03

/I 0 1980 0908 l 1980 2410 dr ! I , ,.!,, 1

, !, ,,,,, I Period. s

IO 100

Fig. 5. Monochromatic magnitudes m(T) for P-waves, for earthquakes from three different regions (see

Fig. 1 and Table I).

4.

i

305

indicates a tendency of the Kuril earthquakes to be blue, and the South-West Asian to be red. For Central America1 earthquakes no specific tendency is noticeable.

The deviations are small, but not insignificant. Nevertheless, the question arises whether more pronounced deviations are possible. It appears, that present-day obse~ational facilities do not permit to give an answer to the question. Earthquakes with a maximum monochromatic magnitude of, say, 6.5 at filter position 1 (see Fig. 6) would saturate regionally distributed seismographs, due to the limited dynamic range of the instruments. At the same time, the small pe~iousness of the earths mantle would prevent such earthquakes to be recognized at teleseismic distances. On the other hand, earthquakes with a maximum monochromatic magni- tude of 6.5 at filter position 5 (see Fig. 6) would remain unnoticed at both regional and teleseismic distances, due to insufficient sensitivity of seismometers at the corresponding periods.

In conclusion, it appears from the investigation of 23 earthquakes that significant deviations from a normal spectral characteristic are given. Regions can be indicated with earthquakes deviating towards a preponderance of either short-period or long-period radiation. Present-day observational facilities, however, generally do not favour the recognition of earthquakes with energy density spectra strongly deviating from some average behavior. Broad-band large dynamic range seismological ob- servatories in sufficient number would probably yield the answer to the question whether a significant portion of the seismicity of the earth is occurring in additional modes, others than the one of normal earthquakes.

The concept of monochromatic magnitudes offers a new means of quantifying the energy density spectrum of the waves radiated from the earthquake focus, as well as a means of classifying earthquakes in accordance with their spectral characteristic.

ACKNOWLEDGEMENT

The investigation was performed under a research grant of Deutsche For- schungsgemeinschaft, Bonn-Bad Godesberg.

One of us (R.N.) wishes to acknowledge the support of IASPEI for his participa- tion in the General assembly in London, Ontario, Canada.

REFERENCES

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Berckhemer, H. and Jacob, K.H., 1968. Investigation of the dynamical process in earthquake foci by

analyzing the pulse shape of body waves. Ber., inst. Meteorol. Geophys., Univ. Frankfurt, 13.

Brune, J.N., 1970. Tectonic stress and spectra of seismic shear waves from earthquakes. J. Geophys. Res.,

75: 4997-5009.

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Duda, S.J. and Nuttli, O.W., 1974. Earthquake magnitude scales. Geophys. Surv.. 1: 429-45X. Flinn, E.A., Engdahl. E.R. and Hill, A.R., 1974. Seismic and geographical regionalization. Bull. Seismol.

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Geller. R.J., 1976. Scaling relations for earthquake source parameters and magnitudes. Bull. Seiamol. Sot.

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Hirasawa. T. and Stauder. S.J.. 1965. On the seismic body waves from a finite moving source. Bull.

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magnitudes. In: S.J. Duda and K. Aki (Editors), Quantification of Earthquakes. Tectonophysics. 93:

251-275.

Savage, J.C., 1972. Relation of corner frequency to fault dimensions. J. Geophys. Res.. 77: 3788-3795.