tectonophysics volume 93 issue 3-4 1983 duda; r. nortmann -- normal, blue and red earthquakes—a...
TRANSCRIPT
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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.
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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.
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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.
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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.
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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
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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.,
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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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