-
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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Res., 72: 1217-1231. Aki, K., 1972. Scaling law of earthquake
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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
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306
Duda, S.J. and Nuttli, O.W., 1974. Earthquake magnitude scales.
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Haskell. N.A., 1964. Total energy and energy spectral density of
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faults. Bull. Seismol. Sot. Am., 54: 181 l- 1841.
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Seismol. Sot. Am.. 55: 2377262.
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properties of earthquakes from their
magnitudes. In: S.J. Duda and K. Aki (Editors), Quantification
of Earthquakes. Tectonophysics. 93:
251-275.
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