Bulletin of the Seismological Society of America, 89, 2, pp. 442-455, April 1999
Moment-Magnitude Relations Based on Strong-Motion Records in Greece
by B. N. Margaris and C. B. Papazachos
Abstract
In this work, the variation of the local magnitude, MLSM, derived from
strong-motion records at short distances is examined, in terms of moment magnitude,
M w. Strong-motion data from Greek earthquakes are used to determine the strongmotion local magnitude, MLSM, by performing an integration of the equation of motion of the Wood-Anderson (WA) seismograph subjected to an input acceleration.
The most reliable strong-motion data are utilized for earthquakes with seismic moments log M 0 -----22.0 dyne • cm and calculated local magnitudes, MLsM >-- 3.7. The
correlation between the seismic moments, log M0, and the calculated local magnitudes, MLSM, using strong-motion records is given by log M 0 = 1.5*Mcsu + 16.07,
which is very similar to that proposed by Hanks and Kanamori (1979). Moreover, it
is shown that MLsM is equal to moment magnitude, Mw, for a large MLsM range (3.9
to 6.6). Comparison of the strong-motion local magnitude and the ME magnitude
estimated in Greece (ML~n) and surrounding area shows a systematic bias of 0.4 to
0.5, similar to the difference that has been found between M w and MLGRfor the same
area. The contribution of the local site effects in the calculation of the local magnitude, MLSM, is also considered by taking into account two indices of soil classification,
namely, rock and alluvium or the shear-wave velocity, vs30, of the first 30 m, based
on NEHRP (1994) and UBC (1997). An increase of MLsM by 0.16 is observed for
alluvium sites. Alternative relations showing the MLSM variation with, v3° are also
presented. Finally, examination of the WA amplitude attenuation, - l o g A0, with
distance shows that the Jennings and Kanamori (1983) relation for A < 100 km is
appropriate for Greece. The same results confirm earlier suggestions that the 0.4 to
0.5 bias between MLGR and Mw (also MLsa4) should be attributed to a low static
magnification ( - 8 0 0 ) of the Athens WA instrument on which all other M L relations
in Greece have been calibrated.
In~oduction
tude recorded by the Wood-Anderson (WA) torsion seismograph located within a few hundred kilometers of the
earthquake source, with a natural period of 0.8 sec, a critical
damping factor ~ = 0.80, and a static magnification V =
2800. In addition, My is determined closer to the seismic
source than are other magnitude scales, thus the ground motion at the instrument site resembles more closely to the
strong ground motion recorded by accelerographs, both in
frequency content and duration. For short epicentral distances (A N 25 kin), the standard WA seismograph goes off
scale for events with My >--4.5, so no reliable measurements
can be made on this instrument for strong motion in these
distances that have significant engineering importance. For
this reason, Trifunac and Brune (1970) have proposed a
method for the determination of local magnitude, MLSM, using strong-motion accelerograms, for moderate to large
earthquakes at distances for which the standard WA instrument would be driven off scale. This method, which enhances the data base from which ML can be found, relies on
Seismic ground motion depends on the size of the corresponding earthquake, the most common relative measure
being magnitude. Ordinary measures of magnitude are defined in terms of peak motions recorded on seismograms
from particular instruments after correction for the attenuation to a reference distance. The seismic waves radiated from
a seismic source are made up of a wide spectrum of frequencies, and the seismic instruments provide views into
different frequency ranges of the released energy. Due to
this fact, the size of any earthquake can be measured by
various magnitude scales. The magnitudes for any earthquake do not necessarily agree with one another, while it
must be emphasized that each scale provides information
concerning the spectral content of the seismic source at different frequencies. The most commonly used magnitudes in
engineering design are the Richter (1935) local magnitude,
ML, the surface-wave magnitude, Ms (Gutenberg, 1945), and
the moment magnitude, M w (Hanks and Kanamori, 1979).
The local magnitude, ML, is based on the trace ampli442
Moment-Magnitude Relations Based on Strong-Motion Records in Greece
calculating a synthetic WA seismogram response using an
input recorded strong-motion acceleration time series. A basic assumption in order to compare the MLSM, derived from
str0ng-motion records, and the My, from real WA recordings,
is that the response of the WA seismograph is sufficiently
known in the calculations. However, this assumption is not
always correct. For instance, some studies have shown that
the effective magnification of WA instruments may be much
lower than the design value of 2800 (Luco, 1982; Boore,
1989; Uhrhammer and Collins, 1990). Moreover, the basis
of the calculation of My from the maximum WA response is
the amplitude attenuation curve, log A0, in terms of distance,
constructed by Richter (1935) and linearly extended to A =
0 km by Gutenberg and Richter (1942) for a reference event.
Possible bias at close distances has been shown by many
studies (Luco, 1982; Jennings and Kanamori, 1983; Bakun
and Joyner, 1984; Bonamassa and Rovelli, 1986; Hutton and
Boore, 1987; Trifunac, 1991a; Lee, 1991).
The seismic moment, M0, has been accepted as one of
the most reliable measures of the size of an earthquake. This
physical parameter, which controls the amplitude of longperiod seismic waves, is the product of the average slip on
the fault surface, the area of the fault surface, and the modulus of rigidity of the material surrounding the fault. The
seismic moment, M o, and local magnitude, ML, have been
related in a number of studies, and some discrepancies in
the linear relations have been observed (Bakun, 1984; Hanks
and Boore, 1984).
The significance of the measure of the earthquake size
has been recognized for a long time, and a number of studies
have been published concerning various magnitude scales in
Greece and surrounding areas. Ms relations have been derived from Greek earthquakes using records from intermediate-period seismographs (Papazachos and Vasilicou, 1967;
Papazachos and Conminakis, 1971) or long-distance recordings of surface wave with periods 18 to 22 sec (Ambraseys
and Free, 1997). For the Aegean area, empirical relations
have been proposed for the estimation of local magnitude,
M L (Kiratzi, 1984; Kiratzi and Papazachos, 1984, 1986), and
of duration magnitude, M D (Kiratzi and Papazachos, 1985;
Papanastasiou, 1989). Macroseismic data have also been
utilized to propose relations calculating the magnitude of
strong events (Galanopoulos, 1961; Drakopoulos, 1978; Papazachos, 1992). The calculation of local magnitude, MLSM,
using strong-motion records was first applied for a limited
number of strong earthquakes in Greece (Papastamatiou et
aL, 1991), although alternative determinations of M r from
strong-motion data have also been made (Hatzidimitriou et
al., 1993). The work on the correlation of different magnitude scales and the procedure for the determination of a homogeneous moment-magnitude scale for Greek earthquakes
was carried out by Papazachos et al. (1997).
In this work, we propose a relation of log M0 and the
corresponding moment magnitude, Mw, versus the local
magnitude determined from the Greek strong-motion data,
MLSM, for a wide range of earthquake sizes (3.9 --< Mw <-
443
6.6). The proposed empirical relation is compared to a homogeneous moment-magnitude relation for Greece and surrounding area proposed by Papazachos et al. (1997), and an
average difference of 0.4 to 0.5 unit of magnitude is revealed
for the same range of magnitudes between MLSM and MLG~
reported from regional seismological networks. A study of
the site-effects contribution in the calculation of the local
magnitude of strong motion, MLSM, is attempted and a correction factor is used in the calculations. In order to compare
the proposed empirical relation of moment magnitude, based
on strong-motion data in Greece, with data from similar seismotectonic regions, we incorporate data from California for
which local and moment magnitudes were available. These
data are in very good agreement with the Greek strongmotion data. Finally, the WA amplitude attenuation curve
with distance is examined.
Calculation of Local Magnitude (MLsM)
by Strong-Motion Records
To determine local magnitude, ML, using Greek strongmotion data, we adopted the technique that is based on
calculating synthetic WA seismograph responses from corrected accelerograms (Kanamori and Jennings, 1978). A
computer program developed to calculate response spectra
(Anagnostopoulos, personal comm.) was modified in order
to compute equivalent WA recordings from corrected acceleration time histories. The typical bandwidth of these records
was approximately 0.05 to 25 Hz. This bandwidth is clearly
acceptable for the estimation of synthetic WA responses because the effective low-cut frequency of the WA instrument
is close to its resonant frequency (0.8 Hz). For the estimation
of local magnitude, MLSM,w e used zer0-to-peak amplitudes
rather than the standard one-half peak-to-peak amplitudes
(Kanamori and Jennings, 1978; Bakun and Joyner, 1984;
Hutton and Boore, 1987) because zero-to-peak have been
traditionally used in previous studies for Greece (Papazachos
and Comninakis, 1971; Kiratzi and Papazachos, 1984). Using the maximum zero-to-peak WA amplitudes and the attenuation corrections proposed by Kiratzi and Papazachos
(1984), which are identical to Kanamori and Jennings (1978)
for A < 100 kin, the local magnitudes, MLSM, were calculated for all the examined earthquakes. A lower static magnification (2080 instead of 2800) was used in our calculation,
in agreement with the values reported by various researchers
(Boore, 1989; Uhrhammer and Collins, 1990) for other WA
seismographs located in the United States. Figure 1 presents
the transverse component of the accelerogram of the wellknown destructive Greek earthquake at Kalamata 1986 (Mw
= 5.9), the corrected ground velocity and displacement
along with the synthetic WA response. The waveform characteristics of the synthetic WA record are very similar to the
ground velocity record than either the displacement or the
acceleration, as already indicated by Kanamori and Jennings
(1978).
Strong earthquakes (112) that occurred in Greece (Fig.
444
B.N. Margaris and C. B. Papazachos
2OO
-~
o
-200
2O
g
o
>
-20
4
E
63
E
0
-2
-4
40
20
v
.<
_20
°
-40
0
5
10
15
20
25
30
Time (sec)
Figure 1. Acceleration, velocity, displacement,
and synthetic WA record of the transverse component
of the 1986 Kalamata (southern Greece) M = 5.9
earthquake. Notice the similarity between ground velocity and the synthetic WA record.
2) were used in the present study, including 11 events from
the Argostoli seismic sequence of 1983, 2 from the Kalamata
seismic sequence of 1986, 6 from the Pyrgos seismic sequence of 1993, 6 from the Arnea seismic sequence of 1995,
21 from the Kozani seismic sequence of 1995, and 26 from
the Konitsa seismic sequence of 1996. The strong-motion
records are from earthquakes that mainly occurred in the
Greek mainland, where the majority of strong-motion instruments is deployed (Fig. 2). The data are presented in
Table 1 where the date, origin time, geographical coordinates of the epicenter, seismic moment, M 0, and moment
magnitude, M w [based on the Hanks and Kanamori's (1979)
relation] are presented for each shock. In addition, the local
magnitude ML*, determined from seismological networks as
proposed by Papazachos et al. (1997) for the examined
earthquakes, and the local magnitudes MLA, of the earthquakes for which WA records were available from the Geodynamic Institute of the National Observatory of Athens, are
also included.
An important parameter for the estimation of MLSM is
the distance considered from the seismic source to the accelerograph station. The use of the strong-motion data permits the determination of the WA response in the near field.
Four different distances, that is, epicentral distance, hypocentral distance, distance to the center of fault, and the closest distance to the surface trace of the fault, were used by
Jennings and Kanamori (1983), and they concluded that the
most consistent results were derived using the last of these
quantities. Moreover, Trifunac (1991a) considered the same
distance definitions, with the addition of the normal distance
to the fault. The definition of the distance becomes critical
when strong-motion records for the calculation of Mcs~t in
distances A _-< 25 km are used. However, in regions as
Greece where a large number of events occurs at sea or
where earthquakes often do not exhibit surface fault traces,
the use of the epicentral distance is the best alternative, since
it leads to similar results with the shortest fault distances, as
has been shown for Italy (Bonamassa and RoveUi, 1986),
which has a similar geotectonic environment with Greece.
For this reason, in the present study, we use epicentral distances, A, for the MLSM estimation from each strong-motion
record. For earthquakes that have been recorded by more
than one accelerograph, an average local magnitude was calculated. These average local magnitudes (MLsM) calculated
from strong-motion data, the number of accelerograph components utilized, NO, and the standard deviation of the calculated mean M f s M are also presented in Table 1. The distribution of the epicentral distances, A and the magnitudes
of the examined earthquakes in Greece are presented in Figure 3. The data set is quite complete for epicentral distances
5 _<- A _-< 60 km and for the magnitude range 3.5 _-__M =<
6.0. However, a lack of data can be seen for strong earthquakes with M ->_5.0, recorded at the near field (A < 5 kin).
M o m e n t Magnitude Based
on Strong-Motion Records
The seismic moment, M0, of earthquakes is widely accepted as the most preferable measure of an earthquake's
size. This preference is based on the fact that the seismic
moment is a physical parameter representing the strength of
the earthquake, and it can be calculated using various independent methods (seismological, geodetic, tectonic, etc.).
Moreover, the corresponding moment magnitude, Mw, does
not saturate, as observed for all the other magnitude scales.
Because of the importance of this quantity, numerous attempts have been made to relate Mo to various magnitude
scales and to determine moment magnitude scale, Mw
(Hanks and Kanamori, 1979). Several studies have focused
on the correlation of the M0 and ML, for example, Hanks
and Boore (1984), who incorporated data from a large number of studies for the determination of the M w - M r relation
for Californian earthquakes. Also, a nonlinear dependence
of log M 0 to ML, for various magnitude ranges, has been
shown by Bakun (1984) for earthquakes in central California.
Table 1 includes seismic moments for 33 earthquakes
in Greece, taken from Papazachos et aI. (1997), who mainly
adopted seismic moments calculated by teleseismic waveform modeling instead of the locally determined values
(Hanks and Boore, 1984). Some of these seismic moments
for smaller events were taken from calculations using shortperiod records and an appropriate spectral analysis method
(Chouliaras and Stavrakakis, 1997). Because we had only
one earthquake with moment magnitude, M w, smaller than
4.0, it was excluded from this analysis. In Figure 4, the plot
Moment-Magnitude Relations Based on Strong-Motion Records in Greece
20"
22 °
24"
445
26"
42"
42"
40"
40 °
38 °
8~
36"
36"
20 °
22 °
24"
26 ~
of log M0 versus local magnitude Mfs~ is presented. The
best-fit, in the least-squares sense, linear relation (also shown
in Fig. 4) is given by
logM0 = 1.5MLsM + 16.07,
3.9----<MLsM<=6.6,
(1)
with a standard error of 0.39 and a linear correlation coefficient of R = 0.94. This relation is in very good agreement
with that defined by Thatcher and Hanks (1973) for southern
California and a similar magnitude range (3.0 _-<Mr --< 7.0).
The correlation of the moment magnitude with the strongmotion local magnitude, MLs~, was estimated to be
M w = 1.0MzsM -- 0.01, 3.9--< MLSM
6.6 (zero to peak-WA amplitudes),
(2)
with a standard error of 0.26 and a linear correlation coefficient of R = 0.94. The data and the best-fit line are presented in Figure 5. Relations (1) and (2) can be applied to
derive moment magnitudes based on strong-motion records.
It should be noted that equation (2) implies that the local
magnitude determined from strong-motion data, MLSM, is
practically equal to M w, which is expected according to the
original definition of Mw by Hanks and Kanamori (1979).
However, in the present study, we utilized zero-to-peak am-
Figure 2. Geographical distribution of the
112 earthquakes (circles) as well as the recording stations (triangles) for which data are used
in the present study. Almost all recorded earthquakes have occurred in the Greek mainland.
plitudes that are systematically larger than the corresponding
half peak-to-peak amplitudes traditionally used. Examination of the 430 synthetic WA Waveforms shows that the ratio
(half peak-to-peak)/(zero-to-peak) is equal to 0.85 ___ 0.1,
which suggests that the use of zero-to-peak amplitudes leads
to a systematic overestimation of MLsM by 0.07. Therefore,
if half peak-to-peak WA amplitudes are used, equation (2)
is transformed to
M W = 1.0Mfs ~ + 0.06, 3.9--< MLSM
--< 6.6 (half peak-to-peak WA amplitudes)
(3)
The remaining M w - M L S M difference of 0.06 is small, compared to various other error sources. Therefore, Mcs~t can be
considered practically equal to moment magnitude, whichever type of amplitude is used (half peak-to-peak or zeroto-peak), at least for the specified magnitude range (3.9 =<
MCSM <=6.6).
In order to compare our relation with those that have
been proposed in different regions with similar geotectonic
setting, our data and the proposed MLSM to Mw relation
(equation 2) are presented in Figure 6, where data from Californian earthquakes are also plotted. Data for central California were taken from Hanks and Boore (1984, Table 2)
until 1983. For the time period 1984 to 1995, all earthquakes
446
B. N . M a r g a r i s a n d C. B. P a p a z a c h o s
Table 1
I n f o r m a t i o n o n t h e 112 E a r t h q u a k e s U s e d i n t h e P r e s e n t S t u d y
DATE
OR. TIME
LAT
LON
MLSM
NO
062078
071680
200321
002330
40.80
39.23
23.20
22.72
6.3
5.3
2
2
0.0
0.1
3
4
081180
091559
39.30
22.82
5.6
2
0.1
092680
041918
39.24
22.74
5.2
2
0.1
5
022481
205338
38.22
22.93
6.6
2
0.04
6
011783
124129
38.09
20.19
6.6
6
0.27
7
8
011783
165330
38.11
20.37
5.1
2
0.04
011983
000214
38.17
20.23
5.5
2
0.1
5.85"10"24(1)
013183
152700
38.11
20.30
5.3
4
0.2
1.41"10"'24(1)
5.4
4.9
5.2
11
022083
031683
124229
211939
37.76
38.80
21.11
20.88
5.2
4.9
2
2
0.008
0.04
---
5.0
4.8
4.9
4.9
12
13
032383
032383
190400
235106
38.78
38.33
20.83
20.22
5.3
5.9
2
6
0.12
0.2
-6.2
4.8
5.7
4.8
5.6
14
032483
041732
38.18
20.32
5.5
2
0.15
1.35"10"'24(1)
5.4
4.6
5.0
15
16
080683
082683
154353
125210
40.18
40.51
24.73
23.92
6.3
5.6
4
2
0.21
0.04
116.0"10"'24(1)
0.641"10"'24(1)
6.6
5.1
6.3
4.5
5.9
4.4
17
18
021984
070984
100484
034722
185710
101512
40.61
40.69
37.64
23.40
21.82
20.85
4.9
5.3
5.2
2
4
2
0.15
0.43
0.06
-0.759"10"'24(1)
--
-5.2
--
4.5
5.0
4.6
4.2
4.8
4.5
102584
032285
094916
203739
36.83
38.98
21.71
21.11
5.3
4.8
3
2
0.54
0.15
---
---
4.6
4.0
4.7
4.0
22
032285
203854
38.91
21.06
4.5
2
0.007
--
--
4.0
4.1
23
24
25
083185
110985
091386
060346
233042
172434
38.99
41.24
37.03
20.59
23.93
22.20
5.5
5.7
6.1
4
4
2
0.11
0.04
0.03
-5.2
5.9
4.8
5.1
5.5
4.7
5.0
5.5
26
27
28
091586
101688
122190
114130
123406
065744
37.04
37,95
40,98
22.13
20.90
22.34
5.5
6.0
6.2
6
4
4
0.28
0.19
0.08
-5.8
6.1
5.0
5.5
5.4
4.9
---
29
3O
032693
032693
114516
115613
37,66
37,69
21.39
21,43
5.3
5.1
2
2
0.13
0.06
---
4.5
4.3
---
1
2
9
10
19
20
21
SD
31
032693
115815
37.49
21.49
5.9
2
0.16
32
33
34
032693
032693
122632
124917
37.55
37.77
21.27
21.33
5.2
4.9
2
2
0.12
0.1
042993
071493
075429
123149
37.40
38.24
21.58
21.78
5.8
5.5
2
4
0.04
0.09
061194
092394
235817
113731
40.73
40.61
23.19
23.44
3.7
4.7
2
4
0.1
0.18
092394
092394
092394
092394
100694
115456
115645
120041
140722
043548
40.64
40.61
40.61
40.63
40.60
23.43
23.44
23,41
23.42
23.41
4.8
3.2
3.9
3.4
3.3
4
2
4
4
2
44
45
46
110594
010695 ~
012295
012295
172905
093023
222729
222325
41.10
40.81
40.60
40.59
23.35
22.92
23.41
23.52
3.8
3.9
4.1
4.0
47
48
49
012495
021395
040495
224920
131636
171010
40.79
40.69
40.56
23.46
22.74
23.63
50
51
52
53
54
55
56
57
040495
040495
050395
050395
172706
172943
141641
153956
40.57
40.55
40.56
40.57
050395
050395
050395
050395
164532
185639
213654
214327
40.63
40.56
40.57
40.57
35
36
37
38
39
4O
41
42
43
Mo(dyn.cm)
Mw
ML*(1)
MLA(4)
6.4
--
6.1
4.5
5.9
4.6
--
--
4.8
4.8
--
--
4.4
4.5
90.1"10"'24(1)
6.6
6.2
5.8
235.0"10"'24(1)
6.8
6.5
6.1
--
4.9
4.9
5.8
5.3
5.5
50.0"10"'24(1)
--
--
---22.3"10"'24(1)
-0.755"10"'24(1)
9.82"10"'24(1)
-7.47"10"'24(1)
17.0"10"24(1)
--1.61"10"'24(1)
5.4
5.0
--
---
4.5
4.4
---
-5.6
45
5.1
---
---
---
2.3
4.1
---
0.1
0.2
0.25
0.13
0.15
------
------
3.6
2.2
3.2
2.5
2.7
------
4
2
2
2
0.38
0.05
0.2
0.15
-----
-----
2.8
3.3
4.0
3.6
-----
3.1
4.9
4.7
2
4
6
0.05
0.05
0.11
--6.14'10"22(2)
--4.5
2.5
4.4
4.1
--4.1
23.66
23.65
23.68
23.69
4.4
3.9
4.2
4.4
6
4
6
6
0.12
0.04
0.21
0.29
--2.94"10"'22(2)
5.95'10"'22(2)
--4.3
4.5
3.8
2.8
3.9
4.3
--3.8
4,0
23.48
23.65
23.67
23.66
3.4
4.3
4.9
5.1
4
6
6
4
0.11
0.33
0.11
0.07
--1.30"10"'23(2)
1.13"10"'23(2)
--4.7
4.6
2.7
3.8
4.6
4.7
--4.3
4.5
---3.20"10"'24(1)
(continued)
447
Moment-Magnitude Relations Based on Strong-Motion Records in Greece
Table
1
Continued
DATE
OR. TIME
LAT
LON
MLSM
NO
SD
58
050395
223303
40.56
23.69
59
050495
003411
40.54
23.63
60
050495
004342
40.57
61
050495
010716
62
050495
011405
63
050495
64
3.9
4
0.18
5.5
14
0.25
1.10"10"'24(3)
23.93
4.0
4
0.07
4.66"10"22(2)
40.56
23.62
3.8
2
0.0
40,58
23.61
4.0
6
0.18
044549
40.56
23.60
3.6
2
0.1
050495
174743
40.57
23.63
4.0
4
65
050795
092627
40.56
23.58
4.0
66
051395
084715
40.16
21.67
6.2
67
051495
144657
40.13
21.66
4.9
2
0.2
68
051595
041357
40.07
21.67
5.0
8
0.19
69
051595
081700
40.11
21.50
4.6
2
0.05
70
051695
230042
40.02
21.56
4.8
2
0.03
1.27"10"23(2)
71
051695
235728
40.09
21.62
4.9
4
0.08
5.89'10"'23(2)
72
051795
041426
40.07
21.61
5.2
8
0.2
8.65"10"'23(2)
73
05•795
094507
40.01
21.56
4.8
4
0.08
--
74
051895
062255
40.03
21.56
4.5
2
0.08
--
75
051995
064850
40.03
21.62
5.1
8
0.4
76
051995
073649
40.06
21.61
4.4
2
0.05
77
052095
210625
40.00
21.58
4.5
4
0.37
78
060495
031809
40.58
23.60
3.8
2
0.0
79
060695
043600
40.14
21.61
4.7
10
0.24
80
060895
021348
39.99
21.54
4.0
2
0.0
81
061195
185195
39.96
21.58
4.8
12
0.36
82
061295
013121
40.44
23.86
4.4
4
0.15
--
3.7
--
83
071795
231815
40.10
21.58
5.0
2
0.15
3.79"10"'23(2)
5.0
5.0
4.6
84
071895
074255
40.12
21.61
4.6
2
0.0
7.18"10"'22(2)
4.5
4.3
4.4
85
082096
224019
40.54
23.60
3.7
4
0.18
--
--
3.1
--
86
091395
102953
40.53
23.17
3.8
4
0.19
--
--
3.2
--
87
073196
151824
40.12
20.68
4.4
3
0.17
--
--
3.2
--
88
080396
132010
40.03
20.74
4.2
3
0,28
--
--
3.0
--
89
080496
080321
40.04
20.70
4.7
3
0.12
--
--
3.4
--
90
080496
100847
40.04
20.70
4.8
3
0.25
--
--
3.7
--
91
080596
224642
40.06
20.66
6.3
3
0.09
--
--
5,1
--
92
080596
235846
40.03
20.72
4.5
3
0.24
--
--
3.6
--
93
080696
051351
40.03
20.69
4.5
1
0.0
--
--
3.6
--
94
080696
061907
40.06
20.71
4.4
1
0.0
--
--
3.7
--
95
080696
080331
40.01
20.72
4.1
1
0.0
--
--
3.1
--
96
080796
194956
40.03
20.71
4.1
2
0.25
--
--
3.0
--
97
080896
073215
40.02
20.67
4.4
2
0.3
--
--
3.0
--
98
081096
055539
40.02
20.66
4.2
3
0.08
--
--
2.9
--
99
081196
030843
40.02
20.73
4.1
2
0.2
--
--
2.8
--
100
081196
075715
40.08
20.73
5.4
5
0.47
--
--
4.4
--
101
081196
083027
40.04
20.74
4.5
3
0.25
--
--
3.0
--
102
081796
014939
40.04
20.74
4.1
2
0.3
--
--
2.9
--
103
082096
012649
40.04
20.70
5.4
2
0.1
--
--
4.8
--
104
082096
054800
40.02
20.66
4.1
2
0.15
--
--
3.4
--
105
082196
071034
40.02
20.78
4.7
2
0.05
--
--
3.3
--
106
090196
065612
40.05
20.69
4.4
2
0.0
--
--
3.1
--
107
090196
074145
40.07
20.72
4.7
4
0.13
--
--
3.9
--
108
090196
181033
40.01
20.71
4.2
2
0.05
--
--
3.4
--
109
090196
211500
40.01
20.74
5.0
5
0.28
--
--
3.9
--
110
090196
214003
40.05
20.74
3.9
2
0.05
--
--
3.1
--
11l
090396
210537
40.02
20.73
4.4
2
0.05
--
--
3.1
--
112
092696
123149
40.05
20.75
5.4
5
0.39
--
--
4.1
--
(1) P a p a z a c h o s
et aL
"
(1997).
(2) C h o u l i a r a s a n d S t a v r a k a k i s ( 1 9 9 7 ) .
(3) T a k e n f r o m H a r v a r d C a t a l o g s .
(4) T a k e n f r o m N a t . O b s e r v . o f A t h e n s , G e o d y n . Inst.
M0(dyn.cm)
Mw
ML*(1)
--
3.3
5.4
5.4
--
4,4
3.6
3.9
--
--
2.5
--
--
--
3.3
--
--
--
3.3
--
0.12
--
--
3.3
--
6
0.21
--
--
3.5
--
22
0.22
6.5
6.1
6.1
--
76.0"10"'24(3)
--
MLA(4)
--
--
4.0
--
5.2
4.7
5.0
--
4.0
--
4.7
4.3
4.3
5.1
4.5
4.6
5.2
4.9
5.1
--
4.6
--
--
4.1
--
5.0
4.7
4.8
--
--
4.4
--
--
--
4.0
--
3.3
3.4
3.2
--
--
4.4
--
--
--
3.9
--
4.4
4.4
4.3
6.08"10"'23(2)
--
3.63"10"'23(2)
8.00"10"'20(2)
4.55"10"'22(2)
--
448
B.N. Margaris and C. B. Papazachos
'
I
'
I
'
I
'
100.0
"• -
%00
~
•
•
•
LO ~ ,
I
3.0
60
I
•
0
000
•
•
•
•
•
O
I
4.0
,
M
I
•
•
•
I
5.0
'
.
•
•
4.0
,
I
6.0
I
7.0
I
I ,,
4,0
l
,
l
6.0
7.0
Figure 5. Plot of the moment magnitude Mw
against MLsM.
•
I
'
Present Study
i
•
t
•
I
Hanks and Boore (1984) - California (-1983)
H a r v a r d C M T / P D E - California
7.0
Q
26.0
I
5.0
MLSM
8.0
'
#
•
•
•
,
"
.
5.0
•
'
:/"
Mw
.
Figure 3. Magnitude-distance distribution of the
data used in the present study. A good coverage is
observed for 3.0 -< M <--7.0 and 5 km --<A -< 60 kin,
although a lack of strong events (M -->5.0) is observed
at small distances (A <- 5 km).
I
'
,3try...
"
aid
2.0
28.0
I
0
r
•|
~o.o ~-
F
'
:
.,
A (km)
7.0
' l .I
-II
~d
I
(1984- 1995) ~
MW= •LSM" 0.01
.;I-
,
/
/
/.-~"#
~
tpazachos et al. (1997)
~i ~ / ~ A
6.0
d
Mw
~, 24.0
O ~ O O
e, o l l i ~ ~ U
•
¢
¢7
5.0
22.0
4.0
/
I
20.0 I
4.0
,
I
5.0
l
I
6.0
4.0
I
7.0
MLSM
Figure 4. Plot of the logarithm of seismic moment, log M0, against MLsM, for 32 earthquakes for
which Mo values were available.
for which PDEs were issued were used for the broader California area, adopting the M w values reported in CMT Harvard solutions and the ML values mainly published from
Berkeley and Pasadena. It is observed that all these data
show a very good agreement between ML and Mw almost for
the whole magnitude range examined (4.0 =< Mr ~ 7.0). It
Figure 6.
1
I
5.0
i
I
6.0
ML
l
l
w
7.0
Comparison of the Mw-ML relation between Greece and California. Greek data of the present study (Mw-MLsM) are shown as solid circles,
while California data are shown as gray (before 1984,
Hanks and Boore, 1984) and white (after 1984, PDEHarvard CMT) diamonds. The best-fit line proposed
in the present study and the relation between M w and
the local magnitude ML~R derived from Greek seismological networks (Papazachos et al., 1997) are also
depicted by a solid and dashed line, respectively. An
excellent agreement is observed between both data
sets. The data exhibit a relatively small magnitude
saturation starting at ML ~ 6.5.
8.0
449
Moment-Magnitude Relations Based on Strong-Motion Records in Greece
is also interesting to note that the data in Figure 6 (both from
Greece and California) do not show a significant magnitude
saturation, although a slight My saturation is starting to be
recognized for M/. > 6.5.
Site-Effect Estimation Based on Local Magnitude
from Strong-Motion Records
It has been widely recognized that the seismic motion
is strongly affected by the local site conditions at the recording site (e.g., Borcherdt, 1970; Aki, 1988). The site effect is more important for accelerographs because they are
usually deployed in urban areas in order to monitor the effect
of strong motion on structures that might be built in a variety
of geological-geotechnical conditions. On the contrary, seisnaological networks follow different criteria for the installation of seismological stations, because remote sites on
some type of bedrock are preferably selected. For this reason, it is important to account for such phenomena and accordingly correct the obtained local magnitude from strongmotion records.
Correction of the estimated M L due to site effects has
not been proposed for Greece, although such corrections are
available for other areas, for example, California (Heaton et
aL, 1986). Because the WA synthetic recordings are very
similar to velocity records (see Fig. 1, also Kanamori and
Jennings, 1978; Boore, 1983), a reasonable alternative is to
use a similar correction proposed for peak ground velocities.
Such a relation has been proposed by Theodulidis and Papazachos (1992) for peak ground velocities in Greece. Use
of this relation implies a - 0.1 units of magnitude correction
for all stations that are located on alluvium sites. This correction was adopted in all calculations of MLSM throughout
this article.
In order to verify this correction, we assumed that a
relation of the form of equation (2) applies between M w and
"'aLSM/. I./.U. , where M /Uncor
~ is
the local magnitude calculated from
strong-motion records without applying any site correction.
Hence, the following relation was used:
/I,4Uncor
Mw = a~,,LSM +
bsite,
(4)
where b~ite has two possible values, one for rock sites and
one for alluvium sites. This categorization is based on the
classification of Theodulidis and Papazachos (1992), who
separate recording sites into two classes, namely, rock and
alluvium. The first class contains mostly basement rocks and
very stiff soils, whereas the second class includes alluvium
and soft-soil sedimentary deposits. Equation (4) represents
an overdetermined linear system to be solved for the calculation of a, brock, and balluvium. Application of equation (4)
to our data set resulted in the following equations:
Mw = 1.04 t,,Ls
~U~°~ _ 0.39
(rock),
(5)
M w = 1.04
~/tUncor
~ vX L S M
_
0.56
(alluvium),
(6)
with a standard error of 0.35 and a linear correlation coefficient of 0.89. The standard error of equations (5) and (6)
is larger than that of equation (2) because the MLsa~ estimates
used in these relations are single-station estimates and not
average MLSM values as those used in equation (2). The observed difference between rock and alluvium sites implies
that for the same earthquake (same Mw), alluvium sites will
require a larger correction than rock sites for MLSM by --0.16,
which is slightly larger than the value predicted from an
independent estimation based on peak ground velocities.
Moreover, this value is not far from the values (0.20 to 0.24)
estimated by Trifunac (1991a) for California, and any difference could be easily attributed by the possibly different
definition of rock and alluvium sites between Greece and
California. This agreement indicates that estimates of siteeffect amplification from peak ground velocities can also be
efficiently applied for the correction of local magnitude estimates from WA recordings.
In order to evaluate the effect of site conditions on
MLSM, we reapplied equation (4) assuming that each recording station has its own characteristic bsite value. This value
represents a station correction to be applied for the estimation M w from MLsM. The new linear system (equation 4) was
solved for 41 recording stations. The final equation has a
slope of 0.98. The difference of the average value of b~ite for
rock and alluvium sites is 0.15, simiIar to the values previously found.
In order to further classify the recording sites, we used
the average Vs3o velocity of the uppermost 30 m at each recording site as an index of the recording station site conditions. In geotechnical engineering, 30 m is a typical depth
of borings, and therefore, a significant number of site-effect
studies is based on the properties of the topmost 30 m. New
U.S. propositions concerning site classification and empirical amplification factors appear to be solely based on the
mean shear-wave velocity of the surficial 30 m (Boore et aI.,
1993; Borcherdt, 1994). This categorization has been
adopted by the recently revised NEHRP (t994) and UBC
(1997) provisions. It is clear that the uppermost 30 m does
not have a significant effect on the wavelengths associated
with the predominant period of the WA seismograph (0.8
sec). However, the use of this average v3° value in engineering seismology has been shown (Boore et al., 1993,
1994; Ambraseys et al., 1996) to be a better semi-empirical
site-classification index than the traditional rock and alluvium categorization. The main reasons for this conclusion is
that (a) soft soils (low v~°) generally lie on top of soft geology, and (b) theory predicts that profiles with strong velocity reduction toward the surface (low v3°) exhibit strong
site amplifications. The combination of these two factors
explains the empirical observation that the average v~° value
is a very good site-classification index, even if the long
wavelengths ( - 1 sec) are not sensitive to this depth range.
A total number of 54 geotechnical boreholes were avail-
450
B.N. Margaris and C. B. Papazachos
able with depths achieving about 50 m for the majority of
them, while a small number of them were shallower and very
few of them deeper than 200 m. Those boreholes are located
at different sites in Greece (Klimis e t al., 1999). The velocity
and density profiles from each borehole were derived from
the work, which has been accomplished by Klimis e t al.
(1998), based on the methodology proposed by Boore and
Joyner (1997). The average travel-time profile was obtained
by interpolating the observed travel times from the shallow
shear velocity measurements at 2-m intervals from the surface to the deepest recording in each borehole. Averaging
the travel time at each depth, for which at least two interpolating values were included, and then fitting a functional
form to the average travel time as a function of depth, a
function of velocity versus depth was determined. Estimates
of v~° were available for 15 recording stations. In Figure 7,
the plot of bsite against vs3o is shown. The linear correlation
coefficient between bsite and v~° was 0,64. The final best-fit
~/~U~co~
M w to ,,,
LSM relation is given by
,I/tUncor
M w = 0.98 ,,~Ls~t
.
,
,
,
,
.
i
.
.
.
.
,
,
.
,"~
,
Soil
.
.
,
,
Rock
0.5
•
bsite
It
0.0
-0.5
-1.0
.
a
2OO
,
400
600
800
I000
Vs(30m)
Figure 7.
30
+ 0.84 vs
< 0.85 km/sec),
- 0.53 (0.25 kin/see < v s30 =
1.0
Plot of the station constant, bsite, of the
M w - M L s M relation as a function of average shear ve-
(7)
where v~° is given in km/sec, with a standard error of 0.18.
Using equation (7), it is possible to estimate moment magnitudes by correcting strong-motion local magnitudes using
the average shear velocity for the first 30 m, v3°. It is important to notice that the use of vs3O as a site-classification
index, rather than the classic rock-alluvium classification,
results in a 50% reduction (from 0.35 to 0.18) of the standard
error of single-station M w estimation from M ~Uncor
s M . However,
if such information is not available but only a general classification is known, application of equations (5) and (6) is a
possible alternative.
M o m e n t Magnitude Based on WA and Short-Period
Records in Greece
Only two WA instruments have been installed and operated in Greece during the last 30 years, both by the Geodynamic Institute of the National Observatol~¢ of Athens
(NOA). As a consequence, many attempts have been made
to estimate WA local magnitude, ML*, from seismograms
recorded by other short-period type seismometers or accelerometers (Kiratzi, 1984; Kiratzi and Papazachos, 1984,
1985, 1986; Papastamatiou e t al., 1991; Hatzidimitriou e t
al., 1993). The local magnitude, Mca, using only WA amplitudes for the examined data set is given in Table 1. The
local magnitudes, Mc~, for the examined strong earthquakes
were calculated using the standard procedure proposed by
Richter (1935) and adopting the attenuation function, - log
A o, proposed by Jelmings and Kanamori (1983) for A < 100
km. Several studies have demonstrated that this function is
valid in several areas of Greece (Kiratzi e t al., 1984; Scordilis e t al., 1989), while it has been appropriately extended
for A > 100 km by Kiratzi and Papazachos (1984).
locity of the first 30 m under each recording station.
A gradual increase of bsite is observed from soil to
rock sites (higher velocities).
Except for the local magnitude based on records from
WA instruments, equivalent local magnitudes, M * , have
been computed in Greece using amplitudes and signal duration of records from short-period seismometers (Papazachos e t al., 1997). In the framework of that study, two relations (6 and 7 in Papazachos e t al., 1997) were proposed
in order to calculate ML* from such data. For the 33 observations of moment magnitude, M w, available in the present
• study, only one event had a M w smaller than 3.5 and was
excluded due to its very low magnitude. Using the local
magnitude, MLA, calculated for 27 events recorded at the WA
seismograph in Athens and the local magnitude, M * , calculated for 32 events from the Geophysical Laboratory of
Thessaloniki seismological network, as well as the corresponding moment magnitudes, M w , the following relation
has been determined:
Mw
= 1.0MLGR + 0.43,
3.6 __<---MrGR ----<6.5,
(8)
with a standard error of 0.21 and a linear correlation coefficient of R = 0.96. In this relation, M/~cRcorresponds to the
local magnitude calculated from Greek records, that is,
MLGR = MZA or MLGR = ML*. In order to avoid the dominance of the large number of small events in the M w to
MLcR relation, equation (8) was calculated after estimated
moving average values for M w and MLcR for the examined
magnitude range. In Figure 8, the proposed M w to MLGRrelation and the original data are presented, where solid and
open circles correspond to Mca and M~*, respectively. Equation (8) is almost identical with that proposed by Papazachos
e t al. (1997, relation 12) that was defined for a smaller mag-
451
Moment-Magnitude Relations Based on Strong-Motion Records in Greece
7.0
I
'
!
'
I
7.0
~
'
/v
ee ,,,I~9 ,,,"
sOSsJS
6.0
5.0
i
'
i
J
'
S
• p/.o,
6.0
_
5.0
MLSM
o
LA
4.0
4.0
'
S •S
S
Mw
I
00
~ ~
0
M~.
s
S
s
s
s
l
4,0
~
1
I
5.0
I
l
6.0
7.0
M t-G~
Figure 8. Plot of the M w against the local magnitude, MLaR, calculated from the Athens WA instrument (solid circles) or the Thessaloniki short-period
instruments (open circles). Notice that ML~~ underestimates Mw by ~0.4 to 0.5 units of magnitude.
nitude range (4.5 =< Mr --< 6.0); hence, this new relation can
be used in Greece for a much wider range of magnitudes
(3.6 -< MLa~ --< 6.5). For this magnitude range, the average
difference between Mw and M r values is 0.4, although it
seems to increase to 0.5 to 0.6 (see Fig. 8) for large events
(M/~R _-->5.5). This difference is well documented for Greece
(Kiratzi, 1984; Latousakis, 1984), where the routinely reported moment-equivalent magnitude, M (Papazachos et aL,
1997), is usually estimated as M = M r + 0.5. The observed
M w to ML bias is identified and is almost constant for all
earthquakes after 1966 when the WA instrument was installed in Athens (Kiratzi, 1984; Papazachos et al., 1997).
However, this systematic bias of Mr is not theoretically expected, because the definition of M W and the observational
data from other regions imply that M W = Mr, for a specific
magnitude range (e.g., Heaton et al., 1986). This problem is
examined in detail in the following section where local magnitude scales in Greece are compared.
C o m p a r i s o n o f Local Magnitude Scales
in G r e e c e - - D i s c u s s i o n
It is interesting to compare the local magnitude, MLsM,
based on strong-motion records (converted to WA waveforms) with the corresponding ones, MraR, derived from
seismological networks in Greece. This comparison is
shown in Figure 9 where the local magnitudes, Mcsg, based
on strong-motion records are plotted against local magnitude, MrGR. For MLGR, we used the local magnitude derived
from the Athens WA seismograph (MLA), and when this es-
3.0
!
3.0
[
4.0
I
I
!
5.0
I
!
6.0
7.0
ML~R
• Figure 9. Comparison of the local magnitude,
MLGR, calculated from the Athens WA instrument
(solid circles) or the Thessaloniki short-period instruments (open circles) against the strong-motion local
magnitude, MLGR.A large but almost constant difference (-- 0.4 to 0.5) between the two magnitude scales
is observed, similar to the Mw-MLGR in Figure 8. The
relation between published ML values and estimated
MLsg for Yugoslavia (Lee et al., 1990) is also shown
for comparison.
timate was not available, we used the M * values given by
Papazachos et al. (1997). MrGR values for those data extend
over a large magnitude range. Moving average Values for
MrcR and MrSM were also calculated for the whole magnitude
range examined, similarly to equation (8). Moreover, in order to avoid large errors in the determination of MLc~ (due
to small recorded amplitudes or ambiguous definitions of
significant signal duration) or MrsM (due to small recording
and filtering effects), we used the most reliable data with
M r > 3.5 (119 events). The following relation between M L
and MLSM was derived for Greece:
MUM = 0.89 * MLaR + 1.01,
3.5 N MLG~ =< 6.5,
(9)
with a standard error of 0.32 and a linear correlation coefficient R = 0.89. If half peak-to-peak amplitudes are used
for the MLSM estimation, equation (9) is modified to
MLS M =
0.89 * M t ~ + 0.94
(half peak-peak WA amplitudes),
3.5 < M r G R < 6.5.
(10)
Differences between MrsM and ML have also been observed in other cases, for example, for California by Trifunac
452
(1991a), who defined this difference as D(MSM). Trifunac
(1991b) examined possible physical causes, mainly related
to attenuation, for D(MSM). In Figure 9, the corresponding
relation between ML (from seismological networks) and
MLS M published for Yugoslavia (Lee et al., 1990) is also
shown. According to this study, this bias between ML and
MLs M exhibits a very strong dependence with the size of the
earthquake, reducing almost linearly from 1.5 to - 0 . 1 4 for
the magnitude range examined in the present study ( M L =
3.5 to 6.5), for example, for M L = 3.5, the average estimated
MLSM is 5.0. However, the bias observed here is very different from the D(MSLM)Yu determined for Yugoslavia. The
MLsM--MLcR difference shown in Figure 9 is practically constant (0.6 to 0.3) with MLoR and does not get the large values
reported for D(MsM)Yu. Moreover, the excellent agreement
of MLSM with Mw further indicates that the constant bias of
MLGR is more related to other factors than those suggested
by Trifunac (t991b), which will be examined in detail.
In order to summarize our results for the magnitude
scale, the best-fit lines for MLsM and MLc~ (equations 2 and
8) versus Mw are presented in Figure 10. It is clear that the
local magnitude, MLaR, reported from seismological networks underestimates Mw by --0.4 to 0.5 units of magnitude.
For the local magnitudes estimated from amplitude and duration recorded at other short-period instruments (not WA),
the reported ML* is almost identical to Mza (e.g., see Fig. 8).
This is expected as M E for these instruments was estimated
by calibrating amplitudes and durations on the available MLA
values reported from the Athens WA instrument (NOA). On
the other hand, the local magnitude determined from strongmotion instruments, MLSM,appears to be almost equal to Mw,
for a large magnitude range.
The systematic difference observed between Mca/M3
and Mw was recently attributed (Papazachos et al., 1997) to
a low magnification of the WA instrument in Athens. The
magnitude difference of ~0.4 to 0.5, also confirmed in the
present study, corresponds to a static magnification of approximately 800 to 1000 for the Athens WA seismograph
(Papazachos et al., 1997), which is even lower than the magnification (V -- 2080) reported for U.S. WA seismographs
(Boore, 1989; Uhrhammer and Collins, 1990). Because no
calibration data are available for this instrument, the ML-Mw
bias could also be attributed to other factors, for example,
very low Q values or special spectral shape of earthquakes
in Greece, special site effects (low Q or deamplification)
near the WA recording sites, etc. However, the results of the
present study show clearly that earthquakes in Greece recorded from strong-motion instruments when input to an
ideal but realistic WA instrument would result in local magnitudes almost equal to the moment magnitude. This observation suggests that the previously described factors could
not have played an important role in MLA--Mw bias, which
confirms that it should be attributed to the specific instrument characteristics of the Athens WA seismograph.
In order to verify this conclusion, we reevaluated the
attenuation correction, - l o g Ao for Greece from both
B.N. Margaris and C. B. Papazachos
7.0
6.5
'
f
¢"
6.0
ML
S(
s.s
(GR, SM)
5.0
4.5
4.0
2,
s, f
! ///
i:':". ......................
3,5
3.5
4.0
4.5
5,0
5.5
6.0
6.5
7,0
Mw
Figure 10. Comparison between the Greek local
magnitude scales ML(GR.SM)and moment magnitude
Mw. Local magnitudes reported from Greek seismological networks, MLGR,exhibit a 0.4 to 0.5 systematic
difference with M w (see Fig. 8). Local magnitudes
estimated from strong ground motion, MzsM, are practically identical to Mw.
strong- and weak-motion data. For this reason, we used the
original definition of M L (Richter, 1935):
ML = log A - log Ao,
(11)
where A is the WA amplitude (in mm) and - log A 0 is the
attenuation term, and required that the local magnitude, ME,
is equivalent to the moment magnitude, Mw. This constraint
is reasonable: Mw was originally calibrated to be equal to
M L (Hanks and Kanamori, 1979), and as a long-period magnitude, it is almost independent of the region for which it is
estimated by international institutes (e.g., Harvard CMT solutions). Therefore, the only way to determine an ML scale
for Greece that is compatible to the original definition (Richter, 1935) is to do it through Mw by assuming that M L =
M w, before M L is saturated. Using this assumption, we can
write
-logA0
=
Mw
-
logA.
(12)
Figure 11 shows the estimated - log A0 values as a function
of the epicentral distance, A. In this figure, circles denote
- log A0 values determined from synthetic WA amplitudes
from strong-motion data (V = 2080), while squares correspond to original WA amplitudes reported from the WA instrument in Athens for the same earthquakes as the strongmotion data. Only earthquakes for which originally reported
M w values were available (gray circles) have been used.
Moreover, eight events for which the equivalent moment
453
Moment-Magnitude Relations Based on Strong-Motion Records in Greece
|
5.0
J
|
I
•
1.9
• -log&
4.0
I ®~'~" "
\~JogA1.6-2.0
® ® i..~
@
"I
-log a o
3.0
o
>y
2.0
#
Kiratzi & Papazachos (1984) (A>100km)
[
Kanamori& Jennings (1978) (A<I00km)
t
/
Present study (A>100km- WA recordings)
~
1
-Str~gomotiondata)
1.0
0
100
200
A (km)
300
magnitude, M~, estimated from MLGR (equation 8), was
larger than 5.0 and no M w estimate was available (open circles) were also incorporated. The Jennings and Kanamori
(1983) curve for A < 100 km is also shown, as well the
relation defined for A > 100 km by Kiratzi and Papazachos
(1984) using the WA recordings from Athens. In general,
strong-motion data and WA recording show a small distance
overlapping (--130 to 160 km) due to the lack of strongmotion records at large distances and the clipping of WA
records for large events at short distances.
Several important conclusions can be deduced from Figure 11. The first observation is that for distances A < 100
kin, the Jennings and Kanamori (1983) correction is quite
appropriate for Greece. This is clearly observed by its very
good correlation with the solid line that was estimated from
the Greek strong-motion data, because only small differences up to - 0 . 0 7 at A = 10 km and +0.16 at A = 100
km are observed. It is clear that this agreement, also identified in earlier studies (Kiratzi et al., 1984; Scordilis et al.,
1989), indicates a similarity in the near-field attenuation
(A < 100 km) between Greece and California. However,
this similarity should only be considered as indicative because our static magnification (V = 2080) is different to the
value (V = 2800) used by Jennings and Kanamori (1983).
Moreover, the distance definition that Jennings and Kanamori (1983) used (closest to fault or closest to center of fanlt)
is quite different from the epicentral distance used here in
400
Figure 11. Plot of the WA amplitude attenuation, - log Ao, versus epicentral distance, A.
Gray-filled circles show estimates from strongmotion data for which original Mw estimates
were available. Eight strong-motion data for
which only M* (> 5.0) estimates from other
magnitudes were available are also shown by
open circles. The corresponding - l o g Ao estimates from the original WA amplitudes recorded for the same earthquakes in the Athens
WA instrument (NOA) are shown (solid
squares) for comparison. The Kanamori and
Jennings (1983) relation proposed for California for A < 100 km (gray solid line) and the
Kiratzi and Papazachos (1994) relation proposed for Greece for A > 100 km (gray shaded
area) are also shown, together with the best-fit
lines determined in the present work for strongmotion (A < 150 km, solid line) and Athens
WA (A > 100 km, dashed line) data. A good
agreement is observed between the Greek
strong-motion data and the prediction of the
Kanamori and Jennings (1983) relation for A
< 100 km. Also, the log A slope (1.9) for A >
100 km determined from WA recordings for
our data set (mainly after t983) is in very good
agreement with those (1.6 to 2.0) found by Kiratzi and Papazaehos (1984) using data before
1982. A clear magnitude bias of the order of
--0.45 is observed between the strong- and
weak-motion estimates for distances between
130 and t60 kin.
the vicinity of the fault (small A). It is also interesting to
notice that the - l o g A 0 value determined here is not completely compatible with Richter' s definition (0.7 ¢tm instead
of 1/zm forML = 0 at A = 100 km). This is not unexpected,
because the adoption of the original Richter M L scale in
Greece through M w can introduce some small bias due to
differences between California and Greece concerning factors other than the local attenuation. Such differences can
concern crustal-upper mantle attenuation affecting M w estimation (Greece is an active subduction area), focal mechanisms (almost exclusively normal in the Greek data set),
high-frequency spectral content due to different stress drop,
etc. However, we do not feel that the available strong-motion
data are adequate, at present, for the determination of a new
attenuation relation for Greece. Such a relation based on a
combined strong- and weak-motion data set is the subject of
further research.
The second observation is the presence of a systematic
shift in the WA recordings of NOA. The best-fit log A 19
variation of - l o g A0 determined from these data (dashed
line), which corresponds to earthquakes mainly after 1983
up to 1996, is in excellent agreement with the corresponding
relation of Kiratzi and Papazachos (1984) using a much
larger number of WA recordings from NOA for earthquakes
between 1966 and 1982. However, although the overlapping
between the two data sets (strong motion and WA) is small,
it is clear from the best-fit lines that the WA data exhibit a
454
B.N. Margaris and C. B. Papazachos
systematic shift of the order of 0.45 magnitude units between
100 and 160 km. This shift does not seem to vary with distance and cannot be attributed to differences in attenuation
because it is present even in the region where the data overlap (~130 to 160 km). This observation clearly verifies that
the Mw-MLG~ bias (equation 8) is due to the specific WA
instrument characteristics. As a result, even using the right
distance correction (Kiratzi and Papazachos, 1984), appropriately calibrated with Richter's definition (ML = 0 for
1 # m at 100 km), leads to biased Mrs ~ estimates.
The presence of this 0.4 to 0.5 magnitude bias can obviously have important implications for hazard estimates, if,
for example, one attempts to import a global PGA attenuation
relation involving M~ to Greece. However, because the presence of this bias, originally between MLGR and M s for M s >=
5.5 (Kiratzi and Papazachos, 1984; Latousakis, 1984), has
been clearly recognized for the last 15 years, all local attenuation relations that have been applied for hazard estimation
in Greece (e.g., Theodulidis and Papazachos, 1992) involve
M = MLoR + 0.5, rather than MLaR itself. This magnitude
M has been shown to be equivalent to Mw (Papazachos et
al., 1997). The results of the present study (equation 8 and
Fig. 11) confirm this result and extend its applicability to a
much larger MLcR range (3.6 to 6.5).
Conclusions
In the present study, it has been shown that strong-motion recordings can be efficiently used to estimate local magnitudes for the range 3.9 <_- MLsM <--<-6.6. This local magnitude, MLsM, calculated from Greek strong-motion records,
can be used to estimate the seismic moment (equation 1) and
is in very good agreement with the moment magnitude, Mw,
for the same magnitude range (equations 2 and 3). Appropriate site-dependent relations have also been proposed for
the estimation of M w from MrsM (equations 5, 6, and 7). The
obtained MLsM does not exhibit the systematic --0.4 to 0.5
difference from Mw, which has been observed for M ~ , derived from the WA instrument in Athens, and M*, derived
from equivalent short-period seismometers from regional
seismological stations, in Greece (equations 8). It has been
shown that this Mw-Mz, difference is observed for a larger
magnitude range than previously thought (equation 8). Comparison of the local magnitudes from strong-motion recordings and seismological networks (equations 9 and 10) suggests that this difference should be attributed to the specific
Wood-Anderson instrument, where all local ML relations
have been calibrated. A low magnification of - 8 0 0 to 1000
instead of 2800 for this instrument (Papazachos et al., 1997)
could explain this difference. This is verified by the variation
of the WA amplitude attenuation curve, - log Ao, with epicentral distance: Comparison between synthetic WA amplitudes from strong-motion records with observed WA amplitudes in Athens for the same earthquake data set exhibits a
similar magnitude deviation (0.4 to 0.5) for the distance
range 130 to 160 kin. These results also confirm that the
Jennings and Kanamori (1983) relation is appropriate for
Greece for short epicentral distances (A < 100 kin).
Acknowledgments
We would like to thank B. Papazachos for his careful reading of the
manuscript and his valuable suggestions, as well as the several discussions
we had with him~ The authors would also like to thank D. Boore for carefully reading the manuscript and several discussions during the evolution
of this work, as well as for providing helpful comments. T. C. Hanks read
the manuscript and made constructive comments and a fruitful discussion
took place with him when the first author was a visiting scientist at USGS
in Menlo Park. N. N. Ambraseys and W. Bakun made several helpful comments for this work. We would also like to thank K. Campbell, A. Rogers,
and an anonymous reviewer for the valuable and instructive review of this
work. This work has been partly financed by the Institute of Engineering
Seismology and Earthquake Engineering-ITSAK (proj. 106197) and the District of Central Macedonia-Greece (proj. 7454 R.C. Univ. Thessaloniki).
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Institute of Engineering Seismology and Earthquake Engineering (ITSAK)
P.O. Box 53
GR 55 102, Finikas
Thessaloniki, Greece
E-mail: margaris @itsak.gr, costas @itsak.gr
Manuscript received 24 March 1998.