Bulletin of the Seismological Society of America, Vol. 76, No. 5, pp. 1225-1239, October 1986
MOMENT MAGNITUDE SCALE FOR LOCAL EARTHQUAKES IN THE
PETATLAN REGION, MEXICO, BASED ON RECORDED PEAK
HORIZONTAL VELOCITY
BY M. MAHDYIAR, S. K. SINGH, AND R. P. MEYER
ABSTRACT
Assigning moment magnitude to local earthquakes based on peak recorded
amplitude and hypocentral distance is the principal concern of this paper. For 38
aftershocks of the Petatlan earthquake (14 March 1979) with moments between
2.8 x 1018 and 1.4 x 1022 dyne-cm, we developed an empirical relationship for
the estimation of moment based on peak horizontal velocity (V) and hypocentral
distance (R). This empirical relationship in conjunction with the definition of
moment magnitude (Hanks and Kanamori, 1979) allows direct estimation of
moment magnitude, knowing peak horizontal velocity and hypocentral distance.
We call this estimation of moment magnitude " M , ' " to distinguish it from its
original definition. Equation for M,,' for our data set is
M,,' = 2.27 + 0.77 Iog(V.R) + 6.59 x 10-3R,
where V is in millimeters/second, and R is in kilometers.
In order to be able to estimate the moment magnitude from coda duration (Tc),
we sought and found correlation between Iog(Tc) and log of moment (Mo) as
follows
log Mo = (2.25 _+ 0.17)1og Tc + (15.88 + 0.29),
where Mo is in dyne-cm, and Tc is in seconds.
INTRODUCTION
Ideally,magnitude should be a measure of"source strength"and thus independent
of the source mechanism, propertiesof the transmitting medium, distance from the
source, and characteristicsof the seismograph. If this was the case,the magnitudes
of earthquakes in differentregions could be directlycompared.
In 1935, using California data, Richter developed the original magnitude scale
based on the peak amplitude recorded on particularWood-Anderson seismographs
(natural period of 0.8 sec, damping ratio of 0.8,and a magnification factor of 2800)
and an empirical amplitude-epicentraldistance relationship.Richter's amplitudedistance relationship may not be valid for regions other than California, since
different regions may have different velocity-depth functions and attenuation
properties.Furthermore, Richter amplitude-distance relationshipdoes not need to
take into account the variationin the depths of earthquakes, as nearly all California
earthquakes are shallow. However, Richter's approach to scale earthquakes based
upon a peak amplitude, a parameter easily determined from analog records,is still
very attractive.
With the advent of digitalrecording, a magnitude scale,Mw, related to seismic
moment, M0, has been developed (Hanks and Kanamori, 1979). M w potentially
provides a transportable magnitude scale,allowing the direct comparison of earthquakes' source strength in different regions, as moment is independent of the
1225
1226
M. MAHDYIAR, S. K. SINGH, AND R. P. MEYER
earthquake source mechanism and explicitly includes corrections for the attenuation
and geometrical spreading from the hypocenter. However, routine determination of
seismic m o m e n t is not especially practical if the data are not in digital form, as
spectra must be computed.
Since most short-period seismographs have outputs t h a t are essentially linear
I
t
I
I
I
I
I
~DIGITAL
15
[]13
~4
LS.C -
~
~
"2
~
O
17
SMOKED PAPER
DIGITAL & SMOKED PAPER
tt
t~
~
•
~
O
.~ --
~2
--
~3
17-0 _
A
~
567
103.0
I
~
I
I
I
102,5
102,0
lOt.5
lOI.O
lO0,S
IO0,O
99,5
w
LONGITUDE
TRENCH
I
I
;
-iO.O
o
-20.0
~-~o.o m
~-4o.o
o
o
m
-50.0 m
-60.0
b
I
-70.0
0.0
50.0
I
I
lO0.O
[50.0
VERTICAL CROSS SECTION A-A Km
FIG. 1. (a) Epicentral locations of 38 earthquakes (circles) recorded at least by four digital instruments
(open squares). Half-solid squares are stations that were occupied by both digital and smoked-paper
instruments. The number above each square is the assigned station number. Smoked-paper stations are
not numbered. (b) Vertical cross-section of the 38 earthquakes projected on the plane shown in (a).
with velocity in the frequency range of 1 to 25 Hz, we can search for an estimator
of Mo (or Mw) through an empirical relationship between M0, peak velocity, and
hypocentral distance, R. It is, therefore, the main objective of this study to obtain
such a relationship and develop an expression for m o m e n t magnitude based on the
peak recorded amplitude.
We derive an empirical equation for the estimation of m o m e n t from peak
M O M E N T MAGNITUDE IN THE PETATLAN REGION~ MEXICO
1227
TABLE 1
SOURCE PARAMETERS OF THE 38 EARTHQUAKES USED IN THIS STUDY
No.
Date
(yr/
m/d)
Origin T i m e
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
79/03/17
79/03/17
79/03/17
79/03/17
79/03/18
79/03/18
79/03/18
79/03/18
79/03/18
79/03/18
79/03/18
79/03/18
79/03/18
79/03/18
79/03/18
79/04/03
79/04/03
79/04/03
79/04/03
79/04/03
79/04/03
79/04/03
79/04/03
79/04/03
79/04/08
79/04/08
79/04/13
79/04/13
79/04/13
79/04/14
79/04/14
79/04/14
79/04/14
79/04/14
79/04/14
79/04/14
79/04/14
79/04/14
20:57
21:47
22:44
23:47
00:12
00:37
1:21
1:22
1:32
1:47
1:53
1:57
2:01
2:11
2:39
0:33
0:36
2:45
4:50
7:45
8:30
11:08
11:50
17:17
00:21
4:47
8:02
11:18
15:09
3:12
3:24
4:24
4:32
4:52
10:49
12:00
12:20
12:32
Latitude( ° N )
17.58
17.48
17.40
17.31
17.39
17.74
17.40
17.46
17.45
17.32
17.47
17.47
17.55
17.60
17.45
17.39
17.39
17.45
17.46
17.51
16.61
17.41
17.33
17.36
16.99
17.24
17~38
17.63
17.44
17.43
17.57
17.41
17.70
17.42
17.55
17A7
17.25
17.28
Longitude
(°W)
Z (km)
Mo* (dyne-cm)
EMot
101.40
101.27
101.23
101.59
101.41
101.47
101.22
101.28
101.29
101.28
101.55
101.24
101.20
101.17
101.31
101.30
101.29
101.26
101.15
101.83
99.86
101.52
100.86
101.14
100.32
101.03
10] .32
1.01.40
101.49
101.20
101.67
101.48
101.59
101.50
101.41
101.61
101.66
101.42
23.81
21.67
19.76
15.77
30.84
31.11
20.25
20.09
20.77
19.65
24.68
22.79
29.84
39.81
16.87
21.90
21.23
24.43
27.37
40.32
33.16
17.37
23.37
24.18
27.52
30.40
~;4.71
19.37
12.21
17.26
17.83
25.35
22.97
17.69
20.50
30.02
13.67
21.28
4.45E19
4.86E18
1.99E19
3.01E20
3.90E20
3.42E19
4.78E19
4.10E18
9.80E19
3.77E19
1.54E19
1.01El9
1.89E20
9.66E18
3.14E20
3.03E19
5.09E19
6.77E19
1.37E19
1.64E20
9.50E19
8.08E18
9.41E18
3.50E20
2.77E19
1.42E22
1.26E21
1.02E20
3.30E19
9.25E18
2.82E18
8.70E19
3.43E20
5.51E18
3.26E19
1.14E19
3.48E18
2.06E19
1.89
1.40
2.23
1.61
1.71
1.59
1.81
1.45
1.11
1.22
1.38
1.47
1.59
1.73
1.42
2.46
2.41
1.88
2.57
2.24
1.59
2.02
1.51
1.54
2.24
2.34
2.56
1.51
3.13
1.61
2.37
2.62
2.60
2.38
1.55
2.03
2.64
1.93
* J~fo, average seismic moment~, was estimated following Archuleta et al. (1982) as
-~o = antilog [ 1 / N j f 1 (log Mo)i],
where (log Mo)j is log of moment at station j, and N is the number of stations that recorded each
earthquake.
t E M o , multiplicative error factor for J~ro, was calculated following Archuleta et al. (1982) as
E M o = antilog[S.D.(log Mo)],
S.D.(log _~ro) =
I
1/(N -
1)
f
j=l
t
[(log Mo)i - log Mo] 2
.
1228
M. MAHDYIAR, S. K. SINGH, AND R. P. MEYER
horizontal velocity (V) and hypocentral distance (R). We determine this equation
from the correlation between log V, log Mo, and R. Using this estimator equation
of log Mo in conjunction with the definition of moment magnitude allows direct
estimation of Mw. We call this estimation of moment magnitude "Mw'" to distinguish it from its original definition.
For the cases t ha t only uncalibrated seismograms are available, we look for an
estimator of log Mo based on coda duration.
Our trial date base is from aftershocks of the Petatlan earthquake of 14 March
1979, M s = 7.6 (Meyer et al., 1980; Valdes et al., 1982) recorded on three-component
portable digital seismographs.
TABLE 2
LISTOF LOCATIONSOFTHE24 STATIONSWHICHWEREOCCUPIEDBYDIGITALINSTRUMENTSAS
SHOWNIN FIGUREla
Station
No.
Latitude ('N)
Longitude (°W)
1
2
3
4
5
6
7
8
9
t0
11
12
13
14
15
16
17
18
19
20
21
22
23
24
17.17
17.24
17.16
17.00
16.87
16.83
16.87
17.65
17.73
17.83
17.94
18.00
18.05
18.06
18.17
17.81
17.63
17.66
17.73
17.67
17.61
17.49
17.42
17.41
100.57
100.43
100.39
100.17
99.88
99.85
99.78
101.59
101.61
101.71
101.78
101.97
102.16
102.57
102.27
101.45
101.47
101.34
101.20
101.26
101.31
101.04
101.04
101.16
DATA
Locations of 38 afCershocks and the recording stations used in this study are
shown in Figure 1. The seismic moments (Mo) were estimated from the displacement
spectra of a 2.5-sec time window, starting 0.3 sec before the shear-wave arrivals as
picked on horizontal components. In the determination of Mo, we corrected the
spectra using rms radiation patterns (a factor of 0.6), free-surface amplification (a
factor of 2), and the assumption of equal vectorial partitioning of the shear energy
into two orthogonal components (a factor of 1/~/2). T he correction for shear-wave
attenuation (Qs) was taken into account using estimated values from Petatlan data,
Qs = 87 fo~s (Mahdyiar, 1984), where f is frequency. For the 38 events studied, Mo
ranges between 2.8 × 10 TM and 1.4 × 1022 dyne-cm. Source parameters of these
1229
MOMENT MAGNITUDE IN THE PETATLAN REGION, MEXICO
earthquakes and the list of stations that recorded them are given in Tables 1 and
2, respectively. The hypocentral range distribution of these earthquakes as a
function of log of moment is shown in Figure 2.
ATTENUATION OF PEAK HORIZONTAL VELOCITY WITH DISTANCE
We approximate the decay of the peak horizontal velocity, Vii, of an earthquake
i recorded by a station j at the hypocentral distance of Rq using an equation in the
23.0
I
I
I
I
22.0
21.0
e~
>,
,i,,,,**e i F - . l l . . .
• **
.
**ileal'.
0
20.0
SF
*
*
m
"ii'.',, :.ii
"ill,
"
*
19.0
.
"18.0
. * *
I
0.0
*
-...*
t
30.0
4
60.0
HYPOCENTRAL
l
90.0
DISTANCE
120.0
Km
FIG. 2. Hypocentral range distribution of stations recorded each earthquake versus log of moment of
the earthquake, averaged over all stations. Average depth of these earthquakes is 22.6 kin.
following form as suggested by Joyner and Boore (1981)
Vii = (SdRq )e-hRi4
(1)
where Si represents source strength, and e -hRi~and 1/Rq are the attenuation (with
constant k) and geometrical spreading decay terms, respectively. As mentioned by
Joyner and Boore (1981), modeling the decay of peak horizontal velocity with
distance in the form of equation (1) is only valid if Si and k are empirically
determined. Equation (1) in its logarithmic form is
log(Vii) = log(Si) - log(Rii) + KRij,
(2)
1230
M. MAHDYIAR, S. K. SINGH, AND R. P. MEYER
where K = -(lOgl0e)k. According to equation (2), plots of log(Vu. Ru) versus Ru of
different earthquakes (Figure 3) ideally are expected to show a series of straight
lines (one for each earthquake) with a slope of K. However, these plots indicate
that some sort of station correction to log(Vu) is needed. We include station
correction in equation (2) as follows
log(Vij) = log(S~) - log(R u) + KRij + Cj,
(3)
3.0
2.0
!
O
O
1.0
4-,
>
~O
O
,-4
I:
0.0
-I.0
"v
-2.0
I
0.0
30.0
I
60.0
HYPOCENTRAL
I
I
90.0
120.0
DISTANCE
Km
FIG. 3. Plot of log(V.R) versus hypocentral distance, R, where V is peak horizontal velocity.Each
continuous line represents one earthquake. According to equation (2), decay rate of log(V.R) with
respect to R of all earthquakes is expected to be constant. However, these plots suggest that some sort
of station correction for log(V) is needed.
where Cj is the station correction at station j. The constraint on Cj, as mentioned
by Bakun and Joyner (1984), is that
N
Cj = O,
(4)
j=l
where the summation is over all the N stations which recorded each earthquake.
We adopted the regression analysis technique of Joyner and Boore (1981) in
conjunction with the constraint on Cj to estimate coefficient K, station corrections
MOMENT MAGNITUDE IN THE PETATLAN REGION, MEXICO
1231
(Cj), a n d source s t r e n g t h (Si). T h i s t e c h n i q u e decouples t h e d e t e r m i n a t i o n of source
s t r e n g t h , Si, f r o m t h e d e t e r m i n a t i o n of p a t h - d e p e n d e n t p a r a m e t e r K. T h e values o f
t h e s t a t i o n c o r r e c t i o n s are given in T a b l e 3, a n d t h e e s t i m a t i o n for coefficient K
a n d its s t a n d a r d e r r o r of e s t i m a t e is
K = - 8 . 5 × 10 -3 +_ 1.24 × 10 -3 k m -1.
W e a p p r o x i m a t e t h e source s t r e n g t h o f e a c h e a r t h q u a k e in t e r m s o f its seismic
m o m e n t as
log(S/) = Ao + A1 (log(/~o)i) + A2 (log(-Mo)i)2.
(5)
TABLE 3
ESTIMATED VALUES OF STATION CORRECTIONS, Cj, AT DIFFERENT STATIONS, j, AND THEIR
STANDARD ERROR OF ESTIMATES*
Station
Ci
Standard Error
of Estimate
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
19
21
22
23
24
0.125
-0.091
0.187
-0.241
0.343
-0.022
-0.053
0.035
-0.188
-0.114
0.436
-0.361
0.304
0.122
0.527
-0.217
0.315
0.012
0.092
-0.097
-0.037
0.135
0.157
0.111
0.007
0.170
0.137
0.121
0.328
0.127
0.138
0.172
0.074
0.116
0.085
0.115
0.266
0.218
0.174
0.165
0.142
0.305
* The values of Cj are additive to log of peak horizontal velocity.
where log(/(to)/is t h e average of log Me at all s t a t i o n s t h a t r e c o r d e d e a r t h q u a k e i. A
p l o t of log(S/) versus log(/~to)i (Figure 4), however, suggests a linear relationship,
i.e.,
Ao = - 1 5 . 9 3 _ 0.73,
A1 = 0.82 _+ 0.04,
(6)
and
A2 = 0.0.
S u b s t i t u t i n g for log(Si) in e q u a t i o n (3) gives a n empirical r e l a t i o n s h i p for t h e
1232
M. MAHDYIAR, S. K. SINGH, AND R. P. MEYER
estimation of log(Vij ) as follows
log(Vij) = Ao + Al(log(-Mo)i) - log(Rij) + KRij + Cj.
(7)
The residuals of the observed log of Vij - estimated log of Vij before and after
considering the stations corrections are shown in Figures 5 and 6. The use of station
correction for log(Vij) has decreased the standard deviation of the average of the
residuals from 0.33 to 0.24, which is significant. Figure 7 shows a plot of log(Vii.
3.0
I
I
I
I
Q
2.0
~1.0
.,.-.
0
Qe
OO
0.0
•
•
-~..0
18.0
19.0
2010
21.0
22.0
l o g (MOMENT) dyne-era
FIG. 4. Plot of log of source strength (S) [equation (1)] versus log of moment, Mo, averaged over all
stations that recorded each earthquake. A least-squares fit to these data suggests a linear relationship
between log(S) and log(Mo), i.e.,
log(S) = (-15.93 _+ 0.78) + (0.82 _ O.04)log(Mo).
Rij) after being corrected for the station correction versus Rii. A comparison between
this figure and Figure 3 shows that using the station correction on log(V;j) has been
effective in removing some of the misbehavior of the data.
For our analysis, however, we need an equation to estimate log Mo from peak
horizontal velocity and hypocentral distance. For this, we rearrange equation (7)
by correcting the peak horizontal velocity for geometrical spreading, attenuation,
and station correction as follows
log(Vij.Rij) - KRij - Ci -- Ao + Al(log(/~0)i):
(8a)
1233
MOMENT MAGNITUDE IN THE PETATLAN REGION, MEXICO
The estimator equation for log Mo can be obtained by taking the left-hand side of
equation (8a) as the independent variable and log -~fo as the dependent variable as
follows
(Sb)
log(A{o)i = Bo + B l [ l o g ( Vij. Rij ) - K R u - Cj ].
A least-squares fit of equation (8b) to the data, using the estimated values of K and
Cj from the previous analysis, results in
Bo = 19.43 __+0.22
1.0
I
.
I
I
i
*
t
o
~)
*
., • . ,
v
b~
0
0.0-
!
~
":;
:.
"N
o
,o
.
.
"
0
0
I
--1 0
0.0
I
30.0
60.0
I
I
90.0
120.0
HYPOCENTRAL DISTANCE Km
FIG. 5. Log[observed peak horizontal velocity (Vobs)] - log[estimated peak horizontal velocity (Vest)]
versus hypocentral distance. Log(Vest) does not include station correction. Average value of these
differences at various stations (solidline) and __I S.D. (# = 0.33) (broken lines) are shown.
and
B1 = 1.05 + 0.03,
with the standard deviation of the best fit a = 0.29.
MOMENT MAGNITUDE
Hanks and Kanamori (1979) proposed the moment magnitude scale as
Mw = ~ log Mo - 10.67.
(9)
M. MAHDYIAR, S. K. SINGH, AND R. P. MEYER
1234
Our purpose is to develop a relationship for the estimation of Mw in terms of peak
horizontal velocity and hypocentral distance. Substituting for log Mo in equation
(9), using its estimation from equation (8b), gives
2
( M ~ t) i j = ~(Bo
+ B~[log(Viy.Rij)
- KRij -
Cj]} -
10.67,
(lO)
where the notation M w ' is used to distinguish the estimation of M w from its original
definition. Subscripts i and j specify earthquake and station number, respectively.
1.0
I
i
I
I
6
0
$'*
~,
00
O
*
0
*B
Ol
O
• % -
"
>
~0
0
0.0
!
~-.~.
o
•
-I.o
t
0
• "g Jb, .,S
1
**
I
0.0
.g
I
30.0
60.0
HYPOCENTRAL
I
i
90.0
DISTANCE
120.0
Kin
F~G. 6. Similar to Figure 5 except that log(Ve~t)includes station correction.Standard deviation of the
average value of log(Vow) - log(Ve~),because of including station correction, decreased from ~ = 0.33
(Figure 5) to a = 0.24.
The values of stations correction in equation (10) are particular for the set of
stations in this study. However, averaging equation (10) over all stations, N, which
recorded each earthquake in conjunction with the assumption on the station
corrections [equation (4)] makes the average value of Mw' independent of the
station correction
(M~')i = ~
o -'l- W
j=l
j=l
Substituting for B0, B1, and K, equation (11) for a single station, after dropping
MOMENT MAGNITUDE IN THE PETATLAN REGION, MEXICO
1235
subscripts i a n d j, is
M ~ ' = 2.28 + 0.70 l o g ( V . R ) + 5.94 x 10-3R,
(12)
where V is in millimeters/second, a n d R is in kilometers. Figure 8 shows plots of
M~ versus M~ '. A least-squares fit to the d a t a shown in this figure yields
Mw = - 0 . 2 6 + 1.11
3.0
l
(
Mw ',
(13)
I
I
90.0
120.0
2.0
l
0
~I.0
o.o
-I.0
-2.0
0.0
30.0
60.0
HYPOCENTRAL DISTANCE Km
FIG. 7. Plot of log(V.R) versus hypocentral distance, R, where V is peak horizontal velocity after
being corrected for station correction. A comparison between this figure and Figure 3 indicated that
including station corrections has improved the data, in the same sense that the decay rate of log(V-R)
with respect to R, in this figure, can be adequately assumed to be constant.
with the s t a n d a r d error of e s t i m a t e of Mw on M w ' a = 0.13 units of magnitude.
Substituting for M w ' f r o m equation (12) in equation (13) gives the final e s t i m a t o r
equation of M~. W e also called this modified e s t i m a t i o n of m o m e n t m a g n i t u d e
"Mw'" to avoid introducing a second n o t a t i o n for e s t i m a t i o n of M~. E q u a t i o n for
modified M ~ ' is
M w ' = 2.27 + 0.77 l o g ( V . R ) + 6.59 x 10-3R,
which should not be confused with
Mw' in equation (12).
(14)
1236
M. MAHDYIAR, S. K. SINGH, AND R. P. MEYER
MOMENT MAGNITUDE IN TERMS OF CODA DURATION
During the recording of the aftershocks, four stations were equipped with smokedpaper, vertical-component seismographs (two Kinemetrics and two Teledyne Portacoders, b o t h with 1-Hz seismometers) (see Figure 1). Of the 38 aftershocks
analyzed here, four are recorded on four stations, six on three, 11 on two, and 17
on one of these stations. Although gains and filter settings are different, coda
A
2
I
I,
I
I
1
2
3
t~
Fro. 8. Plot of estimated moment magnitude (Mw') [equation (11)] versus moment magnitude (Mw)
[equation (9)]. A least-squares fit to this data (solid line) with standard deviation of ~ = 0.13 (broken
lines) indicates a small correction necessary for Mw' [equation {13)] as an est.mation of Mw.
durations, To, at different stations recording one earthquake are reasonably consist e n t . Following Lee et al. (1972), Tc was measured from the beginning of the P wave
up to the time at which signal amplitude became twice the noise level. Figure 9
shows plots of log of average Tc versus log M0. Straight-line fit to the data gives
log Mo = (2.25 + 0.17)log Tc + (15.88 ± 0.29).
(15)
MOMENT MAGNITUDE IN THE PETATLAN REGION, MEXICO
1237
The largest event in Figure 9 has smaller coda duration than expected from the
regression. However, it is possible that the relationship between log M0 and log Tc
is not linear. A relation of the form log M0 = ao + al(log To)2 has been reported by
Bakun and Lindh (1977) for Oroville, California. The present data, however, do not
cover a sufficient M0 range to establish this. Using equation (15) in conjunction
with the definition of Mw [equation (9)] enables direct estimation of M~ from coda
duration.
23.0
I
I
22.0
S
21.0
0
C:
20.0
01)
0
19.0
18.0
17.0
II
1.0
I
I
1.0
2.0
log ('r c) sec
FIG. 9. Log of coda duration, To in sec versus log of moment, Mo, averaged over all stations that
recorded each earthquake. Each point represents one earthquake. Tcwas measuredfromP-wave arrival
to the point where signal-noiseratio drops below 2. A least-squares fit to the data (solidline) [logMo =
(2.25 _+0.17)log Tc + {15.88_+0.29)] and _+_1S.D. (a = 0.31) (broken lines) are shown.
DISCUSSION
The procedure used here to develop an estimator equation of log Mo and thus Mw
based on peak horizontal velocity and hypocentral distance is a practical technique
to estimate log Mo and Mw from analog data.
For our data set, we first determined the propagation characteristics of peakrecorded amplitude, horizontal velocity, of earthquakes in the region regarding
attenuation coefficient and geometrical spreading. In doing that, we isolated source
strength from path parameters. Then, we developed an empirical equation for
estimation of moment from peak horizontal velocity, taking into account the
corrections necessary for attenuation and geometrical spreading. The estimator
equation of log Mo enables direct estimation of moment magnitude [equation (12t],
1238
M. MAHDYIAR, S. K. SINGH, AND R. P. MEYER
which we called Mw'. The correlation between Mw and Mw' indicated a small
correction necessary for Mw' [equation (13)] as an estimation of Mw, with standard
error of estimate a = 0.13 unit of magnitude.
Although the results obtained here are primarily for earthquakes in the Petatlan
region, they may be applicable to earthquakes occurring in other regions of pacific
subduction zone of Mexico. Earthquakes in the entire area are mainly subductionrelated ones with the average depth of 20 km and presumably have a similar log V
log Mo relationship as the earthquakes in this study for similar range of moment.
Also, the attenuation properties of the whole area are very possibly similar to those
of the Petatlan region.
The results are valid for range of moment from 2.8 x 10 is to 1.4 × 1022 dyne-cm.
However, using these results for estimating Mw of earthquakes with Mo > 1.26 ×
1021 dyne-cm should be done with the understanding that only one data point
beyond this moment was used in the analysis.
The equation for calculating Mw' should not be used for range of moments beyond
this study. The reason is the dependency of the scaling relationship between moment
and peak horizontal velocity upon size of earthquakes (Boore, 1986). For example,
coefficient A1 in equation (7) is about 2.3 times the similar coefficient in Joyner
and Boore's (1981) study for earthquakes with M > 4. It should be remembered
that coefficient A~, i.e., the relationship between log V - log M0, in our study and
in Joyner and Boore's study was calculated in such a way to be mainly sourcedependent. Our estimation of coefficients B1 = 1.04, i.e., log 1140 o: 1.04 log V, and
A~ = 0.82, i.e., log V ~ 0.82 log i o , is in relative agreement with Boore's (1986)
study that, for small earthquakes, log V ~ 1.0 log Mo. For large earthquakes, he
predicts log V ~ 0.37 log 11//0.
-
ACKNOWLEDGMENTS
We thank Dee Kruger for typing parts of the manuscript and Carlos Valdes for help on data gathering
coda durations. This study was supported by grants from the National Science Foundation (EAR8390506 and EAR80-00048).
REFERENCES
Aki, K. (1980). Attenuation of shear-waves in the lithosphere, Phys. Earth Planet. Interiors 21, 50-60.
Bakun, W. H. and A. H. Lindh (1977). Local magnitudes, seismic moments, and coda durations for
earthquakes near Oroville, California, Bull. Seism. Soc. Am. 67, 615-629.
Bakun, W. H. and W. B. Joyner (1984). The Mz scale in central California, 79th Annual Meeting of the
Seismological Society of America, Anchorage, Alaska (abstract), Earthquake Notes 55, 13.
Bakun, W. H., S. T. Houck, and W. H. K. Lee (1978). A direct comparison of "synthetic" and actual
Wood-Anderson seismograms, Bull. Seism. Soc. Am. 68, 1199-1202.
Boore, D. M. (1986). The effect of finite bandwidth on seismic scaling relationships, Proc. Fifth Ewing
Symposium on Earthquake Source Mechanics, American Geophysical Union (in press).
Hanks, T. and H. Kanamori (1979). A moment magnitude scale, J. Geophys. Res. 84, 2348-2350.
Hanks, T. and D. M. Boore (1983). Moment-magnitude relations in theory and practice (submitted for
publication).
Joyner, W. B and D. M. Boore (1981). Peak horizontal acceleration and velocity from strong motion
records including records from the 1979 Imperial Valley, California, Bull. Seism. Soc. Am. 71, 20112038.
Lee, W. H. K., R. E. Bennett, and K. L. Meagher (1972). A method of:estimating magnitude of local
earthquakes from signal duration, U.S. Geol. Surv. Open-File Rept. 28.
Mahdyiar, M. (1984). Attenuation properties of the Petatlan region, Mexico, and a local magnitude scale
for microearthquakes in this area, Ph.D. Thesis, University of Wisconsin-Madison, Madison,
Wisconsin.
Meyer, R. P., W. D. Pennington, L. A. Powell, W. L. Unger, M. Guzm~n, J. Havskov, S. K. Singh, C.
MOMENT MAGNITUDE IN THE PETATLAN REGION, MEXICO
1239
Vald~s, and J. Yamamoto (1980). A first report on the Petatlhn, Guerrero, M~xico, earthquake of
14 March 1979, Geophys. Res. Letters 7, 97-100.
Richter, C. F. (1958). Elementary Seismology, W. H. Freeman and Co., San Francisco, California, 768
pp.
Singh, S. K. and J. Havskov (1980). On moment-magnitude scale, Bull. Seism. Soc. Am. 70, 379-383.
Valdes, C., R. P. Meyer, R. Zuniga, J. Havskov, and S. K. Singh (1982). Analysis of Petatlan aftershocks:
numbers, energy release, and asperities, J. Geophys. Res. 87, 8519-8527.
DEPARTMENTOF GEOLOGYAND GEOPHYSICS
UNIVERSITYOF WISCONSIN-MADISON
MADISON,WISCONSIN53706 (M.M., R.P.M.)
Manuscript received 31 July 1985
INSTITUTODE GEOFISICA
U.N.A.M., C.U.
MEXICO 04510 (S.K.S.)