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Comparison of dynamic source parameters for earthquakes in different tectonic regions of the northern Cascadia subduction zone
205
Tectonophysics, 217 (1993) 205-215
Elsevier Science Publishers B.V., Amsterdam
Comparison of dynamic source parameters for earthquakes in different tectonic regions of the northern Cascadia subduction zone Rutger Wahlstriim Jeamological Department, Uppsala University, Box 2101, S-750 02 Uppsala, Sweden
(Received December l&1991, revised version accepted February 29, 1992)
ABSTRACT WahlstrGm, R., 1993. Comparison of dynamic source parameters for earthquakes in different tectonic regions of the northern Cascadia subduction zone. In: S.J. Duda and T.B. Yanovskaya (Editors), Estimation of Earthquake Size. Tectonophysics, 217 (spec. sect.): 205-215. Based on characteristics of displacement amplitude spectra of near-distant S-waves from 52 earthquakes in the magnitude CM,) range - 0.6 to 5.4, dynamic source parameters were computed and compared for three tectonic regions in the northern Cascadia subduction zone: a downgoing slab of the Juan de Fuca Plate with earthquake depths of about 30 km; the same slab further east with deeper events, about 60 km; and an overriding part of the North American Plate. No distance dependence of observed corner frequencies was obtained, nor any significant regional difference in source parameters, although there is an indication of smaller stress drop in the North American Plate for larger events. Factors which may distort a regional comparison were examined, but neither source radiation directivity nor propagation path and station site characteristics have significant influence. The structural model has influence, however, and two different density/velocity models were used for the deeper Juan de Fuca slab events. Seismic moments (M,) range from E + 17 to 0.4E + 24 dyn cm, source radii from 0.07 to 1.6 km, stress drops from less than 0.1 to 40 bar and average dislocations from less than 0.1 to 7 cm. In the range E -t 18 to E + 21 dyn cm, in which the vast majority of the events are confined, both the stress drop and displacement increase rapidly with event size (seismic moment or magnitude) as the seismic moment increases rapidly with fault dimension. The relation between seismic moment (dyn cm) and M, magnitude computed from data from all three regions is similar to relations presented for California and reads log(&) = 17.65 + l.O2M,. There are, however, differences between events in the North American Plate and the Juan de Fuca Plate, with larger M, for the former at equivalent seismic moment.
Introduction The purpose of this study is to co&pare source parameters and spectral scaling relations between earthquakes in different tectonic environments within the northern Cascadia subduction zone. Various methods exist to calculate earthquake source characteristics using ground amplitude spectra of seismic waves. The seismic moment is computed from the spectral level at low frequencies and the source dimension is usually computed from the corner frequency.
In this study, S-wave ampiitude spectra are derived from local station records of earthquakes ranging over six magnitude units. Although the study is not focusing on source parameters for individual events, factors that may influence the basic spectral characteristics and their interpretation in the applied source models, such as path and station site conditions, symmetrical radiation pattern approximation, and choice of structural model, are investigated and discussed in connection with possible discrepancies between the three regions. Data and method
Correspondence
to: Rutger Wahlstriim, Seismological Depart-
ment, Uppsaia University, Box 2101, S-750 02, Uppsala, Sweden. ~40-195~/93/$06.~
The study is based on S-waves from 56 earthquakes near Vancouver Island recorded in the
0 1993 - Elsevier Science Publishers B.V. All rights reserved
206
R. WAHLSl’R6M
TABLE 1 Investigated earthquakes Region
Sub-
and
region
event
Time
Date Y
m
d
h
Location m
“N
“W
Focal
Magnitude
depth
Ml_
N
(km)
Al
1975
11
30
10
48
49.23
123.62
10
4.9
3
A2
1975
12
11
15
02
49.26
123.69
16
3.8
3
A3
1976
03
10
03
54
49.26
123.69
18
3.6
3
A4
1977
06
23
23
26
49.05
123.33
21
3.5
0
A5
1982
01
30
02
37
48.81
122.70
24
3.2
2
6
2.4
4 1
A6
AI
1982
07
07
03
59
49.87
123.48
A7
AI
1984
03
06
09
47
49.94
124.20
1
2.2
A8
AI1
1985
04
28
18
35
48.46
123.35
8
0.6
1
1985
06
23
19
23
48.92
122.78
15
2.5
3
A9 A10
AI1
1985
07
30
17
01
48.40
123.32
15
3.0
4
All
AI1
1985
08
06
23
48
48.58
123.06
21
0.1
0
Al2
AI
1986
02
27
11
46
49.96
123.74
1
2.0
3
Al3
AI1
1986
04
16
18
10
48.78
123.41
15
0.6
1
1986
04
20
16
40
48.84
122.50
24
2.8
6 2
Al4 Al5
AI
1986
11
11
23
26
49.86
123.83
0
0.4
Al6
AI
1986
11
23
18
57
49.94
123.66
0
1.2
1
1986
12
08
18
14
49.23
124.01
11
1.0
4
Al7 Al8
AI
1986
12
09
04
28
49.65
123.71
0
1.4
5
Al9
AI
1986
12
15
02
17
49.87
123.85
4
1.6
3
A20
AI1
1986
12
27
10
53
48.70
123.32
22
0.8
3
A21
AI1
1986
12
27
13
24
48.62
123.00
11
1.8
6
A22
AI
1988
09
25
08
15
49.71
123.59
10
0.2
1
1980
03
07
21
36
49.28
126.42
30
4.7
1
1983
02
05
06
38
48.73
125.36
37
3.6
2
Bl B2
BI
B3
1983
10
30
16
34
48.39
124.71
32
1.8
1
B4
1984
08
28
22
15
49.03
125.53
31
2.8
4
B5
198.5
04
13
10
53
49.11
125.52
33
2.4
4
B6
1986
02
23
09
09
49.15
125.87
29
2.2
3
1986
03
02
04
58
48.74
124.93
36
3.0
2
B8
1986
03
26
02
41
48.98
125.94
26
2.0
2
B9
1986
06
08
05
17
49.00
125.33
32
3.2
6
BlO
1986
06
21
07
13
48.26
124.64
28
0.4
0
B7
BI
Bll
BI
1986
07
27
19
44
48.59
124.96
21
0.8
1
B12
BI
1986
08
15
04
01
48.59
125.23
34
1.0
3
B13
BI
1986
09
06
14
46
48.74
125.26
33
3.5
4
B14
1986
10
11
10
41
49.31
125.56
32
1.4
4
B15
1986
12
06
07
45
49.32
126.14
37
0.5
2
B16
1986
12
12
15
39
49.39
126.24
33
1.6
4
B17
1986
12
17
13
29
49.45
126.48
31
2.5
3
Cl
1976
05
16
08
35
48.92
123.10
62
5.4
1
c2
1978
08
19
01
51
48.64
123.57
51
3.5
1 1
c3
CI
1979
06
05
16
50
49.40
123.91
71
3.0
c4
CI
1979
11
29
16
19
49.39
123.91
69
3.4
1
C5
CI
1981
02
28
23
32
49.35
123.88
65
2.7
6
C6
CI
1983
10
15
20
46
49.33
123.95
65
2.5
4
c7
1984
02
24
15
00
48.36
123.31
44
1.2
3
C8
1984
09
02
03
50
48.75
123.12
58
2.1
7
1985
06
16
07
03
49.34
123.92
66
1.6
5
c9
CI
207
DYNAMICSOURCEPARAMETERSINCASCADIASUBDU~IONZONE
TABLE 1 (continued) Region and event
Subregion
Cl0
CI
Cl1
Cl2 Cl3 Cl4 Cl5 Cl6 Cl7
CI CI
Date
Time
Location
Y
m
d
h
m
“N
“W
Focal depth (km)
1985 1985 1985 1985 1986 1986 1986 1987
07 08 12 12 03 04 11 07
24 21 04 04 01 15 19 06
02 09 03 15 05 08 21 03
37 58 02 32 50 48 52 29
49.36 48.92 48.78 48.80 48.44 49.29 49.33 48.54
123.98 123.17 122.81 123.25 123.14 123.96 123.94 123.38
69 58 63 53 54 64 64 44
Magnitude M,
N
2.3 0.8 1.8 1.4 0.6 1.0 2.0 0.4
8 4 5 3 2 2 7 0
Solutions are revised from the Canadian Earthquake Epicentre File provided by G. Rogers, Pacific Geoscience Centre. Regions and subregions are shown in Figure 2. N is number of useful spectra (see text).
time period 1975-1988 by short-period, verticalcomponent seismometers of the digital (60 samples/s) telemetered network on and adjacent to Vancouver Island. The events represent the range of existing magnitudes in each of three regions: the overriding North American Plate (A); the concentration of seismicity in the Juan de Fuca Plate where it begins to bend to subduct at a depth of approximately 30 km (B); and the concentration of seismicity where the dip of the subducting Juan de Fuca Plate becomes steeper at a depth of about 60 km CC>.Figure 1 shows the area, and the locations of the stations used. Earthquake parameters are listed in Table 1 and
Fig. 1. Locations of 20 stations of the digital telemetered network on and adjacent to Vancouver Island from which short-period, vertical-component seismometer records have been used to derive amplitude spectra.
locations shown in Figure 2. To diminish the possibility of interference of other, e.g. refracted, phases the data are confined to readings at hypocentral distances smaller than 125 km. An exception was made for the largest event (No. Cl in Table 1) for which the only unsaturated signal, recorded by a station at a distance of 146 km, was included. Records with high background noise were omitted. Trace amplitude spectra were obtained from FFT processing using cos-windowed time samples of S-waves of typically several seconds duration (see Fig. 3). Correcting for the instrumental response, log-log plots of 165 ground displacement amplitude spectra from 52 of the investigated earthquakes show a fairly constant level, L,,, at low frequencies, and an approximately linear decrease with increasing frequency starting at the corner frequency, fR. L, and fR were obtained from these spectra by visual inspection. Many additional spectra do not have the simple features and were not used. Thus, four earthquakes have no useful spectrum (see Table 1). The combined effect of instrumentation, data time resolution and data processing is to distort the spectra towards very low and very high frequencies, but this effect does not influence the measurements of L, and fR. For events with magnitude CM,_) 1 or smalIer, spectra were also computed from adjacent segments of background noise. It was generally found that the noise does not distort the measurements
R. WAHLSTRdM
a w-1
ML<
127O
l
126”
Region A
Fig. 2. Locations
l Region B of selected
and C in the downgoing as of Table
1. Magnitudes
the cross section size of symbol,
123”
124”
125’
/
0 Region C
earthquakes.
distribution.
are indicated minimum,
distribution
projected
increase
along the profile
The seismic moment, M,, for an earthquake is computed as the arithmetic average from individual stations from (Keilis-Borok, 1960; Boatwright, 1980; Fletcher, 1980): u~(s)]~‘~ (1)
where p is density and U, is S-wave velocity, with indices s and r denoting source and receiver, respectively. R ishypocentral distance and 0.62 is the average S-wave radiation pattern factor (Fletcher, 1980). The influence of physical attenuation on L, is assumed minor at the distances and frequencies dealt with in this study (see, e.g.,
,‘I
b
“1
+
i
a
-t-t
201
;20
,A
(km)
North American
Plate, regions
from the locations
from ML = - 0.6 to 5.4. The profile line given in (a). Magnitudes
size for ML up to 1 and continuous increase studied regions are clearly separated.
Seismic moment
X [u,(r)] 1’2RL,/0.62
A is in the overlying
AI, All, BI and CI are determined
by size of symbol, with continuous
of L, and fR in the S-signal spectrum. This is exemplified in Figure 3, displaying seismogram traces and spectra from various stations, of Swaves and noise, for a small earthquake in the deeper section of the Juan de Fuca Plate (No. Cl1 in Table 1). The complete set of S-wave spectra for all earthquakes and stations are plotted in Wahlstriim (1989). Seismic moment, source radius, dislocation and stress drop were computed from the spectral parameters, L, and fR, assuming the circular-fault model of Brune (1970).
M, = 47r[p(~)]i’~[p(r)]i’~[
Region
,
!,I
Distance
(a) Epicentral
used in (b). (b) Hypocentral
/
I:,
1 I’
slab of the Juan de Fuca Plate. Subregions
with constant,
1
122” w
for ML > 1. Events
B
of events line marks
are indicated
by
in each of the three
Kim et al., 1989). Effects of the free surface and of energy partition on horizontal and vertical components are not quantified but are not considered relevant for the comparison between different regions of seismic moment and other parameters dependent on the moment, i.e., dislocation and stress drop (see below). Crustal physical parameters are taken from Spence (1984): p(r) = p(s) = 2.9 g/cm3, u,(r) = 3.46 km/s and U,(S)= 3.87 km/s. Since the deeper events involve a region where phase changes take place in the oceanic crust (Grow and Bowin, 1975; Rogers, 1983) also a second, deep-crustal, model was adopted for region C: p(s) = 3.4 g/cm3 and U,(S)= 4.47 km/s @pence, 1984). Seismic moments obtained from the deepcrustal model are approximately 55% larger than from the first model, where they range from E + 17 to 0.4E + 24 dyn cm (see Fig. 5). The effect of applying a constant radiation factor would be problematic if there is a general difference in the earthquake focal mechanism between different regions and such a difference is not averaged by the distribution of recording stations. For fourteen events in the subregions AI, AII, BI and CI (Table 1; Fig. 2a), obtained P-polarity focal mechanisms show no clear pattern, nor do composite solutions performed for each of the subregions. Although the directivity
DYNAMlC
SOUKCE
PARAMETERS
IN CASCADIA
SUBDUCTION
209
ZONE
PGC
36 km dist.
1 6s
7
t
lost
(a) Fig. 3. Examples noise ground
of, from left to right, the S-wave trace, S-wave ground
displacement
amplitude
spectrum,
Juan de Fuca subducted
slab. Each row corresponds
S-wave trace, the station
code also above each spectrum;
traces
are close to the detection
of relative
amplitudes
level. The spectral
of the signal vs. noise spectra.
and have the low-frequency
level and corner
displacement
for a small event on August to one station. density
The station
the time sample
amplitude
spectrum,
21, 1985 (No. Cl1 in Table
length
E-9 m s is indicated
code and epicentral is given beneath
adjacent
distance
to facilitate
have the simple shape described
frequency indicated. Generally, there is no influence of the signal spectral parameters.
part of the
are given above each
each signal and noise trace. Noise
by a circle at each spectrum
Four of the shown S-wave spectra
noise trace and
1) in the deeper
comparison in the text,
of the noise on the determination
210
R. WAHLSTRGM
1 10s '
VDB
d’[\_I
t 10s '
t 10s (b)
‘o-’
too&
m’ Fig. 3 continued.
1
DYNAMIC
SOURCE
PARAMETERS
IN CASCADIA
SUBDUCTION
may have introduced errors of different magnitude for different individual events, the multiple events and multiple stations seem to effectively average the radiation pattern effect to justify the approximation made in eq. (1). Comer
211
ZONE
Mo=(0.400E+2
fR (Hz)’ ZO-
Region A Region B RegionC
frequency
Hasegawa (1983) and Kim et al. (1989) found that not only do larger earthquakes have lower corner frequencies than smaller earthquakes (as an implication of lower frequency content in general), but also the decay of observed corner frequencies with increasing distance is smaller for larger events over large distances. The latter may be attributed to frequency-dependent attenuation, but the different distributions of data, with relatively more readings at larger distances for larger earthquakes, may also play a role. To investigate the distance variation of observed corner frequencies in the present case, a simple regression of fR on R was made for each region and each of three event size classes:
-I
.
x
j’” 0
25
=c, +c,R
Source dimension,
dislocation
[(7/16)(1/~)11’2u,(s)/fo
x
50
75
100
125
dyne-cm
f Fl (Hz) ’ zo-
lo-
.
i il xX0( x
am
mx urn-ox X. .“,: I, . x X.JC
L x x
.
.
.
1”
.
q ..rX.
.XLC7.m. ec. Ir, ! x
!x
0.5 1
I 25
0
I 50
*
, 100
75
125
R(km) Mo=(0.400E+
18;O. 125E+20) dyne-cm
10
x
.
x
x
x
. ?CaZ
5
.
x
l;
x
.
Yn-‘w I
.
.
x
.
and stress drop
The f. value obtained for each event is introduced into the Brune (1970) circular-fault model: r=
l
M~=(O.l25E+20:0.4OOE+21)
(2)
The separation into size classes is based on seismic moment obtained from eq. (1). The fR vs.R data are plotted in Figure 4. The investigation, reported in detail in Wahlstrom (1989), demonstrates that attenuation has insignificant effect on the observed corner frequencies for the short distance interval considered. The zero-distance-or source-corner frequency, fo, for an earthquake is therefore calculated as the arithmetic average of the observed values, fR, from all available spectra for that event. It should be noted that the data analysed by Hasegawa (1983) and Kim et al. (1989) spanned much wider distance ranges, more than 1000 km, than that of this study. Figure 5 illustrates the range of corner frequencies.
x
R(km)
5-
l”g(f,)
l;O. 125E+23)
dyne-cm
(3)
0
25
50
75
100
125
R(km)
Fig. 4. Observed distance
corner
R for various
frequency regions classes.
fR plotted (see
vs. hypocentral
Fig. 2) and
event
size
R. WAHLSTROM
212
CORy;R
FR5EQUENC;
Effects of station site and propagation
(Hz) 1
20 I
10-r
erties
/
I
0.05
Fig.
5. Seismic
source gions
radius (see
model
0.2 SOURCE
moment
plotted
Fig. 2). Cf. Table
various
for
increases
with seismic between
for larger
American
km\
vs. corner in the three
2. The
all three moment,
same
regions.
levels of stress drop.
moments
2
0.5 RADIUS
for earthquakes
was used
indicate
0.1
frequency
and
investigated
re-
density/velocity
The
Clearly,
parallel
is largest
at
dyn cm. The stress drop
Plate events tends to be smaller
events of corresponding
lines
the stress drop
and the increase
E+ 18 and E+21
path prop-
than for
size in the slab.
to give an estimate of the effective radius, I-, of the source. Parameters computed from eq. (1) and (3) are used to compute the average dislocation, d (Aki, 1966):
(4) and the static stress drop during the rupture, Au (Brune, 1970):
(5) Source radii from 0.07 to 1.6 km, dislocations up to 7 cm and stress drops up to 40 bar were calculated for the investigated earthquakes (cf. Fig. 5). The effect of the deep-crustal model is to increase r by about 16% and decrease d by about 26%, whereas there is virtually no effect on to the stress drop, since it is proportional [p(s)/u,h>11’2,which has nearly the same value for both structural models.
Difficulties with the spectral method have been pointed out in several studies, e.g., Somerville et al. (19871, who instead use waveform modeling. Boore (1986) discusses various factors influencing the spectrum and limiting the use of corner frequency as an indicator of source parameters. The main concern is to account for the propagation path and station site effects. Frankel and Wennerberg (1989) found in a study based on near-distant (R < 50 km) microearthquake recordings from the Anza network in California that amplitude spectra mainly reflect station site conditions and that the source corner frequency is significantly higher than the observed corner frequencies, an effect ascribed to low Q at shallow depth. Whereas, in Frankel and Wennerberg’s study, source parameters for the smallest earthquakes are beyond determination by spectral means, the parameters for larger earthquakes, magnitude above 3, can be retrieved by removing the transfer function through spectral division with a small earthquake. However, to be successful this requires that the two shocks have very similar locations and focal mechanisms. The strong influence of non-source parameters on the amplitude spectra of small earthquakes in California has also been pointed out in studies by Archuleta (1986) and Fletcher et al. (1986) among others. Mueller and Cranswick (1985) found a strong site influence on the spectra of very local station records (less than 12 km distance) of Miramichi aftershocks. They were able to isolate and remove much of the site effect by applying a resonance model. Like Mueller and Cranswick (1985), Haar et al. (1984) demonstrated that spectra from very local stations, in their case less than 5 km, give significantly higher observed corner frequencies than from more remote stations. To investigate the non-source effects on the spectra in the present case, where data are taken from a wider distance range, events from four subregions were selected (Table 1; Fig. 2a). A comparison of the spectra with respect to any given station or subregion reveals no clear pattern (all spectra are displayed in Wahlstriim,
DYNAMIC
TABLE Values
SOlJRCE
PARAMETERS
IN CASCADIA
SUBDUCTION
213
ZONE
2 of a, and a,, with standard
errors,
in log(M,J
= a, +
M,, in dyn cm, r in km
a2 log(r), Region
Number
a2
[‘I
of data A
22.07 (0.36)
4.67 (0.43)
20
B
22.98 (0.96)
6.59 (1.56)
16
C
22.5 1 (0.50)
5.45 (0.72)
16
C*
22.35 (0.44)
5.43 (0.72)
16
A+B+C
22.37 (0.30)
5.17 (0.41)
52
Regions
are shown in Figure 2. * denotes
that the deep-crustal
model was used.
1989). This is different from, e.g., Frankel and Wennerberg (1989), who found that the spectral similarity with respect to stations outweighs that with respect to earthquakes, i.e., a strong site dependency. The main task of the present study being a comparison of source parameters in different regions, the eventual minor contamination of non-source effects on the spectra is not a major concern. Scaling
relations
Relationships between seismic moment and source radius (Table 2; Fig. 51, and seismic moment and magnitude (Table 3; Fig. 61, were computed separately for each region and also for all regions taken together. The seismic moment for North American Plate earthquakes tends to increase more slowly both with source radius and M,
than for events
regions.
TABLE Values b, M,,
in the two Juan
Application
of the
de Fuca slab
deep-crustal
model
3 of h, and b,, with standard
errors,
in log(M,)
= b, +
M,, in dyn cm
Region
Number
b,
of data A
17.64 (0.09)
0.94 (0.03)
20
B
17.69 (0.20)
1.08 (0.06)
16
C
17.65 (0.10)
1.06 (0.03)
16
C*
17.84 (0.10)
1.06 (0.03)
16
A+B+C
17.65 (0.09)
1.02 (0.03)
52
Regions
are shown in Figure
model was used.
2. * denotes
that the deep-crustal
Region A n Region B A Region C 0 10'6 i
,0171 21 I
I
I
0
-1
1
MAdTUDE
Fig. 6. Relationships M,,
for separate
between regions
Earthquakes than
in the North those
in the
I
I
4
5
seismic moment
1 6
and magnitude,
(see Fig. 2) and all regions
Cf. Table 3. The same crustal M,
I
iL
together.
model was used for all regions.
American
two Juan
Plate mostly de Fuca
slab
have larger regions
for
similar seismic moment.
implies merely a change of the constant term in the moment-magnitude relation (an increase of 0.19 in b, in Table 3, corresponding to the 55% increase in M,, mentioned above), whereas for the moment-radius relation both the slope and intercept are different, since the source radius itself is dependent on the model [factor L:,(S) in eq. (3)l. In Figure 5 it is seen that for the vast majority of earthquakes, with seismic moment between approximately E + 18 and E + 21 dyn cm, there is a rapid increase in seismic moment with decreasing corner frequency, i.e., with increasing source dimension. The resulting rapid increase in stress drop with event size has been observed for small and intermediate size earthquakes in many areas, see, e.g., Chouet et al. (1978); Rautian et al. (1978); Fletcher (1980); Frankel(1981); Archuleta et al. (1982); Hasegawa (1983); Haar Mueller and Cranswick (1985); Kim So has the less rapid or non-existing stress drop for larger events (Fig. increase in stress drop with event for the few smallest earthquakes
et al. (1984); et al. (1989). increase in 5). The slow size observed (M,, < E + 18
214
dyn cm corresponding roughly to M, < 0.5) may be just an artifact of insufficient data or due to non-source effects (attenuation, site, etc.) predominantly determining the spectral characteristics, in particular fR. Coefficients a, and a2 in Table 2 for the North American Plate region are similar to those proposed by Nuttli (1983) as the linear approximation for the whole seismic moment range from E + 19 to E + 26 dyn cm for eastern North America. The fairly large error estimates for the slope (coefficient a2 in Table 2) for the Juan de Fuca slab regions are worth noting (see below). There is a linear dependence between the logarithm of the seismic moment and the M, magnitude, with a tendency towards larger magnitudes, for an equivalent seismic moment, for events in the selected region of the North American Plate than in the Juan de Fuca slab (Table 2; Fig. 6). This is particularly notable for the larger earthquakes and may be related to the shallower focal depth of the events in region A, since no depth correction is used in the M, computations. Hanks and Boore (1984) found that a positive curvature function accurately describes the log(M,,)-M, relation for all southern and central California earthquakes in the M, range from 0 to 7. In several studies of other areas, the momentmagnitude relation is described by two lines, the steeper for events with seismic moment larger than about E + 21 to E + 22 dyn cm [see, e.g., Hasegawa (1983) for M,, and Nuttli (1983) for m,; both studies relate to mid-plate earthquakes]. Although the present relations show a good linear fit over the entire range of events and are similar to those found in various studies of Californian earthquakes (see table 1 in Hanks and Boore, 19841, extrapolation should not be made to larger or smaller events than those used to derive the relations. Conclusions
There is no obvious distance dependence of the observed corner frequencies. The source corner frequency for an earthquake is therefore calculated as the arithmetic mean of observed corner frequencies from all simple-feature spectra.
R. WAHLSTRiJM
For the different tectonic regions, relationships between various source parameters are given in Table 2 and Figure 5, and between seismic moment and magnitude in Table 3 and Figure 6. There is a rapid increase in seismic moment with source dimension, at least for earthquakes up to about M, = 5, implying a rapid increase in stress drop with seismic moment. The influences of radiation pattern directivity, and station site and propagation path properties, on the source parameters are similar and minor, except, probably, for the smallest earthquakes with high observed corner frequency. The influence of crustal model, i.e., density and shear wave velocity, is large, particularly on the seismic moment. No major differences are found in the spectral scaling relations between the three regions, but there are indications that, for equivalent seismic moments, the stress drop is smaller in the North American Plate region than in the underlying slab of the Juan de Fuca Plate for the largest earthquakes. There is a rapid increase in stress drop with seismic moment for the small earthquakes, up to about E + 21 dyn cm, except for the very smallest events. This corresponds to an only slightly increasing or constant source radius. An alternative interpretation is that the length of the rupture is smaller than the fault width, so that the former is not reflected by the corner frequency (see Aki, 1987). The smaller increase in stress drop for the few smallest events is probably only apparent and may be due to insufficient data, uncertain distance dependence of the high observed corner frequencies or sensitivity to site conditions, one of several factors which may disguise the source properties from being obtained from the spectra. The largest earthquakes, with seismic moment above E + 21 dyn cm, show small, if any, increase in stress drop with increasing moment. There is a good log-lin fit of seismic moment vs. M, magnitude over the entire investigated magnitude range for events in the North American Plate on one hand and those in the two Juan de Fuca Plate regions on the other hand. For earthquakes with similar seismic moment, the North American Plate events have the higher magnitudes.
DYNAMIC
SOURCE
PARAMETERS
IN CASCADIA
SUBDUmION
215
ZONE
scaling
Acknowledgements The research was carried out at the Pacific Geoscience Centre (PGC), Geological Survey of Canada, Sidney, B.C., Canada with financial support from the Swedish Natural Science Research Council, Contracts G-GU 4012-300 and -302, Sweden-America Foundation and Royal Swedish Academy of Sciences. The spectral conversion program was written by W.-Y. Kim, Uppsala University and modified by R. Baldwin, PGC. I greatly appreciate comments on the text made by G. Rogers, PGC, and D. Boore and L. Wennerberg, United States Geological Survey, Menlo Park, CA.
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the active subduc-
Thesis,
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in the northern Geoscience
Cen-
Tectonophysics, 217 (1993) 205-215
Elsevier Science Publishers B.V., Amsterdam
Comparison of dynamic source parameters for earthquakes in different tectonic regions of the northern Cascadia subduction zone Rutger Wahlstriim Jeamological Department, Uppsala University, Box 2101, S-750 02 Uppsala, Sweden
(Received December l&1991, revised version accepted February 29, 1992)
ABSTRACT WahlstrGm, R., 1993. Comparison of dynamic source parameters for earthquakes in different tectonic regions of the northern Cascadia subduction zone. In: S.J. Duda and T.B. Yanovskaya (Editors), Estimation of Earthquake Size. Tectonophysics, 217 (spec. sect.): 205-215. Based on characteristics of displacement amplitude spectra of near-distant S-waves from 52 earthquakes in the magnitude CM,) range - 0.6 to 5.4, dynamic source parameters were computed and compared for three tectonic regions in the northern Cascadia subduction zone: a downgoing slab of the Juan de Fuca Plate with earthquake depths of about 30 km; the same slab further east with deeper events, about 60 km; and an overriding part of the North American Plate. No distance dependence of observed corner frequencies was obtained, nor any significant regional difference in source parameters, although there is an indication of smaller stress drop in the North American Plate for larger events. Factors which may distort a regional comparison were examined, but neither source radiation directivity nor propagation path and station site characteristics have significant influence. The structural model has influence, however, and two different density/velocity models were used for the deeper Juan de Fuca slab events. Seismic moments (M,) range from E + 17 to 0.4E + 24 dyn cm, source radii from 0.07 to 1.6 km, stress drops from less than 0.1 to 40 bar and average dislocations from less than 0.1 to 7 cm. In the range E -t 18 to E + 21 dyn cm, in which the vast majority of the events are confined, both the stress drop and displacement increase rapidly with event size (seismic moment or magnitude) as the seismic moment increases rapidly with fault dimension. The relation between seismic moment (dyn cm) and M, magnitude computed from data from all three regions is similar to relations presented for California and reads log(&) = 17.65 + l.O2M,. There are, however, differences between events in the North American Plate and the Juan de Fuca Plate, with larger M, for the former at equivalent seismic moment.
Introduction The purpose of this study is to co&pare source parameters and spectral scaling relations between earthquakes in different tectonic environments within the northern Cascadia subduction zone. Various methods exist to calculate earthquake source characteristics using ground amplitude spectra of seismic waves. The seismic moment is computed from the spectral level at low frequencies and the source dimension is usually computed from the corner frequency.
In this study, S-wave ampiitude spectra are derived from local station records of earthquakes ranging over six magnitude units. Although the study is not focusing on source parameters for individual events, factors that may influence the basic spectral characteristics and their interpretation in the applied source models, such as path and station site conditions, symmetrical radiation pattern approximation, and choice of structural model, are investigated and discussed in connection with possible discrepancies between the three regions. Data and method
Correspondence
to: Rutger Wahlstriim, Seismological Depart-
ment, Uppsaia University, Box 2101, S-750 02, Uppsala, Sweden. ~40-195~/93/$06.~
The study is based on S-waves from 56 earthquakes near Vancouver Island recorded in the
0 1993 - Elsevier Science Publishers B.V. All rights reserved
206
R. WAHLSl’R6M
TABLE 1 Investigated earthquakes Region
Sub-
and
region
event
Time
Date Y
m
d
h
Location m
“N
“W
Focal
Magnitude
depth
Ml_
N
(km)
Al
1975
11
30
10
48
49.23
123.62
10
4.9
3
A2
1975
12
11
15
02
49.26
123.69
16
3.8
3
A3
1976
03
10
03
54
49.26
123.69
18
3.6
3
A4
1977
06
23
23
26
49.05
123.33
21
3.5
0
A5
1982
01
30
02
37
48.81
122.70
24
3.2
2
6
2.4
4 1
A6
AI
1982
07
07
03
59
49.87
123.48
A7
AI
1984
03
06
09
47
49.94
124.20
1
2.2
A8
AI1
1985
04
28
18
35
48.46
123.35
8
0.6
1
1985
06
23
19
23
48.92
122.78
15
2.5
3
A9 A10
AI1
1985
07
30
17
01
48.40
123.32
15
3.0
4
All
AI1
1985
08
06
23
48
48.58
123.06
21
0.1
0
Al2
AI
1986
02
27
11
46
49.96
123.74
1
2.0
3
Al3
AI1
1986
04
16
18
10
48.78
123.41
15
0.6
1
1986
04
20
16
40
48.84
122.50
24
2.8
6 2
Al4 Al5
AI
1986
11
11
23
26
49.86
123.83
0
0.4
Al6
AI
1986
11
23
18
57
49.94
123.66
0
1.2
1
1986
12
08
18
14
49.23
124.01
11
1.0
4
Al7 Al8
AI
1986
12
09
04
28
49.65
123.71
0
1.4
5
Al9
AI
1986
12
15
02
17
49.87
123.85
4
1.6
3
A20
AI1
1986
12
27
10
53
48.70
123.32
22
0.8
3
A21
AI1
1986
12
27
13
24
48.62
123.00
11
1.8
6
A22
AI
1988
09
25
08
15
49.71
123.59
10
0.2
1
1980
03
07
21
36
49.28
126.42
30
4.7
1
1983
02
05
06
38
48.73
125.36
37
3.6
2
Bl B2
BI
B3
1983
10
30
16
34
48.39
124.71
32
1.8
1
B4
1984
08
28
22
15
49.03
125.53
31
2.8
4
B5
198.5
04
13
10
53
49.11
125.52
33
2.4
4
B6
1986
02
23
09
09
49.15
125.87
29
2.2
3
1986
03
02
04
58
48.74
124.93
36
3.0
2
B8
1986
03
26
02
41
48.98
125.94
26
2.0
2
B9
1986
06
08
05
17
49.00
125.33
32
3.2
6
BlO
1986
06
21
07
13
48.26
124.64
28
0.4
0
B7
BI
Bll
BI
1986
07
27
19
44
48.59
124.96
21
0.8
1
B12
BI
1986
08
15
04
01
48.59
125.23
34
1.0
3
B13
BI
1986
09
06
14
46
48.74
125.26
33
3.5
4
B14
1986
10
11
10
41
49.31
125.56
32
1.4
4
B15
1986
12
06
07
45
49.32
126.14
37
0.5
2
B16
1986
12
12
15
39
49.39
126.24
33
1.6
4
B17
1986
12
17
13
29
49.45
126.48
31
2.5
3
Cl
1976
05
16
08
35
48.92
123.10
62
5.4
1
c2
1978
08
19
01
51
48.64
123.57
51
3.5
1 1
c3
CI
1979
06
05
16
50
49.40
123.91
71
3.0
c4
CI
1979
11
29
16
19
49.39
123.91
69
3.4
1
C5
CI
1981
02
28
23
32
49.35
123.88
65
2.7
6
C6
CI
1983
10
15
20
46
49.33
123.95
65
2.5
4
c7
1984
02
24
15
00
48.36
123.31
44
1.2
3
C8
1984
09
02
03
50
48.75
123.12
58
2.1
7
1985
06
16
07
03
49.34
123.92
66
1.6
5
c9
CI
207
DYNAMICSOURCEPARAMETERSINCASCADIASUBDU~IONZONE
TABLE 1 (continued) Region and event
Subregion
Cl0
CI
Cl1
Cl2 Cl3 Cl4 Cl5 Cl6 Cl7
CI CI
Date
Time
Location
Y
m
d
h
m
“N
“W
Focal depth (km)
1985 1985 1985 1985 1986 1986 1986 1987
07 08 12 12 03 04 11 07
24 21 04 04 01 15 19 06
02 09 03 15 05 08 21 03
37 58 02 32 50 48 52 29
49.36 48.92 48.78 48.80 48.44 49.29 49.33 48.54
123.98 123.17 122.81 123.25 123.14 123.96 123.94 123.38
69 58 63 53 54 64 64 44
Magnitude M,
N
2.3 0.8 1.8 1.4 0.6 1.0 2.0 0.4
8 4 5 3 2 2 7 0
Solutions are revised from the Canadian Earthquake Epicentre File provided by G. Rogers, Pacific Geoscience Centre. Regions and subregions are shown in Figure 2. N is number of useful spectra (see text).
time period 1975-1988 by short-period, verticalcomponent seismometers of the digital (60 samples/s) telemetered network on and adjacent to Vancouver Island. The events represent the range of existing magnitudes in each of three regions: the overriding North American Plate (A); the concentration of seismicity in the Juan de Fuca Plate where it begins to bend to subduct at a depth of approximately 30 km (B); and the concentration of seismicity where the dip of the subducting Juan de Fuca Plate becomes steeper at a depth of about 60 km CC>.Figure 1 shows the area, and the locations of the stations used. Earthquake parameters are listed in Table 1 and
Fig. 1. Locations of 20 stations of the digital telemetered network on and adjacent to Vancouver Island from which short-period, vertical-component seismometer records have been used to derive amplitude spectra.
locations shown in Figure 2. To diminish the possibility of interference of other, e.g. refracted, phases the data are confined to readings at hypocentral distances smaller than 125 km. An exception was made for the largest event (No. Cl in Table 1) for which the only unsaturated signal, recorded by a station at a distance of 146 km, was included. Records with high background noise were omitted. Trace amplitude spectra were obtained from FFT processing using cos-windowed time samples of S-waves of typically several seconds duration (see Fig. 3). Correcting for the instrumental response, log-log plots of 165 ground displacement amplitude spectra from 52 of the investigated earthquakes show a fairly constant level, L,,, at low frequencies, and an approximately linear decrease with increasing frequency starting at the corner frequency, fR. L, and fR were obtained from these spectra by visual inspection. Many additional spectra do not have the simple features and were not used. Thus, four earthquakes have no useful spectrum (see Table 1). The combined effect of instrumentation, data time resolution and data processing is to distort the spectra towards very low and very high frequencies, but this effect does not influence the measurements of L, and fR. For events with magnitude CM,_) 1 or smalIer, spectra were also computed from adjacent segments of background noise. It was generally found that the noise does not distort the measurements
R. WAHLSTRdM
a w-1
ML<
127O
l
126”
Region A
Fig. 2. Locations
l Region B of selected
and C in the downgoing as of Table
1. Magnitudes
the cross section size of symbol,
123”
124”
125’
/
0 Region C
earthquakes.
distribution.
are indicated minimum,
distribution
projected
increase
along the profile
The seismic moment, M,, for an earthquake is computed as the arithmetic average from individual stations from (Keilis-Borok, 1960; Boatwright, 1980; Fletcher, 1980): u~(s)]~‘~ (1)
where p is density and U, is S-wave velocity, with indices s and r denoting source and receiver, respectively. R ishypocentral distance and 0.62 is the average S-wave radiation pattern factor (Fletcher, 1980). The influence of physical attenuation on L, is assumed minor at the distances and frequencies dealt with in this study (see, e.g.,
,‘I
b
“1
+
i
a
-t-t
201
;20
,A
(km)
North American
Plate, regions
from the locations
from ML = - 0.6 to 5.4. The profile line given in (a). Magnitudes
size for ML up to 1 and continuous increase studied regions are clearly separated.
Seismic moment
X [u,(r)] 1’2RL,/0.62
A is in the overlying
AI, All, BI and CI are determined
by size of symbol, with continuous
of L, and fR in the S-signal spectrum. This is exemplified in Figure 3, displaying seismogram traces and spectra from various stations, of Swaves and noise, for a small earthquake in the deeper section of the Juan de Fuca Plate (No. Cl1 in Table 1). The complete set of S-wave spectra for all earthquakes and stations are plotted in Wahlstriim (1989). Seismic moment, source radius, dislocation and stress drop were computed from the spectral parameters, L, and fR, assuming the circular-fault model of Brune (1970).
M, = 47r[p(~)]i’~[p(r)]i’~[
Region
,
!,I
Distance
(a) Epicentral
used in (b). (b) Hypocentral
/
I:,
1 I’
slab of the Juan de Fuca Plate. Subregions
with constant,
1
122” w
for ML > 1. Events
B
of events line marks
are indicated
by
in each of the three
Kim et al., 1989). Effects of the free surface and of energy partition on horizontal and vertical components are not quantified but are not considered relevant for the comparison between different regions of seismic moment and other parameters dependent on the moment, i.e., dislocation and stress drop (see below). Crustal physical parameters are taken from Spence (1984): p(r) = p(s) = 2.9 g/cm3, u,(r) = 3.46 km/s and U,(S)= 3.87 km/s. Since the deeper events involve a region where phase changes take place in the oceanic crust (Grow and Bowin, 1975; Rogers, 1983) also a second, deep-crustal, model was adopted for region C: p(s) = 3.4 g/cm3 and U,(S)= 4.47 km/s @pence, 1984). Seismic moments obtained from the deepcrustal model are approximately 55% larger than from the first model, where they range from E + 17 to 0.4E + 24 dyn cm (see Fig. 5). The effect of applying a constant radiation factor would be problematic if there is a general difference in the earthquake focal mechanism between different regions and such a difference is not averaged by the distribution of recording stations. For fourteen events in the subregions AI, AII, BI and CI (Table 1; Fig. 2a), obtained P-polarity focal mechanisms show no clear pattern, nor do composite solutions performed for each of the subregions. Although the directivity
DYNAMlC
SOUKCE
PARAMETERS
IN CASCADIA
SUBDUCTION
209
ZONE
PGC
36 km dist.
1 6s
7
t
lost
(a) Fig. 3. Examples noise ground
of, from left to right, the S-wave trace, S-wave ground
displacement
amplitude
spectrum,
Juan de Fuca subducted
slab. Each row corresponds
S-wave trace, the station
code also above each spectrum;
traces
are close to the detection
of relative
amplitudes
level. The spectral
of the signal vs. noise spectra.
and have the low-frequency
level and corner
displacement
for a small event on August to one station. density
The station
the time sample
amplitude
spectrum,
21, 1985 (No. Cl1 in Table
length
E-9 m s is indicated
code and epicentral is given beneath
adjacent
distance
to facilitate
have the simple shape described
frequency indicated. Generally, there is no influence of the signal spectral parameters.
part of the
are given above each
each signal and noise trace. Noise
by a circle at each spectrum
Four of the shown S-wave spectra
noise trace and
1) in the deeper
comparison in the text,
of the noise on the determination
210
R. WAHLSTRGM
1 10s '
VDB
d’[\_I
t 10s '
t 10s (b)
‘o-’
too&
m’ Fig. 3 continued.
1
DYNAMIC
SOURCE
PARAMETERS
IN CASCADIA
SUBDUCTION
may have introduced errors of different magnitude for different individual events, the multiple events and multiple stations seem to effectively average the radiation pattern effect to justify the approximation made in eq. (1). Comer
211
ZONE
Mo=(0.400E+2
fR (Hz)’ ZO-
Region A Region B RegionC
frequency
Hasegawa (1983) and Kim et al. (1989) found that not only do larger earthquakes have lower corner frequencies than smaller earthquakes (as an implication of lower frequency content in general), but also the decay of observed corner frequencies with increasing distance is smaller for larger events over large distances. The latter may be attributed to frequency-dependent attenuation, but the different distributions of data, with relatively more readings at larger distances for larger earthquakes, may also play a role. To investigate the distance variation of observed corner frequencies in the present case, a simple regression of fR on R was made for each region and each of three event size classes:
-I
.
x
j’” 0
25
=c, +c,R
Source dimension,
dislocation
[(7/16)(1/~)11’2u,(s)/fo
x
50
75
100
125
dyne-cm
f Fl (Hz) ’ zo-
lo-
.
i il xX0( x
am
mx urn-ox X. .“,: I, . x X.JC
L x x
.
.
.
1”
.
q ..rX.
.XLC7.m. ec. Ir, ! x
!x
0.5 1
I 25
0
I 50
*
, 100
75
125
R(km) Mo=(0.400E+
18;O. 125E+20) dyne-cm
10
x
.
x
x
x
. ?CaZ
5
.
x
l;
x
.
Yn-‘w I
.
.
x
.
and stress drop
The f. value obtained for each event is introduced into the Brune (1970) circular-fault model: r=
l
M~=(O.l25E+20:0.4OOE+21)
(2)
The separation into size classes is based on seismic moment obtained from eq. (1). The fR vs.R data are plotted in Figure 4. The investigation, reported in detail in Wahlstrom (1989), demonstrates that attenuation has insignificant effect on the observed corner frequencies for the short distance interval considered. The zero-distance-or source-corner frequency, fo, for an earthquake is therefore calculated as the arithmetic average of the observed values, fR, from all available spectra for that event. It should be noted that the data analysed by Hasegawa (1983) and Kim et al. (1989) spanned much wider distance ranges, more than 1000 km, than that of this study. Figure 5 illustrates the range of corner frequencies.
x
R(km)
5-
l”g(f,)
l;O. 125E+23)
dyne-cm
(3)
0
25
50
75
100
125
R(km)
Fig. 4. Observed distance
corner
R for various
frequency regions classes.
fR plotted (see
vs. hypocentral
Fig. 2) and
event
size
R. WAHLSTROM
212
CORy;R
FR5EQUENC;
Effects of station site and propagation
(Hz) 1
20 I
10-r
erties
/
I
0.05
Fig.
5. Seismic
source gions
radius (see
model
0.2 SOURCE
moment
plotted
Fig. 2). Cf. Table
various
for
increases
with seismic between
for larger
American
km\
vs. corner in the three
2. The
all three moment,
same
regions.
levels of stress drop.
moments
2
0.5 RADIUS
for earthquakes
was used
indicate
0.1
frequency
and
investigated
re-
density/velocity
The
Clearly,
parallel
is largest
at
dyn cm. The stress drop
Plate events tends to be smaller
events of corresponding
lines
the stress drop
and the increase
E+ 18 and E+21
path prop-
than for
size in the slab.
to give an estimate of the effective radius, I-, of the source. Parameters computed from eq. (1) and (3) are used to compute the average dislocation, d (Aki, 1966):
(4) and the static stress drop during the rupture, Au (Brune, 1970):
(5) Source radii from 0.07 to 1.6 km, dislocations up to 7 cm and stress drops up to 40 bar were calculated for the investigated earthquakes (cf. Fig. 5). The effect of the deep-crustal model is to increase r by about 16% and decrease d by about 26%, whereas there is virtually no effect on to the stress drop, since it is proportional [p(s)/u,h>11’2,which has nearly the same value for both structural models.
Difficulties with the spectral method have been pointed out in several studies, e.g., Somerville et al. (19871, who instead use waveform modeling. Boore (1986) discusses various factors influencing the spectrum and limiting the use of corner frequency as an indicator of source parameters. The main concern is to account for the propagation path and station site effects. Frankel and Wennerberg (1989) found in a study based on near-distant (R < 50 km) microearthquake recordings from the Anza network in California that amplitude spectra mainly reflect station site conditions and that the source corner frequency is significantly higher than the observed corner frequencies, an effect ascribed to low Q at shallow depth. Whereas, in Frankel and Wennerberg’s study, source parameters for the smallest earthquakes are beyond determination by spectral means, the parameters for larger earthquakes, magnitude above 3, can be retrieved by removing the transfer function through spectral division with a small earthquake. However, to be successful this requires that the two shocks have very similar locations and focal mechanisms. The strong influence of non-source parameters on the amplitude spectra of small earthquakes in California has also been pointed out in studies by Archuleta (1986) and Fletcher et al. (1986) among others. Mueller and Cranswick (1985) found a strong site influence on the spectra of very local station records (less than 12 km distance) of Miramichi aftershocks. They were able to isolate and remove much of the site effect by applying a resonance model. Like Mueller and Cranswick (1985), Haar et al. (1984) demonstrated that spectra from very local stations, in their case less than 5 km, give significantly higher observed corner frequencies than from more remote stations. To investigate the non-source effects on the spectra in the present case, where data are taken from a wider distance range, events from four subregions were selected (Table 1; Fig. 2a). A comparison of the spectra with respect to any given station or subregion reveals no clear pattern (all spectra are displayed in Wahlstriim,
DYNAMIC
TABLE Values
SOlJRCE
PARAMETERS
IN CASCADIA
SUBDUCTION
213
ZONE
2 of a, and a,, with standard
errors,
in log(M,J
= a, +
M,, in dyn cm, r in km
a2 log(r), Region
Number
a2
[‘I
of data A
22.07 (0.36)
4.67 (0.43)
20
B
22.98 (0.96)
6.59 (1.56)
16
C
22.5 1 (0.50)
5.45 (0.72)
16
C*
22.35 (0.44)
5.43 (0.72)
16
A+B+C
22.37 (0.30)
5.17 (0.41)
52
Regions
are shown in Figure 2. * denotes
that the deep-crustal
model was used.
1989). This is different from, e.g., Frankel and Wennerberg (1989), who found that the spectral similarity with respect to stations outweighs that with respect to earthquakes, i.e., a strong site dependency. The main task of the present study being a comparison of source parameters in different regions, the eventual minor contamination of non-source effects on the spectra is not a major concern. Scaling
relations
Relationships between seismic moment and source radius (Table 2; Fig. 51, and seismic moment and magnitude (Table 3; Fig. 61, were computed separately for each region and also for all regions taken together. The seismic moment for North American Plate earthquakes tends to increase more slowly both with source radius and M,
than for events
regions.
TABLE Values b, M,,
in the two Juan
Application
of the
de Fuca slab
deep-crustal
model
3 of h, and b,, with standard
errors,
in log(M,)
= b, +
M,, in dyn cm
Region
Number
b,
of data A
17.64 (0.09)
0.94 (0.03)
20
B
17.69 (0.20)
1.08 (0.06)
16
C
17.65 (0.10)
1.06 (0.03)
16
C*
17.84 (0.10)
1.06 (0.03)
16
A+B+C
17.65 (0.09)
1.02 (0.03)
52
Regions
are shown in Figure
model was used.
2. * denotes
that the deep-crustal
Region A n Region B A Region C 0 10'6 i
,0171 21 I
I
I
0
-1
1
MAdTUDE
Fig. 6. Relationships M,,
for separate
between regions
Earthquakes than
in the North those
in the
I
I
4
5
seismic moment
1 6
and magnitude,
(see Fig. 2) and all regions
Cf. Table 3. The same crustal M,
I
iL
together.
model was used for all regions.
American
two Juan
Plate mostly de Fuca
slab
have larger regions
for
similar seismic moment.
implies merely a change of the constant term in the moment-magnitude relation (an increase of 0.19 in b, in Table 3, corresponding to the 55% increase in M,, mentioned above), whereas for the moment-radius relation both the slope and intercept are different, since the source radius itself is dependent on the model [factor L:,(S) in eq. (3)l. In Figure 5 it is seen that for the vast majority of earthquakes, with seismic moment between approximately E + 18 and E + 21 dyn cm, there is a rapid increase in seismic moment with decreasing corner frequency, i.e., with increasing source dimension. The resulting rapid increase in stress drop with event size has been observed for small and intermediate size earthquakes in many areas, see, e.g., Chouet et al. (1978); Rautian et al. (1978); Fletcher (1980); Frankel(1981); Archuleta et al. (1982); Hasegawa (1983); Haar Mueller and Cranswick (1985); Kim So has the less rapid or non-existing stress drop for larger events (Fig. increase in stress drop with event for the few smallest earthquakes
et al. (1984); et al. (1989). increase in 5). The slow size observed (M,, < E + 18
214
dyn cm corresponding roughly to M, < 0.5) may be just an artifact of insufficient data or due to non-source effects (attenuation, site, etc.) predominantly determining the spectral characteristics, in particular fR. Coefficients a, and a2 in Table 2 for the North American Plate region are similar to those proposed by Nuttli (1983) as the linear approximation for the whole seismic moment range from E + 19 to E + 26 dyn cm for eastern North America. The fairly large error estimates for the slope (coefficient a2 in Table 2) for the Juan de Fuca slab regions are worth noting (see below). There is a linear dependence between the logarithm of the seismic moment and the M, magnitude, with a tendency towards larger magnitudes, for an equivalent seismic moment, for events in the selected region of the North American Plate than in the Juan de Fuca slab (Table 2; Fig. 6). This is particularly notable for the larger earthquakes and may be related to the shallower focal depth of the events in region A, since no depth correction is used in the M, computations. Hanks and Boore (1984) found that a positive curvature function accurately describes the log(M,,)-M, relation for all southern and central California earthquakes in the M, range from 0 to 7. In several studies of other areas, the momentmagnitude relation is described by two lines, the steeper for events with seismic moment larger than about E + 21 to E + 22 dyn cm [see, e.g., Hasegawa (1983) for M,, and Nuttli (1983) for m,; both studies relate to mid-plate earthquakes]. Although the present relations show a good linear fit over the entire range of events and are similar to those found in various studies of Californian earthquakes (see table 1 in Hanks and Boore, 19841, extrapolation should not be made to larger or smaller events than those used to derive the relations. Conclusions
There is no obvious distance dependence of the observed corner frequencies. The source corner frequency for an earthquake is therefore calculated as the arithmetic mean of observed corner frequencies from all simple-feature spectra.
R. WAHLSTRiJM
For the different tectonic regions, relationships between various source parameters are given in Table 2 and Figure 5, and between seismic moment and magnitude in Table 3 and Figure 6. There is a rapid increase in seismic moment with source dimension, at least for earthquakes up to about M, = 5, implying a rapid increase in stress drop with seismic moment. The influences of radiation pattern directivity, and station site and propagation path properties, on the source parameters are similar and minor, except, probably, for the smallest earthquakes with high observed corner frequency. The influence of crustal model, i.e., density and shear wave velocity, is large, particularly on the seismic moment. No major differences are found in the spectral scaling relations between the three regions, but there are indications that, for equivalent seismic moments, the stress drop is smaller in the North American Plate region than in the underlying slab of the Juan de Fuca Plate for the largest earthquakes. There is a rapid increase in stress drop with seismic moment for the small earthquakes, up to about E + 21 dyn cm, except for the very smallest events. This corresponds to an only slightly increasing or constant source radius. An alternative interpretation is that the length of the rupture is smaller than the fault width, so that the former is not reflected by the corner frequency (see Aki, 1987). The smaller increase in stress drop for the few smallest events is probably only apparent and may be due to insufficient data, uncertain distance dependence of the high observed corner frequencies or sensitivity to site conditions, one of several factors which may disguise the source properties from being obtained from the spectra. The largest earthquakes, with seismic moment above E + 21 dyn cm, show small, if any, increase in stress drop with increasing moment. There is a good log-lin fit of seismic moment vs. M, magnitude over the entire investigated magnitude range for events in the North American Plate on one hand and those in the two Juan de Fuca Plate regions on the other hand. For earthquakes with similar seismic moment, the North American Plate events have the higher magnitudes.
DYNAMIC
SOURCE
PARAMETERS
IN CASCADIA
SUBDUmION
215
ZONE
scaling
Acknowledgements The research was carried out at the Pacific Geoscience Centre (PGC), Geological Survey of Canada, Sidney, B.C., Canada with financial support from the Swedish Natural Science Research Council, Contracts G-GU 4012-300 and -302, Sweden-America Foundation and Royal Swedish Academy of Sciences. The spectral conversion program was written by W.-Y. Kim, Uppsala University and modified by R. Baldwin, PGC. I greatly appreciate comments on the text made by G. Rogers, PGC, and D. Boore and L. Wennerberg, United States Geological Survey, Menlo Park, CA.
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