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Modelling of stress patterns along the western part of the north anatolian fault zone
Tecf~nff~hy~jc~,152 (1988) 215-226 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
215
Modelling of stress patterns along the western part of the North Anatolian Fault Zone FRANK ROTH Institute of Geophysics, Ruhr-University Bochum, P.0. Box 102148, D-4630 Bochum (Federal Republic of Germany) (Received December 3,1986; accepted Aprii 8, 1987)
Abstract Roth, F., 1986. Model@ of stress patterns along the western part of the North Anatolian Fault Zone. In: 0. Kulhanek (Editor), Seismic Source Physics and Earthquake Prediction Research. Tectonophysics, 152: 215-226. The stress field before and after strong (M 2 6) earthquakes in the western part of the North Anatolian Fault Zone is modelied. Assuming an initially homogeneous state of stress, the elastic co-seismic stress-drops, the inelastic post-seismic stress variations and the increase of stress due to plate motion are taken into account, using the theory of dislocations. The model consists of an elastic layer (upper crust) above a half-space which is described by elastic properties and alternatively by a standard linear solid. The results of the latter inelastic model differ only slightly from that of the purely elastic one. One of the main results is that most of the earthquakes fall into regions for which the model calculations predict high stress levels prior to the events. At present, the highest stress values are obtained for an area around 34 o E to 35 ’ E. They are higher than the average pre-seismic stress vahte for the series of eight earthquakes investigate in this study. All results are critically dependent on the assumption of the initial stress field being homogeneous along the western part of the North Anatolian Fault Zone.
Introduction The North Anatolian Fault Zone (NAFZ) is the northern boundary of the Turkish plate (McKenzie, 1972) as shown in Fig. 1. Along this right-lateral transform fault the Turkish plate is squeezed westward from the area in eastern Turkey where the northward movement of the Arabian plate is resisted by the Eurasian plate (all movements are given relative to the Eurasian plate). The NAFZ is a fault which has been the site of many destructive earthquakes. For quite some years now, the pattern of earthquakes in the NAFZ has been analyzed and the migration of large earthquakes as well as gaps have been reported (Richter, 1958; Mogi, 1968; Dewey, 1976; Toksoz et al., 1979; Purcaru and Berckhemer, 1982). In these pub~cati~ns, it is 0040-1951,‘88/$03.50
0 1988 Elsevier Science Publishers B.V.
mainly the time, epicenter, magnitude and length of surface rupture of large events that are used. In addition to these studies, there have been attempts to calculate the elastic (Canitez and Toksiiz, 1979; Wang and Toksijz, 1984) and v&co-elastic changes in the stress field of the eastern part (35”-42O E) of the NAFZ (Roth, 1983; Roth and Zschau, in prep.). In this paper the results of similar calculations for the western part (31°-35“E) are reported and compared to those of the eastern part.
The theory of elastic dislocations is applied to a layered half-space (for more details see Roth, 1983), and v&o-elastic properties are included in one of the layers using the correspondence principle (Fung, 1965; Nur and Mavko, 1974). The
216
after each earthquake tion of both
results
from the superposi-
the stress field before
the stress changes
caused
the event
and
by it.
Earthquake data The following
catalogues
used: Ergin et al. (1967) (1969)
Karnik
Data Fig. 1. Sketch of plate boundaries region.
The arrows
Eurasia.
The
I -Eurasian, S-Turkish
plates
and motion
show the directions are
assigned
2 -Aegean,
the
relative
following
3 -African,
and 6-Arabian.
in the Turkish
of motion
4 -Black
The boundary
Sea and
the Turkish
plate
in northern
Anatolian
Transform
Fault.
(After McKenzie,
between
Turkey
to
numbers: Sea, the Black
is the North
1972.)
Epicenter Center
dislocations from which is calculated. Stress is
obtained directly from this deformation. only normalized stress values for a unit
So far slip and
et al. (1979) and an Earth-
File of the U.S. Nat.
(NGDC,
Geophys.
1981). Earthquakes
occur-
ring since 1802 with epicenters not farther than 50 km from the NAFZ between 30 o and 35 o E were considered. The limitations to a change in the strike
towards the east is due of the fault at about
35” C (see
lateral
Fig.
2). This
causes serious difficulties tions performed here. The limitation
sources are point shear the surface deformation
were
and Zatopek
(1969 and 1971), Alsan et al. (1975),
Dewey (1976), Toksoz quake
and publications Ambraseys
inhomogeneity
in the model
calcula-
to the west is due to a branching
of the NAFZ in this area (see Pavoni, 1961; Tanoglu et al., 1961; Ketin, 1966; McKenzie, 1972). There seems to be a point of difficult a triple junction
around
30 ’ E including
slip or
a change
unit fault dimension have been calculated. The seismic moment of the earthquakes is introduced via a factor to the normalized values. This factor
in fault type from strike-slip to graben formation (Dewey and Sengbr, 1979), a change in focal mechanism from strike-slip to dip-slip faulting
is the product of the co-seismic the rupture area.
and a seismicity
slip and the size of
The stress changes caused by an earthquake are modelled as a superposition of the effect of sources
pattern
showing
high regularity
in
time inside a small area (Zschau et al., 1981). The range of magnitudes was confined to &I, > 6, using the catalogue
of Alsan et al. (1975).
distributed over the plane ruptured by the earthquake at a depth of 5, 10 and 15 km in a vertical direction and at a distance of 10 km along the strike of the fault. Stress build-up by plate motion is calculated like the stress-drop of an earthquake using the opposite sign for the shear stress values. To obtain the stress field immediately before an earthquake the following fields are considered and superimposed: the initial stress field, the stress build-up between the time of the initial situation and the earthquake, the elastic stress changes due to all preceding earthquakes as well as the corresponding inelastic stress relaxation after these events. Earthquake-related changes in stress are negative and positive, the latter due to the increase in stress noticeable
at the tips of the rupture area, best in Fig. 4d. The stress field immediately
TABLE Strong
1 earthquakes
in the western
part of the North
Fault Zone Year 1844
Intensity
Magnitude
VII
1881
VII
1907
VII
1910
6.2
1942
6.1
6/1943
6.6
11/1943
7.2
1944
7.2
1951
6.9
1953
6.4
1957
7.1+ 6.0 + 6.25
1967
7.2
Anatohan
217
.6%Mll Fig. 2. Position
of the epicenters
used in the eastern
test points of the stress field for the western
.7SM and western
part are placed.
parts of the NAFZ.
surrounds
the area in which the
in to show its approximate
position.
shocks, in which high stress accumulated in large areas is simultaneously adjusted to an even level by smaller events and by creep. As between the activity in 1907-1910 and 1942 there were no significant earthquakes, the calculations start in 1942.
2
Earthquake No.
200
The rectangle
The fault zone is sketched
Table 1 shows the sequence of earthquakes found after applying the above-mentioned criteria. As the initial stress field in the NAFZ is not known, the modelling starts with a homogeneous stress field along the fault. This assumption might be best met after a long period without strong TABLE
Irn ID0
0
data used in the model calculations Date
Epicenter
year
mon.
’
Magnitude,
lat.
day
long.
(ON)
a
M,
( o E)
Surface
Rupture
(slip)
length
x 102’
(m)
(km)
(dyn cm)
Moment
1
1942
12
11
40.76
34.83
6.1
0.23
20
0.027
2
1943
6
20
40.85
30.51
6.6
0.69
30
0.120
3
1943
11
26
41.05
33.72
7.2
1.5
280
4
1944
2
1
41.41
32.69
7.2
3.5
180
3.65
5
1951
8
13
40.88
32.87
6.9
1.0
50
0.295
6
1953
9
7
41.09
33.01
6.4
0.38
30
0.066
7
1957
5
26
40.67
31.0
7.1 =
1.6
60
0.46
8
1967
7
22
40.67
30.69
7.2
1.9
80
0.88
from Alsan,
Tezucan
of the rupture
plane of 20 km were used for
Data
For the determination
and B&h (1975).
of the moment,
those cases for which the co-seismic
a shear modulus slip and the length
(1976) or Toksijz et al. (1979). For the remaining Schtitt,
pers. commun.,
This earthquake
2.44
1983). Slip and surface
was used including
of surface
Pa and a width rupture
events the moment
rupture
two aftershocks
of 3 X 10”
follow directly
were given in Ambraseys
was calculated
and Zatopek
(1969), Dewey
from log MO (dyn cm) = 1.3OM, + 17.5 (W.
from this.
of M, = 6.0 and 6.25, following
Ambraseys
and Zatopek
(1969).
Fig. 3. Rupture lines of strong earthquakes in the weste:
Table 2 gives the data of the events used for the calculations. As in the data sources there is usually only the indication “shallow earthquake”, the hypocentral depth of all earthquakes is restricted to 12okm. The displacement and the size of the rupture area are determined using the length of the surface rupture and the surface displacement given in the publications mentioned above and assuming a vertical width of the rupture plane of 20 km. In cases where there are no data, the relation: Ma = 1.3OM, + 17.5 (W. Schttt, pers, commun., 1983) which is similar to that of Ezen (1981) for 6 < M, I 8, is used to find the seismic moment. From this the product of displacement and rupture area is obtained assuming the shear modulus to be 2.9 X 10” Pa. The position of the observed surface rupture is supposed to be that of the rupture plane and was taken from Ambraseys and Zatopek (1969), McKenzie (1972) and Dewey (1976), when available. Further, the epicenter was assumed to be the center of the rupture area. The rupture planes and lines were projected on the trace of the NAFZ. Figure 2 shows the area under consideration, the position of the fault, the epicenters of the earth-
part of’yhe NAl%
quake considered here, as well as those in the eastern part of the NAFZ, used in the previous calculations (Roth, 1983; Roth and Zschau, 1986). The position and rupture length of the events is given in Fig. 3. The Model for the Crust and Upper Mantle There is no detailed information about the crustal structure beneath Turkey. From a study of travel-time residuals (Necioglu et al., 1981) we find P,, = 8.05 f 0.17 km/s, Ps = 5.89 f 0.03 km/s, and an average crustal thickness of 28.4 f 3.45 km. Chen et al. (1980) and Camtez and Toksijz (1980) give 7.73 f 0.08 km/s and 8.1 km/s respectively for P,. This leads to a model of an elastic layer above a half-space and the elastic shear modulus of the layer is set to 0.47 to that of the half-space. The method does not permit any lateral variation in the layer thickness, which would have been useful to model a zone of low viscosity that moves upwards just below the fault. Thus a constant thickness of 25 km was assumed for the elastic layer, a compromise which seems reasonable for intermediate distances (5-155 km) from the fault.
219
TABLE
3
Model parameters MS>_6
Magnitude
20 km
Fault width Hypocentral Crustal
< 15 km
depth
25 km
thickness
Constitutive
standard
law for the aseismic layer
with relaxation
time
and relaxation
strength
75% of the elastic modulus 3 cm/yr
Plate velocity Number
and spacing
linear solid
0.5 year
42 x 32
of testpoints
10 km in both directions The values set for the initial stress field were equal to the stress drop calculated earthquake
for the M, = 7.9
of 1939 in the eastern part of the NAFZ
The half-space is assumed to behave elastically and as a standard linear solid alternatively. The rate of plate motion is set at 3 cm/yr. In other publications values of between 1 cm/yr (Allen, 1982) and 11 cm/yr (Brune, 1968) have been used. All input parameters for the calculations are listed in Table 3. The initial stress field The stress field in 1942 at the western part of the NAFZ is assumed to be homogeneous, besides some stress enhancement at both ends due to the crack tips (see Fig. 4a). The level of shear stress is set-sign reversed-at the same value as the stress drop calculated by this method for the MS= 7.9 earthquake of 26.12.1939 in the eastern part of the fault. This is the strongest event in the NAFZ since at least 1800. It should give a rough estimate of the range of stress drops for all the events in the eastern and western parts of the fault zone. Results
In each figure the area of highest right lateral shear stress is shaded. The situation immediately before and after the event is indicated by “ - ” and “ + ” respectively (appended to the date). The small rectangle above the post-seismic stress field shows in which part of the fault the earthquake occurred. The stress fields show that six out of eight earthquakes occurred in areas of very high TABLE
4
Average
pre-seismic
shear stress in bars at the rupture
the earthquakes Average
Date
pre-seismic
shear stress
(bar) constitutive
law for aseismic
substratum; elastic 1942 6/1943 11/1943 1944
inelastic
- 28.6
- 28.6
-25.6
- 25.6
- 28.5
- 28.6
-28.1
-28.1
1951
- 2.4
- 5.9
1953
3.1
- 3.7
1957
- 34.9
- 35.8
1%7
-25.4
- 26.9
- 21.3 + 12.9
- 22.9 f 10.8
-28.5+
-28.9+
Mean value
In Fig. 4 the stress situation before and after each earthquake is shown, assuming elastic behaviour of the half-space. Figure 5 shows the stress field in 1986 twice: once in the case of a purely elastic model (Fig. 5a) and once assuming inelastic properties of the aseismic layer (Fig. 5b).
and std. dev. Mean value and std. dev. without
the
events of 1951 and 1953
3.1
3.2
area of
220
stress, including all those with magnitude MS 2 7.0. Only the earthquakes of 1951 (AI, = 6.9) and 1953 (MS = 6.4) took place in an area of very low stress. They are situated near the common tip of the Nov. 1943 and the 1944 earthquakes, which would have reduced the stress considerably. The stress build-up between 1944 and 1951 did not change this situation essentially, as can be seen from Fig. 4e.
wsw
Table 4 summarizes the values of average shear stress on the fault before each earthquake. These values are usually taken from the test points 5 km away from the fault. There might be places with higher stress between 0 and 5 km or between 5 and 15 km from the fault, but stress was not calculated at distances in between these. Therefore the absolute values of stress drop given might be too low, but the stress pattern would not be
ENE ‘SW
42%
Contour id X 18.00bar
Y 0
DATE:
12.1942
ENE
-
9.00 0.00
I
I
"B-;::,": C -27.00
DATE:
20.06.1943
-
DATE:
20.06.1943
t
L a
DATE: M, =
11.12.?942 6.1
+
b
M, =
6.6
Fig. 4. Stress patterns in the NAFZ for the model with an elastic seismogenic layer and an elastic substratum. In each figure (4a-h) the area under consideration striking SW-NE in northern Turkey is shown. The fault runs from left to right in the middle of the figure. Every upper figure gives the stress field immediately before, the lower one immediately after the earthquake. This is also indicated by “-” and “+” respectively, attached to the date. Above each lower figure the position of the rupture area (to be projected on to the fault) is marked. Further, the magnitude of the events and in Fig. 4a, the stress values corresponding to the labels at the isolines for stress, are given. Negative values are right-lateral shear stress. The shaded areas are those with highest stress according to the right-lateral movement of the fault.
221
TABLE
5
Average
pre-seismic
shear stress at stress concentrations
Date
on the rupture
plane
Shear
Shear stress
Fraction
stress
at stress con-
stress concentration
(bar)
centr. (bar)
the total rupture
1942 6/1943
- 28.6
- 28.9
50
-25.6
-31.6
61 20
- 28.5
-31.5
1944
- 28.1
- 29.1
17
1951
-2.4
-2.6
60
11/1943
1953
3.1
- 12.0
17
1957
- 34.9
-35.8
50
1967
-25.4
-31.7
38
Mean value and std. dev.
-21.3
f 12.9
- 25.4 f 10.9
-28.5
i
-31.4
of the area of to area (W)
Mean value and std. dev. without
the events of 1951
and 1953
3.1
wsw
ENE
‘SW
DATE:
26.11.1943
+ 2.3
-
ENE
DATE:
01.02.1944
-
DATE:
01.02.1944
t
/_
L-.
1 DATE:
26.11.1943
C M,
=
+
d
7.2
M, = Fig. 4 (continued).
7.2
222
changed qualitatively by choosing different testpoints. Table 4, like Fig. 5, shows no significant difference between the elastic and inelastic model for the relaxation time and relaxation strength chosen. In both cases the standard deviation of the stress level before the earthquakes is ll%, if those of 1951 and 1953 are excluded. This indicates a rather common shear resistance on the different rupture planes. This is supported by the following analysis. The stress field before each earthquake in the area of the impending event is inspected for stress concentrations: the difference between the maximum and the minimum values of each area is determined and only sub-areas of testpoints with values higher than the maximum stress reduced by
““iSW
i
one third of the difference were taken into consideration for the pre-seismic stress level. Table 5 gives the pre-seismic stress levels and the percentage of the rupture area in which it is found. Considering all events, the mean stress level at the stress concentrations is higher than before, which is as expected. But also the standard deviation decreases from 10.9 to 7.3% (the events of 1951 and 1953 again excluded). Next, the areas of high stress not ruptured at the time of the earthquakes are considered. The shaded areas in Fig. 4 give the overall impression and Table 6 provides more details. The threshold in shear stress is set at -25.3 bar. This is, again excluding the events of 1951 and 1953, about the lowest pre-seismic level and about the mean pre-
6q
I
L_/ O\.. \
e
DATE:
13.08.1951
-
DATE:
13.08.1951
+
M, =
6.9
1
-.
DATE:
07.09.1953
-
DATE:
07.09.1953
+
f M, = Fig. 4 (cont~ued).
6.4
223
wsw
ENE
DATE:
26.05.1957
-
DATE:
22.07.1967
-
DATE:
22.07.1967
t
i DATE: M, =
26.05.1957
t h
7.1
M, =
7.2
Fig. 4 (continued).
a
DATE:
30.06.1986
-
b
DATE:
30.06.1986
-
Fig. 5. The stress field of June 30, 1986. The upper field resulted using the purely elastic model, the lower one assuming the constitutive law of the standard linear solid for the substratum.
224 TABLE
6
Area of high pre-seismic of the impending
shear stress outside
earthquake
area
*
Percentage
Date
the rupture
of test points
constitutive
law for aseismic
substratum: elastic
inelastic
100
100
100
100
96
96
1944
30
30
1951
22
22
1953
23
23
1957
6
6
1967
3
24
1942 6/1943 D/1943
* The
threshold
termined outside absolute
is set at
for test points the rupture stress
total number
values
area.
-25.3
bar.
5 km away The number
above
The from
fraction
is de-
the fault
of test points
that level is compared
and with
to the
of those points.
seismic level reduced by one standard deviation, as stated in Table 4. Besides the rupture area, the remaining area is analyzed for the fraction of high stress testpoints. The results are poor at the beginning of the earthquake series. This is caused by the fact that the initial stress field is assumed to be homogeneous and is above the threshold all along the fault, but the series then starts with two events rather limited in size, and there is no stress release in large areas until Nov. 1943 and 1944. This indicates that the initial stress field may not have been as homogeneous as was assumed. The extrapolation to the situation in 1986 (Fig. 5) shows stress above - 25.3 bar (up to - 31 bar) east of 33.6’C, at the site of the earthquakes of 1942 and Nov. 26, 1943. This area would be the site of the next earthquake according to this model.
conditions might be satisfied just below the rupture plane, but there are no data to support this assumption for the NAFZ. In modelling the stress field in the eastern part of the NAFZ (35”-42”E) (Roth and Zschau, in prep.), the same method was used as in this paper. Nine earthquakes of magnitude MS 2 6.0 were taken into account. Their dates and positions can be seen in Fig. 6. The area of calculations was extended towards the west to include the events of Dec. 11, 1942 and Nov. 26, 1943 which might be attributed to either part of the NAFZ. Thus these two earthquakes are included in both models. The fit to the western part is as follows: the pre-seismic stress of the 1942 event is - 27.8 bar in the eastern and - 28.6 bar in the western part, and the corresponding values in the overlapping area of the 1943 event are - 28.9 and - 28.5 bar. Both stress fields match very well. The fact that the 1951 and the 1953 earthquakes do not fall into regimes of high stress can certainly not be attributed to the plate velocity being too small. Assuming a velocity of 3 cm/yr, the annual stress increase due to plate motion is only 0.22 bar (at the test points 5 km from the fault). Thus, a velocity of more than 50 cm/yr would be needed to give a 27 bar stress level in the
1 0.
Discussion and comparison with the eastern part of the North Anatolian Fault Zone
The differences between the elastic and the inelastic model are small. As pointed out previously (Roth, 1983), the effects of an inelastic substratum would only become stronger if it reached up to shallower depths and if the viscosity was significantly lower than assumed here. Both
1,
110.
Fig. 6. The shear stress values at the stress concentrations to all 15 earthquakes
in the NAFZ.
event of Dec. 1942 and for that of Nov. 1943 display the models match
for the eastern
prior
The two levels given for the
and the western
part
how well
of the fault
each other. The values for Nov. 1943 are closer together
if for the eastern
part only the value in the overlapping
both models is considered
(- 28.9 bar).
area of
225
TABLE
7
Mean values and standard Average
deviation
of average
shear stress
shear stress (bar)
at the total rupture
at stress concentrations
plane
oart of the NAFZ
total
part of the NAFZ
west
NAFZ
west
east
(1)
- 21.3 f 12.9
(2)
-28.5
(1) all earthquakes;
f
- 23.8 & 7.4
3.1 (2) without
the earthquakes
- 22.2 * 10.6
- 25.4 + 10.9
-25.4
-31.4
It 6.8
of 1951 and 1953 in the western
of the two earthquakes 7 years after the 1944 stress drop. This is an unreasonably high velocity, and it would lead to extraordin~ly high stresses in 1986. Table 7 shows the average stress values for both models and for all 15 earthquakes. If all events in the NAFZ are considered, the pre-seismic stress level scatters about 48% (or 40% if stress concentrations are considered). The standard deviation for the eastern part is only 60% of that for the west. This result is strongly influenced by the events of 1951 and 1953, which are discussed below. If they are omitted, the standard deviation of the pre-seismic stress level would be reduced to about 27% for the NAFZ as a whole. This relatively high value could mean that there is no specific stress level at which strong earthquakes occur in the NAFZ, i.e. local and perhaps transient conditions dominate. On the other hand, this value would be greatly reduced if the model took into account the existence of asperities in locations of concentrated stress. The reduction in the variation of the pre-seismic stress level when looking for stress concentrations indicates that these might really exist on the fault. Furthermore, the problem of the low stresses before the 1951 and 1953 earthquakes and the poor results obtained for the unruptured areas of high stress (especially in the first years of the earthquake series) could be solved by assuming stress concentrations in the initial stress field. In this case, the events of 1943 and 1944 might not have fully released a stress concentration at about 33S*E and the process would only have been terminated by the 1951 and 1953 events. Such asperities could be included in a model using both an inhomogearea
+ 2.3
total east
NAFZ
- 25.4 * 7.6
- 24.9 * 9.9 .- 27.6 * 7.1
part.
neous initial field and an inhomogeneous field for stress build-up by plate motion iteratively fitted to the place and time of the earthquake sequence. Although the record of strong events with reliable epicenter locations is rather limited, there is some evidence for the existence of an asperity to be found in seismic data for magnitudes greater than five for the area between 30.5 and 31.5”E. This area was the site of the June 1943, the 1957 and the 1967 events and shows stresses of up to 22 bar in 1986, according to the model calculations. A statistical analysis by Zschau et al. (1981) showed a high release of seismic energy between 1863 and 1967 every 15 + 6 years for this area. Thus, from the statistical point of view, a further earthquake is imminent. The calculated stress level, on the other hand, seems low compared with the average critical values in Table 5. The presence of asperities where stress has accumulated to the critical level, while the areas in between give much lower stress values, could also explain this discrepancy. Conclusions Using simple assumptions, a model was constructed which shows that most of the events in a sequence of earthquakes in the western part of the NAFZ occurred in areas of high right lateral shear stress. According to this model, critical stresses are predicted at present for the region around 34’E to 35*E. The pre-seismic stress level along the western NAFZ is less homogeneous than that along the eastern NAFZ. However, if two extreme events are omitted, the stress level shows deviations of less than 10%. The assumptions of a homogeneous initial stress field and of homoge-
226 neous stress increase great influence
on the results.
these uncertainties and
zones
needed.
spread
creep
predict
earthquake. better
the method several
might
available.
proposed
of an
be improved
In its present
as
form,
here could only be useful in
the seismic
decades.
levels just
of occurrence
hazard
over a period
Thus more than
pass before
the next earthquake
area around
34” E and 35”E.
K., Gli+t,
quakes
U. and Uz, Z., 1967. A catalogue
for
Turkey Tech.
and
Univ.
of
ten years might in the high stress
Istanbul,
nitude
along
the North
the Earth’s
Interior
Hamburg,
1983,
China
Harjes,
C.
Milkereit and J. Zschau for many fruitful comments and discussions and H. Kamplade for drawing the figures.
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Approach
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M.N., 1980. Crustal Am. Geophys.
Chen C.-Y., Chen W.-P. and Molnar, mantle
P wave velocities
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J.W.,
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Seismicity
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Dewey, J.F. and Sengiir, A.M.C., ing regions:
complex
multiplate
1979. Aegean and continuum
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Satel-
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Horizontalverschiebung. and
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Elementary
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J., in prep.
at the eastern
Space-time
Kiel.
development
part of the North
of
Anatolian
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A., Erin9, S. and Tttmertekin,
Toksoz,
M.N.,
Shakal,
A.F.
migration Fault
E.. 1961. Ttirkiye
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Atlasi
Istanbul. along
gaps.
A.J.,
1979.
the
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Pure Appl.
Geo-
phys. 117: 1258-1270. Zschau,
and Toksoz,
J., Nehl,
B., Roth,
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str). Terra Cognita,
and surround-
Nat.
F., 1983. Oberfllchendeformationen
earthquake
Seismol. Sot. Am., 66: 843-868.
a convergent
CF.,
Wang Qi-ming of Northern
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H., 1982. Regularity
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Anatolian
P., 1980. The uppermost
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Roth,
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A, Boulder,
51: 122-139,
potential
nungen
Bull. Earthquake
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Service,
1974.
G. and Berckhemer,
Space-time
phys. Res. Lett., 7: 77-80. Dewey,
G.,
(Atlas of Turkey).
(Unpublished.) Camtez,
Epicenter
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Roth,
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183: 204-206.
Rundsch.
Richter,
Res.
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Science,
stress patterns
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Anatolian
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Information
ihrer zeitlichen
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Sot., 30: 109-185.
B. and Tiirkelli,
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bound.
Francisco,
Rep. No. 7-75. Ambraseys,
Part
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of seismic activity.
1981. Earthquake
Purcaru,
M., 1975. An earthquake
I.
Res. Lett., 8: 33-35.
ETH Zurich,
pp. 67-85.
Part
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and upper mantle
Geophys.
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J.R. Astron.
A., Maddison,
crustal
Geol.
Vieweg, Braunschweig,
Area, Area,
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Pavoni N., 1961. Die Nordanatolische
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66: 23-24.
D.P., 1972. Active Geophys.
Res. Inst., Tokyo,
Nur,
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Committee
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Center/World between
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of the European
Seismicity
I., 1966. Tectonic
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C.R., 1982. Comparison
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Reidel, Dordrecht.
merce, Natl. Ocean.
Allen,
to mag-
Reidel, Dordrecht.
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References
related
fault zone. Bull. IISEE,
of Solid Mechanics.
Englewood
Magi, K., 1968. Migration
H.P.
to Publ.
for the 18th Gen. Assoc. of the IUGG,
Beijing. Prentice-Hall,
Explor.
to thank
Eng.,
19: 33-55.
region,
wishes
(1la.D.
Mining
parameters
Anatolian
Fung, Y.C., 1965. Foundations
McKenzie,
author
of earth-
areas,
Fat.
Ezen, U., 1981. Earthquake-source
Ketin,
Acknowledgements The
surrounding
No. 24.
is
is too large to allow us to
This situation
determining
the fault
Ergin,
1964a.D.).
on asperities
along
the time
data become
have a
to reduce
of 10% in stress
the earthquakes
accurately
In order
more information
of aseismic
The
before
due to plate motion
33.
M.N., 1984. (In preparation.) F. and
Noel],
near Adapazari, spec. issue, spring
U., 1981. Cyclic
Western
Turkey,
1981. Abstr.
(ab-
B32, p.
215
Modelling of stress patterns along the western part of the North Anatolian Fault Zone FRANK ROTH Institute of Geophysics, Ruhr-University Bochum, P.0. Box 102148, D-4630 Bochum (Federal Republic of Germany) (Received December 3,1986; accepted Aprii 8, 1987)
Abstract Roth, F., 1986. Model@ of stress patterns along the western part of the North Anatolian Fault Zone. In: 0. Kulhanek (Editor), Seismic Source Physics and Earthquake Prediction Research. Tectonophysics, 152: 215-226. The stress field before and after strong (M 2 6) earthquakes in the western part of the North Anatolian Fault Zone is modelied. Assuming an initially homogeneous state of stress, the elastic co-seismic stress-drops, the inelastic post-seismic stress variations and the increase of stress due to plate motion are taken into account, using the theory of dislocations. The model consists of an elastic layer (upper crust) above a half-space which is described by elastic properties and alternatively by a standard linear solid. The results of the latter inelastic model differ only slightly from that of the purely elastic one. One of the main results is that most of the earthquakes fall into regions for which the model calculations predict high stress levels prior to the events. At present, the highest stress values are obtained for an area around 34 o E to 35 ’ E. They are higher than the average pre-seismic stress vahte for the series of eight earthquakes investigate in this study. All results are critically dependent on the assumption of the initial stress field being homogeneous along the western part of the North Anatolian Fault Zone.
Introduction The North Anatolian Fault Zone (NAFZ) is the northern boundary of the Turkish plate (McKenzie, 1972) as shown in Fig. 1. Along this right-lateral transform fault the Turkish plate is squeezed westward from the area in eastern Turkey where the northward movement of the Arabian plate is resisted by the Eurasian plate (all movements are given relative to the Eurasian plate). The NAFZ is a fault which has been the site of many destructive earthquakes. For quite some years now, the pattern of earthquakes in the NAFZ has been analyzed and the migration of large earthquakes as well as gaps have been reported (Richter, 1958; Mogi, 1968; Dewey, 1976; Toksoz et al., 1979; Purcaru and Berckhemer, 1982). In these pub~cati~ns, it is 0040-1951,‘88/$03.50
0 1988 Elsevier Science Publishers B.V.
mainly the time, epicenter, magnitude and length of surface rupture of large events that are used. In addition to these studies, there have been attempts to calculate the elastic (Canitez and Toksiiz, 1979; Wang and Toksijz, 1984) and v&co-elastic changes in the stress field of the eastern part (35”-42O E) of the NAFZ (Roth, 1983; Roth and Zschau, in prep.). In this paper the results of similar calculations for the western part (31°-35“E) are reported and compared to those of the eastern part.
The theory of elastic dislocations is applied to a layered half-space (for more details see Roth, 1983), and v&o-elastic properties are included in one of the layers using the correspondence principle (Fung, 1965; Nur and Mavko, 1974). The
216
after each earthquake tion of both
results
from the superposi-
the stress field before
the stress changes
caused
the event
and
by it.
Earthquake data The following
catalogues
used: Ergin et al. (1967) (1969)
Karnik
Data Fig. 1. Sketch of plate boundaries region.
The arrows
Eurasia.
The
I -Eurasian, S-Turkish
plates
and motion
show the directions are
assigned
2 -Aegean,
the
relative
following
3 -African,
and 6-Arabian.
in the Turkish
of motion
4 -Black
The boundary
Sea and
the Turkish
plate
in northern
Anatolian
Transform
Fault.
(After McKenzie,
between
Turkey
to
numbers: Sea, the Black
is the North
1972.)
Epicenter Center
dislocations from which is calculated. Stress is
obtained directly from this deformation. only normalized stress values for a unit
So far slip and
et al. (1979) and an Earth-
File of the U.S. Nat.
(NGDC,
Geophys.
1981). Earthquakes
occur-
ring since 1802 with epicenters not farther than 50 km from the NAFZ between 30 o and 35 o E were considered. The limitations to a change in the strike
towards the east is due of the fault at about
35” C (see
lateral
Fig.
2). This
causes serious difficulties tions performed here. The limitation
sources are point shear the surface deformation
were
and Zatopek
(1969 and 1971), Alsan et al. (1975),
Dewey (1976), Toksoz quake
and publications Ambraseys
inhomogeneity
in the model
calcula-
to the west is due to a branching
of the NAFZ in this area (see Pavoni, 1961; Tanoglu et al., 1961; Ketin, 1966; McKenzie, 1972). There seems to be a point of difficult a triple junction
around
30 ’ E including
slip or
a change
unit fault dimension have been calculated. The seismic moment of the earthquakes is introduced via a factor to the normalized values. This factor
in fault type from strike-slip to graben formation (Dewey and Sengbr, 1979), a change in focal mechanism from strike-slip to dip-slip faulting
is the product of the co-seismic the rupture area.
and a seismicity
slip and the size of
The stress changes caused by an earthquake are modelled as a superposition of the effect of sources
pattern
showing
high regularity
in
time inside a small area (Zschau et al., 1981). The range of magnitudes was confined to &I, > 6, using the catalogue
of Alsan et al. (1975).
distributed over the plane ruptured by the earthquake at a depth of 5, 10 and 15 km in a vertical direction and at a distance of 10 km along the strike of the fault. Stress build-up by plate motion is calculated like the stress-drop of an earthquake using the opposite sign for the shear stress values. To obtain the stress field immediately before an earthquake the following fields are considered and superimposed: the initial stress field, the stress build-up between the time of the initial situation and the earthquake, the elastic stress changes due to all preceding earthquakes as well as the corresponding inelastic stress relaxation after these events. Earthquake-related changes in stress are negative and positive, the latter due to the increase in stress noticeable
at the tips of the rupture area, best in Fig. 4d. The stress field immediately
TABLE Strong
1 earthquakes
in the western
part of the North
Fault Zone Year 1844
Intensity
Magnitude
VII
1881
VII
1907
VII
1910
6.2
1942
6.1
6/1943
6.6
11/1943
7.2
1944
7.2
1951
6.9
1953
6.4
1957
7.1+ 6.0 + 6.25
1967
7.2
Anatohan
217
.6%Mll Fig. 2. Position
of the epicenters
used in the eastern
test points of the stress field for the western
.7SM and western
part are placed.
parts of the NAFZ.
surrounds
the area in which the
in to show its approximate
position.
shocks, in which high stress accumulated in large areas is simultaneously adjusted to an even level by smaller events and by creep. As between the activity in 1907-1910 and 1942 there were no significant earthquakes, the calculations start in 1942.
2
Earthquake No.
200
The rectangle
The fault zone is sketched
Table 1 shows the sequence of earthquakes found after applying the above-mentioned criteria. As the initial stress field in the NAFZ is not known, the modelling starts with a homogeneous stress field along the fault. This assumption might be best met after a long period without strong TABLE
Irn ID0
0
data used in the model calculations Date
Epicenter
year
mon.
’
Magnitude,
lat.
day
long.
(ON)
a
M,
( o E)
Surface
Rupture
(slip)
length
x 102’
(m)
(km)
(dyn cm)
Moment
1
1942
12
11
40.76
34.83
6.1
0.23
20
0.027
2
1943
6
20
40.85
30.51
6.6
0.69
30
0.120
3
1943
11
26
41.05
33.72
7.2
1.5
280
4
1944
2
1
41.41
32.69
7.2
3.5
180
3.65
5
1951
8
13
40.88
32.87
6.9
1.0
50
0.295
6
1953
9
7
41.09
33.01
6.4
0.38
30
0.066
7
1957
5
26
40.67
31.0
7.1 =
1.6
60
0.46
8
1967
7
22
40.67
30.69
7.2
1.9
80
0.88
from Alsan,
Tezucan
of the rupture
plane of 20 km were used for
Data
For the determination
and B&h (1975).
of the moment,
those cases for which the co-seismic
a shear modulus slip and the length
(1976) or Toksijz et al. (1979). For the remaining Schtitt,
pers. commun.,
This earthquake
2.44
1983). Slip and surface
was used including
of surface
Pa and a width rupture
events the moment
rupture
two aftershocks
of 3 X 10”
follow directly
were given in Ambraseys
was calculated
and Zatopek
(1969), Dewey
from log MO (dyn cm) = 1.3OM, + 17.5 (W.
from this.
of M, = 6.0 and 6.25, following
Ambraseys
and Zatopek
(1969).
Fig. 3. Rupture lines of strong earthquakes in the weste:
Table 2 gives the data of the events used for the calculations. As in the data sources there is usually only the indication “shallow earthquake”, the hypocentral depth of all earthquakes is restricted to 12okm. The displacement and the size of the rupture area are determined using the length of the surface rupture and the surface displacement given in the publications mentioned above and assuming a vertical width of the rupture plane of 20 km. In cases where there are no data, the relation: Ma = 1.3OM, + 17.5 (W. Schttt, pers, commun., 1983) which is similar to that of Ezen (1981) for 6 < M, I 8, is used to find the seismic moment. From this the product of displacement and rupture area is obtained assuming the shear modulus to be 2.9 X 10” Pa. The position of the observed surface rupture is supposed to be that of the rupture plane and was taken from Ambraseys and Zatopek (1969), McKenzie (1972) and Dewey (1976), when available. Further, the epicenter was assumed to be the center of the rupture area. The rupture planes and lines were projected on the trace of the NAFZ. Figure 2 shows the area under consideration, the position of the fault, the epicenters of the earth-
part of’yhe NAl%
quake considered here, as well as those in the eastern part of the NAFZ, used in the previous calculations (Roth, 1983; Roth and Zschau, 1986). The position and rupture length of the events is given in Fig. 3. The Model for the Crust and Upper Mantle There is no detailed information about the crustal structure beneath Turkey. From a study of travel-time residuals (Necioglu et al., 1981) we find P,, = 8.05 f 0.17 km/s, Ps = 5.89 f 0.03 km/s, and an average crustal thickness of 28.4 f 3.45 km. Chen et al. (1980) and Camtez and Toksijz (1980) give 7.73 f 0.08 km/s and 8.1 km/s respectively for P,. This leads to a model of an elastic layer above a half-space and the elastic shear modulus of the layer is set to 0.47 to that of the half-space. The method does not permit any lateral variation in the layer thickness, which would have been useful to model a zone of low viscosity that moves upwards just below the fault. Thus a constant thickness of 25 km was assumed for the elastic layer, a compromise which seems reasonable for intermediate distances (5-155 km) from the fault.
219
TABLE
3
Model parameters MS>_6
Magnitude
20 km
Fault width Hypocentral Crustal
< 15 km
depth
25 km
thickness
Constitutive
standard
law for the aseismic layer
with relaxation
time
and relaxation
strength
75% of the elastic modulus 3 cm/yr
Plate velocity Number
and spacing
linear solid
0.5 year
42 x 32
of testpoints
10 km in both directions The values set for the initial stress field were equal to the stress drop calculated earthquake
for the M, = 7.9
of 1939 in the eastern part of the NAFZ
The half-space is assumed to behave elastically and as a standard linear solid alternatively. The rate of plate motion is set at 3 cm/yr. In other publications values of between 1 cm/yr (Allen, 1982) and 11 cm/yr (Brune, 1968) have been used. All input parameters for the calculations are listed in Table 3. The initial stress field The stress field in 1942 at the western part of the NAFZ is assumed to be homogeneous, besides some stress enhancement at both ends due to the crack tips (see Fig. 4a). The level of shear stress is set-sign reversed-at the same value as the stress drop calculated by this method for the MS= 7.9 earthquake of 26.12.1939 in the eastern part of the fault. This is the strongest event in the NAFZ since at least 1800. It should give a rough estimate of the range of stress drops for all the events in the eastern and western parts of the fault zone. Results
In each figure the area of highest right lateral shear stress is shaded. The situation immediately before and after the event is indicated by “ - ” and “ + ” respectively (appended to the date). The small rectangle above the post-seismic stress field shows in which part of the fault the earthquake occurred. The stress fields show that six out of eight earthquakes occurred in areas of very high TABLE
4
Average
pre-seismic
shear stress in bars at the rupture
the earthquakes Average
Date
pre-seismic
shear stress
(bar) constitutive
law for aseismic
substratum; elastic 1942 6/1943 11/1943 1944
inelastic
- 28.6
- 28.6
-25.6
- 25.6
- 28.5
- 28.6
-28.1
-28.1
1951
- 2.4
- 5.9
1953
3.1
- 3.7
1957
- 34.9
- 35.8
1%7
-25.4
- 26.9
- 21.3 + 12.9
- 22.9 f 10.8
-28.5+
-28.9+
Mean value
In Fig. 4 the stress situation before and after each earthquake is shown, assuming elastic behaviour of the half-space. Figure 5 shows the stress field in 1986 twice: once in the case of a purely elastic model (Fig. 5a) and once assuming inelastic properties of the aseismic layer (Fig. 5b).
and std. dev. Mean value and std. dev. without
the
events of 1951 and 1953
3.1
3.2
area of
220
stress, including all those with magnitude MS 2 7.0. Only the earthquakes of 1951 (AI, = 6.9) and 1953 (MS = 6.4) took place in an area of very low stress. They are situated near the common tip of the Nov. 1943 and the 1944 earthquakes, which would have reduced the stress considerably. The stress build-up between 1944 and 1951 did not change this situation essentially, as can be seen from Fig. 4e.
wsw
Table 4 summarizes the values of average shear stress on the fault before each earthquake. These values are usually taken from the test points 5 km away from the fault. There might be places with higher stress between 0 and 5 km or between 5 and 15 km from the fault, but stress was not calculated at distances in between these. Therefore the absolute values of stress drop given might be too low, but the stress pattern would not be
ENE ‘SW
42%
Contour id X 18.00bar
Y 0
DATE:
12.1942
ENE
-
9.00 0.00
I
I
"B-;::,": C -27.00
DATE:
20.06.1943
-
DATE:
20.06.1943
t
L a
DATE: M, =
11.12.?942 6.1
+
b
M, =
6.6
Fig. 4. Stress patterns in the NAFZ for the model with an elastic seismogenic layer and an elastic substratum. In each figure (4a-h) the area under consideration striking SW-NE in northern Turkey is shown. The fault runs from left to right in the middle of the figure. Every upper figure gives the stress field immediately before, the lower one immediately after the earthquake. This is also indicated by “-” and “+” respectively, attached to the date. Above each lower figure the position of the rupture area (to be projected on to the fault) is marked. Further, the magnitude of the events and in Fig. 4a, the stress values corresponding to the labels at the isolines for stress, are given. Negative values are right-lateral shear stress. The shaded areas are those with highest stress according to the right-lateral movement of the fault.
221
TABLE
5
Average
pre-seismic
shear stress at stress concentrations
Date
on the rupture
plane
Shear
Shear stress
Fraction
stress
at stress con-
stress concentration
(bar)
centr. (bar)
the total rupture
1942 6/1943
- 28.6
- 28.9
50
-25.6
-31.6
61 20
- 28.5
-31.5
1944
- 28.1
- 29.1
17
1951
-2.4
-2.6
60
11/1943
1953
3.1
- 12.0
17
1957
- 34.9
-35.8
50
1967
-25.4
-31.7
38
Mean value and std. dev.
-21.3
f 12.9
- 25.4 f 10.9
-28.5
i
-31.4
of the area of to area (W)
Mean value and std. dev. without
the events of 1951
and 1953
3.1
wsw
ENE
‘SW
DATE:
26.11.1943
+ 2.3
-
ENE
DATE:
01.02.1944
-
DATE:
01.02.1944
t
/_
L-.
1 DATE:
26.11.1943
C M,
=
+
d
7.2
M, = Fig. 4 (continued).
7.2
222
changed qualitatively by choosing different testpoints. Table 4, like Fig. 5, shows no significant difference between the elastic and inelastic model for the relaxation time and relaxation strength chosen. In both cases the standard deviation of the stress level before the earthquakes is ll%, if those of 1951 and 1953 are excluded. This indicates a rather common shear resistance on the different rupture planes. This is supported by the following analysis. The stress field before each earthquake in the area of the impending event is inspected for stress concentrations: the difference between the maximum and the minimum values of each area is determined and only sub-areas of testpoints with values higher than the maximum stress reduced by
““iSW
i
one third of the difference were taken into consideration for the pre-seismic stress level. Table 5 gives the pre-seismic stress levels and the percentage of the rupture area in which it is found. Considering all events, the mean stress level at the stress concentrations is higher than before, which is as expected. But also the standard deviation decreases from 10.9 to 7.3% (the events of 1951 and 1953 again excluded). Next, the areas of high stress not ruptured at the time of the earthquakes are considered. The shaded areas in Fig. 4 give the overall impression and Table 6 provides more details. The threshold in shear stress is set at -25.3 bar. This is, again excluding the events of 1951 and 1953, about the lowest pre-seismic level and about the mean pre-
6q
I
L_/ O\.. \
e
DATE:
13.08.1951
-
DATE:
13.08.1951
+
M, =
6.9
1
-.
DATE:
07.09.1953
-
DATE:
07.09.1953
+
f M, = Fig. 4 (cont~ued).
6.4
223
wsw
ENE
DATE:
26.05.1957
-
DATE:
22.07.1967
-
DATE:
22.07.1967
t
i DATE: M, =
26.05.1957
t h
7.1
M, =
7.2
Fig. 4 (continued).
a
DATE:
30.06.1986
-
b
DATE:
30.06.1986
-
Fig. 5. The stress field of June 30, 1986. The upper field resulted using the purely elastic model, the lower one assuming the constitutive law of the standard linear solid for the substratum.
224 TABLE
6
Area of high pre-seismic of the impending
shear stress outside
earthquake
area
*
Percentage
Date
the rupture
of test points
constitutive
law for aseismic
substratum: elastic
inelastic
100
100
100
100
96
96
1944
30
30
1951
22
22
1953
23
23
1957
6
6
1967
3
24
1942 6/1943 D/1943
* The
threshold
termined outside absolute
is set at
for test points the rupture stress
total number
values
area.
-25.3
bar.
5 km away The number
above
The from
fraction
is de-
the fault
of test points
that level is compared
and with
to the
of those points.
seismic level reduced by one standard deviation, as stated in Table 4. Besides the rupture area, the remaining area is analyzed for the fraction of high stress testpoints. The results are poor at the beginning of the earthquake series. This is caused by the fact that the initial stress field is assumed to be homogeneous and is above the threshold all along the fault, but the series then starts with two events rather limited in size, and there is no stress release in large areas until Nov. 1943 and 1944. This indicates that the initial stress field may not have been as homogeneous as was assumed. The extrapolation to the situation in 1986 (Fig. 5) shows stress above - 25.3 bar (up to - 31 bar) east of 33.6’C, at the site of the earthquakes of 1942 and Nov. 26, 1943. This area would be the site of the next earthquake according to this model.
conditions might be satisfied just below the rupture plane, but there are no data to support this assumption for the NAFZ. In modelling the stress field in the eastern part of the NAFZ (35”-42”E) (Roth and Zschau, in prep.), the same method was used as in this paper. Nine earthquakes of magnitude MS 2 6.0 were taken into account. Their dates and positions can be seen in Fig. 6. The area of calculations was extended towards the west to include the events of Dec. 11, 1942 and Nov. 26, 1943 which might be attributed to either part of the NAFZ. Thus these two earthquakes are included in both models. The fit to the western part is as follows: the pre-seismic stress of the 1942 event is - 27.8 bar in the eastern and - 28.6 bar in the western part, and the corresponding values in the overlapping area of the 1943 event are - 28.9 and - 28.5 bar. Both stress fields match very well. The fact that the 1951 and the 1953 earthquakes do not fall into regimes of high stress can certainly not be attributed to the plate velocity being too small. Assuming a velocity of 3 cm/yr, the annual stress increase due to plate motion is only 0.22 bar (at the test points 5 km from the fault). Thus, a velocity of more than 50 cm/yr would be needed to give a 27 bar stress level in the
1 0.
Discussion and comparison with the eastern part of the North Anatolian Fault Zone
The differences between the elastic and the inelastic model are small. As pointed out previously (Roth, 1983), the effects of an inelastic substratum would only become stronger if it reached up to shallower depths and if the viscosity was significantly lower than assumed here. Both
1,
110.
Fig. 6. The shear stress values at the stress concentrations to all 15 earthquakes
in the NAFZ.
event of Dec. 1942 and for that of Nov. 1943 display the models match
for the eastern
prior
The two levels given for the
and the western
part
how well
of the fault
each other. The values for Nov. 1943 are closer together
if for the eastern
part only the value in the overlapping
both models is considered
(- 28.9 bar).
area of
225
TABLE
7
Mean values and standard Average
deviation
of average
shear stress
shear stress (bar)
at the total rupture
at stress concentrations
plane
oart of the NAFZ
total
part of the NAFZ
west
NAFZ
west
east
(1)
- 21.3 f 12.9
(2)
-28.5
(1) all earthquakes;
f
- 23.8 & 7.4
3.1 (2) without
the earthquakes
- 22.2 * 10.6
- 25.4 + 10.9
-25.4
-31.4
It 6.8
of 1951 and 1953 in the western
of the two earthquakes 7 years after the 1944 stress drop. This is an unreasonably high velocity, and it would lead to extraordin~ly high stresses in 1986. Table 7 shows the average stress values for both models and for all 15 earthquakes. If all events in the NAFZ are considered, the pre-seismic stress level scatters about 48% (or 40% if stress concentrations are considered). The standard deviation for the eastern part is only 60% of that for the west. This result is strongly influenced by the events of 1951 and 1953, which are discussed below. If they are omitted, the standard deviation of the pre-seismic stress level would be reduced to about 27% for the NAFZ as a whole. This relatively high value could mean that there is no specific stress level at which strong earthquakes occur in the NAFZ, i.e. local and perhaps transient conditions dominate. On the other hand, this value would be greatly reduced if the model took into account the existence of asperities in locations of concentrated stress. The reduction in the variation of the pre-seismic stress level when looking for stress concentrations indicates that these might really exist on the fault. Furthermore, the problem of the low stresses before the 1951 and 1953 earthquakes and the poor results obtained for the unruptured areas of high stress (especially in the first years of the earthquake series) could be solved by assuming stress concentrations in the initial stress field. In this case, the events of 1943 and 1944 might not have fully released a stress concentration at about 33S*E and the process would only have been terminated by the 1951 and 1953 events. Such asperities could be included in a model using both an inhomogearea
+ 2.3
total east
NAFZ
- 25.4 * 7.6
- 24.9 * 9.9 .- 27.6 * 7.1
part.
neous initial field and an inhomogeneous field for stress build-up by plate motion iteratively fitted to the place and time of the earthquake sequence. Although the record of strong events with reliable epicenter locations is rather limited, there is some evidence for the existence of an asperity to be found in seismic data for magnitudes greater than five for the area between 30.5 and 31.5”E. This area was the site of the June 1943, the 1957 and the 1967 events and shows stresses of up to 22 bar in 1986, according to the model calculations. A statistical analysis by Zschau et al. (1981) showed a high release of seismic energy between 1863 and 1967 every 15 + 6 years for this area. Thus, from the statistical point of view, a further earthquake is imminent. The calculated stress level, on the other hand, seems low compared with the average critical values in Table 5. The presence of asperities where stress has accumulated to the critical level, while the areas in between give much lower stress values, could also explain this discrepancy. Conclusions Using simple assumptions, a model was constructed which shows that most of the events in a sequence of earthquakes in the western part of the NAFZ occurred in areas of high right lateral shear stress. According to this model, critical stresses are predicted at present for the region around 34’E to 35*E. The pre-seismic stress level along the western NAFZ is less homogeneous than that along the eastern NAFZ. However, if two extreme events are omitted, the stress level shows deviations of less than 10%. The assumptions of a homogeneous initial stress field and of homoge-
226 neous stress increase great influence
on the results.
these uncertainties and
zones
needed.
spread
creep
predict
earthquake. better
the method several
might
available.
proposed
of an
be improved
In its present
as
form,
here could only be useful in
the seismic
decades.
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