ISSN 10693513, Izvestiya, Physics of the Solid Earth, 2014, Vol. 50, No. 2, pp. 151–168. © Pleiades Publishing, Ltd., 2014.
Original Russian Text © A.A. Soloviev, A.D. Gvishiani, A.I. Gorshkov, M.N. Dobrovolsky, O.V. Novikova, 2014, published in Fizika Zemli, 2014, No. 2, pp. 161–178.
Recognition of EarthquakeProne Areas:
Methodology and Analysis of the Results
A. A. Solovieva, A. D. Gvishianib, A. I. Gorshkova,
M. N. Dobrovolskyb, and O. V. Novikovaa
a
Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences,
ul. Profsoyuznaya 84/32, Moscow, 117997 Russia
email: [email protected]
b
Geophysical Center of the Russian Academy of Sciences,
ul. Molodezhnaya 3, Moscow, 119296 Russia
Received July 21, 2013
Abstract—We present the results of verifying the areas that were detected as prone to strong earthquakes by
the pattern recognition algorithms in different regions of the world with different levels of seismicity and,
therefore, different threshold magnitudes demarcating the strong earthquakes. The analysis is based on the
data presented in the catalog of the U.S. National Earthquake Information Center (NEIC) as of August 1,
2012. In each of the regions considered, we examined the locations of the epicenters of the strong earthquakes
that occurred in the region after the publication of the corresponding result. There were 91 such earthquakes
in total. The epicenters of 79 of these events (87%) fall in the recognized earthquakeprone areas, including
27 epicenters located in the areas where no strong earthquakes had ever been documented up to the time of
publication of the result. Our analysis suggests that the results of the recognition of areas prone to strong
earthquakes are reliable and that it is reasonable to use these results in the applications associated with the
assessment of seismic risks. The comparison of the recognition for California with the analysis of seismicity
of this region by the Discrete Perfect Sets (DPS) algorithm demonstrates the agreement between the results
obtained by these two different methods.
DOI: 10.1134/S1069351314020116
1. INTRODUCTION
In the evaluation of seismic risks in a seismically
active region, one should answer the following ques
tion: which areas within the region of interest are
prone to strong earthquakes? One of the approaches to
the solution of this problem was formulated in the
early 1970s in (Gelfand et al., 1972a; 1972b). This
approach is based on the hypothesis that the epicen
ters of quite strong earthquakes (with magnitude M ≥
M0, where M0 is a given threshold) are confined to the
intersections of tectonically active fault zones—mor
phostructural nodes. The location of the nodes is
determined by a special method of morphostructural
zoning (MSZ), which is described in (Alekseevskaya
et al., 1977a; 1977b; Ranzman, 1979; Gorshkov, Kos
sobokov, and Soloviev, 2003; Gorshkov, 2010). The
hypothesis that the epicenters of the strong earth
quakes originate near the intersections is supported by
the statistical analysis of their mutual location, as
described in (Gvishiani and Soloviev, 1981). The
probable violations of this hypothesis can probably be
explained by the errors in both determining the place
and intensity of the earthquakes and in the location of
the morphostructural nodes.
In all the seismically active regions considered,
strong earthquakes have only been detected at rela
tively few nodes identified in the region. Since the
instrumental seismological observations were started
slightly less than 100 years ago, it is reasonable to
assume that not all the potentially hazardous nodes
have activated into strong earthquakes during this
interval. Thus, it is required to determine the entire set
of hazardous nodes by formulating the criteria for dis
tinguishing these nodes against the other nodes using
the geological and geophysical information about
them. This task is solved by the pattern recognition
methods (Bongard, 1967). The nodes are considered
as the objects of recognition, and each of them is
described by the vector of geological and geophysical
characteristics measured for the corresponding node.
The training sample, which is required for applying
the pattern recognition algorithm, is formed from the
data on the seismicity of the region. The results of rec
ognition are formulated in the form of classification of
the nodes into those prone to strong earthquakes and
those where only the earthquakes with magnitude M <
M0 are probable, together with the criteria (the deci
sion rule) governing this classification.
In the past, the problem of locating the areas that
are prone to strong earthquakes has been solved for a
number of seismically active regions, and the informa
tion about the earthquakes that occurred in these
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SOLOVIEV et al.
regions after obtaining the corresponding results
allows the geophysicists to assess the reliability of these
predictions. The results of such verification were pre
viously presented in (Ranzman, 1979; Gorshkov et al.,
2001; 2010). In the present paper, we carry out such
verification using the data provided by the U.S.
National Earthquake Information Center (NEIC) as
of August 1, 2012. We also compare the results of rec
ognition for California with the analysis of the seis
micity of this region by applying the Discrete Perfect
Sets (DPS) algorithm, which identifies dense areas.
2. FORMULATION OF THE PROBLEM
AND MAIN STAGES OF SOLUTION
The problem of locating the areas that are prone to
strong earthquakes consists in subdividing the territory
of the seismic region into two parts. One part com
prises highly seismically active areas, which can host
the epicenters of strong earthquakes; another part
includes the areas where seismic activity is weak and
the epicenters of such events are absent.
The solution of this problem includes the following
steps:
• outlining the region and specifying the threshold
magnitude M0 which determines the earthquakes that
are assumed to be strong;
• morphostructural zoning of the region and for
mulation of the problem in terms of pattern recogni
tion;
• determining the training set for applying the algo
rithm of pattern recognition;
• selecting the characteristics that describe the
objects of recognition and measuring their values;
• discretization of the values of the studied charac
teristics and coding them in terms of the components
of binary vectors;
• application of a pattern recognition algorithm in
order to classify the objects of recognition into two
classes: the highly seismically active objects, close to
which strong earthquakes are probable, and the
objects characterized by low seismicity, whose neigh
borhoods are not likely to be hit by strong earthquakes;
• estimating the reliability of the obtained classifi
cation by control tests;
• interpretation of the obtained classification of
recognition objects in terms of subdividing the region
into highly seismic zones and zones with low seismic
ity; and
• interpretation of the obtained recognition rule.
The first stage of the analysis is to delineate the
region for which the problem of recognition of earth
quakeprone areas should be solved. Since the criteria
(yielded by the solution of the problem) for demarcat
ing the areas prone to strong earthquakes from the
areas where such events are not expected should be
common for the entire region of study, the territory
should be sufficiently tectonically homogeneous. This
means that the strong earthquakes throughout the
entire region should be caused by similar reasons.
Simultaneously with delineation of the region, the
threshold magnitude M0 should be specified. The fol
lowing criteria are taken into account here: the num
ber of strong earthquakes in the region should not be
too small (at least 10–20), and the vicinities of these
events, which are commensurate in size with their
sources, should not cover an excessively large part of
the territory. Fulfillment of the first criterion provides
the conditions for forming a sufficiently large training
sample (which contains the examples of the areas
where strong earthquakes have been documented so
far) in order to apply the pattern recognition algo
rithm. The second criterion controls the presence of
the areas where strong earthquakes do not occur and,
therefore, the problem will not have a trivial solution
corresponding to the situation when strong earth
quakes are equally probable everywhere across the
entire studied territory. Thus, the threshold value M0
depends on both the rate of seismic activity of the
region and the size of the region.
The experience in solving problems on recognition
of earthquakeprone areas yields the following values
for the threshold magnitude M0: 5.0 for the Western
Alps (Weber et al., 1985; Cisternas et al., 1985),
Pyrenees (Gvishiani, Gorshkov, and Kossobokov,
1987; Gvishiani et al., 1987a; 1987b), Greater Cauca
sus (Gvishiani et al., 1988), and the Iberian Plate
(Gorshkov, 2010; Gorshkov et al., 2010); 5.5 for the
Greater Caucasus (Gvishiani et al., 1987c) and Lesser
Caucasus (Gorshkov et al., 1991); 6.0 for Italy (Gor
shkov et al., 1979; Caputo et al., 1980), the joint region
of Alps and Dinarides (Gorshkov et al., 2009; Gorsh
kov, 2010), and the junction zone of the Alps and
Dinarides (Gorshkov et al., 2009); 6.5 for Tien Shan
and Pamir (Gelfand et al., 1972a; 1972b; 1973), the
united region of Balkans, Asia Minor, Transcaucasia
(Gel’fand, 1974a), California and Nevada (Gelfand
et al., 1976a; 1976b), Greater Caucasus (Gvishiani
et al., 1986), and Himalaya (Bhatia et al., 1992a;
1992b); and 7.75 for the Andean South America
(Gvishiani, Zhidkov, and Soloviev, 1982; Gvishiani
and Soloviev, 1984) and Kamchatka (Gvishiani, Zhid
kov, and Soloviev, 1984).
The next step after selecting the region and specify
ing the threshold magnitude, which defines strong
earthquakes, is specifying the objects for recognition.
Recognition in the works of Gelfand et al. (1972a;
1972b) was focused on the morphostructural nodes—
the vicinities of the intersections of morphostructural
lineaments. The morphostructural lineaments, which
form the boundaries of the crustal blocks, are con
structed as a result of the MSZ of the region, which
relies on the concept of the block structure of the
Earth’s crust. The MSZ technique applicable to
mountain regions is described in detail in (Alek
seevskaya et al., 1977a; 1977b; Ranzman, 1979; Gor
shkov, Kossobokov, and Soloviev, 2003; Gorshkov,
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RECOGNITION OF EARTHQUAKEPRONE AREAS
2010). The MSZ scheme is a model of the presentday
block crustal structure of the region under consider
ation. The MSZ reveals three elements of the block
structure: the hierarchically ordered blocks; the mor
phostructural lineaments—the boundaries of the
blocks; and the morphostructural nodes—the junctions
of the blocks where intersections of the lineaments
occur. The location of the elements of the block struc
ture is determined by a targeted analysis of the Earth’s
surface topography using topographical maps and sat
ellite images and taking into account the information
of geological and tectonic maps.
Ranzman et al. (1979) formulated the main geo
morphological arguments in favor of the assumption
that the strong earthquakes, just as other extreme nat
ural events, originate within the nodes. This assump
tion is also supported by the positions of the epicenters
of the strong earthquakes known in these regions. The
probable deviations can be associated with the errors
in recording the locations and magnitudes of the
earthquakes and determining the locations of the
nodes. Due to the fact that strong earthquakes are spa
tially correlated to morphostructural nodes, the prob
lem of locating earthquakeprone areas can be formu
lated as the patternrecognition problem where the
role of the objects to be recognized is played by the
nodes. The patternrecognition algorithm is applied in
order to classify the nodes into two groups: the highly
seismically active (“dangerous”) nodes (hereinafter,
referred to as Dnodes), which can host the epicenters
of strong earthquakes, and the nodes where the seis
micity is low (“not dangerous”, or Nnodes) and
strong earthquakes do not occur.
The nodes as objects of recognition were used in
(Gelfand et al., 1972a; 1972b; 1973; 1974a; Gvishiani
et al., 1986; 1987c; Gorshkov, Kossobokov, and Solov
iev, 2003). However, delineating the boundaries of the
nodes is a cumbersome task whose solution requires
largescale MSZ of lineament intersection areas based
on field studies (Ranzman, 1979; Glasko and Ran
zman, 1992). Therefore, the intersections (or groups
of closely located intersections) of morphostructural
lineaments are also used as the objects of recognition
(Gelfand et al., 1974b; 1976a; 1976b; Zhidkov and
Kossobokov, 1978; Gorshkov et al., 1979; 1991; 2004;
2010; Caputo et al., 1980; Gvishiani, Gorshkov, and
Kossobokov, 1987; Gvishiani, Zhidkov, and Soloviev,
1982; 1984; Gvishiani et al., 1987a; 1987b; Gvishiani
and Soloviev, 1984; Weber et al., 1985; Cisternas et al.,
1985; Bhatia et al., 1992a; 1992b). Gelfand et al.
(1974b) were the first who used intersections as recog
nition objects, and their results agree well with the
results obtained for the same region by the recognition
of the nodes (Gelfand et al., 1974a). Gvishiani and
Soloviev (1981) suggested the algorithm for testing the
hypothesis that epicenters of the strong earthquakes
originate close to the intersections.
The application of recognition algorithms with
training requires that the training sample W0 is prelim
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inarily constructed. This sample consists of two non
intersecting subsets: the D0 objects that a priori belong
to class D, and the N0 objects that a priori belong to
class N. Sample W0 = D0 ∪ N0 is constructed in the fol
lowing way. If the nodes are used as the objects of rec
ognition, the subset D0 is composed of nodes that con
tain the epicenters of the strong earthquakes known
for a given region. The subset N0 is either formed of the
remaining objects of W, N0 = W\D0, or of the objects
in which the epicenters of the earthquakes with M ≥
M0 – δ (δ > 0 and is typically about 0.5) are absent. We
note that it is impossible to construct the subset N0 that
contains pure data for training in the N class. The
earthquakes with M ≥ M0 can occur in some of these
objects but are not known, as the interval of observa
tions is short. The task of the recognition is to find
these objects.
If recognition seeks to revealing the intersections of
the lineaments, the subset D0 is composed of objects
that are located within a certain threshold distance r
from the epicenters of strong earthquakes. The value
of r depends on the threshold magnitude M0) specified
for the studied region. For example, in the recognition
of intersections of the lineaments in Pamir and Tien
Shan with M0 = 6.5, r is 40 km (Gelfand et al., 1974b);
and in the recognition of intersections on the Pacific
coast of South America with M0 = 7.75 – r = 75 km
(Gvishiani, Zhidkov, and Soloviev, 1982). The value of
r should satisfy the condition that requires that the dis
tance from all the reliably determined epicenters of
strong earthquakes to the closest intersections do not
exceed r. The subset N0 in such cases is composed of
the remaining intersections located at a distance of at
least r1 (r1 ≥ r) from the epicenters of the events with
M ≥ M0 – δ (δ > 0). In this case, the subset N0 can also
include the objects that potentially belong to class D.
If the subset D0 contains quite a few objects, some
of them can be excluded from D0 and used for control
ling the obtained classification. If nodes are used as the
objects of recognition, the reliability of the results is
primarily determined by whether the condition that
D0 ⊆ D is satisfied, where D are the objects that are
classified by the recognition as dangerous. To put it
another way, all the locations of the earthquakes with
M ≥ M0) known in the region under study should be
classified as highly seismicprone areas. If the recogni
tion is carried out for the intersections, one epicenter
can simultaneously occur within the rvicinities of a
few intersections. All these intersections are included
in D0, although it cannot be ruled out that some of
them belong to the class N. Correspondingly, the con
dition D0 ⊆ D is replaced by the following one: the
vicinity of each epicenter of a strong earthquake
within a distance r should contain at least one inter
section that is related to the class D.
The recognition algorithms are applied to the vec
tors whose components are the characteristics describ
ing different properties of the classified objects. The
earthquakes occur in the fault zones of tectonically
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SOLOVIEV et al.
active regions. In the problems of recognition of earth
quakeprone areas, the characteristics of the objects
should describe the properties of the location of the
object that reflect, directly or indirectly, different fac
tors causing seismic activity. Therefore, it is reasonable
to use the parameters that describe, in some way, the
intensity of tectonic movements. The long studies on
recognition of the areas prone to strong earthquakes
(Gelfand et al., 1972b; 1972a; 1973; 1974a; 1974b;
1976a; 1976b; Zhidkov and Kossobokov, 1981; Gorsh
kov, Kossobokov, and Soloviev, 2003; Gorshkov et al.,
1979; 1991; 2001; 2004; 2009; 2010; Caputo et al.,
1980; Gvishiani and Soloviev, 1984; Weber et al., 1985;
Cisternas et al., 1985; Gvishiani et al., 1987a; Bhatia
et al., 1992a; 1992b; Gorshkov, 2010) have formulated
the set of the characteristics describing the objects of
recognition. These characteristics include the mor
phometric indices of the landforms, the geometry of
the network of lineaments, and the gravimetric param
eters.
In principle, any information characterizing the
particular features of seismic areas can be used for rec
ognition. The only necessary condition here is that the
value of this characteristic should be possible to
equally accurately determine for all the objects within
the studied territory. Once the values of the character
istics have been determined, all the objects contained
in W are converted into the vectors wi = {w1i , w2i ,..., wmi },
i = 1, 2, …, n, where m is the total number of the char
acteristics; n is the total number of the objects in the
set W; w ki is the value of the kth characteristics mea
sured for the ith object.
The recognition problem considered here is solved
by the Cora3 recognition algorithm (Bongard, 1967),
which is applied to the vectors with binary compo
nents. Therefore, the initial vectors of the characteris
tics should be converted into binary vectors. The con
version is carried out by the procedures of quantization
and coding described, e.g., in (Gelfand et al., 1976a;
1976b; Gvishiani et al., 1988; Gorshkov, Kossobokov,
and Soloviev, 2003; Gorshkov, 2010).
After this conversion, the recognition algorithm
carries out the classification of the objects using the
training sample W0 = (D0, N0): W = D ∪ N, where D
and N are the vectors related by the algorithm to the
classes D and N, respectively. The Cora3 algorithm
and the procedures of its application are described in
detail, e.g., in (Gelfand et al., 1976a; 1976b; Gvishiani
et al., 1988; Gorshkov, Kossobokov, and Soloviev,
2003; Gorshkov, 2010). In order to avoid the trivial
solution when all the objects of the studied region are
classified as D, the following condition is introduced:
|D| ≤ β|W|, where |D| and |W| are the numbers of the
objects in the sets D and W, respectively; β (0 < β < 1)
is the realvalued parameter which a priori specifies
the upper limit of the number of the objects D in the
set W. The value of β is found by the assessment of seis
mic potential of the studied territory on the basis of the
available seismological, geological, and other infor
mation.
Clearly, the main criterion for assessing the reliabil
ity of the recognition of earthquakeprone areas is
provided by the subsequent strong earthquakes that
occur in the target regions of recognition. However,
when determining the final classification of the objects
during the solution of the recognition problem, one
should control the quality of the obtained classifica
tions. A number of the control experiments are carried
out with this purpose (Gelfand et al., 1976a; 1976b;
Gvishiani et al., 1988; Gorshkov, Kossobokov, and
Soloviev, 2003; Gorshkov, 2010). The positive results
of the control experiments suggest that the objects of
recognition are quite adequately subdivided into the D
and N classes. Besides formally testing the stability and
reliability of the results of recognition, these results
can also be validated by applying the decisive rule to
the part of the sample D0, which has been a priori
excluded from training and only used for testing the
results. However, the training sample D0 in the recog
nition of seismicprone areas is typically small, which
prevents one from allocating a part of the objects for
testing the obtained classification. In such cases, the
final classification is tested with the use of the data on
the strong historical and/or paleoearthquakes. If the
epicenters of such earthquakes are located close to the
objects that have been recognized as D, this is consid
ered as an additional argument supporting the reliabil
ity of the classification under study. However, it should
be remembered that the epicenters of the historical
events have been probably determined with significant
errors.
In accordance with the classification of the recog
nition objects into the D and N classes, the considered
region is subdivided into highly seismically active ter
ritory and an area that has a low seismic level. In the
case when the objects to be recognized are morpho
structural nodes, the highly seismically active (danger
ous) area is composed of the territories of the nodes
that are included in the D class, while the remaining
territory is classified as lowly seismic. If the recogni
tion objects consist of the intersections of the morpho
structural lineaments, the highly seismically active
area is composed of circles with radius r and centers
located at the intersections related to class D; the
remaining territory forms the low seismic area.
The decisive rule that sorts the recognition objects
into the D and N classes is formulated in terms of the
combinations of nequalities constraining the parame
ters describing the objects. Since the parameters
reflect different factors affecting seismic activity, the
interpretation of the obtained rule can provide a cer
tain contribution in understanding the factors that
cause strong earthquakes (e.g., see (Gvishiani et al.,
1988; Gorshkov, Kossobokov, and Soloviev, 2003;
Gorshkov, 2010)).
After the highly seismic and low seismic zones in
the studied region have been delineated, it makes
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RECOGNITION OF EARTHQUAKEPRONE AREAS
155
44° N
Bishkek
2
5
42° N
Tashkent
40° N
7
3
4
1
Dushanbe
38° N
6
36° N
66° E
68° E
70° E
72° E
74° E
76° E
78° E
80° E
Fig. 1. The scheme of lineaments in the Tien Shan and Pamir, the earthquakeprone area (contoured by the thick lines) according
to (Zhidkov and Kossobokov, 1978), and epicenters of the strong earthquakes (with M ≥ 6.5) that occurred after 1972 (the black
dots with the numbers corresponding to Table 1).
sense to carry out statistical analysis of the spatial dis
tribution of the epicenters of the earthquakes with M <
M0 relative to these areas in the way it is done, e.g., in
(Kossobokov and Soloviev, 1982). Based on the results
of this analysis, it can be concluded that the obtained
highly seismic and low seismic zones are indeed
related to earthquakes with M ≥ M 0' , where the thresh
old magnitude M 0' is slightly lower than M0.
3. THE RESULTS OF RECOGNITION
OF HIGHLY AND LOW SEISMIC AREAS.
THEIR VALIDATION BY THE SUBSEQUENT
STRONG EARTHQUAKES
Below we present the results of recognizing the
highly seismic areas and the areas marked with low
seismicity in a few seismically active regions and com
pare them with the locations of the epicenters of the
strong earthquakes that occurred in these regions after
the completion of the corresponding study. The lists of
such earthquakes are compiled from the NEIC data as
of August 1, 2012 and are presented in Table 1.
The magnitude of each event in the table is the maxi
mal magnitude indicated for this event in the NEIC
catalog.
Tien Shan and Pamir. This is the first region for
which the problem has been formulated and solved.
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The threshold magnitude M0 of strong earthquakes
was assumed to be 6.5. The recognition was carried out
for morphostructural nodes. The result of recognizing
the highly seismic and low seismic areas was obtained
in 1972 (Gelfand et al., 1972a; 1972b). Later, these
findings were supported by the recognition of the
intersections of the morphostructural lineaments
(Zhidkov and Kossobokov, 1978). The last result and
the epicenters of the strong earthquakes that occurred
in the region after 1972 are shown in Fig. 1 (r =
40 km).
From Fig. 1 it follows that since the time of the
solution of the problem, the region has been hit by
seven strong earthquakes, and the epicenters of six of
these events fell in the area recognized as earthquake
prone. We note that one of these earthquakes occurred
in the vicinity of the intersection where strong earth
quakes have not been previously known. One earth
quake (no. 5 in Table 1) occurred outside the vicinities
of the intersections; however, its epicenter is close to
the boundary of the earthquakeprone area.
Balkans, Asia Minor, and Transcaucasia. The
threshold magnitude of the strong earthquakes in this
region is M0 = 6.5. The intersections of the morpho
structural lineaments were used as the objects of rec
ognition. The area prone to strong earthquakes is
composed of circles with radius r = 40 km and the cen
ters located at the intersections related to the Dclass
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SOLOVIEV et al.
Table 1. The earthquakes that occurred in the regions for which the problem of recognition of the earthquakeprone areas
was solved after publication of the results of recognition
Coordinates of epicenter
No.
Date
Magnitude
latitude, deg
longitude, deg
Correspondence to the prediction
Tien Shan and Pamir, M ≥ 6.5
1
2
3
4
5
Aug. 11, 1974
Mar. 24 1978
Nov. 1, 1978
Aug. 23, 1985
Aug. 19, 1992
39.46 N
42.84 N
39.35 N
39.43 N
42.14 N
73.83 E
78.61 E
72.61 E
75.22 E
73.57 E
7.3
7.1
6.8
7.5
7.5
6
7
May 30, 1998
May 15, 2008
37.11 N
39.53 N
70.11 E
73.82 E
7.0
6.9
In Darea
In Darea
In Darea
In Darea
In Narea (outside the vicinities
of intersections)
In Darea*
In Darea
Balkans, Asia Minor, and Transcaucasia, M ≥ 6.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Mar. 27, 1975
Sept. 6, 1975
May 11,1976
Nov. 24, 1976
June 20, 1978
Apr. 15, 1979
Feb. 24, 1981
Dec. 19, 1981
Jan. 18, 1982
Jan. 17, 1983
Aug. 6, 1983
Oct. 30, 1983
Dec. 7, 1988
Mar. 13, 1992
May 13, 1995
June, 15, 1995
Oct. 13, 1997
Nov. 18, 1997
June 27, 1998
40.42 N
38.47 N
37.56 N
39.12 N
40.74 N
42.10 N
38.22 N
39.24 N
40.00 N
38.03 N
40.14 N
40.33 N
40.99 N
39.71 N
40.15 N
38.40 N
36.38 N
37.57 N
36.88 N
26.14 E
40.72 E
20.35 E
44.03 E
23.23 E
19.21 E
22.93 E
25.23 E
24.32 E
20.23 E
24.76 E
42.19 E
44.19 E
39.60 E
21.69 E
22.28 E
22.07 E
20.66 E
35.31 E
6.7
6.7
6.7
7.3
6.6
7.3
6.8
7.6
7.0
7.2
7.3
6.9
7.0
6.9
6.8
6.5
6.7
6.6
6.6
20
21
22
23
24
25
26
27
Aug. 17, 1999
Nov. 12, 1999
July 26, 2001
Feb. 3, 2002
Jan. 8, 2006
Feb. 14, 2008
July 15, 2008
Oct. 23, 2011
40.75 N
40.76 N
39.06 N
38.57 N
36.31 N
36.50 N
35.80 N
38.72 N
29.86 E
31.16 E
24.24 E
31.27 E
23.21 E
21.67 E
27.86 E
43.51 E
7.8
7.5
6.6
6.5
6.7
6.9
6.5
7.3
In Darea
In Darea
In Darea
In Darea
In Darea
In Darea
In Darea*
In Narea
In Darea
In Darea
In Darea*
In Darea
In Darea*
In Darea
In Darea*
In Darea
In Darea
In Darea
In Narea (outside the vicinities of in
tersections)
In Darea
In Darea
In Darea
In Darea*
In Darea*
In Darea
In Darea
In Darea*
32.63 N
37.57 N
36.22 N
37.54 N
115.33 W
118.82 W
120.32 W
118.45 W
7.0
6.7
6.7
6.5
In Darea
In Darea*
In Darea
In Darea*
California and Nevada, M ≥ 6.5
1
2
3
4
Oct. 15, 1979
May 25, 1980
May 2, 1983
July 21, 1986
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Table 1. (Contd.)
Coordinates of epicenter
No.
Date
Magnitude
latitude, deg
longitude, deg
5
6
7
8
9
10
11
12
Nov. 24, 1987
Oct. 18, 1989
Apr. 25, 1992
June 28, 1992
June 28, 1992
Jan. 17, 1994
Oct. 16, 1999
Dec. 22, 2003
33.01 N
37.04 N
40.37 N
34.20 N
34.20 N
34.21 N
34.59 N
35.71 N
115.84 W
121.88 W
124.32 W
116.44 W
116.83 W
118.54 W
116.27 W
121.10 W
6.7
7.1
7.2
7.6
6.7
6.8
7.4
6.6
13
14
Jan. 10, 2010
Apr. 4, 2010
40.65 N
32.30 N
124.69 W
115.28 W
6.5
7.3
Correspondence to the prediction
In Darea
In Darea
In Darea
In Darea
In Darea*
In Darea*
In Darea
In Narea (outside the vicinities
of intersections)
In Darea
In Darea
Italy, M ≥ 6.0
In Darea
In Narea (outside the vicinities
of intersections)
In Darea*
In Narea (outside the vicinities
of intersections)
In Darea
In Narea (outside the vicinities
of intersections)
In Darea
In Narea (outside the vicinities
of intersections)
1
2
Nov. 23, 1980
Apr. 29, 1984
40.91 N
43.26 N
15.37 E
12.56 E
7.2
6.1
3
4
May 7, 1984
Sept. 26, 1997
41.76 N
43.08 N
13.90 E
12.81 E
6.0
6.4
5
6
Apr. 12, 1998
Sept. 6, 2002
46.24 N
38.38 N
13.65 E
13.70 E
6.0
6.0
7
8
Apr. 6, 2009
May 20, 2012
42.33 N
44.90 N
13.33 E
11.23 E
6.3
6.1
33.13 S
23.34 S
16.26 S
13.39 S
36.12 S
71.87 W
70.29 W
73.64 W
76.60 W
72.90 W
7.8
8.4
8.2
8.0
8.8
In Darea
In Darea*
In Narea
In Darea*
In Darea
54.84 N
162.04 E
7.8
In Darea
44.82 N
44.87 N
46.78 N
47.27 N
46.01 N
46.00 N
6.64 E
6.70 E
9.52 E
9.50 E
6.35 E
6.90 E
5.0
5.1
5.1
5.0
5.1
5.3
In Darea
In Darea
In Darea*
In Darea
In Narea
In Darea
42.83 N
42.90 N
42.93 N
2.53 E
0.60 E
0.17 W
5.0
5.1
5.0
In Darea*
In Darea
In Darea
South American Andes, M ≥ 7.75
1
2
3
4
5
Mar. 3, 1985
July 30, 1995
June 23, 2001
Aug. 15, 2007
Feb. 27, 2010
Kamchatka, M ≥ 7.75
1
Dec. 5, 1997
Western Alps, M ≥ 5.0
1
2
3
4
5
6
Oct. 20, 1985
Feb. 11, 1991
Nov. 20, 1991
May 8, 1992
Dec. 14, 1994
Sept. 8, 2005
Pyrenees, M ≥ 5.0
1
2
3
Feb. 18, 1996
Oct. 4, 1999
May 16, 2002
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SOLOVIEV et al.
Table 1. (Contd.)
Coordinates of epicenter
No.
Date
Magnitude
latitude, deg
longitude, deg
Correspondence to the prediction
4
Sept. 18, 2004
42.88 N
1.52 W
5.3
In Narea
5
Sept. 21, 2004
42.30 N
2.46 E
5.1
In Darea
6
Nov. 17, 2006
42.99 N
0.05 W
5.4
In Darea
Greater Caucasus, M ≥ 5.0
1
May 3, 1988
42.47 N
47.66 E
5.1
In Darea*
2
Apr. 29, 1991
42.45 N
43.67 E
7.3
In Darea*
3
June 15, 1991
42.46 N
44.01 E
6.5
In Darea*
4
Oct. 23, 1992
42.59 N
45.10 E
6.8
In Darea
5
Feb. 22, 1993
42.56 N
43.86 E
5.0
In Darea*
6
April 17, 1994
41.95 N
46.32 E
5.0
In Darea
7
Jan. 31, 1999
43.16 N
46.84 E
5.9
In Darea
8
Nov. 9, 2002
45.00 N
37.77 E
5.5
In Darea*
9
Feb. 6, 2006
42.65 N
43.53 E
5.3
In Darea*
10
Sept. 7, 2009
42.66 N
43.44 E
6.0
In Darea*
11
Aug. 18, 2011
42.61 N
42.95 E
5.1
In Darea*
12
May 7, 2012
41.55 N
46.79 E
5.7
In Darea*
13
Oct. 7, 2012
40.75 N
48.44 E
5.4
In Darea
Himalaya, M ≥ 6.5
1
Oct. 19, 1991
30.78 N
78.77 E
7.0
In Darea
2
Mar. 28, 1999
30.51 N
79.40 E
6.6
In Darea
3
Oct. 8, 2005
34.54 N
73.59 E
7.7
In Darea*
4
Sept. 18, 2011
27.73 N
88.16 E
6.9
In Narea (outside the vicinities
of intersections)
* In that part of the Darea where the epicenters of the strong earthquakes have not been known before the solution of the problem
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RECOGNITION OF EARTHQUAKEPRONE AREAS
159
44° N
6
Sophia
Skopje
42° N
5
15
40° N
9
16
38° N
10
3
36° N
11 10
8
22
Ankara
21
12
14
4
23
2
7 Athens
18
Tbilisi
13
Erevan
20
27
19
25
17
24
26
20° E 22° E 24° E 26° E 28° E 30° E 32° E 34° E 36°E 38°E 40°E 42°E 44°E 46°E 48°E
Fig. 2. The scheme of the lineaments for the region that comprises Balkans, Asia Minor, and Transcaucasia; the earthquakeprone
area (contoured by the thick lines) determined according to (Gelfand et al., 1974), and the epicenters of the strong (M ≥ 6.5)
earthquakes that occurred after 1974 (the black dots with the numbers corresponding to Table 1).
(Gelfand et al., 1974a). This area is displayed in Fig. 2,
where the epicenters of the strong earthquakes that
occurred in this territory after 1974 (the date of
obtaining the results) are also shown.
From Fig. 2 it follows that since the solution of the
problem, 27 strong seismic events have occurred in
this region. The epicenters of 25 events fall in the rec
ognized earthquakeprone area. Seven epicenters are
located in the vicinities of the intersections of class D,
where strong earthquakes have not occurred previ
ously. The epicenter of one earthquake (no. 8 in
Table 1) fell in the vicinity of the intersection that is
related to the Nclass, and one earthquake (no. 19 in
Table 1) occurred outside the vicinities of the intersec
tions.
California and Nevada. In this region, the threshold
magnitude of the strong earthquakes was M0 = 6.5.
The recognition was aimed at revealing the intersec
tions of morphostructural lineaments. The earth
quakeprone area consists of circles with radius r =
25 km and the centers at the intersections classified as
D (Gelfand et al., 1976a; 1976b). This area and the
epicenters of the strong earthquakes that occurred
after the year of obtaining the result (1976) are shown
in Fig. 3.
Figure 3 indicates that since the time of the solu
tion of the problem, 14 strong earthquakes have
occurred in this region. The epicenters of 13 events
were located in the predicted earthquakeprone area.
Four epicenters fall in the vicinities of the intersec
tions related to the Dclass, where strong seismic
events have not occurred previously. The epicenter of
one earthquake (San Simeon, 2003, no. 12 in Table 1)
is located outside the vicinities of intersections. This
failure can probably be associated with the fact that,
according to some sources, the magnitude of this
earthquake was 6.4.
Italy. The threshold magnitude of the strong earth
quakes is M0 = 6.0. The intersections of the morpho
structural lineaments were used as the recognition
IZVESTIYA, PHYSICS OF THE SOLID EARTH
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objects. The earthquakeprone area is formed of cir
cles with radius r = 35 km and the centers at the inter
sections related to the Dclass (Gorshkov et al., 1979;
Caputo et al., 1980). This area is shown in Fig. 4,
where the epicenters of the strong seismic events that
occurred in this region after 1979 (the date of obtain
ing the results) are also depicted.
From Fig. 4 it follows that since the solution of the
problem, the region has experienced eight strong
earthquakes. The epicenters of four events fall in the
predicted earthquakeprone area, and one of these
epicenters is located in the neighborhood of the inter
section classified as Dclass, where strong earthquakes
have not occurred previously. The epicenters of four
earthquakes (nos. 2, 4, 6, and 8 in Table 1) fall outside
the vicinities of the intersections. The results of the test
for Italy cannot be considered satisfactory. The failure
is due to the imperfect scheme of morphostructural
zoning for this region. For example, earthquake no. 8
occurred in the valley of River Po, for which a full
scale morphostructural zoning has not been con
ducted. The epicenter of earthquake no. 6 falls in the
sea, where it was impossible to trace the lineaments
with sufficient accuracy due to the insufficient bathy
metric data.
South American Andes. The threshold magnitude
of the strong earthquakes is M0 = 7.75; recognition is
carried out for the intersections of the morphostruc
tural lineaments. The areas prone to the strong earth
quakes are composed of the circles of radius r = 75 km
with the centers at the intersections referred to as
class D (Gvishiani, Zhidkov, and Soloviev, 1982;
Gvishiani and Soloviev, 1984). This area and the epi
centers of the earthquakes that occurred in this region
after 1982 (the date of obtaining the results) are shown
in Fig. 5.
It can be seen in the figure that since the time of
solution of the problem the region has been hit by five
strong seismic events. The epicenters of four of them
fall in the areas recognized as prone to strong earth
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SOLOVIEV et al.
42° N
13
7
40° N
Sacramento
38° N
2 4
San Francisco
6
3
36° N
12
11
10
9
8
34° N
Los Angeles
San Diego
5
Mexicali
1
14
32° N
124° W
122° W
120° W
118° W
116° W
Fig. 3. The scheme of the lineaments in California and Nevada; the earthquakeprone area (contoured by the thick lines) deter
mined according to (Gelfand et al., 1976a; 1976b), and the epicenters of the strong (M ≥ 6.5) earthquakes that occurred after 1976
(the black dots with the numbers corresponding to Table 1).
quakes, and two such epicenters are located in the
vicinity of the intersections related to the Dclass,
where strong earthquakes have not occurred previ
ously. The epicenter of one earthquake is located in the
vicinity of the intersection related to the Nclass.
Kamchatka. In this region, the threshold magni
tude of the strong earthquakes is the same as in the
case of South American Andes (M0 = 7.75). The inter
sections of the morphostructural lineaments were used
as the objects of recognition. The problem of recogni
tion was not solved here; the rule of classification that
was derived for the South American Andes was applied
to the vectors of the characteristics describing the
objects (Gviashiani, Zhidkov, and Soloviev, 1984). The
earthquakeprone area is formed by the circles with
the radius r = 75 km and the centers located at the
intersections classified as D. After 1984, when the
results were obtained, only one earthquake occurred
in the region (Table 1). The epicenter of this event fell
in the earthquakeprone area.
Western Alps. This was the first case when the
described method was applied to identify the earth
quakeprone area in a region of moderate seismicity,
with the threshold magnitude of the strong earth
quakes M0 = 5.0. The recognition was carried out for
the intersections of the morphostructural lineaments.
The seismicprone area consists of the circles with
radius r = 25 km whose centers are located at the inter
sections classified as D (Weber et al., 1985; Cisternas et
al., 1985). This area is shown in Fig. 6. The epicenters
of the strong seismic events that occurred after obtain
ing the results (1985) are also indicated in the figure.
It follows from Fig. 6 that six strong earthquakes
have occurred in the region since the time of the solu
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RECOGNITION OF EARTHQUAKEPRONE AREAS
161
5
46° N
Milan
Turin
44° N
Venice
8
Bologna
Genoa
2
Florence
4
7
3
Rome
42° N
1
Bari
Naples
40° N
6
Palermo
38° N
36° N
8° E
10° E
12° E
14° E
16° E
18° E
Fig. 4. The scheme of the lineaments in Italy; the earthquakeprone area (contoured by the thick lines) determined according to
(Gorshkov et al., 1979; Caputo et al., 1980), and the epicenters of the strong (M ≥ 6.0) earthquakes that occurred after 1979 (the
black dots with the numbers corresponding to Table 1).
tion. The epicenters of five of these events fall in the
earthquakeprone area. One epicenter (no. 5 in
Table 1) is located in the vicinity of an Dclass inter
section where strong earthquakes have not occurred
previously. The epicenter of one earthquake (no. 5 in
Table 1) is located in the vicinity of the intersection
related to class N.
Pyrenees. In this region marked with moderate
seismicity, the threshold magnitude of the strong
earthquakes is M0 = 5.0. The intersections of the mor
phostructural lineaments were used as the recognition
objects. The earthquakeprone area is composed of
circles with radius r = 25 km and the centers located at
the intersections related to the Dclass (Gvishiani,
Gorshkov, and Kossobokov, 1987; Gvishiani et al.,
1987a; 1987b). This area, together with the epicenters
of the earthquakes that occurred after obtaining the
results (1987), is shown in Fig. 7.
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Since the solution of the recognition problem, the
region has been hit by six strong earthquakes. The epi
centers of five of them fell in the predicted earthquake
prone areas, and one of these epicenters was located in
the vicinity of the intersection related to the Dclass,
where strong earthquakes have not occurred previ
ously. The epicenter of one earthquake (no. 4 in
Table 1) is located in the vicinity of the epicenter
related to the Nclass.
Greater Caucasus. The problem of recognition for
this region was solved for different sets of recognition
objects and threshold magnitudes of the strong earth
quakes: (1) morphostructural nodes, M0 = 6.5 (Gvish
iani et al., 1986); (2) morphostructural nodes, M0 =
5.5 (Gvishiani et al., 1987c); (3) intersections of the
morphostructural lineaments, M0 = 5.0 (Gvishiani
et al., 1988). Here, we compare the results of recogni
tion of the intersections (M0 = 5.0) with the locations
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SOLOVIEV et al.
2° N
Quito
2° S
6° S
10° S
Lima
4
14° S
3
La Pas
18° S
22° S
2
26° S
occurred in the region. All their epicenters fall
in the earthquakeprone area. Nine of them are
located in the vicinities of the intersections related to
the Dclass, where strong earthquakes have not
occurred previously.
Himalaya. The threshold magnitude of the strong
earthquakes here is M0 = 6.5. The recognition was car
ried out for the intersections of the morphostructural
lineaments. The area prone to the strong earthquakes
is composed of circles with radius r = 50 km and the
centers at the intersections related to the Dclass
(Bhatia et al., 1992a; 1992b). This area and the epi
centers of the strong earthquakes that occurred in the
region after obtaining the results of recognition (1992)
are shown in Fig. 9.
From Fig. 9 it follows that since the solution of the
problem, the region was hit by four strong earth
quakes, and the epicenters of three of them fell in the
predicted earthquakeprone areas. The epicenter of
one such event was located in the vicinity of the inter
section of the Dclass, where strong earthquakes were
previously absent. One epicenter (no. 4 in Table 1) is
located outside the vicinities of the intersections but in
the immediate proximity of the boundary of the earth
quakeprone area.
In the other seismically active regions, where rec
ognition of the earthquakeprone and low seismic
areas was carried out, strong earthquakes have not
occurred after obtaining the corresponding results.
30° S
1
Santiago
34° S
5
360° S
84° W
80° W
76° W
72° W
68° W
Fig. 5. The scheme of the lineaments in the South Ameri
can Andes; the earthquakeprone area (contoured by the
thick lines) determined in accordance with (Gvishiani
et al., 1982; Gvishiani and Soloviev, 1984), and the epicen
ters of the strong (M ≥ 7.75) earthquakes that occurred
after 1982 (the black dots with the numbers corresponding
to Table 1).
of the epicenters of the earthquakes with M ≥ 5.0 that
have occurred since 1988 (Fig. 8). The earthquake
prone area is formed of circles of radius r = 25 km with
their centers located at the intersections classified as D
(Gvishiani et al., 1988).
From Fig. 8 it follows that since the time of the
solution of the problem, 13 strong earthquakes have
4. THE ANALYSIS OF SEISMICITY
IN CALIFORNIA BY DISCRETE
PERFECT SETS ALGORITHM
The method for recognizing areas prone to the
strong earthquakes described above has some disad
vantages, which include the necessity to construct the
scheme of morphostructural lineaments and to use the
training sample of the objects of recognition; in addi
tion, the earthquakeprone areas recognized by this
method are too large. Therefore, the attempts to
design new methods for recognizing the seismicprone
areas are quite reasonable. One such method is based
on applying the Discrete Perfect Sets (DPS) algorithm
(Agayan, Bogoutdinov, and Dobrovolsky, 2011) to the
analysis of seismicity. This algorithm is applied to the
set of the epicenters of relatively weak regional earth
quakes with M ≥ Mb, where the threshold Mb is signif
icantly lower than M0. This results in identifying the
clusters of epicenters whose union is considered as the
earthquakeprone area.
The clusters of the epicenters of the earthquakes
with M ≥ 3.0 that occurred in California in 1980–2011
are shown in dark gray in Fig. 10 (Gvishiani et al.,
2013a; 2013b). The analyzed set of the epicenters is
compiled from two catalogs: the earthquake catalog of
the Northern California Earthquake Data Center
(NCEDC) accessible at http://www.ncedc.org/
ncedc/catalogsearch.html and the catalog of the
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RECOGNITION OF EARTHQUAKEPRONE AREAS
Zurich
163
4
47° N
3
5
46° N
6
Lyon
Milan
Turin
45° N
2
1
Genoa
44° N
5° E
6° E
7° E
8° E
9° E
10°E
Fig. 6. The scheme of the lineaments of the Western Alps; the earthquakeprone area (contoured by the thick lines) in accordance
with (Weber et al., 1985; Cisternas et al., 1985), and the epicenters of the strong earthquakes (M ≥ 5.0) that occurred after 1985
(the black dots with the numbers corresponding to Table 1).
44° N
Toulouse
Bilbao
6
43° N
3
4
2
1
Pamplona
5
42° N
Zaragoza
Barcelona
3° W
2° W
1° W
0°
1° E
2° E
3° E
4° E
Fig. 7. The scheme of the lineaments in Pyrenees; the earthquakeprone area (contoured by the thick lines) determined in accor
dance with (Gvishiani et al., 1987a; 1987b; 1987), and the epicenters of the strong earthquakes (M ≥ 5.0) that occurred after 1987
(the black dots with the numbers corresponding to Table 1).
Southern California Earthquake Center (SCEC)
(http://www.data.scec.org/ftp/catalogs/SCEC_DC/).
Merger of these catalogs yields some duplicated infor
mation for some events; however, this does not affect
the obtained clusters due to the specificity of the DPS
algorithm.
Figure 11 illustrates the comparison of the obtained
clusters with the earthquakeprone area (Fig. 3)
according to (Gelfand et al., 1976a; 1976b). The com
parison shows that the total area covered by the clus
ters is noticeably smaller than the earthquakeprone
area (Fig. 3), and almost all clusters are located within
IZVESTIYA, PHYSICS OF THE SOLID EARTH
Vol. 50
this area. We note that the only epicenter of the strong
earthquake that fell outside of the recognized earth
quakeprone area in Fig. 3 (event no. 12 with M = 6.5
that occurred on December 22, 2003 near San Sim
eon) falls in one of the clusters.
5. CONCLUSIONS
Table 2 summarizes the results of testing the reli
ability of the predictions for the probable occurrence
of the strong earthquakes (the earthquakeprone
areas), which were yielded by the recognition of the
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SOLOVIEV et al.
8
44° N
Anapa
Pyatigorsk
Groznyi
Sochi
Makhachkala
Vladikavkaz
7
Sukhumi
95
11
10
4
1
3
2
6
42° N
Batumi
Tbilisi
12
13
Baku
40° N
38° E
40° E
42° E
44° E
46° E
48° E
50° E
Fig. 8. The scheme of the lineaments in the Greater Caucasus; the earthquakeprone area (contoured by the thick lines) deter
mined in accordance with (Gvishiani et al., 1988), and the epicenters of the strong earthquakes (M ≥ 5.0) that occurred after 1988
(the black dots with the numbers corresponding to Table 1).
36° N
3
34° N
32° N
1
2
30° N
28° N
Katmandu
4
26° N
74° E
76° E
78° E
80° E
82° E
84° E
86° E
88° E
90° E
92° E
94° E
96° E
Fig. 9. The scheme of the lineaments in the Himalaya; the earthquakeprone area (contoured by the thick lines) determined in
accordance with (Bhatia et al., 1992a; 1992b), and the epicenters of the strong earthquakes (M ≥ 6.5) that occurred after 1992
(the black dots with the numbers corresponding to Table 1).
intersections of the morphostructural lineaments.
After obtaining these results, 91 strong earthquakes
have occurred in these regions. The epicenters of
79 events (87%) fall in the earthquakeprone areas.
The epicenters of 27 of these earthquakes are located
within the vicinities of the intersections related to the
Dclass, where strong seismic events were previously
absent. The test study provides the arguments indicat
ing that the results of the recognition of the earth
quakeprone areas are reliable.
In the case of California, the correlation of the
earthquakeprone area, which was recognized by Gel
fand et al. (1976a; 1976b), to the clusters of the epi
centers revealed by the DPS algorithm by Gvishiani
et al. (2013a; 2013b) provides an additional argument
supporting the reliability of the results yielded by two
different methods. It appears reasonable to apply these
methods when solving the problems associated with
seismic risk assessment.
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RECOGNITION OF EARTHQUAKEPRONE AREAS
165
Table 2. Summary results of testing the reliability of recognition of the earthquake prone areas
Region and year
of completion of the study
M0
Tien Shan and Pamir, 1972
Balkans, Asia Minor,
and Transcaucasia, 1974
California and Nevada, 1976
Italy, 1979
South American Andes, 1982
Kamchatka, 1984
Western Alps, 1985
Pyrenees, 1987
Greater Caucasus, 1988
Himalaya, 1992
Total
6.5
6.5
Number of the strong earthquakes in the region
Radius r
after obtaining the results of the prediction
of the vicinity
in the Narea
of the intersection, total in the Darea
(including in in the Narea (outside the vicinities
km
number
the D*area)
of the intersections)
40
7
6 (1)
0
1
40
27
25 (7)
1
1
6.5
6.0
7.75
7.75
5.0
5.0
5.0
6.5
25
35
75
75
25
25
25
50
14
8
5
1
6
6
13
4
91
13 (4)
4 (1)
4 (2)
1
5 (1)
5 (1)
13 (9)
3 (1)
79 (27)
0
0
1
0
1
1
0
0
4
1
4
0
0
0
0
0
1
8
* In that part of the Darea where the epicenters of the strong earthquakes have not been known before the solution of the problem.
42° N
13
7
40° N
Sacramento
38° N
2
San Francisco
4
6
3
36° N
12
11
10
34° N
9
8
Los Angeles
San Diego
5
Mexicali
1
14
32° N
124° W
122° W
120° W
118° W
116° W
Fig. 10. The results of application of DPS algorithm in order to cluster the epicenters of the earthquakes with M ≥ 3.0 that
occurred in California in 1980–2011. The epicenters are shown by the gray dots; the recognized clusters are shaded in dark gray.
The epicenters of the strong earthquakes (M ≥ 6.5) that occurred after 1976 are shown by the black dots with the numbers corre
sponding to Table 1.
IZVESTIYA, PHYSICS OF THE SOLID EARTH
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SOLOVIEV et al.
42° N
13
7
40° N
Sacramento
38° N
2 4
San Francisco
6
3
36° N
12
11
10
9
8
34° N
Los Angeles
San Diego
5
1
Mexicali
14
32° N
124° W
122° W
120° W
118° W
116° W
Fig. 11. The comparison of the clusters determined by the DPS algorithm (gray) with the earthquakeprone area (contoured by
the thick lines) recognized in (Gelfand et al., 1976a; 1976b). The epicenters of the strong (M ≥ 6.5) earthquakes that occurred
after 1976 are denoted by the black dots with the numbers corresponding to Table 1.
ACKNOWLEDGMENTS
The work was partially supported by Basic
Research Program 7 of the Earth Science Department
of the Russian Academy of Sciences (“Geophysical
Data: Analysis and Interpretation”) and by the Rus
sian Foundation for Basic Research (grant no. 1205
92699IND_a).
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Translated by M. Nazarenko
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