We used the approach based on a methodology for recognition of possible locations of future large earthquakes (Gelfand et al. 1972) in order to determine tsunamigenic sources; the methodology has been used for a long time to identify potential earthquake-generating nodess. The most recent review of applications of this methodology with a detailed discussion can be found in (Gorshkov and Soloviev 2021). The methodology is efficient, as has been proved by comparing recognition results in the regions of study with the actual relevant earthquakes which have occurred in the regions after the results were published (Gorshkov 2010; Soloviev et al. 2014; Gorshkov and Novikova 2018).
The methodology is based on the idea that large earthquakes tend to occur at nodess of fault zones. The procedure consists of two stages. The first stage involves the application of morphostructural zoning (MSZ) to find the locations of morphostructural nodes which are treated as earthquake-controlling structures (Alekseevskaya et al. 1977; Rantsman 1979).
Morphostructural zoning is based on the concept of a hierarchical block structure of the Earth's crust. The MSZ maps show blocks of three hierarchical levels. The lower level (the third rank) consists of blocks with similar values of information-bearing relief features (altitude level and the orientations of linear relief forms). The boundaries between blocks, or morphostructural lineaments, are assumed to run where at least one feature experiences a sharp and significant change. These blocks are combined to form megablocks that represent the second hierarchical level. If the values of information-bearing features change in a monotone manner from block to block, then the boundaries between megablocks are taken to be where this monotonicity breaks down. The largest zoning unit of the first rank, a mountain country, is an area having a uniform type of relief and the same type of orogenesis. The lineaments are assigned the rank of those morphostructures which they separate.
Morphostructural nodes are a special kind of morphostructures which are formed at intersections of morphostructural lineaments that separate crustal blocks. The natural boundaries of nodes can be determined by detailed field surveys (Rantsman 1979; Gvishiani et al. 1988). In cases where the natural intersection boundaries are not determined, then nodes are defined as vicinities of nodes of lineaments in a circle of some radius, approximately equal to the earthquake source size appropriate for the magnitude under consideration.
The second stage involves discrimination of the nodes found by MSZ into high and low seismicity ones relative to a specified magnitude threshold. Nodes are classified using methods of pattern recognition (Bongard 1967). This is done using recognition algorithms, e.g., the Cora-3 logical-type learning algorithm (Gelfand et al. 1972; Gvishiani et al. 1988; Gorshkov et al. 2003).
The problem of identifying tsunamigenic nodes is formulated in this study similarly to the problem of recognizing high and low seismicity nodes. The objects of recognition are the nodes found by MSZ (Fig. 2). Tsunami-generating earthquakes can emanate from several of the nodes identified by MSZ in the region (Fig. 2). The problem is to find criteria (a decision rule) from geomorphologic parameters to distinguish tsunamigenic nodes (the TsG class) from non-tsunamigenic ones (the NTsG class). The decision rule is worked out during the training stage for the Cora-3 algorithm. The training sample for the TsG class is based on the information concerning documented tsunamigenic earthquakes. The decision rule separates all nodes into the TsG and NTsG classes.
2. The data set
2.1. The morphostructural nodes in mainland Greece
We determined the morphostructural nodes in the region of study earlier to deal with the recognition of earthquake-generating nodes where М7+ earthquakes can occur (Gorshkov et al. 2020). A MSZ map for mainland Greece to scale 1: 1 000 000 is shown in Fig. 2.
The relief of the territory is dominated by mountain ranges of the Hellenides mountain belt; their structure and present-day configuration was formed by a complex interaction of the African and Eurasian plates (McKenzie 1970). The Hellenic belt divides into the northern part (the Pindus mountains) and the southern, which occupies the Peloponnese Peninsula (see Fig. 2). They are separated by the Gulf of Corinth which fills the basin of a young Quaternary rift (Armijo et al. 1996). Lineaments of the first rank separate the Hellenides mountain country from the adjacent major geostructures of the first rank. In the west, east, and south, lineaments of the first rank separate the Hellenides from the deep-sea basins of the Ionic, Aegean, and Cretan seas, respectively (Fig. 2). These lineament zones follow along the continental slope and include major tectonic faults (Kilias et al. 2002).
Lineaments of the second rank separate territorial units of the second rank (megablocks). Five megablocks have been identified with different altitude levels and the strikes of the large constituent relief elements. The mega-blocks are discussed in (Gorshkov et al. 2020). The megablock that includes the Peloponnese is separated from the mega-blocks of central Greece by a transverse lineament of the second rank which can be followed along the active southern side of the Gulf of Corinth (Armijo et al. 1996). The lineament extends westward across the Gulf of Patras.
Lineaments of the third rank separate blocks. They can be followed by observing sharp changes in the altitude and strike of large relief elements. The relief of the area of study is heavily dissected, so that a dense network of rank 3 transverse lineaments has been identified striking northeast and nearly east--west; they cut obliquely through the north--northwestern trend of the Hellenides mountain ranges (Fig. 2).
MSZ has identified 139 nodes (Fig. 2) whose boundaries are defined as circles of radius 30 km around intersections of lineaments.
2.2. The tsunamigenic earthquakes in Greece
The information on the tsunamigenic earthquakes in the region was taken from the Global Historical Tsunami Database (http://www.ngdc.noaa.gov/hazard/tsu_db.shtml), which has a separate section on Mediterranean tsunamis. A description of the data base along with other tsunami data bases and the principles underlying their creation can be found in (Goff 2020).
This data base contains parameters of tsunamigenic earthquakes (date, geographic coordinates, magnitude, and depth of focus) and characteristics of the tsunamis themselves (intensity and runup). The reliability of the raw data on each event is given by a numeral on a scale from -1 to 4. Tsunami intensity is given on the Soloviev-Imamura scale (Soloviev 1972; Soloviev and Go 1974) based on average runup values on the coast that was the nearest to the epicenter. Each event is supplied with a reference to a source describing the event. The depths of focus in the data base are available for recent earthquakes only. Papadopoulos and Chalkis (1984) say that the absolute majority of tsunamigenic earthquakes in Greece were at depths of 10--15 km in the crust, and it was only occasionally that hypocentral depths could reach 70 km.
There is no unambiguous relationship between tsunami intensity and the magnitude of the responsible earthquake (Soloviev 1990; Levin et al. 2005). Smaller earthquakes occasionally give rise to greater tsunami intensities than events of higher magnitudes. Bearing this in mind, we selected the training material for the Cora-3 recognition algorithm to identify tsunamigenic nodes by relying on tsunami characteristics rather than the responsible earthquake. The Cora-3 algorithm was trained by earthquakes and associated tsunamis for which the reliability factor was greater than 1 and tsunami intensity was ≥ 3. With this intensity, the mean wave height could reach 5.7 meters according to the Soloviev relation, which can pose immediate threat to coastal communities and infrastructure.
A list of events such as specified above is given in Table 1, and their epicenters are displayed in a map of morphostructural zoning (Fig. 2). It is apparent from this figure that the epicenters of these tsunamigenic earthquakes lie close to nodes of morphostructural lineaments to be treated as morphostructural nodes.
Table 1. The tsunamigenic earthquakes in Greece (http://www.ngdc.noaa.gov/hazard/tsu_db.shtml)
Year
|
north latitude
|
east longitude
|
M
|
Intensity
|
Source
|
-426
|
38.9
|
22.7
|
Ms,7.1
|
5
|
Freitag and Reicherter 2019
|
-373
|
38.25
|
22.25
|
Ms, 7.3
|
5
|
Papadopoulos 2000
|
551
|
38.4
|
22.3
|
7.1
|
4
|
Ambraseys 2009
|
1402
|
38.11
|
22.41
|
7
|
5
|
Soloviev et al. 2000
|
1817
|
38.3
|
22.1
|
Ms, 6.8
|
3
|
Galanopoulos 1960
|
1861
|
38.2
|
22.2
|
7.3
|
4
|
Galanopoulos 1960
|
1866
|
36
|
23
|
Ms, 6
|
4
|
Ambraseys 1962
|
1867
|
36.4
|
22.2
|
Ms, 7.1
|
4
|
Ambraseys 1962
|
1881
|
38.4
|
21.4
|
6.5
|
3
|
Papadopoulos 2000
|
1894
|
38.7
|
23.1
|
Ms, 7
|
4
|
Galanopoulos 1960
|
1915
|
38.5
|
20.7
|
Ms, 6.7
|
3
|
Galanopoulos 1960
|
1948
|
38.53
|
20.42
|
Mw, 6.5
|
4
|
Galanopoulos 1960
|
2.3 The nodes parameters used for recognition
We did recognition of tsunamigenic nodes using those parameters which we employed to recognize those earthquake-generating nodes in mainland Greece which can produce М7+ earthquakes (Gorshkov et al. 2020). The parameters used to recognize tsunamigenic nodes (Table 2) include morphometric terrain indicators and the geometry of the lineament-and-block structure of the region under study as displayed in the map of morphostructural zoning shown in Fig. 2. We also included a parameter defined as the fraction of unconsolidated Quaternary deposits within an intersection. Taken as a whole, these parameters provide indirect data to characterize the intensity of tectonic movements and the degree of crustal fragmentation at nodes. The parameters were found by inspection of topographic and geological maps, as well as the MSZ map. The parameter values were measured in a circle of radius 30 km treated as a node and which is centered at the intersection.
Table 2. The parameters that were used for recognition of tsunamigenic nodes
Parameters
|
Discretization thresholds
|
Morphometric parameters
|
|
Maximum relief altitude, m (Hmax)
|
1600
|
Minimum relief altitude, m (Hmin)
|
- 106
|
Altitude range, m (ΔH) (Hmax - Hmin)
|
1952
|
Distance between points of Hmax and Hmin, km (L)
|
32
|
Altitude gradient, (ΔH/L)
|
63
|
Geological parameter
|
|
Percentage of Quaternary deposits in % at a node (Q)
|
20
|
Geometry of lineament-and -block structure
|
|
Highest rank of lineament at a node, (HR)
|
2
|
Number of lineaments that make an a node, (NL)
|
2
|
Distance between intersection and nearest lineament of first rank, km, (D1)
|
50
|
Distance between intersection and nearest lineament of second rank, km, (D2)
|
30
|
Distance to nearest intersection at adjacent intersection, km, (Dn)
|
21
|
The Cora-3 recognition algorithm used in this study (Bongard 1967; Gvishiani et al. 1988; Gorshkov et al. 2003; Gorshkov 2010) is applied to objects in the form of binary vectors. For this reason the application of the recognition algorithm is preceded by parameter discretization to divide the entire range of a parameter using discretization thresholds into two or three intervals so that each interval should contain approximately the same number of recognition objects. Afterwards, the algorithm deals, not with measured parameter values, but with the fact of falling in an interval: "small" and "large" in the case of two intervals, and "small, "intermediate", and "large" when there are three intervals. The discretization thresholds for each parameter are listed in Table 2. The discretization procedure is described in detail in (Gvishiani et al. 1988; Gorshkov et al. 2003).
3. Recognition Of Tsunamigenic Nodes
The training material for the Cora-3 algorithm was based on the information for the tsunamigenic earthquakes in the study region; see the list in Table 1.
The set of recognition objects for mainland Greece included 139 nodes. The training sample TsG0 of the tsunamigenic class had 12 nodes: 71, 72, 83, 84, 86, 90, 91, 98, 139,140, 145, and 150 (Fig.3). The remaining 127 nodes made the training material NTsG0.
Recognition results. The characteristic features for nodes in class TsG and class NTsG as selected by Cora-3 during the training phase are listed in Table 3. The intervals of parameter values in Table 3 are specified by the discretization thresholds.
The classification of nodes into classes TsG and NTsG was produced by Cora-3 using a voting procedure. For each intersection the algorithm counts the numbers of features for each class that a current intersection has. Tsunami-generating nodes are recognized to be those for which the difference between the number of features in class TsG and that in class NTsG was ≥1. As a result, of the 139 nodes in the region, 27 were classified as being tsunamigenic ones, including the 12 that were used for training in class TsG.
Table 3. Characteristic features of tsunamigenic (TsG) and non-tsunamigenic (NTsG) nodes
PARAMETERS (for notation see Table 2)
|
FeatureN
|
Hmax,
m
|
Hmin,
m
|
L,
km
|
dH,
m
|
dH/L
|
Q,
%
|
NL
|
D1
km
|
D2,
km
|
Dn,
km
|
HR
|
features of nodes in class TsG
|
|
1
|
|
≤-106
|
|
|
|
|
|
|
|
>21
|
>2
|
2
|
|
|
|
|
|
|
>2
|
>50
|
|
|
≤2
|
3
|
|
≤-106
|
>32
|
|
|
|
|
|
≤30
|
|
|
4
|
≤1600
|
|
>32
|
|
|
|
|
|
≤30
|
|
|
5
|
|
≤-106
|
|
|
|
≤20
|
|
>50
|
|
|
|
6
|
≤1600
|
|
|
>1952
|
|
|
>2
|
|
|
|
|
7
|
|
|
>32
|
|
>63
|
|
|
≤2
|
|
|
|
8
|
|
≤-106
|
≤32
|
>1952
|
|
|
|
|
|
|
|
9
|
≤1600
|
|
>32
|
|
>63
|
|
|
|
|
|
|
features of nodes in class NTsG
|
|
1
|
|
|
|
|
≤63
|
|
|
|
|
≤21
|
|
2
|
|
|
≤32
|
|
|
|
|
|
≤30
|
|
|
3
|
|
|
≤32
|
|
|
|
|
>50
|
|
|
|
4
|
|
|
≤32
|
|
>63
|
|
|
|
|
|
|
5
|
|
|
≤32
|
≤1952
|
|
|
|
|
|
|
|
6
|
>1600
|
|
≤32
|
|
|
|
|
|
|
|
|
7
|
|
>-106
|
|
|
|
|
|
|
|
|
|
The reliability of the resulting classification was checked by three control experiments (Gelfand et al. 1972; Gvishiani et al. 1988). In the first experiment, the training material TsG0 and NTsG0 consisted in the nodes recognized as being TsG and NTsG in the main variant shown in Fig. 3. Overall, the classifications obtained by the experiment were identical with the main variant. In the other two experiments, recognition objects were excluded one by one from the training, and in the same manner the parameters of these objects, one by one. The classifications obtained in these experiments show some insignificant departures from the main variant. The results of the experiments are adjudged to be positive, since less than 10% of the objects changed classification; this is consistent with the empirical criteria for stability as formulated in (Gvishiani et al. 1988), and one can say that the resulting classification of nodes into tsunamigenic and non-tsunamigenic ones is stable.