APPENDIX I
Methodology
Delineation of the nodes with the morphostructural zoning method(MZ)
The MZ is based on the idea that the lithosphere is built up by different-scale blocks separated by mobile boundaries and earthquakes are generated due to the relative movement of the blocks (e.g. Keilis-Borok 1990). The MZ has been especially developed with a goal to delineate the block structure of a region that was created at the latest stages of tectonic evolution. The youngest tectonic deformations built the present-day topography in tectonically/seismically active regions. Therefore the topography features are the main subject of the analysis in MZ.
In MZ the target region is divided into a system of hierarchically ordered areas characterized by homogeneous present-day topography and tectonic structure. MZ distinguishes (1) areas of different rank, called blocks; (2) their boundary zones, called morphostructural lineaments; and (3) sites where lineaments intersect, called nodes.
All elements of the hierarchical system compose a single system. A morphostructural lineament is viewed as a boundary zone between areas delineated by MZ. The rank of the lineament is determined by the rank of an area bounded by it. MZ differs from the standard morphostructural analysis (e.g. Korzhuev, 1974) where the term “lineament” (Hobbs, 1911) was defined as the complex of alignments detectable on topographic and geological maps. According to that definition the lineament is locally defined and the existence of the lineament does not depend on the surrounding areas. In MZ, the primary element is the block – a relatively homogeneous area, while the lineament is a secondary element of the morphostructure. A morphostructural lineament is viewed as a boundary zone between blocks. Therefore, the existence and the position of the lineaments are determined not locally, but as a part of a broad pattern. If a certain alignment does not separate two topographically different areas, that alignment cannot be viewed as a lineament in MZ.
In the Iberian Peninsula, large-scale geostructures such as the Pyrenees or Betics developed within the collisions zones by a common orogenesis and characterized by uniform relief are considered the highest first rank units, called mountain countries. First rank unit areas can be also delineated in intraplate terrains. In Iberia some of the major morphostructures, developed within the Hercynian basement are represented by basins with a flat topography. The largest of them, like the Ebro basin, are classified by MZ as first rank areas that we call macroblocks, in order to distinguish them from mountain country units. Mountain countries and macroblocks are divided into second rank areas, megablocks, which are further subdivided into third rank areas, blocks.
A morphostructural lineament is viewed as a boundary zone between territorial units delineated by MZ. Actually, a lineament is the superficial expression of a zone of tectonic deformations and/or zone of tectonic weakness of the crust. The rank of the lineament is determined by the rank of a territorial unit bounded by it, according to the hierarchical procedure of MZ. Morphostructural lineaments are linear zones (not lines) of tens, usually hundreds of kilometers long and of few, sometimes tens of kilometers wide. The lineament width depends on the character and intensity of the tectonic motion and indicates indirectly the rank of morphostructures involved. With respect to the regional trend of the tectonic structure and topography, one can distinguish the longitudinal and transverse lineaments. Longitudinal lineaments are approximately parallel to the regional trend of the tectonic structure and of the topography and, as a rule, include the prominent faults. In general, they are more evident than transverse lineaments. Transverse lineaments go across the regional trend of the tectonic structure and of the topography. Normally, they appear on the Earth’s surface as a discontinuous chain of tectonic escarpments, rectilinear parts of river valleys, and partly faults.
Higher rank lineaments include the wider zone of deep-seated deformation.For instance, Gvishiani et al. (1988) for the Caucasus and Cisternas et al. (1985) for the Western Alps demonstrated that first and second rank lineaments can be associated with considerable changes in the thickness and in the configuration of Moho discontinuity, while third rank lineaments correspond to the escarpments in the crystalline basement. The real size of the lineament zone can be mapped from fieldwork; according to our experience, the width of the first rank lineaments, for example, varies from 5 – 8 km to 25 – 30 km (Gvishiani et al. 1988). Additionally, the width of this complex zone may vary along a given lineament.
Morphostructural nodes (from here on, nodes) are formed around the intersections or junctions of two or more lineaments. A node may include more than one intersection or junction (Gvishiani et al. 1988). Lineament zones become wider at nodes. Nodes are characterized by a mosaic combination of various topographic forms and by an increased number of linear topographic forms of various strikes that reveal the instability of the area. Stream offsets and topographic breaks of slopes are characteristic features of a node. In the vicinity of nodes, tectonic faults branch and/or become bent; sometimes a fault system with one orientation merges into a fault system with another orientation.
Identification of seismogenic nodes with the pattern recognition
The use of pattern recognition approach suggests that nodes already marked by one or more strong earthquakes might have a similar portrayal that can be used to identify nodes, which did not yet explicitly show up as earthquake-prone. The goal of the recognition is to classify all the nodes delineated within a region into the two classes:
(1)class D containing the nodes where earthquakes with magnitude MM0 may occur;
(2)class N containing the nodes where only earthquakes with MM0 may occur.
Nodes are characterized by a set of topographical, geologic, and geophysical parameters. A vector of values of these parameters represents each node. The set of these vectors is the input for the recognition algorithms.
In this work we used the CORA-3 and CLUSTERS pattern recognition algorithms (Gelfand et al. 1976; Gvishiani et al. 1988; Gorshkov et al. 2003).
Application of the CORA-3 algorithm consists of the following two steps:
(1)Learning step - selection of the distinctive features of each class on the basis of the training set composed by D0 and N0 subsets, which are constituted by all the sample nodes representative of the classes D and N, respectively (the training set N0 may also contain nodes that potentially belong to class D);
(2) Classification step – determination of the class to which each node belongs.
The distinctive features (characteristic traits) for classes D and N are selected at the learning stage as follows. Let l be the number of components of the binary vectors representing the node. The trait is a matrix A defined as:
,
where i1, i2, i3 are natural numbers, such that 1 i1i2i3l and 1, 2, 3 are equal to 0 or to 1. A node (binary vector) numbered i, i = (1i, 2i, ...,li) posses the trait A if
The characteristic traits are selected with four parameters of the algorithm, , which must be integer non-negative values. Let W be the set of all the nodes considered and K(W, A) the number of nodes iW that posses the trait A. The trait A is a characteristic trait of class D, when K(D0, A) k1 and K(N0, A) , and the trait A is a characteristic trait of class N, when K(N0, A) k2 and K(D0, A) . The classification is made as follows. For each node i the algorithm calculates the number nDi of the characteristic traits for class D, the number nNi of the ones for class N, and the difference i = nDi - nNi. Class D includes the nodes i for which iwhile class N includes the nodes for which i. and as well as are the parameters of the algorithm.
The second algorithm,CLUSTERS, is a modification of CORA-3 (Gelfand et al. 1976; Gorshkov et al. 2003), and it is useful when there is ambiguity in attributing an epicenter to a certain node.
Let Kbe the number of epicenters. Each epicenter defines a subclass D0k consisting of points located at distances that do not exceed r (k= 1, 2, ..., K). A subclass may consist of one or many natural objects. The training set of class D includes all D0k (k= 1, 2, ...,K). The condition D0D must be modified. Specifically, CLUSTERS uses Ksubsets = D01D02 ... D0K, instead of D0; each must have a vector that belongs to D, although some vectors from may belong to N; the same vector may enter several times.
The learning step in CLUSTERS differs from that of CORA-3. First, by definition, a subclass has a trait if it contains a vector with this trait. Some vectors without this trait may belong to this subclass. Trait A is a characteristic trait of class D if
KS(, A) k1 and K(N0, A)
where KS(, A) is the number of subclasses that have the trait A.
Second, trait A is a characteristic trait of class N if K(N0, A) ≥ and
K(, A) D0 is used here to represent a set of vectors.
Third, the definition of weaker and equivalent traits for characteristic traits of class D is different. A characteristic trait A1 of class D is weaker than a characteristic trait A2 of the same class if any subclass that has the trait A1 also has A2 and there is at least one subclass, which has trait A2 but does not have trait A1. Traits A1 and A2 are equivalent if they are found in the same subclasses.
CLUSTERS forms the sets of characteristic traits of classes D and N like CORA-3. The stage of voting and classification is the same as in CORA-3. However, ∆ is determined from the condition
where, first, the maximum is taken over the vectors belonging to D0k, and, second, the minimum is searched over all Ksubclasses. The classification of a vector wiW is made, as CORA -3.