Computer-based self-organized tectonic zoning revisited: Scientific criterion for determining the optimum number of zones

Tectonophysics 510 (2011) 207–216

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Tectonophysics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t e c t o

Computer-based self-organized tectonic zoning revisited: Scientific criterion for determining the optimum number of zones Ahmad Zamani a,⁎, Marziyeh Khalili a, Abbas Gerami b a b

Department of Earth Sciences, College of Sciences, Shiraz University, Shiraz, Iran School of Mathematics, Statistics and Computer Sciences, Tehran University, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 5 February 2011 Received in revised form 30 June 2011 Accepted 7 July 2011 Available online 20 July 2011 Keywords: Optimum zoning Stopping rule Wilk's Lambda Seismotectonics Neotectonics Iran

a b s t r a c t As multivariate numerical classification become increasingly available to Earth Scientists, there is a corresponding need to introduce a scientific criterion or stopping rule to determine the optimum number of classifications. The increasing interest in comparative, experimental numerical zoning makes such a criterion highly desirable. In this research multivariate data comprising new and updated geological and geophysical characteristics of Iran have been used to construct Automatic Integrated Self-Organized Optimum Zoning (AISOOZ) maps. The Wilk's Lambda Criterion and the relative discrepancy of Wilk's Lambda have been applied for the first time as stopping rules to measure the relative usefulness of zoning maps. The application of these criteria has eventually led to an optimum map with 11 zones. Our AISOOZ map reveals some remarkable features that cannot be observed on conventional tectonic maps of Iran. For example: contrary to the conventional maps, the AISOOZ map reveals the much disputed extent and rigidity of the microplate in the central and eastern parts of Iran and makes a clear distinction between the Makran ranges and the eastern Iran mountains. The AISOOZ method is a new approach to zoning, organized in a hierarchy of increasing complexity, and developed from reductionist approach. Based on this logic, the AISOOZ method casts an interesting light on the connection between the zoning hierarchy and the geodynamic evolution of the study area. It also helps to estimate the likelihood of earthquake occurrence for each zone. The AISOOZ map not only can be re-assessed quite often, but also provides us with a means for online information availability. The information can be tailored to the user's specific needs and down-loaded to the user's computer. Furthermore, the general approach presented in this paper could readily be adapted to pattern recognition and zoning maps of any space, regardless of context or scale. © 2011 Elsevier B.V. All rights reserved.

1. Introduction A major task in the Earth Sciences is to map any desired surface or subsurface part of the Earth characterized by similar geological history and development (Aghanabati, 1986, 2004; Alavi, 1991, 1994; Berberian, 1976, 1979, 1983; Berberian and King, 1981; Berberian and Yeats, 1999; Davoudzadeh et al., 1986; Davoudzadeh and Weber-Diefenbach, 1987; Eftekharnezhad, 1980; McCall, 1996; Nowroozi, 1971, 1976, 1979; Stöcklin, 1968; Stöcklin and Nabavi, 1973) (Fig. 1). Typically, the attribute measurements gathered are not only correlated with each other, but each attribute is also influenced by the other attributes. Thus, in many instances the attributes are interwoven in such a way that when analyzed individually they yield little information about the region under investigation. In the past, geologists have primarily dealt with conventional maps on the basis of their appearance. However the development of more sophisticated technol-

⁎ Corresponding author. Tel./fax: + 98 71 2284572. E-mail address: [email protected] (A. Zamani). 0040-1951/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2011.07.004

ogy to collect numerical data has outpaced geologists' ability to use it to full potential (Zamani and Hashemi, 2004; Zamani and Khalili, 2006, hereafter referred to as Ι and ΙΙ respectively). Today, it is common to have massive numbers of observations which contain far more information about the Earth than can be modeled by conventional methods of geologic mapping. Such massive amounts of data require both statistical reduction and the ability to compute theoretical solutions in Earth models with many parameters. Since the publication of the first computer-based self-organized tectonic zoning (Fig. 2) (Ι; ΙΙ) there was a need to come up with some scientific criteria for objective selection of the final or optimum number of zones to be recognized (also known as the stopping rule). In this paper, which is an extension of Ι and ΙΙ, many new and updated geological and geophysical characteristics of Iran have been used to construct computer-based self-organized tectonic zoning maps. For this purpose, Ward's method, which is most intuitive and computationally efficient, was chosen (Duda et al., 2001; Ward, 1963, Ι; ΙΙ). This agglomerative (bottom-up) hierarchical clustering procedure results in tectonic zones of approximately equal size and avoids problems with “chaining” found in other agglomerative methods (Ι; ΙΙ). Perhaps the most

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Fig. 1. Generalized tectonic map of Iran (modified from Stöcklin, 1968; Stöcklin and Nabavi, 1973 by Zamani and Hashemi, 2004).

perplexing issue in computer-based self-organized tectonic zoning using statistical methods is the objective selection of the final number of tectonic zones. In order to alleviate this deficiency, a stopping rule algorithm has been used for determining the final number of zones. To illustrate, Computer-Based Self-Organized Tectonic Zoning maps of Iran have been produced utilizing a large amount of new and updated geological and geophysical characteristics of Iran (Ι, ΙΙ). Finally, by

assessing the statistical significance of differences between tectonic zones the best, in the sense of most generally useful zoning, was identified. 2. Method of analysis Cluster analysis is the generic name for a variety of statistical methods that search for patterns in a set of objects by grouping them

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Fig. 2. Computer-based self-organized tectonic zoning map of Iran. Zones are numbered according to their hierarchical orders. Larger differences between any two zone numbers correspond to greater diversity between their specified characteristics, and vice versa (modified from Zamani and Hashemi, 2004; Zamani and Khalili, 2006).

into clusters (Everitt et al., 2001; Kaufman and Rousseeuw, 1990). The goal is to find an optimal grouping for which the objects within each cluster are similar; however, the groupings are dissimilar. Cluster analysis is useful in all fields that need to make and continually revise classifications. It can be used to help raise interesting scientific questions and research hypotheses that stimulate further research. Cluster analysis is also useful for making decisions in planning and management (Everitt et al., 2001; János and Balázs, 2007). There is a variety of mathematical methods that can be used to perform cluster analysis. Cluster analysis differs from classification analysis. Classification analysis allocates the objects to a known number of predefined groups or populations. Some researchers use the term classification analysis to describe cluster analysis in which the objects are clustered according to attribute values rather than into predefined groups. Cluster analysis is usually referred to as pattern recognition, classification, unsupervised learning and numerical taxonomy (Hair, 2005; Rencher, 2002; Tabachnick, 2006). But, in cluster analysis neither the number of clusters nor the cluster themselves are known in advance. The methods of cluster analysis have been extensively applied to make classifications in many fields. However, perhaps the

most perplexing hurdle for the researcher is determining the final number of clusters to be formed (also called the stopping rule) that provides the best fit to the data (Ansari et al., 2009). We have used Ward's minimum variance index (Duda et al., 2001; Ward, 1963), as a pattern recognition technique to seek and separate zones for which the tectonics within each zone are similar, while the tectonic zones are dissimilar to each other. We do this as we consider Ward's minimum variance index to be more intuitive and computationally efficient than possible alternatives. Because there is no internal statistical criterion used for determining the final numbers of tectonic zones to be formed, researchers have developed several criteria and guidelines for this purpose. The decision to make a selection from the classifications depends on whether we want a general-purpose classification to seek and separate the most basic structures or a specific-purpose classification to be related to a more well-defined and detailed structure (I, II).In Ι and ΙΙ the agglomeration coefficient has been used as a measure for the stopping rule. This semi-qualitative measure examines the similarity or distance between tectonic zones at each successive step, with the zoning pattern defined when the similarity makes a

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sudden jump. The quantitative statistical measures, namely Wilk's Lambda Criterion and the relative discrepancy of Wilk's Lambda are here applied for the first time to seek and separate the optimum number of zones and construct an Automatic Integrated SelfOrganized Optimum Zoning (AISOOZ) map. Wilk's Lambda is also referred to as the maximum likelihood criterion or U statistic is defined as:

/

Λ =jSW j

jSW + SB j

Where SW is the matrix of the sum of the squares of deviations within tectonic zones, and SB is the matrix of the total sum of the squares of deviations between zones (Yin and Tian, 2007). This criterion describes the ratio of the determinants of the within-class and total dispersion matrices. It proved to be a useful diagnostic for measuring the relative usefulness of a general purpose hierarchical numerical tectonic zoning where the number of variables is likely to be large. Wilk's Lambda is a test statistic used in multivariate analysis of variance which measures the discrepancy amongst individuals within groups. The best tectonic zoning has the smallest Wilk's Lambda Criterion (Everitt and Dunn, 1991; Rencher, 2002). Wilk's Lambda and the relative discrepancy of Wilk's Lambda statistical inference procedures take into account both the observed value of each variable as well as correlations between each pair of variables. In doing so, two things should be taken into account. First, the number of clusters should not be very small, because this causes heterogeneity between individuals within each cluster. Second, the number of clusters should not be very large, since this would contradicts with any stratification. Wilk's Lambda and the relative discrepancy of Wilk's Lambda are test statistics applied post-hoc for testing the null hypothesis in multivariate analysis of variance (MANOVA). They test whether there are differences between the means of identified groups of subjects based on more than one dependent variable (Jackson, 1997). More subtly, these statistical tests are effectively performed by the researcher after the experiment has ended. They seek patterns in the data that were not specified a priori. These criteria measure the relative usefulness of a general-purpose tectonic zoning. They can be used to determine the final or optimal partitioning of a data set. The increasing interest in comparative, experimental, and automatic tectonic zoning makes such criteria very desirable. While using the Wilk's Lambda Criterion as a stopping rule is not new, its application to tectonic zoning is a novel approach to this problem. Everitt and Dunn (1991) and Polit (1996) provide more detail about the application and interpretation of this criterion. This statistic takes values between zero and one. Smaller values increase the differences between groups and provide a means to measure the relative usefulness or better grouping of a general purpose numerical tectonic zoning. It should be noted that as the number of zones is increased, the value of this measure will decrease. Let us denote ΛK as Wilk's Lambda statistics based on K tectonic zones (K= 2, 3… n, where n is the maximum number of sites to be classified). In order to obtain an appropriate value for K, we define two criteria: (1) the values of Wilk's Lambda and (2) the relative discrepancy of Wilk's Lambda. The small values of these criteria provide a good value for K. As the number of tectonic zones is increased, similarities shared by members of each zone will be increased and vice versa. Therefore, we need a compromise. This can be done either by considering the absolute value of Wilk's Lambda or by the relative discrepancy of Wilk's Lambda. The smallest value of K, which has Λ K substantially different from Λ 2 … Λ K − 1 and also is not large compared to (Λ K + 1… Λ n), can be regarded an optimum number of tectonic zones. These criteria are useful diagnostics and can be used as statistical inference measures for assessing the statistical significance of differences between tectonic zones. These criteria could be built into computer programs as stopping rules for determining the optimum number of tectonic zones.

3. Data analysis In order to classify zones and construct an Automatic Integrated SelfOrganized Optimum Zoning (AISOOZ) map of Iran, large numbers of new and updated geological and geophysical characteristics (Table 1) have been compiled for the 175 quadrangular sites of 1º area. As in Ι and ΙΙ the quadrangles from west to east are numbered beginning with 1 for the quadrangle between 44° E and 45° E meridians and increasing to 175 for the quadrangle between 61° E and 62° E meridians. In order to perform any multivariate or integrated classifications, the multivariate data matrix first has to be prepared, with rows as cases and columns as

Table 1 Attributes used for constructing Automatic Integrated Self-Organized Optimum Zoning (AISOOZ) map, measured within 1° quadrangular area⁎. No.

Attributes

No.

Attributes

1

a — value in the Gutenberg– Richter's formula, AVGRF b — value in the Gutenberg– Richter's formula, BVGRF Maximum earthquake magnitude(mb), MXEMG Number of earthquakes with mb ≥4.5, NEGMB Number of earthquakes with mb ≤4.5, NESMB Maximum seismic energy released (j), MXSER Range of isostatic anomaly (mgal), RA ISO Average isostatic anomaly (mgal), AVISO Maximum isostatic anomaly (mgal), MXISO Minimum isostatic anomaly (mgal), MIISO Range of regional Bouger anomaly (mgal), RAEGB Average regional Bouger anomaly (mgal), AVREG Maximum regional Bouger anomaly (mgal), MXREG Minimum regional Bouger anomaly (mgal), MIREG Range of residual Bouger anomaly (mgal), RARES

26

Minimum gravity anomaly (mgal), MIGRV Range of free air anomaly (mgal), RAFRA Average free air r anomaly (mgal), AVFRA Maximum free air anomaly (mgal), MXFRA Minimum free air anomaly (mgal), MIFRA Range of magnetic intensity (gamma), RAMGI Average magnetic intensity (gamma), AVMGI Maximum magnetic intensity (gamma), MXMGI Minimum magnetic intensity (gamma), MIMGI Average moho depth (km), AVMOD Range of elevation (m), RAELV Average elevation (m), AVELV Maximum elevation (m), MXELV Minimum elevation (m), MIELV Relative area of surface unconsolidated sediments rocks (%), RAUNR Relative area of surface sedimentary rocks (%), RASER Relative area of surface metamorphic rocks (%), RAMER Relative area of surface igneous rocks (%), RAIGR Relative area of surface ophiolitic rocks (%), RAOPR Relative area of surface Cenozoic rocks (%), RACER Relative area of surface Mesozoic rocks (%), RAMER Relative area of surface Paleozoic rocks (%), RAPAR Relative area of surface Proterozoic rocks (%), RAPTR Fault length density (km−1), FLTLD

2 3 4 5 6 7 8 9 10 11 12 13 14 15

16 17 18 19 20 21 22 23 24 25

Average residual Bouger anomaly (mgal), AVRES Maximum residual Bouger anomaly (mgal), MXRES Minimum residual Bouger anomaly (mgal), MIRES Range of Bouger anomaly (mgal), RABUG Average Bouger anomaly (mgal), AVBUG Maximum Bouger anomaly (mgal), MXBUG Minimum Bouger anomaly (mgal), MIBUG Range of gravity anomaly (mgal), RAGRV Average gravity anomaly (mgal), AVGRV Maximum gravity anomaly (mgal), MXGRV

27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49

⁎ Geological data have been obtained from digitized and regular geological maps of Iran (Geological Survey of Iran, 2004). Seismological data were taken from earthquakes that occurred between the years 1900 up to 2010 (Engdahl et al., 2006; Gutenberg and Richter, 1954; ISC, 2010; NEIC, 2010). Geophysical data have been taken from Dehghani and Makris (1983), total magnetic intensity maps of Iran (Yousefi, 1989), Seismicity and fault map of Iran (Mohajer-Ashjai and Nabavi, 1982) and digital data from Geological Survey of Iran.

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Table 2 Wilk's Lambda (Λ) and the relative Wilk's Lambda discrepancy (ΛK − ΛK + 1)/Λk + 1 calculated for 25 Automatic Integrated self-organized Optimum Zoning (AISOOZ) maps, showing how11 zone model decreases (Λ) and (ΛK − ΛK + 1)/Λk + 1 and gives a better tectonic zoning map. Although these criteria have been calculated for the 175 zoning maps, for the purpose of economy, only the results for 25 maps are presented; however, this does not change the results. Number of zones

Wilk's Lambda

Log Wilks

Wilk's Lambda discrepancy

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

9.66E-02 1.89E-03 4.97E-04 7.33E-05 4.90E-06 1.39E-06 4.56E-07 2.14E-07 6.59E-08 3.00E-08 1.67E-06 5.88E-07 1.97E-07 1.13E-07 4.79E-08 3.38E-08 1.48E-08 7.34E-09 3.33E-09 1.38E-09 8.45E-10 3.47E-10 1.65E-10 6.72E-11

−1.01 −2.72 −3.35 −4.13 −5.31 −5.86 −6.34 −6.67 −7.18 −7.52 −5.78 −6.23 −6.70 −6.95 −7.32 −7.47 −7.83 −8.13 −8.48 −8.86 −9.07 −9.46 −9.78 −10.17

50.13 3.20 5.13 13.95 2.53 2.04 1.13 2.25 1.20 −0.98 1.84 1.98 0.74 1.36 0.41 1.29 1.01 1.20 1.41 0.64 1.44 1.10 1.45 1.99

0

log Wilks Lambda

-2 -4 -6 -8 -10 -12

2

4

6

8

10

12

14

16

18

20

22

24

number of tectonic zones

Fig. 3. Wilk's Lambda criterion (Λ), calculated for Automatic Integrated Self-Organized Optimum Zoning (AISOOZ) maps, showing how 11-zone model decreases (Λ) and gives an optimum number of tectonic zones.

Wilks Lambda discrepancy

variables. Each of the 175 quadrangular cells of 1° area has been considered as a case. Each case has been characterized by 49 attributes or variables that seem to characterize the intensity and degree of contrast between tectonic structures in Iran. Ward's hierarchical clustering technique is used to determine the statistical similarities between quadrangular cases, on the bases of the collective treatment of the geological and geophysical attributes presented in Table 1. The classification procedure starts with “n” tectonic zones (where n = 175 in this paper); each zone consists of one case, and finishes up with one classification containing all cases (Ι; ΙΙ). If there are n cases, then there will be n(n − 1)/2 similarities and the classification will take (n − 1) steps (Duda et al., 2001; Everitt et al., 2001; Hair, 2005). Then the two criteria, namely Wilk's Lambda Criterion and the relative discrepancy of Wilk's Lambda are applied for the first time to measure the relative usefulness of a classification. This step determines the final or optimum number of tectonic zones present on the map. The resulting AISOOZ map not only reveals some remarkable features but also shows trends in tectonic evolution of an area that cannot be shown on conventional maps. The values of Wilk's Lambda and the relative discrepancy of Wilk's Lambda for each classification are given in Table 2 and have been plotted in Figs. 3 and 4. Although these criteria have been calculated for 175 zoning maps, for the purpose of economy, only the values for 25 maps are presented in Table 2 and Figs. 3 and 4; however, this does not change the outcome. These statistics are post-hoc procedures. They refer to examining the data for patterns that were not specified a priori after each experiment ended. These criteria, eventually led to an AISOOZ map displaying 11 optimum tectonic zones (Fig. 5). For comparison, the 10- and 12-zone models have been presented in Fig. 6. The 10-zone model represents the combination of the magmatic and metamorphic formations into one zone, i.e. zone 4 (Fig. 6a). The division of the Makran Zone into two zones, i.e. zones 10 and 11 on the 12-zone model has been presented in Fig. 6b. Both models contradict the tectonic zones currently recognized in Iran (Stöcklin, 1968; Stöcklin and Nabavi, 1973).

211

45 35 25 15 5 -5

2

4

6

8

10

12

14

16

18

20

22

24

number of tectonic zones 4 Fig. 4. Showing how 11-zone model which has smallest relative discrepancy gives an optimum number of tectonic zones.

Since the 11-zone model recognizes major units that fit with current structurally recognized zones, the results of determining Wilk's Lambda and the relative discrepancy of Wilk's Lambda are unlikely to be misleading. Therefore, these criteria could be usefully applied as stopping rules to hierarchical numerical zoning, with a large number of variables, where it is often difficult to visualize where to stop the division or fusion process. Any AISOOZ map cannot only be re-assessed quite often, but also provides a measure of on-line information availability. The information can be tailored to the user's specific needs and down-loaded to the user's computer. Easy access to information about such maps will assist researchers and the general public both within Iran and elsewhere. 4. Result and discussion Because of the geological complexities of Iran, a study of the heterogeneity of its tectonic situation may not be well served by too many or too few clusters of tectonic zones (Ι; ΙΙ). For the final or optimum selection of the number of tectonic zones, Wilk's Lambda and the relative discrepancy of Wilk's Lambda criteria have been used as stopping rules to decide among the alternative clusters of computer-based self-organized tectonic zones. These criteria are particularly amenable for use in stopping rules that evaluate the

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Fig. 5. Shows Automatic Integrated Self-Organized Optimum Zoning (AISOOZ) map of Iran, representing 11 optimum tectonic zones. The map has been processed for outliers and inliers and the corners of zones have been rounded slightly for cosmetic reasons. Description of the zone numbers as in Fig. 2.

change in the criteria at each stage of the hierarchical process. Among the clusters of tectonic zones, the 11-zone model (Fig. 5) has the optimum number of tectonic zones. This model balances well the description of structures against the homogeneity of the tectonic zones, and picks out major units that fit rather well with the currently recognized structural zones. There are many similarities between this AISOOZ map and conventional maps; the optimum 11-zone map reveals some significant features and structural trends not shown by the current tectonic maps (Alavi, 1991; Stöcklin, 1968; Stöcklin and Nabavi, 1973). Thus, for illustrative purpose as well as the assessment of the practical significance of the AISOOZ map, the optimum 11-zone model has been correlated with the conventional tectonic map constructed from field observations. An examination of the AISOOZ (Fig. 5) reveals a distinctive pattern developed from the specified geological and geophysical parameters presented in Table 1. The tectonic zones are numbered according to their hierarchical order. Therefore, a larger difference between any two zone numbers corresponds to greater tectonic diversity and vice versa. Contrary to

the conventional maps (Stöcklin, 1968; Stöcklin and Nabavi, 1973), the AISOOZ map draws a clear distinction between the East Iranian Ranges (6 on Fig. 5) and the Makran Mountains Ranges (10 on Fig. 5). It also reveals the much disputed extent and rigidity of the central and eastern Iran microplate (6 on Fig. 5). The AISOOZ illustrates a new approach to tectonic zoning, organized in a hierarchy of increasing complexity. This approach is based on a reductionist analysis of development (i.e. change to a more general or basic form from particular facts or examples). The underlying assumption is that the more properties shared by the tectonic zones, the closer they are related, and therefore are unlikely to have changed from any common ancestor. Those zones surfaced by ancient (Proterozoic) crustal rocks have relatively lower rates of tectonic evolution and tend to be more stable. In other words, their characteristics diverge little after ~500 million years of crustal evolution. By contrast, tectonic zones sharing fewer common characteristics consist of relatively younger parts of the Earth's crust. These are more active and currently undergoing faster tectonic evolution. The

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distinction of tectonically stable zones from active ones allows a qualitative estimate of the likelihood of earthquake occurrence in each zone. Therefore, the AISOOZ method casts an interesting light on the connection between the optimum multivariate numerical zoning hierarchy and the geodynamic evolution of zones in the study region. The following tectonic zones produced by AISOOZ method are characterized below and numbered according to Fig. 5. For illustrative purposes only, the original and widely used generalized tectonic maps of Stöcklin (1968) and Stöcklin and Nabavi (1973) have been compared to the tectonic zones generated by AISOOZ method. It is important to recognize that the AISOOZ procedure is based purely on the geological and geophysical attributes presented in Table 1. So, correspondences and differences between the AISOOZ map and a given map based on conventional methods deserve careful thought. In this paper the AISOOZ approach has been applied to zoning tectonic maps for illustrate purposes only. However, the attributes used to construct the AISOOZ map could readily be adapted to take additional or alternative Earth Sciences data sets, whether they are on- or off-shore. The same approach could also be used to zoning maps of any space, such as sedimentary basins, ecosystems, ground water basins, fauna and flora territories, architecture, or even star maps. This new approach to tectonic zoning is a starting point and is expected to be improved and refined by collection of new data (Ι; ΙΙ).

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1) The Urumiyeh Zone. The general tectonic characteristics of this zone are maximum metamorphic exposure; maximum area of Paleozoic and Proterozoic rocks, highest average elevation, moderate gravity anomaly, moderate seismic activity and moderate fault length density (Table 3). This zone coincides with the northwestern end of the Sanandaj–Sirjan Zone introduced by Stöcklin (1968) and Stöcklin and Nabavi (1973). 2) The Eilam Zone. A high gravity anomaly, moderate isostatic anomaly relief, moderate magnetic intensity and moderate seismic activity play important roles in separating this domain from the rest of country (Table 3). This zone covers a small part of the Zagros Mountains, part of the Simply Folded Belt introduced by Stöcklin (1968) and Stöcklin and Nabavi (1973). 3) The Western Alborz Zone. Maximum area of igneous exposure, largest isostatic anomaly, moderate seismic activity, and moderate fault length density are the main characteristics of this zone (Table 3). Most of this zone coincides with part of the western Alborz Mountains introduced by Stöcklin (1968) and Stöcklin and Nabavi (1973). 4) The Hashtrud–Natanz Zone. This zone is characterized by the maximum magnetic intensity relief, a high percentage area of igneous exposure, high faulting density, a deep Moho (thick crust) and low seismic activity (Table 3). It covers parts of the Zagros Thrust Zone and Igneous Rocks of Stöcklin (1968) and Stöcklin and Nabavi (1973).

Fig. 6. (a) Shows the combination of the magmatic and metamorphic formations into one zone, i.e. zone 4 on the 10-zone model. (b) Illustrates the division of the Makran Zone into two zones, i.e. zones 10 and 11 on the 12-zone model. Both models contradict the tectonic zones currently recognized in Iran (Stöcklin, 1968; Stöcklin and Nabavi, 1973). . Description of the zone numbers as in Fig. 2.

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Fig. 6 (continued).

5) The Central and Eastern Alborz–Kopeh Dagh Zone. High fault length density, a large area of sedimentary rock exposures, large gravity anomaly relief and moderate seismicity are important features of this zone (Table 3). Its structures are the result of Alpine–Himalayan (Mesozoic–Tertiary) orogenic process (Axen, et al., 2001; Stöcklin, 1974). Most of this his zone occupies the Central Alborz and Kopeh Dagh Mountains of Stöcklin (1968) and Stöcklin and Nabavi (1973). 6) The Central–East Iran Zone. This zone is differentiated from surrounding regions by the largest percentage area of unconsolidated sediments, moderate gravity anomaly, and magnetic intensity reliefs and low seismic activity (Table 3). It comprises major parts of the East Iranian Ranges, the Grate Kavir, the Yazd Block, the Lut Rigid Block and the young depression described by Stöcklin (1968) and Stöcklin and Nabavi (1973). 7) The Sanandaj–Baft Zone. High crustal thickness (~46 km), high fault length density, moderate elevation and moderate seismicity play important roles in separating this domain from the rest of the country (Table 3). This zone comprises most of the Sanandaj– Sirjan, the Zagros Thrust Zone, and Central Iran of Stöcklin (1968) and Stöcklin and Nabavi (1973). 8) The Zagros Folded Belt. This zone is characterized by the highest values of seismic activity, Moho depth and sedimentary rock exposure, plus high gravity anomaly and moderate topography reliefs (Table 3). This structural unit was deformed by the late Tertiary (Pliocene and Quaternary) Zagros orogeny when the sediments deformed into a series of parallel folds that gradually

die out southwestward near the northeastern shore of the Persian Gulf. This zone occupies large parts of the Zagros Thrust Zone and part of Zagros Folded Belt formed by the interaction of the Arabian and the Persian plates (Stöcklin, 1968 and Stöcklin and Nabavi, 1973). 9) The Ahvaz–Bandar Abbas Zone. The general tectonic characteristics of this zone are high seismic activity, moderate values of Moho depth and gravity anomaly (Table 3). According to plate tectonic theory, this zone covers areas of recently (Neogene– Quaternary) deformed deposits of Phanerozoic platform facies. This zone is closely related to parts of Simply Folded Belt of (Stöcklin, 1968 and Stöcklin and Nabavi, 1973). 10) The Makran Zone is characterized by high fault density and areas of ophiolite exposures, moderate seismic activity, low elevation and low Moho depth (Table 3). This zone comprises the southern East Iranian Ranges and the northern part of the Makran's accretionary prism. Parts of it correlate with the Makran Ranges and Ophiolites introduced by Stöcklin (1968) and Stöcklin and Nabavi (1973). 11) The Chabahar Zone. This zone is characterized by a high percentage of very low grade metamorphic rock exposures, moderate fault length density, moderate gravity anomaly, low seismic activity and low elevation (Table 3). It contains the onshore component of the accretionary prism, where sediments are transferred onto the Iranian Plate from the Oman plate across an active subduction zone (Farhoudi and Karig, 1977; Jacob and Quittmeyer, 1979). This zone partly coincides with southern part of Makran Ranges named by Stöcklin (1968) and Stöcklin and Nabavi (1973).

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Table 3 Geophysical and geological attributes of 11 Automatic Integrated Self-Organized Optimum Zoning (AISOOZ) map presented in Fig. 5 (units and symbols are shown in Table 1). Variables

Zone 1

Zone 2

Zone 3

Zone 4

Zone 5

Zone 6

Zone 7

Zone 8

Zone 9

Zone 10

Zone 11

MIGRV MXGRV RAGRV AVGRV MIFRA MXFRA RAFRA AVFRA MIBUG MXBUG RABUG AVBUG MXISO MIISO RAISO AVISO AVRES MXRES MIRES RARES AVREG MXREG MIREG RAEGB AVMOD MXMGI MIMGI AVMGI RAMGI RAOPR RACER RAMER RAPAR RAPTR RAIGR RAMER RASER RAUNR MXELV MIELV RAELV AVELV NESMB NEGMB MXEMG MXSER BVGRF AVGRF FLTLD

9.80E + 08 9.80E + 08 315,756 9.80E + 08 −1372.12 10,502.9 11,891.4 3468.27 −18,030 −9767 8262.86 −13,362 46.14 3.57 42.57 26.78 −8.17 39.28 −57.7 97 −274.3 −91.4 −151.4 60 44.69 40,157.7 39,407.9 39,643.4 749.86 3.68 37.91 16.71 6.27 9.43 6.89 8.18 32.78 25.59 3185.71 1050 2135.71 2070.52 16 15.20 5.70 7.90E + 18 1.12 4.53 0.005

5.00E + 08 1.00E + 09 165,300 1.00E + 09 −4807.4 4442.4 9249.9 −677.45 −10,978 −5241.4 5736.3 −7977.8 16.99 −5.06 22.04 7.04 6.85 24.86 −11.97 36.83 −88.4 −77.6 −1000 21.4 39.30 39,810 39,423 39,571 387.51 0.24 22.22 6.98 0.07 0 0.36 0 14.42 17.22 1778.6 310.71 1467.9 899.69 8.87 9.22 5.32 1.00E + 20 1.12 4.50 0.002

1.00E + 09 1.00E + 09 446,113 1.00E + 09 −8666 13,658 22,324 4315.5 −15,840 2931.3 18,771 −5336 78 25 53 51.25 3.83 44.25 −36.75 81 −51 −12.5 −87.88 75.37 32.12 40,263 39,264 39,619 998.75 0.02 58.51 10.72 2.11 0.72 24.52 1.95 28.82 23.54 2437.5 437.5 2000 1297 13.64 13.15 5.44 2.00E + 19 1.18 4.77 0.004

979,085,828 979,377,824 291,996.88 979,226,737 −3558.75 13,100 16,658.75 3795.18 −18,382.5 −10,873.12 7509.37 −14,929.24 27.06 0.56 26.5 15.35 3.56 22.19 −16.81 39 −136.70 −114.87 −158.19 43.31 44.38 40,375.5 39,270.69 39,649.56 1104.81 0.21 82.34 13.97 1.22 2.13 12.91 3.49 38.30 44.77 3137.5 1062.5 2075 1996.69 5.41 5.10 4.89 3.64E + 19 1.12 4.49 0.005

9.80E + 08 9.80E + 08 366,423 9.80E + 08 −3928 11,378.9 15,307.2 2275.81 −14,979 −6757 8222.22 −10,860 19.5 −10 29.83 6.07 −1.82 25.2 −29.4 54.67 −95 −82.4 −107 25.05 40.82 39,798.3 39,282.3 39,490.8 516 0.05 56.07 33.16 4.12 1.06 1.73 1.66 54.56 39.30 3338.89 425 2913.89 1755.74 13.70 13.31 5.63 2.70E + 20 1.09 4.36 0.009

9.80E + 08 9.80E + 08 169,759 9.80E + 08 −3186.7 6116.46 9303.13 816.45 −13,169 −6965 6203.75 −10,104 5.9 −18 24.04 −4 7.8 31.94 −16 47.9 −108 −97 −119 21.29 41.55 40,114.6 39,152.9 39,539.1 961.73 1.73 86.57 9.08 0.99 0.98 10.96 1.78 26 57.73 2462.5 587.5 1875 1306.14 9.47 8.83 5.45 1.00E + 20 1.05 4.14 0.005

978,867,344 979,075,115 207,771.04 978,975,656 −2889.30 8074.09 10,963.39 2045.30 −19,014.61 −11,824.09 7190.52 −15,262.08 16.48 −18.61 35.09 0.25 −9.39 17.43 −35.13 52.56 −141.36 −128.87 −153.35 24.48 46.94 39,935.39 39,243.22 39,534.07 692.17 2.50 68.11 22.43 1.28 0.72 5.47 1.94 45.00 38.20 3365.65 609.80 2755.85 1861.26 23.47 17.52 5.33 9.70E + 19 1.15 4.79 0.006

1.00E + 09 1.00E + 09 3.00E + 05 1.00E + 09 −7073 5131 12,204 −2022 −17,791 −9801 7990 −13,509 9.36 −36.8 46.18 −13.5 6.86 36.55 −22.6 59 −149 −129.7 −168.5 38.82 47.75 39,576 39,475 39,527 101.5 0.33 77.99 20.61 0.77 0.20 0.27 0.23 75.31 23.85 3657 350 3307 1615 61.8 44.25 5.67 1.00E + 20 1.26 5.67 0.004

1.00E + 09 1.00E + 09 122,056 1.00E + 09 −9551 −2256 7294.3 −6782 −11,108 −6511 4597 −8974 −13 −71.6 58.29 −42.79 4.26 30 −23.9 53.86 −96.3 −54.8 −137.4 82.5 41.74 39,549 39,451 39,493 97.89 0 76.35 3.44 0.28 0.28 0 0 39.10 50.72 1671.1 62.86 1608.2 621.61 52.95 40.49 5.46 1.00E + 20 1.28 5.64 0.002

1.00E + 09 1.00E + 09 234,478 1.00E + 09 −5545.8 8127.5 13,673 842.85 −13,300 −3185 10,116 −8858 44 −31 75.08 5.98 30.09 69.25 −9.7 79 −95.9 −58.6 −132.8 74.25 38.59 39,991 39,286 39,543 705.42 5.83 79.28 10.82 2.18 0.9 2.56 5.80 54.38 25.31 2441.7 258.33 2183.3 1218.4 21.25 22.13 5.66 1.00E + 21 1.24 5.35 0.015

9.80E + 08 9.80E + 08 47,462.5 9.80E + 08 1117.5 6177.5 5060 3467.8 −110 5582.5 5692.5 2992.6 63.75 24.25 39.5 45.16 12.35 40.5 −16.2 56.75 29.09 82 −21.75 103.75 28.25 39,475.8 39,421.5 39,451.5 54.25 0 57.20 0 0 0 1.78 6.33 33.97 49.40 1325 0 1325 276.20 3.07 3.12 5.23 4.60E + 20 1.67 7.36 0.004

5. Conclusions Conventional methods of tectonic zoning, especially for general purposes, rely largely on individual researchers applying their skill to judge how tectonic zones are delineated. These methods are “deductive” or “top-down” in their operation and depend on the general vision of the researcher and the prevailing philosophies that influence the process of zoning. They are time consuming, and zoning tends to be made only once. The application of Automatic Integrated Self-Organized Optimum Zoning (AISOOZ) using the multivariate numerical method of statistical analysis allows a more flexible approach. This new approach to tectonic zoning is organized in a hierarchy of increasing complexity, based on “inductive” or “bottomup” reasoning of geological development. The most perplexing issue of this approach is the objective selection of the final number of zones to be identified. The Wilk's Lambda (Λ) and the relative discrepancy of Wilk's Lambda (ΛK − ΛK + 1)/Λk + 1 criteria have been applied for the first time in this paper as stopping rules to determine the relative usefulness of maps produced. The application of these criteria to computer-based self-organized multivariate numerical maps, have

eventually led to an Automatic Integrated Self-Organized Optimum Zoning (AISOOZ) map of Iran with 11 zones. Since these optimum11 zones fit rather well with current structurally recognized zones, the application of these criteria are unlikely to be misleading. The AISOOZ map reveals the much disputed extent and rigidity of the microplate of Central–East Iran and makes a clear distinction between the Makran ranges and eastern Iran Mountains. These features are not distinguished on conventional tectonic maps of Iran produced by Stöcklin (1968) and Stöcklin and Nabavi (1973). The optimum multivariate numerical zoning hierarchy produced by the AISOOZ method not only picks out zones with different rates of crustal deformation but also casts an interesting light on the connection between zoning hierarchy and the evolution of geodynamic processes in the study areas. Therefore, distinguishing tectonically stable from active regions helps to estimate the likelihood of earthquake occurrence in each region. The AISOOZ map can be re-assessed quite often, and also provides us with a measure of on-line information availability. The information can be tailored to the user's specific needs and down-loaded to the user's computer. This new approach to optimum numerical zoning is in an early stage of

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development and is expected to be improved and refined by the collection of new geological and geophysical data. However, the same approach could also be applied to zoning maps of any space, regardless of context or scale. Acknowledgements We are grateful to Christopher Talbot for his detailed reviewing of the manuscript along with his helpful suggestions. We thank the Editor and an anonymous reviewer for their constructive comments. The assistance of the Editor-in-Chief and the Journal Manager is also appreciated. This study was supported by the Center of Excellence for Environmental Geohazards and the Research Council of Shiraz University. References Aghanabati, A., 1986. 1/5,000,000 Sheet, Geological Map of the Middle East. Commission Map of the World. Geological Survey of Iran. Aghanabati, A., 2004. Geology of Iran. Geological Survey of Iran. . (584 pp.). Alavi, M., 1991. scale 1/5,000,000. Tectonic Map of Middle East. Geological Survey of Iran. Alavi, M., 1994. Tectonics of the Zagros orogenic belt of Iran: new data and interpretations. Tectonophysics 229, 211–238. Ansari, A., Noorzad, A., Zafarani, H., 2009. Clustering analysis of the seismic catalog of Iran. Computer and Geosciences 35, 475–486. Axen, G.J., Lam, P.S., Grove, M., Stockli, D.F., Hassanzadeh, J., 2001. Exhumation of the west central Alborz Mountains, Iran, Caspian subsidence and collision-related tectonics. Geology 29, 559–562. Berberian, M., 1976. Contribution to the seismotectonics of Iran. Geological Survey of Iran, Part III. . Report No.39. Berberian, M., 1979. Discussion of the paper A. A. Nowroozi, 1976 seismotectonic province of Iran. Bulletin of the Seismological Society of America 69, 293–297. Berberian, M., 1983. The Southern Caspian: a compressional depression floored be a trapped, modified oceanic crust. Canadian Journal of the Earth Sciences 20, 163–183. Berberian, M., King, G.C.P., 1981. Towards a paleogeography and tectonic evolution of Iran. Canadian Journal of the Earth Sciences 18, 1764–1766. Berberian, M., Yeats, R.S., 1999. Patterns of historical earthquake rupture in the Iranian Plateau. Bulletin of the Seismological Society of America 89, 120–139. Davoudzadeh, M., Weber-Diefenbach, K., 1987. Contribution to the paleogeography, stratigraphy and tectonics of the Upper Paleozoic of Iran. Neues Jahrbnch Fuer Geologie und Palaontologie-Abhandlungen 175, 121–145. Davoudzadeh, M., Lensch, G., Weber-Diefenbach, K., 1986. Contribution to the paleogeography, stratigraphy and tectonics of the Infracambrian and Lower Paleozoic of Iran. Neues Jahrbnch Fuer Geologie und Palaontologie-Abhandlungen 172, 245–269. Dehghani, G.A., Makris, J., 1983. The Gravity Field and Crustal Structure of Iran, in Geodynamic Project (Geotraverse) in Iran. Geological Survey of Iran, pp. 51–68. Duda, R.O., Hart, P.E., Stork, D.G., 2001. Pattern Classification. Wiley, New York. Eftekharnezhad, J., 1980. Subdivision of Iran into different structural realms to sedimentary basins (in Persian). Bulletin of the Iranian Petroleum Institue, pp. 19–28 (Report Number 82). Engdahl, E.R., Jackson, J.A., Myers, S.C., Bergman, E.A., Priestley, k., 2006. Relocation and assessment of seimicity in the Iran region. Geophysical Journal International 167, 761–778.

Everitt, B.S., Dunn, G., 1991. Applied Multivariate Data Analysis. Edward Arnold, London. Everitt, B.S., Landau, S., Leese, M., 2001. Cluster Analysis, fourth ed. Edvard Arnold, London. Farhoudi, G., Karig, D., 1977. Makran of Iran and Pakistan as an active arc system. Geology 5, 664–668. Geological Survey of Iran, 2004. 1/5,000,000 Sheet, Geological Map of Iran. Ministry of Industries and Mines. Gutenberg, B., Richter, C.F., 1954. Seismicity of the Earth and Associated Phenomena. Princeton University Press, New Jersey. Hair, F. Joseph, 2005. Multivariate Data Analysis, sixth ed. Prentice Hall, Englewood Cliffs. ISC, 2010. International Seismological Centre. Newbury, Berkshire, UK. Jackson, C., 1997. Establishing a classification of traditional local retail centers. Centre for Property Research, Department of Land Economy, University of Aberdeen, Elphinstone Road, Old Aberdeen. (AB24 3UF). Jacob, K.H., Quittmeyer, R.L., 1979. The Makran region of Pakistan and Iran: trench–arc system with active plate subduction. In: Farah, de Jong, K. (Eds.), Geodynamics of Pakistan. Geological Survey of Pakistan, Quetta, pp. 305–317. János, A., Balázs, F., 2007. Cluster Analysis for Data Mining and System Identification. Boston and Basel, Switzerland, Birkhäuser Basel. Kaufman, L., Rousseeuw, P.J., 1990. Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, Interscience. McCall, G.J.H., 1996. The inner Mesozoic to Eocene Ocean of south and central of Iran and associated microcontinents. Geotectonics 29, 490–499. Mohajer-Ashjai, A., Nabavi, M.S., 1982. 1/2,500,000 Sheet, Seismicity and Fault Map of Iran. Atomic Energy Organization of Iran. NEIC, 2010. National Earthquake Information Center. Colorado, USA. Nowroozi, A.A., 1971. Seismotectonics of the Persian Plateau, eastern Turkey, Caucasus, and Hindu–Kush regions. Bulletin of the Seismological Society of America 61, 317–341. Nowroozi, A.A., 1976. Seismotectonics provinces of Iran. Bulletin of the Seismological Society of America 66, 1249–1276. Nowroozi, A.A., 1979. Reply to M. Berberian comparison between instrumental and macroseismic epicenter. Bulletin of the Seismological Society of America 69, 641–649. Polit, D.F., 1996. Data Analysis and Statistics for Nursing Research. Appleton and Lange, Stamford. Rencher, A.C., 2002. Method of Multivariate Analysis, second ed. John Wiley. Stöcklin, J., 1968. Structural history and tectonics of Iran: a review. American Association Petroleum Geological Bulletin 52, 1229–1258. Stöcklin, J., 1974. In: Spencer, A. (Ed.), Northern Iran: Alborz Mountains. : Mesozoic Cenozoic Organic Belts: Data for Orogenic Studies, 4. Geol. Spec. Publ, London, pp. 213–234. Stöcklin, J., Nabavi, M.H., 1973. Tectonic Map of Iran. Geological Survey of Iran. Tabachnick, B., 2006. Using Multivariate Statistics, fifth ed. Allyn and Bacon. Ward, J.H., 1963. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association 58, 236–244. Yin, Y., Tian, X., 2007. Classification of Chinese drinks by a gas sensors array and combination of the PCA with Wilks distribution. Sensors and Actuators 124, 393–397. Yousefi, E., 1989. 1/250,000 Sheets, Total Magnetic Intensity Maps of Iran. Geological Survey of Iran. Zamani, A., Hashemi, N., 2004. Computer-based self-organized tectonic zoning: a tentative pattern recognition for Iran. Computer and Geosciences 30, 705–718. Zamani, A., Khalili, M., 2006. Application of multivariate statistical methods for integrated mapping in Geology. 8th Iranian Statistical Conference, Shiraz University, Shiraz, Iran (in Persian).