Fuzzy cognitive mapping vs. statistic approach of geomorphological analysis of active faults: Preliminary results from a case study within the Corinth Graben, Greece

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Fuzzy cognitive mappingIFAC vs.PapersOnLine statistic approach of geomorphological analysis of 51-30 (2018) 372–377 Fuzzy faults: cognitive mapping vs. statistic of geomorphological analysis of active Preliminary results fromapproach a case study within the Corinth Graben, Fuzzy faults: cognitive mapping vs. statistic approach of geomorphological analysis of active Preliminary results from a case study within the Corinth Graben, Greece Fuzzy cognitive mapping vs. statistic approach of geomorphological analysis of active faults: Preliminary results from a case study within the Corinth Graben, Greece active faults: Preliminary Vasiliki resultsZygouri*, from a case study within the Corinth Graben, Sotirios Verroios*, Greece Antigoni Anninou**, Ioannis Greece Vasiliki Zygouri*, SotiriosKoukouvelas* Verroios*,  Ioannis Koukouvelas* Antigoni Anninou**, Vasiliki Zygouri*, Sotirios Verroios*,  Vasiliki Zygouri*, SotiriosKoukouvelas* Verroios*, Antigoni of Anninou**, Ioannis *Department Geology, University of Patras,Rion,26504 Antigoni Anninou**, Ioannis Koukouvelas*  Greece (e-mail: [email protected]; [email protected],[email protected] ).

*Department of Geology, University of Patras,Rion,26504 **Department of Electrical and Computer[email protected],[email protected] Engineering, University of Patras, Rion 26504 ). Greece (e-mail: [email protected]; *Department of Geology, University of Patras,Rion,26504 (e-mail: [email protected]) **Department of Electrical and Computer Engineering, University of Patras, Rion 26504 *Department of Geology, University of Patras,Rion,26504 Greece (e-mail: [email protected]; [email protected],[email protected] ). (e-mail: [email protected]) Greece (e-mail: [email protected]; [email protected],[email protected] ). **Department of Electrical and Computer Engineering, University of Patras, Rion 26504 **Department of Electrical (e-mail: and Computer Engineering, University of Patras, Rion 26504 [email protected]) Abstract: This paper is presenting(e-mail: a [email protected]) methodology for classifying faults that host destructive earthquakes based on their morphometric analysis of basins for draining the footwall of thedestructive fault. The Abstract: This paper is presenting a new methodology classifying faults block that host morphometric analysis is morphometric based on fouranalysis indices.ofThese indices are drainage basin shape (Bs), The the earthquakes based on their basins draining the footwall block of the fault. Abstract: This paper is presenting a new methodology for classifying faults that host destructive asymmetry factor (AF), the stream length-gradient index (SL), and the valley floor width to valley height morphometric analysis based on afour indices. are shape (Bs), The the Abstract: This paper isispresenting new methodology for classifying faults basin that host earthquakes based on their morphometric analysis ofThese basinsindices draining thedrainage footwall block of thedestructive fault. ratio (Vf) which are integrated with the use of statistically induced “Iat” index. This newly proposed asymmetry factor (AF), the stream length-gradient index (SL), and the valley floor width to valley height earthquakes based on their morphometric analysis of basins draining the footwall block of the fault. The morphometric analysis is based on four indices. These indices are drainage basin shape (Bs), the methodology triesare to integrated correlate the causality between indicesinduced considered here as This concepts that allows ratio (Vf) which with the of statistically index. newly proposed morphometric analysis is based on fouruse indices. These indices are“Iat” drainage (Bs), the asymmetry factor (AF), the stream length-gradient index (SL), and the valley floorbasin widthshape to valley height degrees of causality and not the usual binary logic of the “Iat” statistical index. These very interesting methodology triesare to integrated correlate the causality considered here as width concepts that allows asymmetry factor (AF), the stream length-gradient indexindices (SL),induced and the “Iat” valley floor to valley height ratio (Vf) which with the use between of statistically index. This newly proposed results will be presented for athe well analyzed seismically normal fault within the Gulf of Corinth degrees of which causality not usual binary logic of indices theactive “Iat” statistical very that interesting ratio (Vf) integrated with the use between of statistically induced “Iat”index. index. This newly proposed methodology triesare toand correlate the causality considered here asThese concepts allows Graben, Greece. results betries presented for athe well analyzed normal fault within the Gulf of Corinth methodology toand correlate the causality between here asThese concepts allows degreeswill of causality not usual binary seismically logic of indices theactive “Iat”considered statistical index. very that interesting Graben, Greece. degrees of causality and not the usual binary logic of the “Iat” statistical index. These very interesting results will be presented for a well analyzed seismically active normal fault within the Gulf of Corinth © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Seismically active faults, morphometric analysis, geomorphic indices, fuzzy cognitive results will be presented for a well analyzed seismically active normal fault within the Gulf of Corinth Graben, Greece. mapping, of indices. Keywords:causality Seismically active faults, morphometric analysis, geomorphic indices, fuzzy cognitive Graben, Greece. mapping, of indices. Keywords:causality Seismically active faults, morphometric analysis, geomorphic indices, fuzzy cognitive  Keywords:1. Seismically active faults, morphometricthe analysis, geomorphic indices, fuzzy mapping, causality of indices. results in order to extract classes of cognitive tectonic activity for INTRODUCTION  mapping, causality of indices. each landscape (Table 1). the results in order to extract classes of tectonic activity for 1. INTRODUCTION Tectonic geomorphology represents the study of the interplay each landscape (Table  results order to 1). extract classes of tectonic activity for However ifinwe review the methodologies applied by each 1. INTRODUCTION between tectonic and surface the the Tectonic geomorphology representsprocesses the study that of theform interplay the results in order to extract classes of tectonic activity for each landscape (Table 1). 1. INTRODUCTION researcherifand usedthe tools we come across a complex landscape tectonic (Keller and 1996). During the last decades we the review methodologies applied by each between andPinter surface the However Tectonic geomorphology representsprocesses the study that of theform interplay each landscape (Table 1). image that emphatically shows that there is no consensus in tectonic has increased its influence by using researcher usedthe tools we come across a complex landscapegeomorphology (Keller and 1996). During lastform decades However ifand we the review methodologies applied by each Tectonic geomorphology represents the studythe of the interplay between tectonic andPinter surface processes that the the way the geomorphic indices are derived and particularly data from geomorphology, seismology, geochronology, thatifand emphatically shows that there is no consensus in However we the review methodologies applied by each tectonic geomorphology has increased its influence by using researcher usedthe tools we come across a complex between tectonic andPinter surface processes thatlastform the image landscape (Keller and 1996). During the decades interpretation of the outcoming data is rather arbitrary and stratigraphy and structural geology. Its interdisciplinary role the the way the geomorphic indices are derived and particularly researcher and the used tools we come across a complex data from geomorphology, seismology, geochronology, image that emphatically shows that there is no consensus in landscape (Keller and Pinter 1996). During the last by decades tectonic geomorphology has increased its influence using based on statistical approaches. Serious to address along with the technological advances allow earth scientists interpretation of the outcoming isattempts rather arbitrary and image shows there is no in stratigraphy and structural Itsits interdisciplinary role the the waythat theemphatically geomorphic indicesthat aredata derived andconsensus particularly tectonic geomorphology hasgeology. increased influence by using data from geomorphology, seismology, geochronology, this problem are the research papers of Silva et al. (2003), El to use new techniques that represent cost – effective, fast based on statistical approaches. Serious attempts to address the way the geomorphic indices are derived and particularly along with the technological advances allow earth scientists interpretation of the outcoming data is rather arbitrary and data from and geomorphology, seismology, geochronology, stratigraphy structural geology. Its interdisciplinary role Hamdouni et al. (2008) and Koukouvelas et al. (2018). The performed accurate tools for estimating future landscape this interpretation problem are the research papers of Silva et al. (2003), El of the outcoming data isattempts rather arbitrary and to usewith newand techniques thatgeology. represent – earth effective, fast the based on statistical approaches. Serious to address stratigraphy and structural Its cost interdisciplinary role along the technological advances allow scientists two research teams try to group etmore than The two evolution asand a proxy fortools hazard assessment in geology. The first Hamdouni et al. (2008) and Koukouvelas al. (2018). based on statistical approaches. Serious attempts to address performed accurate for estimating future landscape this problem are the research papers of Silva et al. (2003), El along with the technological advances allow earth scientists to use new techniques that represent cost – effective, fast geomorphic indices in order to obtain a decisive tectonic geomorphology uses drainage pattern morphometry first two research teams try to group more than two this problem are the research papers of Silva et al. (2003), El evolution as a proxy for hazard assessment in geology. The Hamdouni et al. (2008) and Koukouvelas et al. (2018). The to use new techniques that represent cost – effective, fast performed and accurate tools for estimating future landscape characterization for fault activity. Silva et al. (2003) succeed extracting the so called uses geomorphic indices represented by Hamdouni geomorphic indices inandorder obtain a than decisive et al. (2008) Koukouvelas etmore al. (2018). The tectonic geomorphology drainage pattern two research teams try to togroup two performed accurate for estimating future landscape evolution asand a proxy fortools hazard assessment in morphometry geology. The first acharacterization graphical result,forwhereas El Hamdouni et al. al. (2003) (2008) succeed adopted mathematical that highlightindices the interplay between et two research teams try toSilva morea than two extractinggeomorphology theaequations so called geomorphic by first geomorphic indicesfault inactivity. order togroup obtain decisive evolution as proxy for uses hazard assessment inrepresented geology. The tectonic drainage pattern morphometry a new geomorphic index “Iat”, representing a simple endogenic (plate tectonicthat processes) and exogenic landscape acharacterization graphical result, Elorder Hamdouni et al. (2003) (2008) adopted indices to et obtain a decisive mathematical highlight the interplay between forwhereas faultinactivity. Silva al. succeed tectonic geomorphology drainageindices pattern morphometry extracting the equations so called uses geomorphic represented by geomorphic approach of index adding “Iat”, variables, geomorphica indices, shaping processes (climaticprocesses) forcing). and exogenic landscape astatistical new geomorphic representing simple fault activity. Silva et endogenic (plate a graphical result,forwhereas El Hamdouni et al. al. (2003) (2008) succeed adopted extracting the so tectonic called that geomorphic represented by characterization mathematical equations highlightindices the interplay between and dividing by the total number of them in every indices, studied statistical approach of adding variables, geomorphic graphical result, whereas El Hamdouni et al. (2008) adopted shaping processes (climatic forcing). a new geomorphic index “Iat”, representing a simple mathematical equations that highlight theexogenic interplaylandscape between site. On the other hand, Koukouvelas et al. (2018) deal endogenic (plate processes) and 2. tectonic SETTING THE PROBLEM with and dividing by the total number of them in every studied a new geomorphic index “Iat”, representing a simple statistical approach of adding variables, geomorphic indices, endogenic (plate tectonic shaping processes (climaticprocesses) forcing). and exogenic landscape the errors generated when different satellite or airborne 2. SETTING THE PROBLEM site. dividing On the other hand, Koukouvelas et geomorphic al. (2018) with approach oftotal adding variables, indices, and by the number of them in everydeal studied The dynamic interplay between climatic forcing and plate statistical shaping processes (climatic forcing). techniques are used for the different quantification of the tectonic the when or deal airborne 2. SETTING THE PROBLEM and dividing by the total number of them in every studied site. errors On the generated other hand, Koukouvelas etsatellite al. (2018) with movements on the landscape shaping processes are The dynamic interplay between climatic forcing and plate forces over theused surface In this study “Iat techniques for theprocesses. quantification of the tectonic 2. SETTING THE PROBLEM site. On the are other hand, Koukouvelas etsatellite al. (2018) with the errors generated when different or deal airborne enormously benefited by the rapid technological development movements on the landscape shaping processes are methodology” is also applied but a simple question arises. Is The dynamic interplay between climatic forcing and plate forces overare theused surface In this study “Iat errors generated when different satellite or airborne techniques for theprocesses. quantification of the tectonic of satellite benefited imagery by or the UAV These remote the enormously rapidtechnology. technological development simple statistical method of “Iat” able to describe the The dynamic on interplay between climatic and plate movements the landscape shapingforcing processes are this methodology” isused also applied but a simple arises. Is techniques for theprocesses. quantification of the tectonic forces overarethe surface In question this study “Iat sensing products enableortheUAV application of many geomorphic of satellite imagery These remote surface pattern that ofis “Iat” affected byto external and movements on the by landscape shaping processes are complex enormously benefited the rapidtechnology. technological development this simple statistical method able describe the forces over the surface processes. In this study “Iat indices in different areasthecharacterised various rates of methodology” is also applied but a simple question arises. Is sensing products enable application ofbymany geomorphic earth processes? enormously benefited by rapidtechnology. technological development of satellite imagery or the UAV These remote internal complex surface pattern thatbut byto external methodology” is also applied aaffected simple question arises.and Is simple statistical method ofis “Iat” able describe the fault activity and erosion degrees. Even by if the studied areas indices in different areas characterised various rates of this of satellite imagery technology. These remote sensing products enableortheUAV application of many geomorphic internal earth processes? this simple statistical method of “Iat” able to describe the complex surface pattern that is affected by external and differ, earth scientists made a serious effort to homogenise fault activity and enable erosion Evenofby ifmany the studied areas sensing products application geomorphic indices in different areasthedegrees. characterised various rates of complex surface pattern that is affected by external and internal earth processes? differ, earth scientists made a serious effort to homogenise indices in different areas degrees. characterised various rates of fault activity and erosion Even by if the studied areas internal earth processes? fault and erosion degrees. Eveneffort if thetostudied areas differ,activity earth scientists made a serious homogenise differ, earth scientists Copyright © 2018 IFAC made a serious effort to homogenise372 2405-8963 © IFAC (International Federation of Automatic Control) © 2018, 2018 IFAC 372Hosting by Elsevier Ltd. All rights reserved. Copyright Peer review under responsibility of International Federation of Automatic Control. Copyright © 2018 IFAC 372 10.1016/j.ifacol.2018.11.334 Copyright © 2018 IFAC 372

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Table 1. Representative publications concerning the application of geomorphic indices Morphometric unit/ calculated indices 1

AF, Smf, Vf, SL, T

2

AF, Smf, Vf, SL, Hypsometric curves

3

Hi, AF, Smf, Vf, SL, FD, Bs

4 6

Hi, Hc, E, AF, Smf, Vf, SL. SL, AF, Bs Smf, Vf, Hi, basin area SL, Hi, AF, Vf, Bs, Smf

7

Bs, AF, SL, Vf, Smf, Hc

8

AF, Hi, Vf, Bs, Smf, SL

5

9 10

Smf, Vf, AF, Hi, Bs, Ddf, Fs, facet analysis Smf, AF, SL, Hi, Bs, Vf

373

slightly differs from the paleoseismologically estimated rate. We suggest that this inconsistency between the two methodologies is due to the way “Iat” is calculated. The use of fuzzy logic in order to set weights in the individual geomorphic indices applied is encouraged from our observation that in many studied areas the indices show different behaviour in correspondence to the lithology incorporated.

Source Tsodoulos et al. 2008 Perez-Pena et al. 2010 Mahmood and Gloaguen 2012 Rebai et al. 2013 Arian and Aram 2014 Elias 2015 Zygouri et al. 2015 Tarı and Tüysüz 2016 Topal et al. 2016

Jaberi et al. 2018 Koukouvelas et al 11 Bs, RF, AF, SL, Vf, basin area 2018 SL = stream length gradient index, AF = asymmetrical factor, Hi = hypsometric integral, Hc= hypsometric curves, Vf = valley floor width-to- height ratio, Bs = elongation ratio, T = traverse topographic symmetry, Smf = mountain front sinuosity, E = elongation ratio, FD = Fractal dimension, Ddf= facet drainage density, Fs= facet slope.

Fig. 1. a) Active faults dissecting the Corinth Graben.

It is thus necessary to vigorously reaffirm that even though each geomorphic index highlights a specific earth process, different structural, lithological and climatic environments can affect in multiple ways the interplay between earth processes. Therefore, the scope of this study is to discuss methods that overcome the statistically defined “Iat” fault classification. Being able to visualise the complex nature of the impact of tectonic forcing on landscape evolution will be a reliable tool in lowering the risk of natural hazards in an area, since seismicity induces ruptures cutting across life lines or buildings, trigger voluminous landslides and cause flood hazard. In this contribution we, for the first time, use fuzziness in the interpretation of geomorphic indices. Our intent is to make feasible a worldwide comparison or even better to introduce universal threshold values that every geomorphic index must follow. 3. METHODOLOGY

Fig. 2. Map showing the classification of the basins behind the analysed active fault in the Corinth graben as derived by the application of “Iat” methodology. Lower picture shows the slip rate significance of the fault according to the estimation of a paleoseismological approach and the morphometrical classification.

We selected a case study of a low to moderate active fault in southeastern coast of the Corinth graben an area hosting strong seismicity in the recent past (Koukouvelas et al. 2017) (Fig. 1). This has been systematically studied paleoseismologically (Koukouvelas et al. 2017) and geomorphologically (Koukouvelas et al. 2018; Zygouri et al. 2018). In this fault, near the ancient city of Kenhreai, the “Iat methodology” showed significant influence of the tectonic processes on the drainage pattern (e.g. basin shape, stream channel distribution). The map derived by Koukouvelas et al. 2018 (Fig. 2) classifies the fault’s activity rate as high that

Thus, considering four indices applied in our current study as concepts and characterize its relation to others as positive or negative, then “Iat” evaluation can be defined as weak (W), medium (M) or strong (S). By this method we can have a more reliable technique for the estimation of a fault’s activity. The indices used are drainage basin shape (Bs), the asymmetry factor (AF), the stream length-gradient index (SL), and the valley floor width to valley height ratio (Vf) (Table 2). For the mathematical background of these indices the reader is encouraged to address the Zygouri et al. (2015) study, where these indices are described in detail. 373

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Table 2. Indices used in this study and their activity classes suggested by El Hamdouni et al. (2008). Geomorphological indices Asymmetry Factor

Stream lengthgradient index SL Valley Floor Width– Valley Height Ratio Vf Drainage basin shape Bs

Mathematical formula and activity classes(2)

into consideration this positive and negative relation between the geomorphic indices. Table 3. Interrelations between the inputs and the outputs of the Fuzzy Cognitive Map technique

No of values/ No of valleys 14/14

AF=100(Ar/At) Class 1: AF <35, >65 Class 2: AF 35-45, 55-65 Class 3: AF 45-55 SL= (H/L)L 234/14 Class 1: HA High Anomalies Class 2: NA No Anomalies Class 3: LA Low Anomalies Vf=2Vfw/[(Eld–Esc)+(Erd–Esc)] 113/14 Class 1: Vf<0.5 highly active. Class 2: Vf 0.5-1.0 moderately active. Class 3: Vf>1.0 inactive Bs = Bl/Bw 14/14 Class 1: Bs >4 (highly active) Class 2: Bs 3-4 (active) Class 3: Bs <3 (less active to inactive)

4. FCM METHODOLOGY IN HIGHLIGHTING KEY LANDSCAPE FEATURES ACROSS ACTIVE FAULTS Fuzzy Cognitive Mapping is a soft computing technique that deals with complex systems, incorporating a reasoning process that can even include ambiguous situations. The landscape evolution depends on climate, tectonics bedrock properties and different base levels and therefore consists a complex nature system. To decipher the roles of these influences we included a series of geomorphic indices as concepts (inputs) in a FCM computing technique (Table 3). This graph structure represents the basic concepts of our study and their interrelations. It is primarily based on the positive or negative relations that imprint the accordance or the struggle between the used geomorphic indices and the “Iat” index (Fig. 3). For each concept a single output was performed. Thus all concepts that were used in previous statistical analysis were processed via Fuzzy Cognitive Map method.

W: Weak relation, M: Medium relation, S: Strong relation, VS: Very strong relation.

Longitudinal river profiles indicate that all channels in the study area depend on bedrock properties. Bedrock properties (expressed as hard or soft rocks) strongly control channel incision and hillslope processes in the study area. Further analysis shows that variations in channel and basin metrics are not only linked to different rock types but also in contrasts between slope distribution. These discrepancies can be recorded in maps and change the initial distribution of “Iat” index that we derived from the statistical process. It was stated above that figure 3 provides valuable information for the interrelations of the geomorphic indices with the calculation of “Iat” index of landscape evolution. In addition in figure 3 the red solid line illustrates a positive relation and the blue dashed line a negative one. This is very valuable and useful geological information. Using the theory of Fuzzy Cognitive Maps new results are obtained which take

Fig. 3. The interrelations of the geomorphic indices with the “Iat” index and the various influences of landscape evolution. The red solid line illustrates a positive relation and the blue dashed line a negative one.

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Figure 3 is used and a Fuzzy Cognitive Map is constructed that is similar to the generic FCM model, figure 4. A geomorphic FCM model is obtained based on figure 3 and a corresponding weight matrix is determined and is given in table 4. Simulation studies were conducted using the overall FCM model equations (1) and (2) and the table 4. Due to space limitations graphical results cannot be given but plans are to publish a journal paper in which the obtained results will be provided. However it is of interest to say that the geomorphic FCM model gives us results that have better values than the statistical one by 20-25 %. In addition the FCM model gives us the positive-negative interrelation between the geomorphic indices; a characteristic that the statistical methods cannot provide but it is very important.

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Table 4. Weight matrix table

5. DISCUSSION OF THE POSSIBILITY TO UNRAVEL EVOLVING LANDSCAPES THROUGH FCM The data presented in this contribution suggest that the classification of a fault is not a simple task and have to be handled carefully since the morphometric results and the classification have implications on the earthquake planning and protection of an area. The above analysis was performed using the classical methods based only on probability and statistical theories. The results were as expected. Most scientific explanations are probabilistic. The statistical view of nature is evident implicitly or explicitly when stating scientific predictions of phenomena or explaining the likelihood of events in actual situations. However, so far scientific explanations are limited and many times not acceptable to human kind. Scientific knowledge is necessarily contingent knowledge rather than absolute, and therefore must be evaluated and assessed, and is subject to modification in light of new evidence. It is impossible to know if we have thought of every possible alternative explanation or every variable, and often even technology is limited. New knowledge is created in a dynamic way and cannot be explained sufficiently using only statistical analysis. This is true despite the efforts of many scientists to use Artificial Intelligence (AI) to overcome problems been risen by the Big Data Driven World. This is the case in studying and analyzing geological phenomena which are turning to be more and more complex and big volume of data are selected. A number of theoretical and practical questions arise: How is the big data driven world created in geological phenomena? Can we ignore other new and advanced methods that have been recently used in analyzing systems being driven by big data and are not based solely on statistical methods? How does the human cognition affect these natural physical processes?

Fuzzy Cognitive Maps (FCMs) have come from the combination of the ideas and methods of both fuzzy logic and Neural Networks. They have been used in modelling complex dynamic systems. FCMs consist of concept nodes and weighted arcs, which are graphically illustrated as a signed weighted graph with feedback. Signed weighed arcs, connecting the concept nodes, represent the causal relationship that exists among concepts. In general, concepts of a FCM, represent key-factors and characteristics of the modeled complex system and stand for: events, goals, inputs, outputs, states, variables and trends of the complex system been modeled. This graphic display shows clearly which

Today many believe that the theory of Fuzzy Cognition and Intelligent Systems can provide some very practical and useful solutions. Here, in our study we use the recent developments of Fuzzy Cognitive Maps Kosko (1986) and Groumpos (2010) to investigate for first time the geological phenomena of fault activity. The FCM has also been used for earth science purposes by the research team of Papadopoulou et al. (2017) in order to detect paleoenvironments based on paleontological methods.

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concepts influences with other concepts and what this degree of influence is (Fig.4).

 Fig. 4. A simple Fuzzy Cognitive Map (FCM). The degree of influence between the two concepts is indicated by the absolute value of the weight wij. During the simulation mathematically the value, Ai, of each concept Ci at the iteration step k+1, is calculated applying the following calculation rule: (Groumpos and Stylios 2000). 

  + 1 =   +     1 ,

Where f is the sigmoid function (λ>0 steepness of the function): 1  = 2 1 +   A Fuzzy Cognitive Map is a graph that shows the degree of causal relationship among concepts of the map while the knowledge expressions and the causal relationships are expressed by fuzzy weights. Existing knowledge on the behavior of the system is stored in the structure of nodes and interconnections of the map. Relationships between concepts have three possible types; a) either express positive causality between two concepts (Wij> 0), b) negative causality (Wij< 0) and c) no relationship (Wij = 0). The value of Wij indicates how strongly concept Ci influences concept Cj. The sign of Wij indicates whether the relationship between concepts Ci and Cj is direct or inverse. The direction of causality indicates whether concept Ci causes concept Cj, or vice versa. These parameters have to be considered when a value is assigned to weight Wij. Concepts stand in the interval [0,1]. Causality between concepts allows degrees of causality and not the usual binary logic, so the weights of the interconnections can range in the interval [-1,1]. Important Remark: most people confuse the statistical correlation coefficient with the FCM causality coefficient. This is one reason that the FCM theory needs further investigation and show clearly that are different from statistics. Therefore, we use FCMs to classify the activity of a seismic fault through morphometric analysis based on indices expressing the causality between four concepts.

explained sufficiently using only statistical analysis. The field of Geology becomes a dynamic case and new methods are needed to better study and analyze geological phenomena. A Fuzzy Cognitive Map (FCM) has been developed for the same geological phenomenon studied earlier. Simulation studies have been performed and a good number of interesting results have been obtained. These results are compared with the statistical results been obtained in the first part of this paper. The preliminary application of the new method seems more sensitive to activity variations along the fault length and therefore it is regarded as a better way for evaluating the impact of tectonics on surface processes. In addition, it shows that the classification of the fault’s activity according to the statistical method oversimplifies the particular bedrock properties and erosion factors that prevail in a certain area. Due to drawbacks of existing equations we can’t approach with simple way the weighted Iat1st-3rd values for each drainage basin across the fault. Consequently, we introduce the “Icas” index that will incorporate the three Iat values in one. This new index implements new simulation equations that weight each isolated Iat1st-3rd in a complex dynamic system, such as the seismically active faults. The fuzzy cognitive mapping can provide us a weighted morphotectoning mapping across an active fault. The FCM can compare the linear and areal morhotectonic indices in a different way that is proposed by the traditional statistically calculated “Iat” index. By this way the future morphotectonic studies across active faults can be more reliable.

REFERENCES Arian, M. and Aram, Z. (2014). Relative tectonic activity classification in the Kermanshah area, western Iran. Solid Earth, 5, 1277–1291. El Hamdouni, R., Irigaray, C., Fernandez, T., Chacon, J.and Keller, E.A. (2008). Assessment of relative active tectonics, southwest border of the Sierra Nevada (southern Spain). Geomorphology, 96, 150–173. Elias, Z. (2015). The Neotectonic Activity Along the Lower Khazir River by Using SRTM Image and Geomorphic Indices. Earth Sciences, 4, 50-58. Groumpos, P.P., (2010). Fuzzy cognitive maps: basic theories and their application to complex systems. Fuzzy cognitive maps. Springer,Berlin,Heidelberg. 1-22. Groumpos, P.P. and Stylios, C.D., (2000). Modeling supervisory control systems using fuzzy cognitive maps. Chaos Solitons & Fractals. 113, 329–336. Jaberi, M., Ghassemi, M.R., Shayan, S., Yamani, M. and Zamanzadeh, S.M. (2018). Interaction between active tectonics, erosion and diapirism, a case study from Habble-Rud in Southern Central Alborz (Northern Iran). Geomorphology, 300, 77-94. Keller, E.A. and Pinter, N. (1996). Active tectonics: Earthquakes, Uplift and Landscapes. Prentice Hall, New Jersey. Kosko, B. (1986). Fuzzy Cognitive Maps. International Journal of Man-Machine Studies, 24, 65-75.

6. CONCLUSION AND FUTURE RESEARCH Studies of geological phenomena must take into consideration that as the time passes most systems become dynamic and so is the geomorphic landscape evolution. New knowledge is created in a dynamic way and cannot be 376

IFAC TECIS 2018 Baku, Azerbaidschan, Sept 13-15, 2018

Vasiliki Zygouri et al. / IFAC PapersOnLine 51-30 (2018) 372–377

Koukouvelas I.K., Zygouri V., Papadopoulos G.A. and Verroios S. (2017). Holocene record of slip-predictable earthquakes on the Kenchreai Fault, Gulf of Corinth, Greece. Journal of Structural Geology, 94, 258-274. Koukouvelas I.K., Zygouri V., Verroios S. and Nikolakopoulos, K. (2018). Treatise on the tectonic geomorphology of active faults: The significance of using a universal digital elevation model. Journal of Structural Geology (in press). Mahmood, S.A. and Gloaguen, R. (2012). Appraisal of active tectonics in Hindu Kush: Insights from DEM derived geomorphic indices and drainage analysis. Geoscience Frontiers, 3, 407-428. Papadopoulou, P., Iliopoulos, G., Koukouvelas, I., Anninou, A., Redoumi, E. and Groumpos, P. (2017). Integrated palaeoenvironmental reconstruction of a Lower Pleistocene section (Sousaki basin, Northeastern Corinth Gulf): using Fuzzy logic to decipher long term palaeoenvironmental changes. European Geosciences Union General Assembly 2017. Perez-Pena, J.V., Azor, A., Azanon, J.M.and Keller, E.A. (2010). Active tectonics in the Sierra Nevada (Betic Cordillera, SE Spain): insights from geomorphic indexes and drainage pattern analysis. Geomorphology, 119, 7487. Rebai, N., Achour, H., Chaabouni, R., BouKheir, R. and Bouaziz, S. (2013). DEM and GIS analysis of subwatersheds to evaluate relative tectonic activity. A case study of the North–south axis (Central Tunisia). Earth Science Informatics, 6, 187-198. Silva, P., Goy, J.L., Zazo C. and Bardají T. (2003). Faultgenerated mountain fronts in Southeast Spain: geomorphologic assessment of tectonic and seismic activity. Geomorphology, 50, 203-225 Tarı, U.and Tüysüz, O. (2016). The effects of the North Anatolian Fault on the geomorphology in the Eastern Marmara Region, Northwestern Turkey. Geodinamica Acta, 28, 139–159. Topal, S., Keller, E., Bufe, A.and Koçyiğit, A. (2016). Tectonic geomorphology of a large normal fault: Akşehir fault, SW Turkey. Geomorphology 259, 55-69. Tsodoulos, I.M., Koukouvelas I.K. and Pavlides, S. (2008). Tectonic geomorphology of the easternmost extension of the Gulf of Corinth (Beotia, Central Greece). Tectonophysics, 453, 211 –232. Zygouri, V., Koukouvelas, I.K., Kokkalas, S., Xypolias, P. and Papadopoulos G.A. (2015). The Nisi Fault as a Key structure for understanding the active deformation of the NW Peloponnese, Greece. Geomorphology, 237, 142-156. Zygouri, V., Nikolakopoulos, K., Verroios, S. and Koukouvelas I.K. (2018). Importance of DEM’s accuracy in the activity classification of faults: The case of a fault in the Gulf of Corinth, Greece. Proceedings of SPIE 10773, Sixth International Conference on Remote Sensing and Geoinformation of the Envirionment (RSCy2018), doi:10.1117/12.2326015.

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