Evaluation and comparison of fractal and fuzzy quantitative methods efficiency in analysis of northwest Zagros tectonic situation

Document Type : Original Research

Authors
A. Goorabi 1
S. M. zamanzadeh 2
M. Yamani 2
P. Pirani 2
1 university of tehran
2 university of Tehran
Abstract
Introduction

In order to tectonic analysis northwestern Zagros, we have used fractal geometry against classic geometry and fuzzy logic instead of Aristotelian classic logic to evaluate natural landscapes with non-integer dimension and the complex nature of tectonic processes. The fractal dimension (FD) has been applied to determine anomaly or normality of surface rupture (faults) pattern in association with drainage network that can show the maturity of structures. In other hand, uncertainty of fuzzy logic has been applied to specify the potential of tectonic activity by using morphotectonic factors. At the end, we have compared results of these two methods with surface epicenters of earthquakes.

Methodology

To calculate the FD of faults and drainage network using box-counting, the area was divided to 6 boxes that contain main fault trends horizontally and vertically. In fractal method each box is covered by several network (grid) that their side length (quantity of Size) is decreased at every grid level. Then the relation between reciprocal of side length and boxes containing linear feature (quantity of Number) was drawn Logarithmically as a linear regression that shows FD. In fuzzy model, six main effective factors were determined and 12 layers were produced base on their importance in tectonic analysis. The membership degree of these layers’ effective parts by fuzzy functions were determined and then they were overlaid by fuzzy operators like gamma with different powers.

Results and Discussion

Calculating number-size quantity using box-counting method for faults and drainage network shows both partial and overall FD changes. As partial changes are close, yjey indicate the existence of the self-similarity components. Based on partial FD, there are three communities: back ground with FD larger than slope of linear regression, threshold community with repeating component, and anomaly community with FD value more than three. Based on overall FD, development of faults and drainage network have not entered to chaos phase. The comparison of mean value of fuzzy zoning with different gamma powers for each box indicates that 0.7 power of gamma has the most correlation with overall FD of boxes.

Conclusion

Areas of high value of FD for faults and low value for drainage network are more tectonically active. Here the box labeled A which represent western parts of Kermanshah in folded Zagros, has the highest FD value of faults (1.32) and lower FD value of drainage network (1.432). Epicenter evidences of earthquakes for example 7.3 magnitude earthquake of Ezgeleh, confirm the FD results; whereas, the box labeled E near Dezful Embayment shows the lowest FD value of faults (1.07) and highest FD value of drainage network (1/470). Overlaying fractal boxes (A to F) with fuzzy exports (gamma 0.7) are in line with these results and represent more potential of tectonic activity for northwestern parts of area (box A).



Keywords: Tectonic, Northwestern Zagros, Fractal, Fuzzy.Introduction

In order to tectonic analysis northwestern Zagros, we have used fractal geometry against classic geometry and fuzzy logic instead of Aristotelian classic logic to evaluate natural landscapes with non-integer dimension and the complex nature of tectonic processes. The fractal dimension (FD) has been applied to determine anomaly or normality of surface rupture (faults) pattern in association with drainage network that can show the maturity of structures. In other hand, uncertainty of fuzzy logic has been applied to specify the potential of tectonic activity by using morphotectonic factors. At the end, we have compared results of these two methods with surface epicenters of earthquakes.

Methodology

To calculate the FD of faults and drainage network using box-counting, the area was divided to 6 boxes that contain main fault trends horizontally and vertically. In fractal method each box is covered by several network (grid) that their side length (quantity of Size) is decreased at every grid level. Then the relation between reciprocal of side length and boxes containing linear feature (quantity of Number) was drawn Logarithmically as a linear regression that shows FD. In fuzzy model, six main effective factors were determined and 12 layers were produced base on their importance in tectonic analysis. The membership degree of these layers’ effective parts by fuzzy functions were determined and then they were overlaid by fuzzy operators like gamma with different powers.

Results and Discussion

Calculating number-size quantity using box-counting method for faults and drainage network shows both partial and overall FD changes. As partial changes are close, yjey indicate the existence of the self-similarity components. Based on partial FD, there are three communities: back ground with FD larger than slope of linear regression, threshold community with repeating component, and anomaly community with FD value more than three. Based on overall FD, development of faults and drainage network have not entered to chaos phase. The comparison of mean value of fuzzy zoning with different gamma powers for each box indicates that 0.7 power of gamma has the most correlation with overall FD of boxes.

Conclusion

Areas of high value of FD for faults and low value for drainage network are more tectonically active. Here the box labeled A which represent western parts of Kermanshah in folded Zagros, has the highest FD value of faults (1.32) and lower FD value of drainage network (1.432). Epicenter evidences of earthquakes for example 7.3 magnitude earthquake of Ezgeleh, confirm the FD results; whereas, the box labeled E near Dezful Embayment shows the lowest FD value of faults (1.07) and highest FD value of drainage network (1/470). Overlaying fractal boxes (A to F) with fuzzy exports (gamma 0.7) are in line with these results and represent more potential of tectonic activity for northwestern parts of area (box A).



Keywords: Tectonic, Northwestern Zagros, Fractal, Fuzzy.

Keywords

Subjects

- Aghanbati, S.A. (2004). Geology of Iran. Geological Survey of Iran, 640.
- Agrad, P., Omrani, J., Jolivet, L., & Mouthereau. (2005). “Convergence history across Zagros (Iran): constraints from collisional and earlier deformation”. International Journal of Earth Sciences, 94, 401–419. DOI 10.1007/s00531-005-0481-4
- Ai, T., Zhang, R., Zhou, H.W., & Pei, J.L. (2014). “Box-counting method to directly estimate the fractal dimension of a rock surface”. Applied surface science, 314, 610-621. DOI.org/10.1016/j.apsusc.2014.06.152
- Amini Fasoudi, A. (2005). “Application of Fuzzy Logic Inference to Regional Planning and Development Studies”. Science & Development, -(17), 39-61.
- Angeles.G., Perillo, G., & Pierini, J. (2004). “Fractal analysis of tidal channels in the Bahı́a Blanca Estuary (Argentina)”, Geomorphology, 57(3–4), 263-274. DOI.org/10.1016/S0169-555X(03)00106-5
- Baas, A.C.W. (2002): Chaos, “Fractals and Self-Organization in Coastal Geomorphology: Simulating Dune Landscapes in Vegetated Environments”, Geomorphology, 48 (1-3), 309-328. DOI.org/10.1016/S0169-555X(02)00187-3
- Berberian, M. (1995). “Masterblind thrust faults hidden under the Zagros folds: active basement tectonics and surface morphotectonics”. Tectonophysics, 241, 193-224. DOI.org/10.1016/0040-1951(94)00185-C
- Bi, L., He, H., Wei, Z., & Shi, F. (2012). “Fractal properties of landforms in the Ordos Block and surrounding areas, China”. Geomorphology, 175-176, 151–162. DOI.org/10.1016/j.geomorph.2012.07.006
- Bonham-Carter, G. F. (1991). Geographic Information System for Geoscientists: Modeling with GIS, Pergamon, Ontario, PP. 291-300.
- Caram, A. (2010). “Chaos theory, fractal (fractal) and nonlinear systems in geomorphology”. Natural Geography, 3(8), 67-82.
-Darvishzadeh, A. (1991). Geology of Iran. Amirkabir Publishing Institute, 902.
- Fatehi, M., Mohjal, M., & Khatib, M.M. (2011). “Fractal analysis of faults and their relationship with earthquakes in the Neshan shear zone of Dehshir fault, west of Yazd province”. Earth Science Research, 2(8), 36-45.
- Goorabi, A. (2019). “Detection of landslide induced by large earthquake using InSAR coherence techniques –Northwest Zagros", Iran”. The Egyptian Journal of Remote Sensing and Space Science, In press, DOI.org/10.1016/j.ejrs.2019.04.002
- Han, Z., Zhang, P., Wu, L., & Hou, J. (1998). “Characters about the modern movement of North Qilianshan block”. In: Department of Geology, Peking University, Collection of International Conference on Geological Science in Peking University. Seismological press, Beijing.
- Hovius. N. (1996). “Regular spacing of drainage outlets from linear mountain belts”. Basin Research, 8(1), 29-44. DOI:10.1111/j.1365-2117.1996.tb00113.x
- Jackson. J., & Leeder. M. (1994). “Drainage systems and the development of normal fault: an example from Pleasant Valley Nevada”. Journal of Structural Geology, 16(8), 1041-1059. DOI.org/10.1016/0191-8141(94)90051-5.
- Klir, G.J., & Yuan, B. (1995). “Fuzzy Sets Fuzzy Logic: Theory and Application. Upper Saddle River”. N.J. Prentice Hall PTR. DOI:10.5860/choice.33-2786
- Lifton, N.A., & Chase, C.G. (1992). “Tectonic, climatic and lithologic influences on landscape fractal dimension and hypsometry: implications for landscape evolution in the San Gabriel Mountains, California”. Geomorphology, 5, 77-114. DOI.org/10.1016/0169-555X(92)90059-W
- Lin, H., kao, J., Li, K., & Hwang, H.H. (1996). “Fuzzy GIS assisted landfill siting analysis. Proceedings of International Conference on Solid Waste Technology and Management”. System Theory. Brooklyn, NY: Polytechnic Press. http://hdl.handle.net/11536/19928
- Mandelbrot, B.B. (1982). The Fractal Geometry of Nature. W.H. Freeman and Company, New York.
- Metkkan A.A., Shakiba, A., PoorAli S.H., & Nazimfar, H. (2008). “Locating suitable areas for landfill using GIS (Study Area: Tabriz City)”. Environmental Sciences, 6(2), 121-131.
- Nasrollahi, Kh., Akbari, N., & Heidari, M. (2011). “Comparative Analysis of Ranking Methods in Measuring Development (Case Study: Khuzestan Provinces)”. Land Planning, 3(4), 65-93.
- Phillips, J. D. (2002). Interpreting the fractal dimension of river networks, In: LAM, N. S. N., DECOLA, L. (eds.): Fractals in Geography. PTR Prentice-Hall, Inc., New Jersey, 142–157.
- PourAhmad, A., Habibi, K., MohammadZahrai, S., & NazariAdli, S. (2007). “Using Fuzzy Algorithms and GIS for Urban Equipment Location (Case Study: Babolsar City Landfill)”. Environmental Studies, 33(42), 31-42.
- Ramesh, M.H. (2010). “Space in Geomorphology”. Space Planning and Planning (Teacher of Humanities), 14(4), 111-136.
- Richardson, L.F. (1961). The problem of contiguity: An Appendix to Statistics of Deadly Quarrels. General System Yearbook, 6, 139-187.
- Rodriguez-Iturbe, I., & Rinaldo, A. (1997). Fractal River Basin (Chance and Self-Organization). Cambridge, Cambridge University Press. DOI:10.1063/1.882305
- Sadr, A.H., Alipour, R., & , Ghamarian, S. (1977). “Investigation of the Role of Active Tectonic Structures in Fractal Dimensions of Fractures and Waterways of Hasan Abad Fault (Southwest of Qazvin)”. Tectonics, 2(5), 3-15.
- Saeedi, H., & Afsharijo, P. (2010). “Fuzzy logic in simple language”. Entrepreneur, -(82), 61-64.
- Sahraeyan, M., Seif, H., Haddad, E. E., & Mohammadzadeh, N. (2015). “Sedimentology and Geochemistry of the Late Miocene–Pliocene Succession in the Fars Interior (SW Iran)”.
Chemostratigraphy, 103–129. DOI:10.1016/b978-0-12-419968-2.00005-4
- Schuller , D.J., Rao, A.R., & Jeong, G.D. (2001). “Fractal characteristics of dense stream networks”. Journal of Hydrology, 243 (1-2), 1–16. DOI.org/10.1016/S0022-1694(00)00395-4
- Shahriari, S., & Khatib, M.M (1997). “Fractal analysis of the Nehbandan fault system”. Geosciences, 6(23-24), 22-39.
- Shayan, S. (2004). “Geomorphological evidence in the Great Lakes Stratigraphy of Simare (Zagros Mountains) Zagros, Southwestern Iran”. Space Planning and Planning (Teacher of Humanities), 8(1), 45-70.
- Turcotte, D.L. (1997). Fractal and Chaos in Geology and Geophysics, Cambridge University Press. Cambridge. DOI:org/10.1017/CBO9781139174695
- Verges, J., Goodarzi, M.G.H., Emami, H., Karpuz, R., Efstathiou, J., & Gillespie, P. (2011). “Multiple detachment folding in Pusht-e Kuh arc, Zagros: Role of mechanical stratigraphy”. Thrust fault-related folding: The American Association of Petroleum Geologists Memoir, 94, p. 69–94. DOI:10.1306/13251333M942899
The Journal of Spatial Planning and Geomatics
Volume 24, Issue 4
December 2020
Pages 29-67