ارزیابی و مقایسه کارایی روش‌های کمی فرکتال و فازی در تحلیل وضعیت تکتونیکی زاگرس شمال غرب

ماهیت پیچیده فرایندهای زمین‌ساختی عامل ایجاد توپوگرافی و همچنین ابعاد مناظر طبیعی زمین را نمی‌توان با ساختارهای کلاسیک، مانند هندسه اقلیدسی یا منطق ارسطویی، ارزیابی نمود. برای این منظور، تحلیل فرکتالی آبراهه‌ها و شکستگی‌ها با استفاده از روش شمارش جعبه‌ای برای تعیین بلوغ ساختاری زاگرس شمال‌غرب انجام گرفت. همچنین با کمک معیارهای مرتبط با مورفوتکتونیک، پتانسیل فعالیت تکتونیکی منطقه با روش عدم قطعیت فازی مشخص و نتایج این دو روش با کانون‌های سطحی زلزله مقایسه شدند. مناطق دارای بعد فرکتالی بالای گسل و پایین زهکشی فعالیت تکتونیکی بیشتری دارند. طبق این تحقیق، محدودۀ a یعنی غرب کرمانشاه، دارای بالاترین بُعد فرکتالی (1.32) گسل و بُعد فرکتالی کمتر برای شبکۀ زهکشی (1.432) است و شواهد لرزه‌ای از‌جمله زلزلۀ اخیر کرمانشاه با 7.3 ریشتر نیز پویا بودن آن را تایید می‌کند. محدودۀ e که رو به فروافتادگی دزفول است، کمترین بُعد فرکتالی گسل (1.07) و بیشترین بُعد فرکتالی شبکۀ زهکشی (1.470) را دارا است. با این حال گسل‌های مدفون نقش مهمی در تولید زلزله در شمال این محدوده دارند. هم‌پوشانی مربع‌های فرکتالی با گاماهای مختلف در مدل فازی تا حد زیادی تایید‌کنندۀ نتایج بود و محدودۀ a در این مدل نیز بالاترین پتانسیل فعالیت تکتونیکی را نشان می‌‌دهد.

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

IntroductionIn 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 noninteger 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.MethodologyTo calculate the FD of faults and drainage network using boxcounting, 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  DiscussionCalculating numbersize quantity using boxcounting method for faults and drainage network shows both partial and overall FD changes. As partial changes are close,  yjey indicate the existence of the selfsimilarity 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.ConclusionAreas 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.IntroductionIn 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 noninteger 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.MethodologyTo calculate the FD of faults and drainage network using boxcounting, 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  DiscussionCalculating numbersize quantity using boxcounting method for faults and drainage network shows both partial and overall FD changes. As partial changes are close,  yjey indicate the existence of the selfsimilarity 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.ConclusionAreas 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.