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

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.

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  

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.

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).