Modeling dolines morphometric factors and presenting an index of fractal dimension in studying the faults of karstic regions (a case study of the karstic areas between Paraov and Shahoo)

Introduction Karst is a geomorphic and hydrologic system which is created due to the dissolution of soluble stones like lime, dolomite and Gypsum (Ozyurt et al., 2014). The development of a karstic system is dependent upon climactic, lithologic and structural (wrinkle, fault and gap) factors (Ford and Williams, 2013). The most important landforms in the created perspectives include carnic bands, dolines and swallowing gaps. These shapes are usually but not necessarily formed in the areas which suffer from a fracture or a gap (Kovacic & Ravbar, 2013). Nowadays the theory of fractal collections and multifractal measuring is extensively used in describing some natural processing like the activity of faults (Ayunova et al., 2007 & Feder, 1988). In fact the process of fault creation can be investigated through fractal concepts (Mandelbrot 1983 & Sarp 2014). As the behavior of the faults certainly nonlinear (Turcottee, 1990) and the fractal theory is a method for determining and predicting complex dynamic nonlinear behaviors (Yang et al., 2007) this method can be used to examine the behavior of faults (Torcotte, 1997).
Materials and instrumentation Initially the dolines of the target areas were extracted on the basis of DEM10 meter and method CCLs. after extracting these dolines their morphometric factors which consisted of area, perimeter, depth, slope, large diameter and small diameter were calculated in GIS software. Following that the SPSS software was utilized for the descriptive and regressive analysis the morphometric parameters of dolines. To this end single and multivariable variable linear methods were employed and those models which were of more value were presented.
1/100000 geological maps of Kermanshah, Kamiaran, Miyan Rahan and Paweh were used to determine the fault systems of the examined areas and extract their fault maps. Afterwards, since the faults followed a vector shape, the Number-Size equation was selected to calculate the fractal dimension of the faults. In this equation a self-similar exponential relationship exists which is affected by the number factors and the size of spatial quantities. Therefore, based on what was explained, Number-size equation can be explained according to equation 1 (Mehrnia, 2006).
Equation 1): Log (Ns)= a K Log (s)
In this equation Ns is the number of the phenomena (in this study the number of the faults), S is the size of the network, k is the coefficient of the line slope or the fractal dimension (Mandelbrot, 1983).
Findings and discussion The results of the single variable linear regression shows that the relationships between perimeter with major diameter, area with perimeter, depth with area, minor diameter with perimeter and area with major diameter were statistically significant and the correlation coefficients were 0/93, 0.837, 0/668, 0/860, and 0/850. Moreover, the most degree of significant correlation for second and third degree equations was observed between perimeter and large diameter with correlation coefficients of 0/932 and 0/942 and the estimated error of 0/297 in the area has a possibility of error which is smaller than 0/01. The results of multiple regressions also revealed that the most significant correlation of the depth is with area, slope, and minor diameter with a correlation coefficient of 0/834 and estimated error of 7/85. The estimation of the fractal dimension in the investigated areas shows that Shahoo and Paraov areas have the maximum and minimum fractal fault dimensions which are 1/24 and 1/15 respectively.
Conclusion This study was an attempt to analyze the dolines which exist between Shahoo and Paraov areas using quantitative geomorphology, statistic methods and fractal geometry. The existence of a high correlation between most of the morphometric factors of dolines indicates that that these landforms can be modelled with a high degree of accuracy provided that exact and sufficient data is existent. The employment of fractal geometry and Number-Size equation also showed that by estimating the fractal dimension through the above method the activity of the faults their relative effect on the solution of the soluble stones can be determined. As a matter of fact this method can be utilized as a new index in studying the faults of the karstic areas.