Comparison of Dimensionless Drainage Network Density and Fractal Dimensions in Separating of Lithological Units (Case Study: Taft Watershed, Yazd)

Introduction :

Petrological and geological studies are of great importance in natural resources management. The fractal technique is used as an instrument to achieve accurate results in a shorter time. Geological maps are very useful in natural resources management, industry, especially refineries, and mine exploration. Due to the large scale of available geological maps, small scale geological maps should be provided in details. The fractal dimension, as a measure of surface roughness over a variety of scales, can be used to model the dissipation of erosive products due to climatic elements and fluvial transport. Nowadays, by using new fractal technique and terrestrial survey, more accurate results on geological units can be obtained in a shorter time. This research aims to compare the performance of two techniques of quantitative parameters non-dimensionalization in geomorphology such as drainage network density index, and fractal dimension, to separate geological units in the Taft watershed, Yazd province.

 Materials and Methods:

 Taft watershed, as the study area, located in the Yazd province, that is situated between 53° 43' 38'' to 54° 14' 54'' E. longitude and 31° 33' 22'' to 31° 49' 06'' N. latitude. There is high diversity of geological and lithological units, including gd (Granodiorite), K^(t-1) (Taft lime), and K^S (conglomerate and sandstone) in this watershed. Three geological units selected in the study area. In each geological unit, , 10 plots of 2 km×2 km (samples), and 10 plots of 2 km×2 km (tests) were selected respectively inside and outside of the study area for analysis. To identify and distinguish three studied geological units, drainage network was drawn in each geological units through geological map of the Iranian Geological Survey and satellite images of the Google Earth and field observation. Afterwards, using Fractalyse and ArcGIS softwares, their fractal dimension and density were calculated. Output results of the Fractalyse software is some numbers that one of them indicates the fractal dimension of those lines. Fractal dimension number is between one and two. The area and network length of each plot were calculated by ArcGIS 10.2 software. Then, the drainage network density of each plot was calculated by equation 1. Drainage Network Density= Drainage Network Length (km)/ Plot area (km2) (1) Efficiency of the two dimensionless indices of drainage network density and fractal in separating geological units were compared by two

A) Validation: In each geological unit, the calculated numbers of the samples and tests should be averaged individually. Then, equation 2 is used to calculate the validation of each geological units. Validity= sample/test (2) Sample: Average fractal dimension of drain networks for sample plots. Test: The mean fractal dimension of drainage networks for test plots. Or Sample: Average density of drainage networks for sample plots. Test: The average density of the drainage networks for test plots. B) Comparing the sample and test by using QQ diagram, the line equation, the coefficient of determination and the angel of deviation: In drainage network fractal dimension, QQ diagram is plotted between samples and tests' fractal dimension. Line equation, coefficient of determination and angel of deviation were calculated. Moreover, the QQ graphs were plotted and calculations carried out on the drainage network density.

 Results and discussion:

Results of the first comparing method (validation) in both techniques are very good and similar. In second comparing method (i.e. QQ graph, angle of deviation, and coefficient of determination), coefficient of determination in the drainage network density in K^S, gd and K^(t-1)geological units were 0.99, 0.93 and 0.94, respectively, which are more than drainage network fractal dimension. The standard deviation in drainage network fractal dimension in K^S and gd and K^(t-1)geological units are +17.05, - 1.48, and +8.37 respectively, these values in the drainage network density are much lower (i.e. better). The angle of deviation in drainage network density of K^S, gd and K^(t-1) geological units are + 0.21, -2.4, and +0.22, respectively. According to the results, the drainage network density index is better than the drainage network fractal dimension in identifying and separating of the studied geology and lithological units of K^S, gd and K^(t-1) in the region. 

Conclusion:

 The results of the accuracy assessment of both techniques are very good and similar to each other. Therefore, in this comparison, both techniques of drainage network density index and drainage network fractal dimension have high efficiency in identifying and separating of the geological studies unit. However, The drainage network density technique is the best technique of quantitative parameters non-dimensionalization in geomorphological studies in identifying and separating of geological units in the Taft watershed, Yazd.