mathematical functions

Quantitative description of valley profiles can help us to identify its geomorphologic and dynamic properties and a useful tool for separating the valleys created by various processes. In this study, the Longitudinal and Cross-sections of 15 valleys were investigated in three geological formations of Kahar, Taft and Granite. Fractal properties of valleys along with the mathematical functions and two Vf and Fr indicators were used to study valley morphology. The average of Vf index was calculated in Kahar, Taft and Granit formations 5.56, 3.52 and 1.38, respectively. Also, the average of Fr index in three formations was calculated 0.07, 0.20, and 0.17, respectively. The results indicated heterogeneity in the lithology and structural status of valleys. According to the results, the shape of the valley, from Kahar to Taft formation, is U profile to V-shaped profile. The results showed that less curvature profiles are fitted with linear functions and profiles with more curvature fitted with polynomial functions. In fact, the polynomial functions, especially the fourth order, have high ability in modeling the Longitudinal and Cross-sections of the valleys. Subsequently, multifractal analysis of cross-sectional valley, Using the general multifractal dimensions (Dq) and the technical spectrum f(αq), showed that these sections are transmitted from mono-fractal to multifractal. None of the valley sections in Taft formation has multifractal properties. In a number of Cross-section valleys of Granite and Kahar formations, the multifractal approach seems to be more appropriate. Because of the fractal parameters may vary depending on the locations.