In this paper, a power-law relation modeling called the vario-fractal model is introduced in order to understand the discrepancies between the linear and non-linear distribution of the elements and its application for mineral exploration in the calamine Zn-Pb ore-deposit. From a hypothetical viewpoint, since geochemical zonation of the supra- and sub-ore elements is a crucial evaluation criterion for concealed/underlying mineralization potentials, this hypothesis can be tested by delineating the fractal surfaces of elements as the geometric evidence of primary geochemical zonation of elements in the calamine mine. A comparison of the linear regression results with the Poisson distribution coefficients indicate the relative tendency of the elements towards a non-linear distribution. Therefore, a logarithmic equation derived from the variance-distance relationship (power-law) is used here for the delineation of fractal surfaces of elements as the geometric features related to proper self-organized distributions. In this research work, the vario-fractal expression of geochemical zonation has trace-element tendencies to the non-linear distribution. The results obtained show that the calamine’s fractional surfaces are mostly of self-organized types, situated at 2 < FD < 3 as "real fractal surfaces", although 3 of the elements appear in the quasi-fractal populations called "near Brownies” here. Moreover, the calamine’s fractal surfaces can be extended throughout the anomalous regions or may be distributed as limited types of the finalized model, which is a fractal-based pattern of geochemical zonation of the elements for evaluation of the hypogenic mineralization potential and has been prioritized to 6 target-areas containing 10 elements with real fractal surfaces and 3 more at near Brownies and then validated by the mineralogical evidence.