A modified equation for the downstream dilution of stream sediment anomalies

Abstract

Mixing stream sediments originating from mineralization surface with eroded materials from background areas leads to downstream dilution in metal content of mineralization-sourced sediments. This phenomenon has a negative effect on delineation of anomalous catchment basins. In order to eliminate the dilution effect from the chemical analysis of stream sediments data, Hawkes (1976) proposed the equation “CmAm=Aa(Ca−Cb)+CbAm” through which he calculated the metal concentration at the mineralization surface. Hawkes's equation was a great advancement in interpretation of stream sediment geochemical datasets.However, Hawkes makes some simplifying assumptions to derive his formula from the mass balance equation including the hypothesis that the total sediment produced at a basin surface is delivered to the basin outlet. By this approach, an equation is obtained in which a linear relation is set between the sediment delivery and the area size of the basin. Some of the Hawkes’s assumptions are inevitable, but the aforementioned one is not in general true. In the present research, a new equation is derived by employing the concept of sediment delivery ratio (SDR) and its introduction into the mass balance equation, used by Hawkes (1976). SDR that represents the gap between the gross erosion in a catchment basin and the amount of sediment delivered at the basin outlet is negatively related to the basin size, and, as the basin size increases, the rate of deposition at the basin outlet decreases.SDR plays the main role in our work to attain a modified formula in which the dilution is related to the basin size by a power function. The modified equation “CmAm1+n=CaAa1+n−Cb(Aa−Am)1+n” is a general form of Hawkes's equation where power equals 1 (n=0) corresponds to Hawkes's equation. The new equation was applied to test the data presented by Hawkes, and it emerged that, in his study, n=0 delivers closer results to the reality in the first case study, but n=−0.25 and−0.5 delivers closer Cu values to the actual value in the second case. Similarly, more acceptable results were achieved for Mo if n=−0.25 in the second case. Additionally, the sample catchment basin was tested on the stream sediment dataset in the west of Iran, where orogenic gold occurrences were recognized to exist. Employing the modified equation with those three n values has resulted in repositioning of some catchment basins in terms of their favorability.