| Abstract |
A linear mixing model has generally been used to calculate the thermal end-member composition of a mixed hydrothermal vent fluid when the concentration of a chemical tracer (e.g. magnesium) can be considered zero for the thermal end-member. However, it is necessary to evaluate the feasibility of the linear regression model that is used to calculate the intercept value. After a statistical evaluation of the linear model application, it was found that the calculation of the chemical composition of the thermal end-member using a linear mixing model is feasible. However, a statistical evaluation of this model is necessary before its application. In the examples presented in this paper, it was considered that all of the Mg in the vent fluid originates from the seawater and is added to the vent fluid through a mixing process occurring beneath the seafloor discharges (Bischoff and Seyfried, 1978). Further, at temperatures around 85°C, the magnesium reacts with silicate species to form a Mg-hydroxi-silicate precipitate (Bischoff and Seyfried, 1978). The proposed validation of this regression method was performed in the following steps: (a) establishing the relationship between the chemical variables (Mg vs. concentrations of other dissolved chemical elements) using correlation and determination coefficients, (b) using residual plots as a diagnostic tool of the linearity and presence of possible outliers, (c) statistical validation of the linear regression equation, and (d) proposal of a confidence interval for the Y-intercept calculated using the regression model. For the cases presented here (both coastal hydrothermal systems off the coast of Mexico), it was concluded that Ca, Si, Mn and Ba are supplied by the hydrothermal system, since Na, Cl, SO4 and K are all present due to a seawater mixing process occurring immediately beneath the vent discharges. |