Quantitative geospeedometry based on homogeneous reactions

In the literature, various methods to infer cooling rate from the measured species concentrations of a homogeneous reaction have been developed. These methods are summarized and assessed below. Then two specific geospeedometers based on two homogeneous reactions are presented. 

Four methods are available in the literature for inferring cooling rate or cooling timescale from measured species concentrations in homogeneous reaction geospeedometers temperature-time transformation, Ganguly s method, Zhang s equation, and the empirical method. They are outlined below. 

Temperature-time transformation The temperature-time transformation, or T-t-T method (e.g., Seifert and Virgo, 1975), is the oldest method in geospeedometry. In this method, a reasonably high initial temperature is given, and equilibrium species concentrations are calculated. This speciation is assumed to be the initial speciation. The final species concentrations after cooling down (i.e., at present day) are measured and hence known. To reach the present-day species 

The similarity between the apparent equilibrium temperature equation and the closure temperature equation can be seen by comparing Equation 5-125 and Equation 5-77b by letting Tae and Tc be equivalent, Xr (reaction timescale) and x (diffusion timescale) be equivalent, and G = 2, the two equations become the same. 

Given measured species concentrations for a homogeneous reaction in a rock, cooling rate at Tae can be found as follows if the equilibrium constant K and the forward reaction rate coefficient k as a function of temperature are known. First, the apparent equilibrium temperature is calculated from the species concentrations. Then kf and kb at Tae are calculated. Then the mean reaction time Xr at Tae is calculated using expressions in Table 2-1. From x, the cooling rate q at Tae can be obtained using Equation 5-125. Two examples are given below. 

---