Diagenetic Reactions as Stochastic Processes: Application to the Bermudian Eolianites

Diagenetic reactions in rock bodies are best described as stochastic processes. When the diagenetic environment is fairly constant and when destruction of an unstable mineral is the limiting step, we propose that the rate of a diagenetic reaction can often be expressed by the equation δC( t ) = Λ( t ) C( t ) dt, where C( t ) denotes the concentration of reactant minerals and Λ( t ) is a random function characteristic of the diagenetic environment. In the simplest case, the initial concentration is a constant and Λ is a random variable independent of time. Then, the logarithm of the concentration of an unstable mineral decreases linearly in the mean with time, and its standard deviation is an increasing linear function of time. This model describes well the time dependence of carbonate alterations in the vadose zone of the Bermudian eolianites. We further suggest that, owing to the stochastic nature of fluid flow in natural rock bodies, our model may apply to many diagenetic and metamorphic reactions.