Introduction

Dynamics deals with changes in the state of a system with time. We can think of a geological system evolving in response to changes in geological parameters that are not explicitly time-dependent: although trace-element contents in differentiating magmas may change as a function of descriptive parameters that are time-dependent, they can be adequately described by their degree of fractionation. Likewise, the chemistry of clastic sediments with different provenance can be thought of as resulting from a time-dependent process, but most local chemical aspects of these sediments can be handled efficiently using source composition and mixing proportions. These systems are not described as dynamic systems because the time-dependence is not a critical factor in determining the geochemical variable of interest. In contrast, some other systems have characteristic time-scales involved, such as those in geochemistry through fluxes, that are time-dependent in essence, and homogenization processes that need some time to complete. These are real dynamic systems.

Let us first introduce some important definitions with the help of some simple mathematical concepts. Critical aspects of the evolution of a geological system, e.g., the mantle, the ocean, the Phanerozoic clastic sediments,…, can often be adequately described with a limited set of geochemical variables. These variables, which are typically concentrations, concentration ratios and isotope compositions, evolve in response to change in some parameters, such as the volume of continental crust or the release of carbon dioxide in the atmosphere. We assume that one such variable, which we label ƒ, is a function of time and other geochemical parameters.