The mathematics of early diagenesis: From worms to waves

Abstract

The changes that sediments undergo after deposition are collectively known as diagenesis. Diagenesis is not widely recognized as a source for mathematical ideas; however, the myriad processes responsible for these changes lead to a wide variety of mathematical models. In fact, most of the classical models and methods of applied mathematics emerge naturally from quantification of diagenesis. For example, small‐scale sediment mixing by bottom‐dwelling animals can be described by the diffusion equation; the dissolution of biogenic opal in sediments leads to sets of coupled, nonlinear, ordinary differential equations; and modeling organisms that eat at depth in the sediment and defecate at the surface suggests the one‐dimensional wave equation, while the effect of waves on pore waters is governed by the two‐ or three‐dimensional wave equation. Diagenetic modeling, however, is not restricted to classical methods. Diagenetic problems of concern to modern mathematics exist in abundance; these include free‐boundary problems that predict the depth of biological mixing or the penetration of O2 into sediments, algebraic‐differential equations that result from the fast‐reversible reactions that regulate pH in pore waters, inverse calculations of input functions (histories), and the determination of the optimum choice in a hierarchy of possible diagenetic models. This review highlights and explores these topics with the hope of encouraging further modeling and analysis of diagenetic phenomena.