Diagenesis is one of the branches of geology, which is currently in the process of becoming a quantitative science. Although most of the papers published in the field are still largely descriptive and qualitative, a quantitative understanding of many important diagenetic processes is emerging, and an increasing number of mathematical models describing these processes have been put forward. However, despite the growing interest for quantitative diagenetic models, there are few introductory texts and reference works on the subject. Therefore, geologists interested in developing or understanding quantitative diagenetic models and their implementation as computer codes, often have to consult lengthy mathematical texts focused on other applications to extract the relevant mathematical tools for handling diagenetic problems. This book does much to rectify this situation by presenting many mathematical and numerical techniques commonly applied to diagenetic problems.
The book starts by presenting some general comments concerning the identification, formulation and solution of diagenetic problems before the mathematics needed to formulate a diagenetic problem in quantitative terms are briefly reviewed in the second chapter. This short but useful review defines different types of algebraic and differential equations, introduces different types of series expansion and approximation, and presents a few central theorems and methods such as mean value theorems for integrals and Reynolds decomposition and averaging.
Chapter Three discusses central concepts and methods involved in formulating diagenetic problems in mathematical terms. Topics include formulation of conservation equations for solutes and solids, the type of terms occurring within the conservation equations, how to express these terms mathematically, and choice of appropriate coordinate systems.
In Chapter Four, the constitutive equations used to describe quantities such as diffusive fluxes and chemical reaction rates are discussed, and methods for estimating parameters in the equations are reviewed. Chapter Four also includes a large amount of tabulated values for parameters such as diffusion coefficients.
The different types of boundary conditions that may apply to diagenetic models form the subject of Chapter Five. Concentration conditions, flux conditions, and continuity conditions are reviewed on a general basis and illustrated by the use of examples from early diagenesis.
Chapter Six focuses on the analytical solution of steady-state one-dimensional diagenetic equations, whereas Chapter Seven is concerned with analytical solutions for time-dependent and/or multi-dimensional diagenetic models. Various techniques of solution are reviewed and illustrated by numerous examples.
Chapter Eight explains some of the most commonly applied numerical techniques for solving diagenetic problems: root finding for non-linear equations, numerical evaluation of integrals, finite-difference approximations for ordinary differential equations and for partial differential equations. Lastly, the book includes an appendix explaining where various FORTAN computer programs for solving diagenetic problems can be found on the Internet.
In summary, this book is a very useful reference for geologists and others interested in understanding and/or developing quantitative solutions to diagenetic problems, especially during early diagenesis. By bringing together a large body of relevant mathematical techniques, examples of their application, and references to other work within a single volume, the author has made it much easier to rapidly and efficiently obtain an understanding of many of the quantitative aspects of this field. The book is also well written and well organized, and should form a valuable addition to the library of those interested in the quantitative aspects of diagenesis.
OLAV WALDERHAUG
Statoil a.s.
N-4035 Stavanger
Norway
Source
http://archives.datapages.com/data/sepm/journals/v66-67/data/068/068003/0519.HTM