Statistical analyses of the numbers, lengths, and orientations of fission tracks etched in minerals yield dating and thermal history information valuable in geological and geoscience applications, particularly in oil exploration. Fission tracks can be represented mathematically by a stochastic process of randomly oriented line segments in three dim

Statistical analyses of the numbers, lengths, and orientations of fission tracks etched in minerals yield dating and thermal history information valuable in geological and geoscience applications, particularly in oil exploration. Fission tracks can be represented mathematically by a stochastic process of randomly oriented line segments in three dimensions, and this "line segment" model can describe and explain the essential statistical features of the data, providing a rigorous foundation for quantitative modelling and simulation studies. Statistics for Fission Track Analysis explores the line segment model and its consequences for the analysis and interpretation of data. The author derives the equations for fission track data and the theoretical probability distributions for the number, orientation, and length measurements of the tracks. He sets out the theory of fission track dating and through numerical examples, presents methods for analyzing and interpreting fission track counts. Later chapters address statistical models for situations in which samples contain mixtures of fission track ages. These methods, along with observation features of the various measurements, are illustrated by real examples. Finally, the author brings together the theoretical and observation aspects to formulate a joint likelihood function of counts, lengths, and angles as a basis for parametric thermal history modelling. An appendix provides general notes on statistical concepts and methods. Designed for broad accessibility, this is the first book to fully cover the statistical foundations of fission track analysis. Whether you work in a fission track lab, in archaeological, geological, or geochronological research, or in geological applications of statistics, you will find the background material and practical tools you need to optimize the use of fission track analysis in your work and to make further advances in the field.

This book is focused on the basics of applying thermochronology to geological and tectonic problems, with the emphasis on fission-track thermochronology. It is conceived for relatively new practitioners to thermochronology, as well as scientists experienced in the various methods. The book is structured in two parts. Part I is devoted to the fundamentals of the fission-track method, to its integration with other geochronologic methods, and to the basic principles of statistics for fission-track dating and sedimentology applied to detrital thermochronology. Part I also includes the historical development of the technique and thoughts on future directions. Part II is devoted to the geological interpretation of the thermochronologic record. The thermal frame of reference and the different approaches for the interpretation of fission-track data within a geological framework of both basement and detrital studies are discussed in detail. Separate chapters demonstrate the application of fission-track thermochronology from various perspectives (e.g., tectonics, petrology, stratigraphy, hydrocarbon exploration, geomorphology), with other chapters on the application to basement rocks in orogens, passive continental margins and cratonic interiors, as well as various applications of detrital thermochronology.

Volume 58 of Reviews in Mineralogy and Geochemistry presents 22 chapters covering many of the important modern aspects of thermochronology. The coverage of the chapters ranges widely, including historical perspective, analytical techniques, kinetics and calibrations, modeling approaches, and interpretational methods. In general, the chapters focus on intermediate- to low-temperature thermochronometry, though some chapters cover higher temperature methods such as monazite U/Pb closure profiles, and the same theory and approaches used in low-temperature thermochronometry are generally applicable to higher temperature systems. The widely used low- to medium-temperature thermochronometric systems are reviewed in detail in these chapters, but while there are numerous chapters reviewing various aspects of the apatite (U-Th)/He system, there is no chapter singularly devoted to it, partly because of several previous reviews recently published on this topic.

The collection of papers in this volume is a direct result of the Society of Economic Paleontologists and Mineralogists Research Symposium on "Thermal History of Sedimentary Basins: Methods and Case Histories" held as part of the American Association of Petroleum Geologists Annual Convention in New Orleans in March 1985. The original goal of the sym posium was to provide a forum where specialists from a variety of dis ciplines could present their views of methods that can be used to study the thermal history of a sedimentary basin or an important portion of a basin. An explicit part of that goal was to illustrate each method by presentation of a case history application. The original goal is addressed by the chapters in this volume, each of which emphasizes a somewhat different approach and gives field data in one way or another to illustrate the practical useful ness ofthe method. The significance of our relative ignorance of the thermal conductivities of sedimentary rocks, especially shales, in efforts to understand or model sedimentary basin thermal histories and maturation levels is a major thrust of the chapter by Blackwell and Steele. Creaney focuses on variations in kerogen composition in source rocks of different depositional environments and the degree to which these chem- . ically distinct kerogens respond differently to progressive burial heating.

This book focuses on two general purpose approaches to data analysis that work well in practice: weighting and imputation. The book takes a very practical approach to the methods, with a number of datasets used to illustrate the key aspects. The datasets are taken from randomized trials, observational studies, and sample surveys. Keeping theoretical details to a minimum, the book is suitable for practitioners with only basic knowledge of statistics. The author’s SAS-based software, which can be used for all the examples, is available online.

1. 1 Solution of geological problems-are mathematical methods necessary? A question which is often asked is whether it is necessary for geologists to know and to use mathematics in the practise of their science. There is no simple answer to this question, and it is true that many geologists have had successful careers without ever needing to get involved in anything other than simple mathematics, and all the indications are that this is likely to continue into the future. However, in many branches of the subject the trend has been towards using a numerical approach for the solution of suitable problems. The extent to which this occurs depends on the nature of the area being studied; thus, in structural geology, which is con cerned in its simplest aspects with the geometrical relationships between various features, there are many problems which are easily solved. More recently the use of analytical methods has allowed the solution of more-difficult problems. In another area, geochemistry, two things have happened. On the theoretical side there has been a greater integration with physical chemistry, which itself is a highly mathematical subject; and on the practical side there is the need to analyse and interpret the vast quantities of data which modem instrumentation produces. Within geology the application of numerical methods has been given various names, so we have numerical geology, geo mathematics, geostatistics and geosimulation.