Statistics for Fission Track Analysis

Statistics for Fission Track Analysis

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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 more

Product details

  • Hardback | 240 pages
  • 157.5 x 248.9 x 20.3mm | 476.28g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 30 black & white illustrations
  • 1584885335
  • 9781584885337

Review quote

... The book collates the huge amount of high quality statistical work that the author has contributed to the analysis of fission track data, often in collaboration with G. M. Laslett, over a 20-year period. It seems to me to provide an object lesson in sound statistical practice, grounding the work in appropriate simple physical models, extending models empirically and fitting them by maximum likelihood, always being fully immersed in, and addressing, the context to hand, and providing a deep understanding of the limitations of the laboratory and statistical techniques used. ... an essential handbook for all scientists who are involved with fission track analysis. ... this is an excellent book and I congratulate the author on his contributions to the topic. -M.C. Jones, Journal of the Royal Statistical Society, 2006, Volume 169, Issue 3 The book is a good survey for scientists who have worked in the field. ...This would be an excellent introductory text for those wishing to enter this field, especially if they were also aware of the new statistical tools available. -E. Enns, Short Book Reviews of the ISI I strongly recommend this book to its intended audience and would use it in a course on statistical consulting. -Thomas Burr, Los Alamos National Library, Technometrics, November 2008, Vol. 50, No. 4show more

Table of contents

INTRODUCTION What are Fission Tracks? How are they Observed? Why are they Useful? Applications of Fission Track analysis Mathematical Representation of Fission Tracks Fission Track Dating and Provenance Studies Thermal Histories and Track Length Distributions Sampling by Plane Section Intitial Formation of Tracks Shortening of Tracks by Heat Properties of Apatite Bibliographic Notes THE POISSON LINE SEGMENT MODEL Joint Distribution of Length and Orientation The Number of Tracks with a Given Attribute The Expected Number of Tracks Intersecting a Plane Track Density and Equivalent Isotropic Length Tracks Intersecting a Prismatic Face Effect of Non-Prismatic Face on Track Density Track counts from a Dosimeter Glass Spatial and Temporal Variation Remarks Bibliographic Notes TRACK COUNTS AND DENSITIES: FISSION TRACK DATING The Mathematical Basis of Fission Track Dating The External Detector Method Observed and Theoretical Track Densities A Short Digression Estimates of Fission Track Age Inspection of Single Grain Data Radial Plot of Single Grain Ages Chi-Square Age Homogeneity Test A Measure of Age Dispersion A Protocol for Data Analysis Dealing with Small counts Practical Considerations Remarks Historical Note Bibliographic Notes THE POPULATION METHOD Experimental Method and Data Theoretical and Observed Track Densities An Estimate of the Uranium Dispersion A Uranium Homogeneity Test Estimates of Fission Track Age Summarising and Inspecting the Data Age Homogeneity Test A Measure of Dispersion of True Fission Track Ages Counts over Unequal Areas A Protocol for data Analysis Discussion The Population-Subtraction Method Remarks Bibliographic Notes DISCRETE MIXTURES OF AGES Maximum Likelihood Estimation of a Common Age Discrete Mixture Models Example" A Synthetic Mixture of Two Ages Example: Apatite Data from the Bengal Fan Maximum Likelihood Estimation Formulae How Many Ages to Fit? Example: Zircon Ages from Mount Tom Data from more than One Irradiation Bibliographic Notes CONTINUOUS MIXTURES OF AGES Example: Otway Data from Victoria, Australia General Approach A Random Effects Model with Binomial Errors Maximum Likelihood Estimation Formulae A Random Effects Model with Normal Errors Examples Finite Mixtures of Random Effects Models A Minimum Age Model Data and Statistical Model with Binomial Errors Maximum Likelihood Estimation Formulae A Minimum Age Model with Normal Errors Example: Apatite Data from China A Synthetic Mixture Revisited Grain Age Distributions Remarks Bibliographic Notes PROBABILITY DISTRIBUTIONS OF LENGTHS AND ANGLES All Tracks Having the Same Length Each Track Having One of Two Lengths Several Different Lengths A General Isotropic Length Distribution A General Anisotropic Length Distribution Distributions on a Prismatic Face Horizontal Confined Track Lengths Some explicit Formulae A Two-Component Mixture of Anisotropic Lengths Quantitative Effects of Anisotropy Parametric Models for Length Against Angle Bibliographic Notes OBSERVATIONAL FEATURES OF TRACK MEASUREMENTS Horizontal Confined Tracks Length Bias The Loaded Dog Experiments Empirical Verification of Length Bias Fracture-Thickness Bias Orientation Bias Surface Proximity Bias Estimate of m from Horizontal Confined Tracks Projected Semi-Track Lengths and Angles Semi-Track Lengths and Angles Bibliographic Notes FURTHER DEVELOPMENTS Thermal History Parameters Combined Likelihood for Track Measurements Annealing Experiments Annealing Data Annealing Models Fitting Annealing Models Calculating the Length Distribution Inferring Times and Temperatures from Lengths Multi-Compositional Annealing Models Bibliographic Notes APPENDIX Poisson Processes in One, Two, and Three Dimensions Notes on the Poisson Distribution Relation Between Binomial and Poisson Distribution Standard Errors and Confidence Intervals Components of Error Statistical Significance Tests and p-Values Radial Plots Histograms and "Probability Density" Plots Parametric Models and Likelihood Inferenceshow more