E-Book, Englisch, 240 Seiten
E-Book, Englisch, 240 Seiten
Reihe: Chapman & Hall/CRC Interdisciplinary Statistics
ISBN: 978-1-4200-3492-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
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.
Zielgruppe
Professionals in fission track labs in universities and oil companies; researchers and research students in geology, archaeology, and geochronology; applied mathematicians and statisticians in the geo-sciencesand undergraduate and graduate earth science students
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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 Inference
