Methods of measurement and absolute datings
Academic Year 2022/2023 - Teacher: PAOLA LA ROCCAExpected Learning Outcomes
The course aims at providing the basic knowledge and tools for the analysis of geophical data, for the uncertainties estimation and for statistical analyses. It also gives an introduction to the main dating methods and their application in Geophysics.
The Learning Objectives, within the Dublin Descriptors scheme, are:
- Knowledge and understanding: knowledge of the basic notions of statistics and data analysis techniques; knowledge of the main dating techniques and their field of application;
- Applying knowledge and understanding: ability to analyze and understand experimental data;
- Making judgements: ability to make numerical estimations of physical quantities;
- Communication skills: ability to discuss (in an oral conversation or in writing) a scientific topic using an appropriate scientific language;
- Learning skills: ability to study individually and to keep up-to-date with the new scientific discoveries in this field.
Course Structure
Classroom-taught lessons by the use of interactive power point presentations.
Practical sessions of data analisys and exercises.
Guided tours of nuclear physics and dating laboratories.
N.B. Should the circumstances require online or blended teaching, appropriate modifications to what is hereby stated may be introduced, in order to achieve the main objectives of the course. Exams may take place online, depending on circumstances.
Information for students with disabilities and / or SLD
To guarantee equal opportunities and in compliance with the laws in force, interested students can ask for a personal interview in order to plan any compensatory and / or dispensatory measures, based on the didactic objectives and specific needs. It is also possible to contact the referent teacher CInAP (Center for Active and Participated Integration - Services for Disabilities and / or SLD) of our Department, Prof. Giorgio De Guidi.
Required Prerequisites
Basic knowledge about topics in mathematics, statistics and physics, usually reached during the bachelor degree course in Geological Science.
Attendance of Lessons
Should the circumstances require online or blended teaching, appropriate modifications to what is hereby stated may be introduced, in order to achieve the main objectives of the course.
Detailed Course Content
First part
1) Measurement of a Physical quantity
The scientific method – Physical quantities – Units of measurement – Measurement uncertainty – Estimation of the uncertainty – Absolute and relative uncertainties – How to report uncertainties – Use of tables – – Comparison of two measured numbers – Significant Figures – Graphical representation of the experimental data
2) Propagation of uncertainties
Direct and indirect measurements - Error propagation in sums, differences, products and quotients - Independent uncertainties in a measurement - General formula for error propagation
3) Statistical analysis of random uncertainties
Histograms and distributions - The mean and Standard Deviation – The weighted average - The Gaussian distribution and its properties - The Poisson distribution and its properties - Student test
4) Least-squares fitting
Introduction to the least-squares fit - The Linear best-fit – Calculation of the constants A and B - Uncertainties in the constants A and B - Least-squares fits to other curves – Examples and applications
5) The chi-squared test for a distribution
Comparison between theoretical and experimental data distributions - General definition of chi-squared - Degree of freedom and the reduced chi-squared – The chi-squared test - Examples
Second part
1) Basics of Nuclear Physics
The nucleus and its contents - Mass number and atomic number – Isotopes – Abundance of isotopes in nature
2) Basics of radioactivity
Nuclear stability – The radioactivity - The radioactivity decay law –Decay constant, lifetime and half-life - Types of Radioactive Decay – Alpha decay - Beta decay - Gamma decay
3) Dating methods
Introduction to the dating methods - Radiocarbon dating - AMS dating - Potassium-Argon dating - Argon-Argon dating - Uranium-Thorium dating - Rubidium-Stronzium dating - Fission track dating – Thermoluminescence phenomena and its application in archaeological dating - Electron spin resonance and its use in dating - atcheomagnetic dating technique
Textbook Information
1) J.R. Taylor, “Introduzione all’analisi degli errori”, Zanichelli
2) B.Povh, K.Rith, C.Scholtz, F.Zetsche, “Particelle e Nuclei”, Bollati-Boringhieri
3) W.S.C. Williams, “Nuclear and Particle Physics”, Oxford Science Publications
4) M.J.Aitken, “Science-based Dating in Archeology”, Pearson Education
5) A.Castellano, M.Martini, E.Sibilia, “Elementi di archeometria”, Egea
| Author | Title | Publisher | Year | ISBN |
|---|---|---|---|---|
| J.R.Taylor | Introduzione all’analisi degli errori, seconda edizione | Zanichelli | 1999 | 978880817656 |
| B.Povh, K.Rith, C.Scholtz, F.Zetsche | Particelle e Nuclei | Bollati-Boringhieri | 1998 | 9788833955957 |
| W.S.C. Williams | Nuclear and Particle Physics | Oxford Science Publications | 1991 | 9780198520467 |
| M.J.Aitken | Science-based Dating in Archeology, 1st edition | Pearson Education | 1990 | 9780582493094 |
| A.Castellano, M.Martini, E.Sibilia | Elementi di archeometria, seconda edizione | Egea | 2007 | 9788823820920 |
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | The scientific method | 1) |
| 2 | Physical quantities, units of measurement | 1) |
| 3 | Uncertainty in experimental measurements | 1) |
| 4 | "Qualitative" estimation of uncertainties | 1) |
| 5 | Absolute and relative uncertainties | 1) |
| 6 | Numerical representation of a measurement | 1) |
| 7 | Tables | 1) |
| 8 | Significant digits | 1) |
| 9 | Comparison between different measurements | 1) |
| 10 | Graphycal represention of experimental data | 1) |
| 11 | Direct and indirect measurements | 1) |
| 12 | Uncertainties propagation for sums, differences, ratios and products | 1) |
| 13 | Independent uncertainties | 1) |
| 14 | General formula for uncertainties propagation | 1) |
| 15 | Histograms and data distributions | 1) |
| 16 | Mean and standard deviation | 1) |
| 17 | Combination of measurements with different uncertainties | 1) |
| 18 | Weighted mean | 1) |
| 19 | Limiting distributions | 1) |
| 20 | Gaussian distribution and its properties | 1) |
| 21 | Poissian distribution and its properties | 1) |
| 22 | Method of least squares | 1) |
| 23 | Introduction to the method of least squares | 1) |
| 24 | Linear best-fit | 1) |
| 25 | Evaluation of free parameters in the linear best-fit procedure | 1) |
| 26 | Evaluation of uncertainties of the free parameters in the linear best-fit procedure | 1) |
| 27 | Least squares methos applied to a data distribution | 1) |
| 28 | Applications of the best-fit procedures | 1) |
| 29 | Comparison between theoretical and experimental distributions | 1) |
| 30 | Chi-square | 1) |
| 31 | Degrees of freedom and reduced chi-square | 1) |
| 32 | Chi-square test | 1) |
| 33 | Applications of the chi-square test | 1) |
| 34 | Basic concepts of nuclear physics | 2) 3) |
| 35 | The nucleus and its components | 2) 3) |
| 36 | Atomic and mass numbers | 2) 3) |
| 37 | Isotopes | 2) 3) |
| 38 | Isotopes in nature | 2) 3) |
| 39 | Nuclei stability | 2) 3) |
| 40 | Radioactivity | 2) 3) |
| 41 | Radioactivity decay law | 2) 3) |
| 42 | Decay constant, average lifetime, half-time | 2) 3) |
| 43 | Types of decay | 2) 3) |
| 44 | Alpha decay | 2) 3) |
| 45 | Beta decay | 2) 3) |
| 46 | Gamma decay | 2) 3) |
| 47 | Dating techniques | 4) 5) |
| 48 | Radiocarbon dating | 4) 5) |
| 49 | AMS dating | 4) 5) |
| 50 | Potassium-Argon dating | 4) 5) |
| 51 | Argon-Argon dating | 4) 5) |
| 52 | Uranium-Thorium dating | 4) 5) |
| 53 | Rubidium-Strontium dating | 4) |
| 54 | Dating based on nuclear fission tracks | 4) 5) |
| 55 | Thermoluminescence dating | 4) 5) |
| 56 | Electron spin resonance dating | 4) 5) |
Learning Assessment
Learning Assessment Procedures
The exams dates can be found on the web site of the Master Degree in Geophysical Science http://www.dipbiogeo.unict.it/corsi/lm-79. At least 2 dates are available foor each session.
The exam consists in an oral discussion about the contents of the course. The minimum mark is 18.
The final evaluation will take into account the following aspects:
- knowledge of the contents
- clarity and language skills
- relevance of the answers to the asked questions
- ability to make correct links with other topics in the program
- ability to report examples
- ability to solve simple exercises and make estimates
The verification of learning will be done remotely if the circumstances would require online or blended teaching.
Examples of frequently asked questions and / or exercises
- Discuss the main types of uncertainties in an experimental measurement.
- Explain the difference between accuracy and precision.
- Explain the difference between direct and indirect measurements.
- Discuss the general formula for the uncertainties propagation in an indirect measurement.
- List and describe the indexes of dispersion.
- Explain the meaning of limiting distributions.
- List and discuss the main properties of the Gaussian distribution and give an example of its application in an experimental data analysis.
- List and discuss the main properties of the Poissian distribution and give an example of its application in an experimental data analysis.
- Describe the least squares method.
- Describe the chi-square test.
- Discuss the radioactive decay law.
- Explain the difference between isotope lifetime and half time.
- List the main properties of dating techniques.
- Describe one of the dating methods discussed in the course.
- Discuss the limits of a given dating technique.