Undergraduate Course: Geophysical Inverse Theory (EASC09038)
Course Outline
| School | School of Geosciences |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 9 (Year 3 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | Inverse theory, in the context of this course, is a collection of mathematical techniques used to approach any situation where you can not make a direct measurement of a quantity, but you can measure a different quantity which is related to the one you want by physics which you understand. Problems of this type arise frequently in meteorology and in solid-earth geophysics, and may be encountered in other areas of science.
This course introduces the basic concepts of inverse theory and shows how they may be applied to a variety of geophysical and meteorological examples. The course is mostly lecture based but has two computing exercises. |
| Course description |
PLEASE NOTE: the schedule of lectures shown below is from last year (2013-14). Expect small changes for 2014-15. Note in particular that lectures will continue to the end of week 10 (lecture 20).
Lecture 1
Definition of the forward and inverse problem; how to specify models; continuous functions and parameterised models; examples of pairs of observables and physical properties on which they depend.
Lectures 2-3
Over-constrained and underdetermined models; the least squares method.
Lectures 4-5
The covariance matrix, errors and correlations.
Lectures 6-7
Eigenvectors and eigenvalues; model resolution; fit to the data and information density matrix.
Lectures 8-9
Damping; smoothing and the trade-off curve.
Lectures 10-13
Examples
Lecture 14-15
Linearised methods and iteration
Computer Practicals
Least squares analysis of the Hawaiian-Emperor Chain age-distance data
Residual static shifts for land seismic surveying (including group working and presentation).
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Information for Visiting Students
| Pre-requisites | Equivalent to University of Edinburgh Pre-requisites. Contact course secretary. |
Course Delivery Information
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| Academic year 2014/15, Available to all students (SV1)
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Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 15,
Seminar/Tutorial Hours 4,
Supervised Practical/Workshop/Studio Hours 11,
Feedback/Feedforward Hours 4,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
62 )
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| Assessment (Further Info) |
Written Exam
70 %,
Coursework
30 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
Written Exam: 70%, Course Work: 30 %, Practical Exam: 0%.
The course work is in two parts. The first exercise (Hawaiian-Emperor Chain)is an individual computing problem and will make up 20% of the marks. The second exercise, 10%, is carried out in groups and the results are presented by each group to the rest of the class.
During the exam, which lasts for 1.5 hours, students are expected to answer all five questions in Section A and one of two questions in Section B. |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | | 1:30 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Students will be introduced to Geophysical Inverse Theory and develop an integrated understanding of the essential aspects of parameter estimation.
- A critical understanding of the distinctions between forward and inverse problems, linear and non-linear problems, and the relationships between data and model parameters.
- Formulate and solve least square problems.
- Understand how data uncertainties translate into uncertainties in model parameters; they will also know how and why to weight data by their uncertainties.
- Have a critical understanding of why damping is often a good strategy, know how to do a damped inversion, and be able to explain the effect of damping on model parameter uncertainties and resolution.
6. Understand the eigenvector - eigenvalue decomposition of an inverse problem, and know how the eigenvalue spectrum can be used to help choose an appropriate amount of damping to apply.
7. Know how to treat linearisable problems by an iterative inversion scheme. Through problem sheets, laboratory classes, tutorials and assessment.
8. Formulating, solving and interpreting algebraic and numerical, computer based problems.
9. Making formal and informal presentations on the main aspects of parameter estimation.
10. Applying effectively this knowledge gained to new scenarios.
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Reading List
Time Series Analysis and Inverse Theory for Geophysicists by David Gubbins (CUP)
Geophysical data analysis: Discrete Inverse Theory by William Menke (AP)
Inverse methods for Atmospheric Sounding by Clive D. Rodgers
Inverse Problem Theory and Methods for Model Parameter Estimation by Albert Tarantola (see http://www.ipgp.fr/~tarantola/Files/Professional/Books/index.html)
Inverse Problems in Geophysics} by Roel Snieder and Jeannot Trampert. Only available on the web at http://samizdat.mines.edu/snieder_trampert
Introductory Geophysical Inverse Theory} by John A. Scales, Martin L. Smith and Sven Treitel. Available online from Samizdat Press at http://samizdat.mines.edu/inverse_theory |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Additional Class Delivery Information |
Lectures on Tuesdays and Fridays at 12:10-13:00, Weeks 1-11
Computer Workshop on Mondays at 14:10-16:00, Weeks 3, 6 and 7
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| Keywords | Geophysical_Inverse-Theory |
Contacts
| Course organiser | Dr Hugh Pumphrey
Tel: (0131 6)50 6026
Email: h.c.pumphrey@ed.ac.uk |
Course secretary | Mr Ken O'Neill
Tel: (0131 6)50 8510
Email: koneill3@exseed.ed.ac.uk |
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