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 assessed computing exercises.
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| Course description |
PLEASE NOTE: the schedule of lectures shown below is from last year (2014-15). Expect small changes for 2015-16. Note in particular that lectures will continue to the end of week 10 (lecture 20).
Lecture 1: What is inverse theory? Definition of the forward and inverse problem
Lecture 2: Inverse theory as simultaneous equations. Over-constrained problems and the least squares method.
Lecture 3-4: Errors in a vector quantity: the covariance matrix. Weighted least-squares
Lecture 5: Underconstrained problems and damping
Lecture 6: The diagonalising transformation
Lecture 7: Uniqueness, information density and model resolution; Effective number of parameters
Lectures 8: More on eigenvalues and damping
Lecture 9: Linear example: residual statics
Lecture 10: Linear example: Rayleigh wave attenuation
Lecture 11: Linear example: Magnetic field at the core-mantle boundary
Lecture 12: Linear example: Euler deconvolution
Lecture 13: Non-linear problems
Lecture 14: nonlinear example --- simple gravity models
Lecture 15: Ad-hoc error assessment: Checkerboard test
Lectures 16-20: Further examples and discussion of tutorial exercises. Group exercise presentations.
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. |
| High Demand Course? |
Yes |
Course Delivery Information
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| Academic year 2015/16, 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 is an individual computing problem. The second exercise is carried out in groups and the results are presented by each group to the rest of the class.
The computing exercise should be handed in on the Friday of week 5 (Friday 12 February.
The group exercise will be assessed by presentations to be held on the Friday of week 9 (Friday 18 March).
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| Feedback |
Short problems will be set after most lectures, with the answers provided a week or two later, allowing plenty of self-regulated feedback. Some of these problems are computing exercises, applying skills learned in ¿Computational Modelling¿¿ in semester 1.
Selected problems which are not part of the assessment will be marked and returned to provide formative feedback.
The assessment includes two computing practicals. The first exercise is an individual exercise and will be marked and returned.
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| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
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| Main Exam Diet S2 (April/May) | | 1:30 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Understand the distinction between forward and inverse problems
- Solve both underconstrained and over-determined linear problems
- Understand how data uncertainties translate into uncertainties in model parameters
- Understand the eigenvector - eigenvalue decomposition of an inverse problem
- Solve linearisable nonlinear problems using an iterative inversion scheme.
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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
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Additional Class Delivery Information |
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| Keywords | Geophysical_Inverse-Theory |
Contacts
| Course organiser | Dr Hugh Pumphrey
Tel: (0131 6)50 6026
Email: |
Course secretary | Ms Casey Hollway
Tel: (0131 6)50 8510
Email: |
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