Undergraduate Course: Geophysical Imaging and Inversion (EASC10109)
Course Outline
School  School of Geosciences 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 10 (Year 3 Undergraduate) 
Availability  Available to all students 
SCQF Credits  20 
ECTS Credits  10 
Summary  This is a companion course to Geophysical Measurement and Modelling. That course teaches physics and how to represent/model it computationally, this course teaches how to combine that information with new measurements to constrain model parameters for applications in remote sensing in the atmosphere, on the Earth's surface or in the subsurface. Such skills underpin much of science in all of the Geophysical disciplines taught in the SH year. 
Course description 
This course provides an honourslevel introduction to inverse theory and its use in a variety of geophysical contexts. It also provides an introduction to direct imaging methods, which image the Earth's subsurface without using inverse theory.
The inverse theory part of the course begins with some simplified examples which are either linear inverse problems or can be treated as such. These problems are essentially the solution of simultaneous equations, often with either more or fewer equations than there are unknowns; a variety of methods are presented for finding useful solutions to problems with fewer equations than unknowns. While some methods discussed are adhoc, the inverse problem is also considered from the Bayesian probabilistic point of view. Several techniques for assessing the usefulness of the solution to an inverse problem are covered. Extensions of the linear techniques to moderately nonlinear problems are described next, followed by the use of Markov chain Monte Carlo methods (an explicitly Bayesian approach) for very nonlinear problems.
The imaging part of the course surveys a variety of geophysical techniques, including gravity, magnetics, electromagnetics and resistivity, before providing a detailed description of reflection seismology. The practicalities of marine and landbased seismic surveys are considered. The theoretical background of reflection seismology is described, along with the data processing sequence. The use of Fourier transforms for filtering is described. The course concludes with migrationbased seismic processing, which images the subsurface without solving an explicit inverse problem.
The two parts of the course are linked in various ways: inverse theory is required for the understanding of some aspects of the imaging material, and the imaging material provides a variety of examples used in the inverse theory part of the course. The direct imaging methods are essentially computationally tractable approximations to the full inverse solution for subsurface imaging.

Information for Visiting Students
Prerequisites  Good grounding in Maths and Physics to second year level 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2023/24, Available to all students (SV1)

Quota: None 
Course Start 
Semester 2 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
200
(
Lecture Hours 27,
Seminar/Tutorial Hours 7,
Supervised Practical/Workshop/Studio Hours 9,
Feedback/Feedforward Hours 3,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
148 )

Assessment (Further Info) 
Written Exam
60 %,
Coursework
40 %,
Practical Exam
0 %

Additional Information (Assessment) 
Assessment Details:
¿ Exam (60%); Coursework (40%)
Coursework (40%) This is broken down into:
¿ One individual exercise (20%)
¿ One group exercise (20%)
Individual Exercise, 12:00 Tuesday week 5
Group Exercise, InClass, week 9
Written Exam, May Exam Diet

Feedback 
Homework problems will be set each week, with the answers provided later, allowing students to generate their own feedback. The individual coursework exercise will be marked and returned as usual. The group exercise will be assessed with feedback from both staff and students in the audience. 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)   2:00  
Learning Outcomes
On completion of this course, the student will be able to:
 Understand how to combine the information in modelled representations of physics with measured data
 Impose constraints from data on model parameters
 Apply practical skills in data analysis
 Demonstrate knowledge of several applications of inverse methods, including seismic imaging and remote sounding of the atmosphere

Reading List
Time Series Analysis and Inverse Theory for Geophysicists by David Gubbins. (Cambridge University Press)
Inverse Problem Theory and Methods for Model Parameter Estimation by Albert Tarantola. 
Additional Information
Graduate Attributes and Skills 
1. Knowledge of mathematics and probability for application to a variety of practical problems
2. Teamworking on technical problems
3. Confidence in presenting mathematical results verbally.

Keywords  Inversion,imaging,Bayesian,parameters,constraint,conditioning,eigenvalues,eigenvectors 
Contacts
Course organiser  Dr Hugh Pumphrey
Tel: (0131 6)50 6026
Email: Hugh.Pumphrey@ed.ac.uk 
Course secretary  Mr Johan De Klerk
Tel: (0131 6)50 7010
Email: johan.deklerk@ed.ac.uk 

