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 solidearth 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.

Course description 
PLEASE NOTE: the schedule of lectures shown below is from last year (201415). Expect small changes for 201516. 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. Overconstrained problems and the least squares method.
Lecture 34: Errors in a vector quantity: the covariance matrix. Weighted leastsquares
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 coremantle boundary
Lecture 12: Linear example: Euler deconvolution
Lecture 13: Nonlinear problems
Lecture 14: nonlinear example  simple gravity models
Lecture 15: Adhoc error assessment: Checkerboard test
Lectures 1620: Further examples and discussion of tutorial exercises. Group exercise presentations.
Computer Practicals
Least squares analysis of the HawaiianEmperor Chain agedistance data
Residual static shifts for land seismic surveying (including group working and presentation).

Information for Visiting Students
Prerequisites  Equivalent to University of Edinburgh Prerequisites. Contact course secretary. 
High Demand Course? 
Yes 
Course Delivery Information
Not being delivered 
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 overdetermined 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.

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 

Keywords  Geophysical_InverseTheory 
Contacts
Course organiser  Dr Hugh Pumphrey
Tel: (0131 6)50 6026
Email: Hugh.Pumphrey@ed.ac.uk 
Course secretary  Ms Casey Hollway
Tel: (0131 6)50 8510
Email: earth.sciences@ed.ac.uk 

