Undergraduate Course: Geophysical Inverse Theory (EASC09038)
|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
|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.
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.
Least squares analysis of the Hawaiian-Emperor Chain age-distance data
Residual static shifts for land seismic surveying (including group working and presentation).
Information for Visiting Students
|Pre-requisites||Equivalent to University of Edinburgh Pre-requisites. Contact course secretary.
|High Demand Course?
Course Delivery Information
|Not being delivered|
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.
|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
|Graduate Attributes and Skills
|Additional Class Delivery Information
|Course organiser||Dr Hugh Pumphrey
Tel: (0131 6)50 6026
|Course secretary||Ms Casey Hollway
Tel: (0131 6)50 8510