# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2017/2018

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# 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 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. 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).
 Pre-requisites It is RECOMMENDED that students have passed Introduction to Geophysics (EASC08008) AND Computational Modelling for Geosciences (EASC09035) Co-requisites Prohibited Combinations Other requirements None Additional Costs None.
 Pre-requisites Equivalent to University of Edinburgh Pre-requisites. Contact course secretary. High Demand Course? Yes
 Not being delivered
 On completion of this course, the student will be able to: Understand the distinction between forward and inverse problemsSolve both underconstrained and over-determined linear problemsUnderstand how data uncertainties translate into uncertainties in model parametersUnderstand the eigenvector - eigenvalue decomposition of an inverse problemSolve 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 Not entered Additional Class Delivery Information Keywords Geophysical_Inverse-Theory
 Course organiser Dr Hugh Pumphrey Tel: (0131 6)50 6026 Email: h.c.pumphrey@ed.ac.uk Course secretary Ms Casey Hollway Tel: (0131 6)50 8510 Email: earth.sciences@ed.ac.uk
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