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DRPS : Course Catalogue : School of Geosciences : Earth Science

Undergraduate Course: Geophysical Inverse Theory (EASC09038)

Course Outline
SchoolSchool of Geosciences CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 9 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryInverse 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).
Entry Requirements (not applicable to Visiting Students)
Pre-requisites It is RECOMMENDED that students have passed Introduction to Geophysics (EASC08008) AND Computational Modelling for Geosciences (EASC09035)
Prohibited Combinations Other requirements None
Additional Costs None.
Information for Visiting Students
Pre-requisitesEquivalent to University of Edinburgh Pre-requisites. 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:
  1. Understand the distinction between forward and inverse problems
  2. Solve both underconstrained and over-determined linear problems
  3. Understand how data uncertainties translate into uncertainties in model parameters
  4. Understand the eigenvector - eigenvalue decomposition of an inverse problem
  5. 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
Inverse Problems in Geophysics} by Roel Snieder and Jeannot Trampert. Only available on the web at
Introductory Geophysical Inverse Theory} by John A. Scales, Martin L. Smith and Sven Treitel. Available online from Samizdat Press at
Additional Information
Graduate Attributes and Skills Not entered
Additional Class Delivery Information
Course organiserDr Hugh Pumphrey
Tel: (0131 6)50 6026
Course secretaryMs Casey Hollway
Tel: (0131 6)50 8510
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