Undergraduate Course: Fields and Waves (EASC09033)
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  The course introduces a common framework to address diverse problems of Earth physics based on special cases of the telegraph equation.
The course describes the geophysical applications to acoustic wave propagation and to gravity, magnetic, electrical, electromagnetic, heat flow, and seismic problems.
This course extends the Teaching of U00545 Physics 2A: Forces, Fields and Potentials to general features of waves, fields, and diffusive propagation in continuous media. The course also extends the teaching of electricity and magnetism in Physics 2A to geophysical problems including current flow in the Earth and variations of conductivity within it.
Lastly, the course introduces the concepts of passive and active measurement of geophysical data and discusses the sources required for active geophysical exploration.

Course description 
The apportioning of topics between lectures is approximately as follows.
L12
Derivation of the Telegraph Equation.
Total time derivative and partial time derivative; acceleration of a particle; linearization; equation of continuity; pressure waves in a fluid; constitutive equation; 1D, 2D and 3D acoustic wave equations; solution to the 1D wave equation.
L3
Potential Fields
Newton's law of gravitation; gravity; gravitational potential; Laplace's equation; Poisson's equation; force due to electric charge and magnetic poles.
L45
Seismic Waves
Components of strain and stress; equations of motion in an elastic medium; Hooke's law of elasticity; elastic wave equations, Pwaves and Swaves; particle motion of a plane wave; solutions to the wave equation; normal modes: oscillations of a string.
L67
Electromagnetic (EM) Waves and Heat Flow
Maxwell's equations; constitutive relations; EM wave equations; plane wave solutions of the EM wave equations, skin depth, wavelength; EM propagation in air and free space; EM propagation in conducting media; diffusion equation. Heat flow in solids.
L8
Revision of Fourier Theory
Fourier transform; the deltafunction; resolution and bandwidth; similarity theorem; impulse function; impulse response; linear filters and convolution; convolution theorem; derivative theorem; wavefield transformation.
L910
Passive Geophysical Measurements
Gravity anomalies; gravity meters, measurements and corrections; gravity gradiometry and gravity measurement on a moving vessel or aeroplane; nonuniqeness of gravity interpretation; magnetics; heat flow; the magnetotellurics method; classical seismology; AdamsWilliamson equation.
L1112
Active Geophysical Measurements
Controlled Source Electromagnetics (CSEM) and the role of fluids; conventional CSEM; transient CSEM and MTEM; seismic exploration and data acquisition; seismic exploration and reflection coefficients for acoustic waves; seismic exploration and normal moveout correction and stacking.
L1316
Seismic Sources and Receivers
Monopole source  dynamite on land; the Vibroseis method and vibrator force source; Vibroseis method and correlation with the sweep; Vibroseis method and generation of the sweep; Vibroseis method and the downgoing wavefield; marine airgun source; marine airgun source and spectrum and effect of sea surface; marine airgun source and arrays of air guns; effect of seasurface reflection at receiver; geophones, hydrophones and accelerometers.
L1718
Manipulation of Wavefield Measurements
Sampling theorem and aliasing; sources of noise; filtering; deconvolution; upward and downward continuation.

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information
Not being delivered 
Learning Outcomes
On completion of this course, the student will be able to:
 Familiarity with essential mathematical techniques.
 Familiarity with concepts of classical physics applied to Earth problems.
 Confidence in the conceptual framework of analysing fields and waves.
 Appreciation of the application of physical and mathematical techniques to diverse Earth problems.
 Appreciation of manipulation of geophysical data to obtain physical properties of the Earth.

Reading List
"Fundamentals of Geophysics" by William Lowrie, Cambridge University Press.
"A Student's Guide to Geophysical Equations" by William Lowrie, Cambridge University Press.
Course notes are also provided online.

Additional Information
Graduate Attributes and Skills 
Not entered 
Additional Class Delivery Information 
Thursdays at 11:1013:00, Weeks 111 
Keywords  Fields_and_waves 
Contacts
Course organiser  Prof Anton Ziolkowski
Tel: (0131 6)50 8511
Email: anton.ziolkowski@ed.ac.uk 
Course secretary  Ms Casey Hollway
Tel: (0131 6)50 8510
Email: earth.sciences@ed.ac.uk 

