Prof. Dr. Heiner Igel,
Dr. Cιline Hadziioannou,
Tobias Megies, LMU
February 6 March 2, 2012
Scope: The course aims to provide students with an understanding
of the principles of digital signal processing, filter theory and the
application of spectral methods in the analysis of geophysical data. Topics
include discrete Fourier transforms, convolution, power spectra, coherence,
transfer functions, covariance, correlation, Laplace transforms, Z-transforms,
filters, de-convolution, auto-regressive models, spectral estimation, basic
statistics, 1-D wavelets, model fitting via singular valued decomposition, and
probabilistic methods. The lectures are complemented by extensive practicals with data examples from major recent
earthquakes, as well rotational seismology, and computational wave propagation.
Practicals will be carried out using python based
tools (e.g., ObsPy, www..obspy.org)
as well as Matlab.
Literature:
Most of the
graphics are taken from the following books,
additional material is given with each lecture or tutorial:
Stein and Wysession, An
introduction to seismology, earthquakes and earth structure, Blackwell
Scientific (Chapts.
6, 7 and appendix) see also http://epscx.wustl.edu/seismology/book
.
Shearer, Introduction to Seismology, Cambridge
University Press, 1990, 2nd edition 2009 (section on data processing
and appendices)
Tarantola, Inverse Problem
Theory and Model Parameter Estimation,
Gubbins, Time series
analysis and inverse problems for geophysicists, Cambridge University Press
(e.g., Z-transforms, geophysical applications)
Scherbaum, Basic concepts
in digital signal processing for seismologists (e.g., seismometer equation,
instrument corrections).
Menke: Geophysical data
analysis: discrete inverse theory
Minimum total
lecture time: 10
hrs/week
Minimum total
tutorial time: 6 hrs/week
Tentatative Schedule
Week 1:
Week 2:
Week 3:
Week 4:
Time Plan (L lecture, T tutorial, E exams)
Day/Time |
10:00-11:30 |
12:00-13:00 |
14:00-16:00 |
Mon, Feb 6 |
L |
L |
T |
Tue, Feb 7 |
L |
L |
T |
Wed, Feb 8 |
L |
L |
|
Thu, Feb 9 |
L |
L |
T |
Fri, Feb 10 |
L |
T |
|
|
|
|
|
Mon, Feb 13 |
L |
L |
T |
Tue, Feb 14 |
L |
L |
T |
Wed, Feb 15 |
L |
L |
T |
Thu, Feb 16 |
L |
L |
|
Fri, Feb 17 |
|
|
|
|
|
|
|
Mon, Feb 20 |
|
|
|
Tue, Feb 21 |
L |
L |
T |
Wed, Feb 22 |
L |
L |
|
Thu, Feb 23 |
L |
L |
T |
Fri, Feb 24 |
L |
T |
|
|
|
|
|
Mon, Feb 27 |
L |
L |
T |
Tue, Feb 28 |
L |
L |
T |
Wed, Feb 29 |
L |
T |
|
Thu, Mar 1 |
E |
E |
|
Fri, Mar 2 |
|
|
|
Programm details and lecture material
Lectures:
Note: Lecture material, comprehension questions,
exercises, additional material and recent research papers on the topics will be
given (linked) shortly before the course starts.
L1: Introduction: What are the current hot topics
of seismology and what role do computations and data analysis play? (more
L2: Mathematical
background for data analysis and inverse problems (more)
L3: Seismic waves and sources (more)
L4: Data in
seismology: networks, observables, and instruments (more)
L5: Spectral
analysis: Foundations and applications (more)
L6: Filtering: Be careful! (more)
L7: Windows, Tapers, Wavelets (more)
L8: (Almost
everything is a) Linear system: convolution and
de-convolution, transfer functions, and other transforms (more)
L9: Auto-
and cross-correlations: applications in geophysics (more)
L10: Linear Inverse problems (more)
L11: Probabilistic inverse problems (more)
Tutorials:
Note: The tutorials will be both theoretical and
computational. The computational exercises will be carried out with python and/or
Matlab. Most participants will be familiar with Matlab. An introduction to python will be given. You are
welcome to familiarize yourself with python before the course. We will use
mostly the libraries given in the ObsPy package. There
is a lot of tutorial material on the following www site: www.obspy.org.
T1: Maths exercises: complex numbers, linear
algebra, matrices and vectors, eigenvector analysis, applications to
geophysical problems
T2: Introduction to Python and ObsPy
T3: Spectral
estimation and filtering with data from recent Giant earthquakes
T4: Filtering, time-frequency analysis
T5: Seismic instrument correction
T6: Synthetic seismogram generation
T7: Correlation techniques
:
T8: Linear inverse problems
T9: