ROSE School: Signal Processing Geophysical Data Analysis

Prof. Dr. Heiner Igel, Dr. Cιline Hadziioannou, Tobias Megies, LMU Munich

 

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, SIAM, 2005 (probabilistic inversion, examples in the appendix)

•         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:

  • Problems in seismology, fundamentals of seismic wave propagation
  • Mathematical foundations of signal processing, Fourier Analysis
  • Spectral estimation, Window functions
  • Multitapering, wavelet methods
  • Introduction to Python/ObsPy

 

Week 2:

  • Linear systems, transfer functions
  • Filter theory
  • (De-) convolution, correlations
  • Laplace and Z transforms
  • Seismic instruments, instrument correction

 

Week 3:

  • Correlation techniques, noise analysis
  • Linear inverse problems
  • Singular value decomposition and generalized inverse
  • Probabilistic Inverse theory

 

Week 4:

  • Monte Carlo Methods
  • Applications to geophysical problems
  • Exam

 

 

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: Monte Carlo methods