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Inverse problems in geophysics - MG452P73

Title:	Obrácené úlohy v geofyzice
Czech title:	Obrácené úlohy v geofyzice
Guaranteed by:	Institute of Hydrogeology, Engineering Geology and Applied Geophysics (31-450)
Faculty:	Faculty of Science
Actual:	from 2020
Semester:	winter
E-Credits:	4
Examination process:	winter s.:
Hours per week, examination:	winter s.:2/1, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Level:	specialized
Explanation:	Výuka probíhá s ohledem na situaci dle nařízení hyg. stanice hl.m. Prahy a MŠMT
Note:	enabled for web enrollment

Guarantor:	RNDr. Bohuslav Růžek, CSc.
Teacher(s):	RNDr. Bohuslav Růžek, CSc.

Opinion survey results Examination dates WS schedule

Annotation -

Last update: RNDr. Josef Datel, Ph.D. (01.06.2009)

Forward and inverse problem, linear and non-linear inversion, inversion versus optimization, model parametrization and propagation of errors, stochastic inversion, genetic and evolution algorithms

Literature - Czech

Last update: Mgr. Zdeňka Sedláčková (04.01.2012)

R.C. Aster, B. Borchers, C.H. Thurber: Parameter Estimation and Inverse Problems. Elsevier, Amsterdam 2005.

W. Menke: Geophysical Data Analysis: Discrete Inverse Theory. (Revised Edition). Academic Press, San Diego 1989.

A. Tarantola: Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier, New York 1987.

Starší verze některých dokumentů k přednášce je na

http://www.ig.cas.cz/cz/vyzkum-a-vyuka/

Requirements to the exam - Czech

Last update: Mgr. Zdeňka Sedláčková (04.01.2012)

Podmínkou zápočtu je vypracovaní vybrané inverzní úlohy: sestavení algoritmu, naprogramovaní v Matlabu (nebo jiném programovacím jazyce),

diskuse zadaných dat a výpočet inverzní úlohy.

Zkouška je ústní a je nutno zodpovědět 3 vylosované otázky ze souboru cca 35 otázek.

Syllabus -

Last update: RNDr. Josef Datel, Ph.D. (01.06.2009)

1. Basic notions

Importance of inverse problems in contemporary geophysics. A brief review of the historical development. Inverse problem versus optimisation. Deterministic versus statistical variables. Probability. Operations with random variables. Propagation of errors.

2. Linear algebra and mathematical methods of linear inversions

Matrix operations. The first and second Gauss transformations. System of linear equations with a rectangular matrix, least squares method and minimum norm method. Regularisation of matrices. Inverse matrix, generalised inversion, determinant, eigenvalues, eigenvectors. Projection matrix. Singular value decomposition. Transformation of matrices.

3. Linear inverse problem

Space of parameters and data. Covariance of parameters and data, mutual relation. Null-space and range. Resolution matrix. System identification.

4. Methods of non-linear inversion and non-linear optimisation

Method of tangents/secants. Simplex method. Variable metric method. Newton-Raphson method. Monte Carlo method, Markov?s chains. Genetic/evolution algorithms. Artificial neural networks.

5. Examples of inverse problems in geophysics

Earthquake location, joint estimation of hypocentral and structural parameters. Seismic tomography. Inversion of waveforms. Inversion of seismic data in anisotropic models. Magneto-telluric inversion in 1D a 2D media. Inversion of surface-wave dispersion curves.