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Course, academic year 2024/2025
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Methods of Geophysical Data Processing - NGEO057
Title: Metody zpracování geofyzikálních dat
Guaranteed by: Department of Geophysics (32-KG)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: summer
E-Credits: 5
Hours per week, examination: summer 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, English
Teaching methods: full-time
Guarantor: prof. RNDr. František Gallovič, Ph.D.
Teacher(s): prof. RNDr. František Gallovič, Ph.D.
Classification: Physics > Geophysics
Is co-requisite for: NGEO058
Annotation -
Deterministic and stochastic signals in geophysics. Linear filtration, z-transformation, prediction filters. Autocorrelation and power spectral density of random signals, parametric and nonparametric methods. Multichannel data, polarization analysis.
Last update: T_KG (02.05.2013)
Aim of the course -

The lecture provides basic techniques for analysis, filtration, modeling and prediction of signals and their applications to geophysical temporal and spatial data.

Last update: T_KG (02.05.2013)
Course completion requirements - Czech

Podmínkou udělení zápočtu je aktivní účast na cvičeních.

Povaha kontroly studia předmětu vylučuje opravné termíny zápočtu.

Získání zápočtu je podmínkou pro konání zkoušky.

Last update: Gallovič František, prof. RNDr., Ph.D. (06.10.2017)
Literature - Czech
  • Marple, S. L. (1987). Digital Spectral Analysis With Applications. Prentice-Hall, Englewwod Cliffs, New Jersey.
  • Percival, D. B., and A. T. Walden (1993). Spectral Analysis for Physical Applications - Multitaper and Conventional Univariete Techniques, Cambridge Univ. Press.
  • Gubbins, D. (2004). Time Series Analysis and Inverse Theory for Geophysicists. Cambridge Univ. Press.
  • Claerbout, J. F. (1985). Fundamentals of Geophysical Data Processing with Applications to Petroleum Prospecting, 2nd edn, Blackwell Scientific Publications, http://sep.stanford.edu/sep/prof/

Last update: T_KG (16.11.2011)
Teaching methods -

Lecture + exercises

Last update: T_KG (11.04.2008)
Requirements to the exam - Czech

Zkouška je ústní, požadavky odpovídají sylabu v rozsahu prezentovaném na přednášce.

Last update: Gallovič František, prof. RNDr., Ph.D. (06.10.2017)
Syllabus -
Classification of geophysical data

Deterministic and stochastic processes, stationary random process, mean and autocorrelation, spectrum and power spectral density, ergodicity.

Linear filters

Linearity, time invariance, causality, stability, impulse response, transfer function, ideal filter, convolution in the frequency domain, filter with zero and linear phase, low pass-, band pass- and high pass-filters, Butterworth filter, filtration of a random process.

Discrete signals

Sampling, Nyquist frequency, relation between continuous and discrete Fourier transform, alias. Z-transform and digital filtering, convolution and deconvolution, minimum phase, dipole with minimum phase, bilinear transformation, spectral factorization and Töplitz approach. Wiener filter, Yule-Walker normal equations, optimal filtering, linear prediction.

Nonparametric power spectral density estimates

Data tapering. Sample spectrum, correlograms, periodograms, multitaper approach. Trade-off between estimation variance and resolution.

Parametric power spectral density estimates

Definition of Autoregressive (AR) and Moving Average (MA) random process, AR power spectral density estimation, relation of AR parametry and autocorrelation function, relation to linear prediction filter. Estimates of the AR parameters, model order selection.

Pseudo power-spectral density

Minimum variance (MV) spectral estimation, relationship between MV and AR spectral estimator. Eigenanalysis-based frequency estimation, eigenanalysis of autocorrelation matrix for sinusoids in white noise, signal and noise subspace frequency estimators, order selection.

Multichannel and vector data

Spectral estimates, polarization analysis.

Last update: T_KG (02.05.2013)
 
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