6. Resolution and spectral content

6. Resolution and spectral content - 6. Spectral Content...

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Unformatted text preview: 6. Spectral Content Kurt J. Marfurt CPSGG The University of Oklahoma Petroleum Geology and Geophysics 6-1 Learner Objectives After this section, you will be able to: Visualize time- and space-variant signals in terms of their spectral components Be able to describe the impact of low-pass, high-pass, and band-pass filtering Evaluate strong, constructive interference from thin beds in terms of tuning thickness 6-2 Spatial resolution 6-3 Periodic vibrations (in time) Period, T Frequency, f=1/T (measured in Hz) Radial frequency, =2f=2 /T (measured in radians/s) T i m e ( s ) Amplitude 6-4 Wave length, Distance (m) Radial frequency, =2 /T (measured in Hz) Wavenumber, k=2 / (measured in radians/m) Periodic vibrations (in space) Amplitude 6-5 Any function can be decomposed into sinusoids of different amplitude, phase, and frequency. (Bergbauer et al, 2003) z (m) x (m) 100m cmpt 300m cmpt 1200m cmpt Sum of three cmpts 10 20 40 50 60 30 Spectral analysis of topography 6-6 Spectral analysis of a seismic wavelet w a v e l t (Yilmaz, 2001) 6-7 Forward Fourier Transforms Fourier cosine transform Fourier sine transform Complex Fourier transform 6-8 = =-= T T t even c t t d D ) cos( ) ( ) ( = = T t odd s t t d D ) sin( ) ( ) ( + = = T t t i t d D ) exp( ) ( ) ( ) ( ) ( ) ( s c iD D D + = Inverse Fourier Transforms Fourier cosine transform Fourier sine transform Complex Fourier transform 6-9 = = max ) cos( ) ( ) ( t D t d c even ) ( ) ( ) ( t d t...
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This note was uploaded on 02/04/2012 for the course GPHY 3423 taught by Professor Marfurt during the Fall '11 term at The University of Oklahoma.

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6. Resolution and spectral content - 6. Spectral Content...

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