1 / 18

Fourier Theory in Seismic Processing

Fourier Theory in Seismic Processing. (From Liner and Ikelle and Amundsen). Temporal aliasing Spatial aliasing. Sample Rates. What is the fewest number of times I need to sample this waveform per second?. ?. ?. ?. Sample Rates. Sample Rates. Sample Rates. Sample Rates.

raymond-mcintosh
Télécharger la présentation

Fourier Theory in Seismic Processing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Fourier Theory in Seismic Processing (From Liner and Ikelle and Amundsen) • Temporal aliasing • Spatial aliasing

  2. Sample Rates What is the fewest number of times I need to sample this waveform per second? ? ? ?

  3. Sample Rates

  4. Sample Rates

  5. Sample Rates

  6. Sample Rates What is the fewest number of times I need to sample this waveform per second? At least twice per wavelength or period! OTHERWISE ….

  7. Undersampled waveforms Amplitude True frequency (f -true) Reconstructed frequency (f -aliased)

  8. Oversampled waveforms Nyquist frequency Amplitude Reconstructed frequency frequency is unaliased = True frequency (f -true) Nyquist frequency = 1 / twice the sampling rate Minimum sampling rate must be at least twice the desired frequency E.g., 1000 samples per second for 500Hz, 2000 samples per second for 1000 Hz

  9. Oversampled waveforms Nyquist frequency Amplitude In practice we are best oversampling by double the required minimum i.e. 1000 samples per second for a maximum of 500 Hz i.e., 2000 samples per second for a maximum of 1000 Hz Oversampling is relatively cheap.

  10. Spatial aliasing Spatial frequency, or wavenumber (k) is the number of cycles per unit distance. One spatial cycle or wavenumber = frequency/velocity. Each wavenumber must be sampled at least twice per wavelength (two CMP’s per wavelength) IN PRACTICE each wavenumber must be sampled at least four times per minimum wavelength (two CMP’s per wavelength)

  11. Spatial aliasing However, dip (theta) as well as frequency and velocity event changes the number of cycles per distance, so Liner, 9.7,p.192

  12. Spatial aliasing For aliasing NOT to occur, delta(t) must be less than T/2

  13. Spatial aliasing

  14. Geophone Spacing and Spatial Aliasing K=0

  15. 1/4 wavelength shift per trace total shift across array=3/4 wavelength K=+ or -ve?

  16. 1/4 wavelength shift per trace total shift across array=3/4 wavelength K=?

  17. 1/2 wavelength shift per trace total shift across array=3/2 wavelength K=0

  18. 3/4 wavelength shift per trace total shift across array=2 1/4 wavelength

More Related