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F-K filtering

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- 1. EXTENDED SEISMIC DATA PROCESSING SEISMIC DATA PROCESSING-ZGE 373
- 2. TODAY’S SUBJECTS • Definition of f-k domain • Filtering in the f-kx domain
- 3. WHAT IS F-K DOMAIN? A two-dimensional Fourier transform over time and space is called an F-K (or K-F) transform where F is the frequency (Fourier transform over time) and K refers to wave-number (Fourier transform over space). The space dimension is controlled by the trace spacing and (just like when sampling a time series) must be sampled according to the Nyquist criterion to avoid spatial aliasing. Several noise types such as groundroll or seismic interference may be more readily separated in the FK amplitude domain than the time-space domain and therefore will be easier to mute before the inverse transform is applied.
- 4. F-K AND SPATIAL ALIASING Spatial aliasing, is a common problem to be considered when performing data processing. One way to limit the spatial aliasing of the previous figure would be to remove frequencies above 30Hz. This would be wasteful of primary signal. The trace spacing is also important. Consider the adjacent figure (a) & (b) showing an event of 70Hz dipping at 20 degrees. Sampling every 12.5m samples the signal properly, but at 25m the signal becomes spatially aliased and appears to show reverse dip which confuses interpretation (as well as many processing algorithms such as migration). Reverse dip is shown more clearly in figure (c) where the dip of the dipping event becomes confusing when high frequencies are present. The formula for determining the maximum frequency which can be handled without spatial aliasing is given by:
- 5. F-KX FILTERING In this discussion we will discuss two items: 1- Ground-Roll filtering 2- Multiples Filtering in marine data
- 6. WHAT IS GROUND-ROLL? Ground roll, also called Rayleigh waves, are surface waves that travel as ripples with motions that are similar to those of waves on the surface of water (note, however, that the associated particle motion at shallow depths is retrograde, and that the restoring force in Rayleigh and in other seismic waves is elastic, not gravitational as for water waves). The existence of these waves was predicted by John William Strutt, Lord Rayleigh, in 1885. They are slower than body waves, roughly 90% of the velocity of S waves for typical homogeneous elastic media. In the layered medium (like the crust and upper mantle) the velocity of the Rayleigh waves depends on their frequency and wavelength.
- 7. The problem
- 8. Example
- 9. Discuss:
- 10. Filtering: In one dimension (frequency) filter we usually apply the following : The same concept applies for f-K domain. The input window is multiplied by a filter which is a function of both frequency and wavenumber. As a result we have a freedom to design our filter response to be for example slice band pass or reject. In our case we define a pie-slice filter to remove ground roll.
- 11. Pie-Slice filter
- 12. Output :
- 13. Real Example
- 14. multiples
- 15. Procedure

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