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Experiment

A synthetic data set was generated to test these methods of preventing aliasing. Shot-gathers were modeled over a 2000m/s earth model with one flat reflector at 1000m. Nominal shot, $\Delta s$, and receiver, $\Delta r$, spacing is 10m. Dominant frequency of the wavelet is 30Hz. These experiments were performed using a shot-profile algorithm. However, these analyses and conclusions are valid for both shot-geophone and shot-profile migrations due to their mathematical equivalence Biondi (2003),Shan and Zhang (2003).

The introduction of aliasing artifacts is seen by comparing the panels in Figure [*] constructed at the depth of the reflector. Panels share the characteristics of Figure [*]d, though a frequency axis is now introduced by postponing the summation of frequencies normally required by wave-equation migration imaging conditions. Migrating shot-profiles at every receiver location (left panel) shows marked difference to the wavenumber components that make up the image produced by migrating shots at every tenth shot (center panel). As the kx=0 energy moves into the image from the replicated Fourier spectra, bands of aliased energy appear at multiples of 10 m-1 on the kx axis . Both images were constructed with standard shot-profile migration using a single trace source function.

 
allv10vfat10
allv10vfat10
Figure 2
Panels show image wavenumbers from migrations of different selections of available shots from the data set. Left panel was created by migrating all available shots, while the center and right panels include only every tenth shot. Note the replication of the flat reflector at kx=2i Ny/10 in the center panel. The right panel is the result of restricting the migrated energy with a fat source function. Notice that the length of the reflector energy along the kx=0 axis has been limited from 10m-1 to 5m-1 indicating an imposed restriction on the number of offsets contributing to the image at any given dip. Selective energy imaging yields an identical result to the fat wavelet result.
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The right panel, also produced using every tenth shot, illustrates the effectiveness of our methods in eliminating the aliased energy introduced by subsampling the shot axis. The image does not suffer from aliased energy due to the use of a spatially band-limited (fat) source function. It also shows a diminished kh bandwidth as a result of removing the aliased energy.

Selective energy imaging, our second proposed method, uses band-limited versions of the source and receiver wavefields in the imaging condition. The resultant image is identical to the right panel and is accordingly not shown.


next up previous print clean
Next: Conclusions Up: Artman et al.: Aliasing Previous: METHODOLOGY
Stanford Exploration Project
7/8/2003