Shot-Profile Migration

The introduction of aliasing artifacts is demonstrated by comparing panels a and b in Figure 3. Both images were constructed with the shot-profile migration algorithm using a single trace source function. Each panel shows the Fourier transformed image surface location and subsurface offset axes, $(k_x,k_h,\omega)$. In this manner the spatial energy components of the image from a particular depth in the model can be viewed. These figures capture the model space at the depth of a perfectly imaged flat reflector. Migrating shot-profiles at every receiver location as in panel a, shows marked difference to the wavenumber components that make up the image produced by migrating shots at every tenth shot in panel b. As the k_x=0 aliased energy moves into the image from the replicated Fourier spectra, bands of aliased energy appear at multiples of 10 m^-1 on the k_x axis.

 

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Figure 3 Panels showing 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 every 10 m^-1 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 k_x=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 band-limited wavelet result.

Panel c, also produced using every tenth shot, illustrates the effectiveness of the first two 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 source function with some width in space rather than a single trace. Notice also the diminished k_h bandwidth as a result of restricting energy content of the migration.

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