Prestack Interpolation
Prestack interpolation has numerous applications including minimization of prestack migration artifacts, azimuthal data regularization prior to fracture detection inversion, reconciling sampling differences in merge processing, and footprint removal in CMP stacking.
5D interpolation algorithm (SFINTERP)
Arcis’ 5D Interpolation algorithm is a Fourier reconstruction approach based on the work of Bin Liu and Mauricio Sacchi (Geophysics, 2004). The technique entails posing an inverse problem which essentially seeks to compute an optimal set of spatial Fourier coefficients which at once reconstruct the existing (i.e., sparsely acquired) input traces and also exhibit certain properties of coherence in the frequency-wavenumber domain. At each temporal frequency, a separate inverse problem is posed for which the four spatial interpolation coordinates are typically {cmp-x, cmp-y, offset, azimuth}. Note that the five dimensions in “5D” are temporal frequency plus the four spatial interpolation variables.
Once the spatial Fourier coefficients are computed via solution of the above inverse problem, the algorithm reconstructs the missing traces according to a desired output geometry. This output geometry specification may be either subsurface-consistent (i.e., a set of regularly sampled cmp gathers which in turn are regularly sampled across offset and azimuth) or surface consistent (i.e., a set of regularly sampled shot gathers associated with surface acquisition along regularly sampled shot and receiver lines). In the latter case, output geometry specification is performed via use of an interactive survey design tool which provides great flexibility in defining new source and receiver locations.
Several QC tools guide the 5D interpolation process. Specifically, the user may conveniently toggle between input CMP gathers (after casting onto the 5D interpolation computational grid) and the corresponding output data after interpolation. Also, prestack data visualization tools allow for the ready culling of output traces which lack input data support. Finally, timeslice/inline/crossline viewing of offset (and optionally azimuth) limited stacks and full offset stacks provide and additional confirmation of algorithm efficacy.
The following images are from Arcis' Kaybob dataset
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| PSTM after revised careful offset class selection | PSTM after 5D |
DSINTERP—Coherence-guided data reconstruction
DSINTERP improves the sampling of 3D volumes by inserting new shots and receivers along existing shot and receiver lines. The algorithm operates on individual shot/receiver gathers within spatially and temporally localized windows, and its first task is the identification of dominant dip directions associated with coherent energy. Once these principal dip directions are computed, the algorithm synthesizes the missing traces via local slant stack. The figure immediately below shows the result of a reprocessing effort for a noisy Canadian foothills 3D in which DSINTERP was a major component. Note the tremendous improvement in image quality.
In the 3 frames below we show how DSINTERP may be cascaded with SFINTERP, in effect combining the best of both worlds.
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Stack: raw (uninterpolated) data |
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After DSINTERP (increase shot/rec spacing) |
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| After DSINTERP plus SFINTERP (infill missing shot line) |
AMO –Azimuth Moveout
Arcis offers Azimuth Moveout (AMO), a state-of-the-art wave equation propagation algorithm for regularizing and interpolating poorly sampled 3D data. The AMO operator, which rotates the azimuth and modifies the offset of 3D pre stack data, is analytically derived by cascading the forward and inverse 3D DMO operators. AMO is not a single trace to single trace transformation, but rather a partial-migration operator that moves events across midpoints according to their dip. Click here to see a powerpoint on AMO.
The figure immediately below shows a shallow timeslice before and after application of AMO for a 3D land data set. The AMO algorithm has succeeded in eliminating the acquisition footprint.
