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.  Prestack data visualization tools allow for the ready culling of output traces which lack input data support. Timeslice/inline/crossline viewing of offset (and optionally azimuth) limited stacks and full offset stacks provide an additional confirmation of algorithm efficacy. 

Perhaps the most definitive QC tool is ‘Leakage’.  Unique to Arcis, 5D leakage is a method for illuminating areas where 5D Interpolation may be failing.  The 5D Leakage QC is computed in two steps: first the original geometry is reconstructed from the newly-generated 5D-interpolated data; then this reconstructed data is compared to the true original recorded data.  If the 5D Interpolation is working well, then what’s left in the 5D Leakage display is simply incoherent noise that did not fit to the 5D model of the data in Fourier space, or complex events (such as diffractions) that do not completely satisfy the constraints used by the interpolation algorithm and therefore could not be estimated accurately.

Images from the Blackfoot data set


Input stack                                     5D stack                                   Leakage stack (error of 5D)

Data courtesy: CREWES (Consortium for Research in Elastic Wave Exploration Seismology), University of Calgary

—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.

land Processing Prestack Interpolationland Processing Prestack Interpolation 2

In the 3 frames below we show how DSINTERP may be cascaded with SFINTERP, in effect combining the best of both worlds. 
Prestack Interpolation_raw

Raw (uninterpolated) data

Prestack Interpolation_afterdipscan

After dip-scan interpolation

Prestack Interpolation_afterdipscan+5D
After dip-scan plus 5D interpolation



Back To Top