Fold, offset, azimuth statistics
Learning objectives
- Compute the fold (number of traces per bin) for an orthogonal 3D geometry
- Interpret an offset histogram: what a near-offset gap means for AVO
- Read an azimuth rose: narrow vs wide azimuth distributions and their imaging consequences
- Diagnose edge-effect fold taper and its influence on full-fold area
Every source–receiver pair contributes one trace with a specific midpoint, offset, and azimuth. Collected over a survey, these contributions form a cloud in three variables. Three statistics of the cloud — fold per bin, offset distribution per bin, azimuth distribution per bin — are what survey design optimises.
Fold
Fold = traces per bin. Higher fold = more stacking gain (§0.8). In the interior of a full-fold area fold is roughly
where N_s, N_r are total active sources and receivers and N_bin is the number of bins in the survey. Near the edges fold tapers because bins that lie close to the boundary miss contributions that would have come from beyond it — the edge taper. Full-fold area is always smaller than survey area by roughly the aperture length (§3.6).
Offset distribution
Stacking assumes offsets are well-sampled from 0 (or near 0) up to some maximum X_max. A bin with, say, only far offsets and no near-offsets stacks noisy for shallow targets and misses the AVO intercept (§7.4 of the Processing textbook). Offset histograms per bin should be roughly uniform and extend from close-to-zero to the design X_max.
Near-offset gaps are a marine-streamer disease: the streamer is towed ~150 m behind the source, so no receiver can sit closer. Offset bin 0–150 m is empty for every shot. OBN geometries (§4.6) have no such gap.
Azimuth distribution
Draw a vector from shot to receiver and bin the azimuth angles. A narrow-azimuth survey (2D, typical marine streamer) has azimuths clustered in one direction; wide-azimuth (WAZ, multi-vessel marine or good-aspect-ratio land) distributes azimuths over the full range. Narrow azimuth gives poor imaging of cross-dip features and under-determines FWI. Dedicated land 3D surveys aim for azimuth aspect ratio ≥ 0.5 inside the target area.
Why all three matter together
You can have high fold with bad offset sampling (only far offsets: cannot do AVO). You can have balanced offsets with narrow azimuth (bad for 3D imaging of cross-dip). You can have balanced azimuth with low fold (noisy stack). A good survey design hits reasonable values in all three simultaneously, across the target area. Edge effects are acceptable — just shoot further out (§3.6).
References
- Vermeer, G. J. O. (2002). 3-D Seismic Survey Design. SEG Geophysical References 12.
- Cordsen, A., Galbraith, M., Peirce, J. (2000). Planning Land 3-D Seismic Surveys. SEG Geophysical Developments 9.
- Vermeer, G. J. O. (2012). 3D Seismic Survey Design (2nd ed.). SEG.
- Stone, D. G. (1994). Designing Seismic Surveys in Two and Three Dimensions. SEG Geophysical References 5.