Survey design sanity: fold, offset, azimuth

Every processing decision you will make later is constrained by what the acquisition team recorded. The best algorithm on Earth cannot produce an azimuth-dependent AVO result from a single-azimuth survey, and no deconvolution saves you from undersampling. Survey design is where many of the hardest processing problems are solved, or baked in permanently.

1. The three dimensions of trace coverage

For each CMP bin in your survey, three quantities decide what processing can do:

• Fold, the number of traces in the bin. Stacking them improves the signal-to-noise ratio in proportion to $\\sqrt{\\text{fold}}$ for random noise (Section 0.8).
• Offset distribution, range of source-receiver distances in the bin. Wide range → can measure AVO (amplitude vs angle) and do velocity analysis; narrow range → can only stack.
• Azimuth distribution, spread of directions in the bin. Wide coverage → can measure azimuthal anisotropy (HTI fractures, orthorhombic media), run wide-azimuth FWI, and detect stress orientation. Narrow azimuth → imaging must assume the medium looks the same in every direction. (VTI anisotropy in shales is measured from long offsets, not from azimuths.)

In Figure 1.5 you lay out a survey, pick a CMP bin, and read what reached it: its fold, the angles its offsets reach at your target, and how many directions its far offsets arrive from. The figure opens on an orthogonal 3D survey with a 2500 m maximum offset, and its centre bin falls short of the angle an AVO gradient needs. Try the 2D line, move the bin toward a corner, and narrow the patch, and watch which of the three quantities each change takes away.

2. What each design tells you

• 2D line (single azimuth). Shots and receivers on one line. Every CMP is a single 1D collection of offsets, and every trace has the same azimuth: the bearing of the line, east-west in the figure, where the rose (d) shrinks to two opposite petals. Can do 2D stacking and AVO. Cannot do azimuthal anisotropy, wide-azimuth FWI, or anything crossline.
• Wide-azimuth 3D (orthogonal). Shot lines and receiver lines cross at right angles, and each shot records a patch of several receiver lines. When the patch is close to square (crossline over inline aspect 0.8 or more in Figure 1.5, with a maximum offset of 2500 m or more), the far offsets of nearly every interior CMP arrive from every direction, which is what azimuthal AVO, anisotropy analysis and FWI need; at an aspect of 0.6 the north-south sectors already empty out. It needs the most live channels, and it unlocks the most downstream work.
• Narrow-azimuth 3D swath. The same orthogonal layout with a narrow patch. Narrowing the patch aspect from 1.0 to 0.2 in the figure, at a 3000 m maximum offset, drops the centre bin from 121 to 45 traces and its far-offset azimuth coverage from 9 of 9 merged sectors to 3 of 9: the near traces still arrive from every side, but the far ones, where anisotropy shows, come from east and west only. Reasonable fold for imaging, adequate offsets for AVO, limited azimuths. Use it when the target is a known structural play and wide azimuth is unaffordable.

3. Fold: the S/N multiplier

For an orthogonal design the nominal fold is $N = N\_x N\_y$: the inline fold $X\_h/\\Delta s\_l$ (half the patch length over the source line interval) times the crossline fold $Y\_h/\\Delta r\_l$ (about half the number of live receiver lines). The fold counted in a bin swings around it with the line grid, which is the acquisition footprint. Doubling the receiver line interval in the figure, from 200 m to 400 m at a 3000 m maximum offset, drops the centre bin from 99 to 55 traces and the live channels per shot from 1767 to 837. More fold means better S/N. The trace count grows as shots $\\times$ active channels, while cost grows with the number of source points and receiver stations deployed, so extra active channels are the cheapest fold. The survey designer’s question is: what minimum fold is required for the target to appear above noise at the needed resolution?

A common rule of thumb, quoted with its bin size because fold means little without one (the ranges are indicative):

• Fold 20 to 60 (at 25 m bins) is typical for shallow land and conventional towed-streamer imaging.
• Fold 60 to 120 (at 25 m bins) is standard for deep-water or difficult imaging targets.
• Fold 200 to 500 or more (at 12.5 to 25 m bins) is used for tough subsalt and FWI-centric programs.

4. Offset: the AVO and depth-of-investigation lever

The longest offset in a CMP bin limits the maximum angle of incidence on a target reflector:

For a reservoir at 2500 m depth and a survey with 5 km maximum offset, \\theta\_{\\max} \\approx 45^\\circ, enough for full AVO class discrimination. At 3 km maximum offset, \\theta\_{\\max} \\approx 31^\\circ, marginal. Velocity that increases with depth bends the rays, so true angles are somewhat larger than this straight-ray estimate. An offset equal to the reservoir depth still reaches \\theta\_{\\max} \\approx 27^\\circ, enough for intercept and gradient; offsets well short of the depth (say $x\_{\\max} < z/2$, so \\theta\_{\\max} < 14^\\circ) leave only near angles and no usable AVO gradient.

What counts is the farthest offset actually in the bin, which falls short of $x\_{\\max}$ because the line grid samples a bin’s offsets in steps of twice the line interval. In the figure the centre bin’s farthest trace is 4561 m (42° at 2500 m) with a 5000 m maximum offset, and only 2000 m (22°) with 2500 m.

5. Azimuth: the anisotropy lever

Fractured carbonates, stressed shales, and any HTI (horizontally transversely isotropic) medium have velocities that depend on which direction you look. Two surveys over the same reservoir, one wide-azimuth and one narrow, produce different images of a fractured zone: the wide one shows the fracture orientation as an azimuthal velocity or amplitude anomaly; the narrow one averages it out.

A standard quality metric is azimuth coverage: what fraction of the azimuth sectors (typically 18 × 20° over 360°, or 9 over 0 to 180° once reciprocal pairs are merged: by source-receiver reciprocity a trace at $\\phi$ follows the same raypath, reversed, as one at \\phi + 180^\\circ, so the two carry the same azimuthal information) holds at least a minimum number of traces? Count it on the far offsets: azimuthal differences in moveout and amplitude grow with offset, and near traces arrive from every direction in any design. The figure’s readout counts the far half of the spread, for the minimum you choose.

6. Edge effects

Any survey has edges. Near the edges, fold drops, offset range narrows, and azimuth coverage becomes lopsided. Processing on edge bins is unreliable; most surveys oversize the acquisition footprint so the image area sits comfortably inside the full-fold region. In the figure, with a 3000 m maximum offset, moving the bin from the centre to (300 m, 300 m) drops the fold from 99 to 16 and the farthest offset from 2561 m to 849 m, and no trace in that bin reaches half the maximum offset.

7. What you cannot get back in processing

• Bandwidth you never recorded. A streamer towed at 10 m has a receiver-ghost notch at $f = v/(2d) = 1500/(2 \\times 10) = 75$ Hz at vertical incidence. Deghosting can restore the band around the notch where signal survived above noise, but nothing recovers the null itself.
• Offsets beyond your maximum. Far offsets needed for AVO must be acquired; interpolation does not reach beyond the last trace.
• Azimuths never sampled. If every source-receiver pair was aligned E-W, processing cannot deduce N-S anisotropy.

What processing can do is regularize irregular sampling and fill small gaps by interpolation (Section 9.3), and optimize the imaging aperture for what you have. But the ceiling is set in the field.

Where this goes next

Part 1 is complete. You now know what land and marine acquisition each record, how traces get sorted into CMP bins, what noise to recognize on a shot gather, and how survey design decisions cascade into every later step. Part 2 starts the actual processing: reformatting the data, repairing the amplitude path, applying the first statics corrections, and building the deconvolution operator.

References

• Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge UP.
• Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.
• Claerbout, J. F. (1976). Fundamentals of Geophysical Data Processing. McGraw-Hill.