Bin size & dip aliasing

Part 3 — Survey geometry design

Learning objectives

Apply the spatial-Nyquist condition Δx < V / (4 f_max sinα) for steepest-dip event
Identify aliased events in an f-k spectrum as wrapped diagonals past the Nyquist wavenumber
Choose bin size accounting for both dip and wavelength (λ/3 rule of thumb)
Recognise when bin size is the binding constraint vs aperture or fold

Bin size Δx is the single most consequential number in survey design. It sets what you can image, whether you alias, and how much data you record. Three constraints intersect:

1. Spatial Nyquist for dipping events

A dipping reflector with dominant frequency f_max and dip α has spatial wavenumber k_x = f_max sinα / V along the surface. The spatial-Nyquist condition says neighbouring bin samples must be closer than half a wavelength of that wavenumber. Solving:

\Delta x < \frac{V}{4\,f_{\max}\,\sin\alpha}

Violate it and the dipping event wraps in f-k space and re-emerges as a ghost event with reversed dip. You cannot un-alias it in post-acquisition processing.

2. The λ/3 rule of thumb

Independently of dip, the stack must resolve the dominant-frequency wavelength. If λ_min = V / f_max at the target, a bin size of λ_min / 3 is a safe default that works for most targets below ~50° dip. Deeper / faster targets have larger λ_min and tolerate larger bins.

Example: target depth 2 km, V = 3 km/s, f_max = 60 Hz → λ_min = 50 m, bin size ≈ 17 m. Rounded to a standard 12.5 m or 25 m.

3. Standard bin sizes

Industry uses standardised bins: 6.25 / 12.5 / 25 / 37.5 / 50 m. Every seismic processing system is tuned around these (trace headers, interpolation grids, migration aperture cuts). Pick the nearest standard below your computed constraint.

What aliased data looks like

Aliased dipping events appear as coherent noise with apparent-velocity lower than the true event. They cross main reflectors and look like crisp dipping lines. On the f-k panel the tell is clear — a second diagonal on the opposite side of k = 0, with slope that wraps through ±k_Nyq. If you see one in your stack, the cure is: re-acquire with finer bin, interpolate from well-sampled neighbours (§9.3 of Processing), or accept the loss.

References

Vermeer, G. J. O. (2002). 3-D Seismic Survey Design. SEG Geophysical References 12.
Bracewell, R. N. (1999). The Fourier Transform and Its Applications (3rd ed.). McGraw-Hill.
Vermeer, G. J. O. (1990). Seismic Wavefield Sampling. SEG Geophysical Monograph 4.
Krey, T. (1987). Attenuation of random noise by 2-D and 3-D CDP stacking and Kirchhoff migration. Geophysical Prospecting, 35(2), 135–147.