CMP, CDP, CIG: what we are binning for

Part 3 — Survey geometry design

Learning objectives

Define Common Midpoint (CMP) as the surface location where source–receiver pairs share
Derive the NMO hyperbola t(h) = √(t₀² + h²/V²) for a flat reflector
Explain why CMP equals CDP only for zero dip; why dip causes reflection-point smearing
Distinguish CMP (surface bin), CDP (subsurface depth point), and CIG (post-migration image gather)

The foundation of modern seismic is a simple geometric observation. For a flat reflector at depth z, a source at S and a receiver at R on either side of a midpoint M all illuminate the same reflection point directly beneath M. Their travel times differ by the classic NMO hyperbola

t(h) = \sqrt{t_0^2 + (h/V)^2}, \qquad t_0 = 2z/V

where h is the full source–receiver offset. Gather all traces sharing a midpoint M into a CMP gather, apply the NMO correction to flatten the hyperbola, stack across offsets, and the coherent reflection grows by a factor of N while random noise grows by √N (§0.8). This is the stacking miracle that makes seismic imaging possible at all.

CMP vs CDP

For a flat reflector the common midpoint is also a common depth point — all traces in the gather reflect off the same subsurface point. Add dip and the reflection point shifts toward the up-dip side; different offsets now illuminate slightly different depth points, and the "common midpoint" smears a region of the dipping reflector. The name CDP survives in processing literature but CMP is the accurate surface-geometry name.

For a constant-dip reflector with dip α, the reflection-point shift is approximately

\Delta x_{\text{refl}} \approx \frac{h^2}{4z}\tan\alpha

so a 30° dip with offset 2 km and target depth 1 km shifts the reflection point by ~580 m — substantial. Dip-moveout (DMO) and pre-stack migration move the traces to their true depth locations.

CIG: the migration successor

After pre-stack migration each output image point (x, z) is itself a gather — a common image gather — collecting all source–receiver contributions that imaged to that point. A well-migrated CIG is flat with offset (residual moveout = 0) when the velocity model is correct; residual moveout on CIGs is the input to velocity tomography (§5.9 of the Processing textbook). CIGs are to migrated data what CMPs are to stacked data.

Why the CMP survived 60 years

Because the moveout formula is exact under two weak assumptions (passive isotropic medium, flat or mildly-dipping reflector) and because it turns N traces into one trace with √N better SNR at zero computational cost. Every survey geometry from §3.2 onward is ultimately designed to populate CMP bins with enough traces, at enough offsets, at enough azimuths, to pass this simple test. Bin the survey, stack the bin, image the stack.

References

Mayne, W. H. (1962). Common reflection point horizontal data stacking techniques. Geophysics, 27(6), 927–938.
Yilmaz, Ö. (2001). Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data (2 vols.). SEG Investigations in Geophysics 10.
Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press.
Vermeer, G. J. O. (2002). 3-D Seismic Survey Design. SEG Geophysical References 12.