Questions: Seismic Reflection Surveys and Common Midpoint Processing

Question 1

A seismic survey is designed with 60 traces per CMP gather. After NMO correction and stacking, how does the signal-to-noise ratio of the stacked trace compare to a single raw trace, and why?

• A. 60× better, because the 60 signals add together perfectly while all noise cancels
• B. Approximately √60 ≈ 7.7× better, because coherent reflections add constructively while random noise partially cancels
• C. Unchanged — stacking corrects for moveout but does not affect noise
• D. Worse than a single trace, because summing traces introduces new noise from the NMO correction

Answer: (B)

When N traces are stacked, coherent signals (reflections) add linearly: N traces each with amplitude A produce a stacked amplitude of N·A. Random noise, however, is statistically independent between traces: when N independent noise samples with standard deviation σ are summed, the combined noise standard deviation grows as √N·σ (by the central limit theorem / random walk statistics). The SNR of the stack is therefore (N·A)/(√N·σ) = √N·(A/σ) — exactly √N times the single-trace SNR. Doubling the fold improves SNR by √2, not by 2. This is why high fold (more traces per CMP) is valuable but shows diminishing returns.

Question 2

In a CMP gather, a geologist applies an NMO correction using a velocity that is too high. What will the corrected gather look like?

• A. The reflection event will be perfectly flat — small velocity errors do not affect the NMO-corrected shape
• B. The reflection will be over-corrected, bending downward at far offsets (a 'smile' or 'hockey stick' shape)
• C. The reflection will still show residual upward curvature at far offsets, because the insufficient correction leaves part of the moveout unremoved
• D. The reflection will split into two separate events at near and far offsets

Answer: (C)

Normal moveout creates a hyperbolic increase in travel time with offset. The NMO correction subtracts a time shift calculated from the assumed velocity and offset. If the velocity used is too high, the calculated moveout is too small — the correction is insufficient. The far-offset traces are not shifted up enough, so the event still curves upward at large offsets ('under-corrected' or 'frown' shape). Conversely, a velocity that is too low over-corrects, shifting far-offset traces too far up and creating a downward 'smile.' Velocity analysts search for the velocity that produces the flattest gather — this is velocity picking.

Question 3

A CMP (common midpoint) gather groups seismic traces that all share the same midpoint between their source and receiver, so that each trace in the gather recorded a reflection from approximately the same subsurface point.

• T. True
• F. False

Answer: True

This is the defining property of CMP processing. By sorting traces by their common reflection point rather than by source or receiver, geologists isolate multiple measurements of the same subsurface reflector. Different source-receiver pairs sample the same midpoint but with different offsets (source-to-receiver distances), giving the moveout information needed for velocity analysis, while all traces contain the same geological signal from that reflection point. This organization is the foundation of modern reflection seismology.

Question 4

A stacked seismic section directly shows the depth of geological reflectors below the surface, so a reflection appearing at 2 seconds on the vertical axis corresponds to a reflector 2 kilometers deep.

• T. True
• F. False

Answer: False

The vertical axis of a stacked section shows two-way travel time (TWT) — the time for a seismic wave to travel from the surface down to a reflector and back up. Depth requires multiplying TWT by velocity and dividing by two, but the velocity varies with depth and lithology. A 2-second TWT reflection could correspond to widely different depths depending on whether the overlying rocks are slow shales (~1.5 km/s) or fast carbonates (~6 km/s). Converting from time to depth requires the velocity model estimated during NMO analysis, often supplemented by well log data. Further geometric corrections (migration) are needed when reflectors are dipping.

Question 5

Explain why stacking multiple NMO-corrected CMP traces improves the signal-to-noise ratio, and why the improvement scales as √N rather than N.

Model answer: After NMO correction, all traces in a CMP gather show the same reflection at approximately the same arrival time. Stacking (summing) these traces combines coherent signal constructively: N traces each with amplitude A produce a total signal of N·A. Random noise, by contrast, is incoherent — each trace has independent random fluctuations from sources like ground roll, wind, traffic, and electronic noise. When N independent random noise samples are summed, the noise amplitude grows as √N (not N), because the independent fluctuations partially cancel by random walk statistics. The signal-to-noise ratio is therefore (N·A)/(√N·σ) = √N·(A/σ), improving as √N. This is why seismic surveys are designed with high fold: more traces per CMP improve SNR, but with diminishing returns, so there is an economic tradeoff between acquisition cost and image quality.

The √N scaling is the same phenomenon as the standard error of the mean in statistics: averaging N independent measurements reduces uncertainty by √N. In seismology, 'stacking' is the geophysicist's word for this statistical averaging process.