Common midpoint stacking

Definition

Let $d(s, r, t)$ be reflection traces for sources $s$ and receivers $r$ on a line. The midpoint of a trace is $(s + r)/2$ , and its offset is $x = \abs{r - s}$ . The common midpoint gather at a midpoint $y$ is the set of traces $d_k(t)$ , $k = 1, \dots, N$ , with midpoint $y$ , of offsets $x_k$ . For a stacking velocity $v > 0$ , the common midpoint stack at $y$ is $S_y(t_0) = \frac{1}{N} \sum_{k=1}^{N} d_k\Bigl(\sqrt{t_0^2 + x_k^2 / v^2}\Bigr),$ the average of the gather after normal moveout correction. Common midpoint stacking is the formation of $S_y$ for every midpoint $y$ , which gives a stacked section with one trace per midpoint.

Remarks

Example: suppose each trace is $d_k = a\, w + n_k$ after NMO correction, with a common reflection $a\, w$ and independent noises $n_k$ of variance $\sigma^2$ . The stack is $a\, w + \frac{1}{N} \sum_k n_k$ , whose noise has variance $\sigma^2 / N$ ; for $N = 4$ the noise standard deviation halves while the signal is unchanged. Non-example: averaging the gather without the NMO correction sums reflections at different times, so the reflection is smeared and weakened; this fails the correction in the definition. The number $N$ of traces in a gather is the fold of the survey. Scanning $v$ and measuring the coherence of the corrected gather, for example by semblance, gives the stacking velocity analysis.

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Normal moveout concept
Variance concept
Common midpoint stacking definition

Tag	`ET84JX9ZD9`
URI	`m2://ET84JX9ZD9`
Kind	definition
Writing	W0 stub
MSC	86A22, 94A12
Defines	Common midpoint stacking
Uses	Normal moveout, Variance
Changed	3 November 2026

Common midpoint stacking

Definition

Remarks

Reading path

Further reading

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