What is Common midpoint, fold?

For a source at $x_s$ and a receiver at $x_r$ on a line, the midpoint is $(x_s + x_r)/2$ and the offset $x = |x_r - x_s|$. A common midpoint (CMP) gather is the set of traces, from all the shots, that share the same midpoint; over flat layers they all reflect from the same subsurface point. The fold (of seismic coverage) is the number of traces in a gather. With $N$ channels at the receiver interval $\Delta g$ and a shot every $\Delta s$ along the line, the fold is $N\Delta g/(2\Delta s)$.