The data

Seismic amplitudes d(s,r,t) are recorded over time t as a function of surface horizontal positions for source s and receiver r. Although these positions are one-dimensional we must also be prepared to think of them as vectors indicating a surface position. The time coordinate is sampled evenly and densely enough that we can think of it as continuous.

For a given source, we have a limited range of receivers (perhaps 3-5 kilometers), and vice versa. Receiver positions are often sampled two or four times as densely as source positions. In marine data, both are evenly sampled relatively, but a spatial Fourier transform must pay attention to aliasing or edge effects from the short span. Land data will be much more arbitrarily sampled.

Define the coordinates of offset $h \equiv r-s$ and midpoint $y \equiv (s+r)/2$. Resorted data can be written as d(s=y-h/2, r=y+h/2, t). The well-sampled midpoint coordinate covers the entire span of the survey.