Reciprocity: source / receiver duality

Part 3 — Survey geometry design

Learning objectives

Recall reciprocity from §0.9: swap source and receiver, identical recorded trace
Apply reciprocity at the survey level: the same trace set can be built in many ways
Use reciprocity to read an OBN shot gather as a common-receiver gather
Distinguish the two areas where reciprocity holds and where it fails

§0.9 introduced reciprocity for a single trace: swap source and receiver and the recorded trace is identical. In survey design this becomes a very practical tool.

The survey-design consequence

The set of traces produced by N_s sources firing into N_r receivers is identical (up to permutation) to the set produced by N_r sources firing into N_s receivers. The same midpoints; the same offsets; the same azimuths; the same data. Only the logistics differ.

When to swap

The prevailing direction of swap depends on economics:

Marine streamers: 2 sources × 10,000 receivers. Move sources (cheap — one vessel pulls them); receivers are always live on a streamer.
OBN: many receivers on the sea floor, shot by a marine vessel. Same logic: move sources, keep receivers static.
Land 3D: can go either way. Nodal systems often have 10,000–100,000 receivers laid out; vibroseis trucks move between shot points. Historic dynamite surveys moved sources and receivers together in smaller live patches.
VSP: one deep receiver in a well vs many surface sources. Reciprocity says this is equivalent to one surface source + many downhole receivers — which is exactly the DAS-in-well geometry (§2.6), and why VSP and downhole DAS image the same wavefield.

When reciprocity fails

It fails in time-varying media (4D, by design), in media with non-reciprocal losses (extremely rare in passive seismic), and in strongly-coupled sensor–ground configurations where the energy transfer is non-linear (near-source dynamite). For 99% of passive exploration geophysics, reciprocity is a clean, exploitable symmetry.

Reciprocity as a QC

Cross-correlate the trace from source-at-A receiver-at-B with the trace from source-at-B receiver-at-A: the correlation peak should be at zero lag with unit amplitude. Any deviation flags a timing, polarity, or coupling problem on one side.

References

Aki, K., Richards, P. G. (2002). Quantitative Seismology (2nd ed.). University Science Books.
Vermeer, G. J. O. (2002). 3-D Seismic Survey Design. SEG Geophysical References 12.
Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press.