Fresnel Zone Calculator: Lateral Resolution of Seismic Data

It is tempting to think of a seismic trace as a pencil-thin ray probing the earth directly beneath each point on the surface. The physics disagrees. A reflection is built from constructive interference over a patch of the reflector, and everything inside that patch, the first Fresnel zone, contributes to a single sample. Two channels 200 meters apart under a 400 meter Fresnel zone are not two channels on your section; they are one blurry smudge. Vertical resolution gets most of the attention in seismic interpretation, but lateral resolution is governed by this zone, and it is usually far worse.

The formula and where it comes from

The first Fresnel zone is the region of the reflector where the reflected energy arrives within half a period (a quarter wavelength of two-way path) of the first arrival, so it interferes constructively. For a coincident source and receiver over a flat reflector this works out to:

rF = (V/2) x sqrt(t / f)

with V the average velocity down to the reflector, t the two-way time, and f the dominant frequency. The uncomfortable feature is the square root of time: the zone keeps growing with depth, while frequency, the only thing fighting for you, also decays with depth due to attenuation. Deep targets get hit from both directions.

Worked example

• Target at 2.0 s two-way time, average velocity 3,000 m/s, dominant frequency 30 Hz
• rF = 1500 x sqrt(2.0/30) = 387 m, a zone diameter of about 775 m
• On unmigrated data, any geologic feature narrower than that is laterally unresolvable
• After good 3D migration the effective radius shrinks toward lambda/4 = 25 m, a thirty-fold improvement

What migration does, and what it cannot do

Migration is, at heart, a Fresnel zone collapser: by summing energy along diffraction hyperbolas it undoes the lateral smearing and shrinks the effective zone to roughly a quarter of the dominant wavelength. But there are two honest catches. In 2D data, migration only collapses the zone in the direction of the line; perpendicular to it, the full unmigrated width remains, which is why sideswipe haunts 2D interpretation and why the move to 3D was not a luxury. And migration is only as good as its velocity model; a wrong model leaves the zone partially uncollapsed while looking superficially crisp. When someone asks whether a 3D survey is worth the cost over dense 2D, this calculator quantifies exactly what is being bought: run your target through it and compare the unmigrated radius with lambda over four.

Related Calculators and Reference

Vertical resolution, the other half of the resolution story, lives in the vertical resolution calculator and the tuning thickness calculator, and the frequency decay with depth that shrinks your bandwidth is modeled in the dominant frequency vs resolution calculator. The SEG Wiki entry on the Fresnel zone has the geometric derivation.