Resolution and the wavelength problem

Vertical resolution: the λ/4 rule

Two reflectors separated by vertical time less than about a quarter-wavelength of the dominant frequency cannot be individually resolved on seismic — their wavelets overlap constructively and appear as a single event.

The wavelength in the rock is $\lambda = V / f$, where V is the interval velocity and f is the dominant frequency. The resolution threshold is:

For a 30 Hz wavelet in a 3000 m/s rock, $\lambda = 100$ m and $\lambda/4 = 25$ m. Two reflectors closer than 25 m in depth (or about 16 ms in two-way time in this rock) appear as one event. Above that threshold they progressively separate.

The word "about" does real work here. The precise value depends on wavelet shape, phase, and noise. λ/4 is the rule of thumb; for band-limited data the practical resolution can be closer to λ/6 under favorable conditions and worse than λ/3 for noisy data. Do not treat λ/4 as a sharp cutoff; treat it as the order-of-magnitude constraint.

Tuning: resolution's twin

Below the resolution threshold, reflectors are not simply invisible — their amplitudes interfere. For a thin bed with positive R at the top and negative R at the base (the usual sand-between-shales case), the top and base wavelets overlap and constructively reinforce. The composite event is brighter than either reflector alone. Amplitude peaks at the tuning thickness, which for a zero-phase wavelet is $\lambda/4$. Below the tuning thickness, as the bed gets even thinner, amplitudes drop rapidly because the top and base wavelets cancel more and more.

This creates a trap. A thin sand at the tuning thickness produces a bright reflector that can be mistaken for a thicker, more significant feature — or for a gas accumulation. Conversely, a thinner bed can be invisible, and its absence on seismic does not mean the bed does not exist.

Above tuning, amplitude reflects impedance; below tuning, amplitude reflects thickness

This is the most important sentence in §1.7.

For beds thicker than the tuning thickness, peak amplitude approximates the true reflection coefficient of the top interface. You read amplitude as a proxy for impedance contrast.

For beds thinner than the tuning thickness, peak amplitude varies primarily with bed thickness, not with impedance contrast. You read amplitude as a proxy for thin-bed geometry. Two beds with the same impedance contrast but different thicknesses can have dramatically different amplitudes, and two beds with different impedance contrasts but the same thickness can have similar amplitudes. Any amplitude-to-rock-property interpretation in the thin-bed regime has to account for this.

Lateral resolution: the Fresnel zone

Vertical resolution gets most of the attention because the λ/4 rule is simple. But lateral resolution — the minimum size of a feature that can be distinguished map-view — is just as important and is controlled by a different mechanism.

On unmigrated data, the Fresnel zone is the region of the reflector surface whose echoes arrive within half a wavelength of each other and therefore interfere constructively at the receiver. The radius of the Fresnel zone is approximately:

$r_F \approx \sqrt{\lambda z / 2}$ (z = depth to reflector)

For 30 Hz data at 2000 m depth in 3000 m/s rock, $\lambda = 100$ m and $r_F \approx \sqrt{100 \cdot 2000 / 2} = 316$ m. Anything smaller than the Fresnel-zone diameter (~630 m across) blurs together on unmigrated data.

Migration dramatically improves this. After proper migration, lateral resolution collapses to approximately one spatial sample size — dictated by the survey bin size rather than by the Fresnel zone. Typical 3D bins are 25 × 25 m or smaller, so migrated data can resolve features on the order of tens of metres laterally. This is one of the biggest arguments for why migration is non-negotiable for modern interpretation.

Detection vs. resolution

A subtle but important distinction. Resolution is the ability to see two features as separate. Detection is the ability to see that a feature is present at all. A thin bed below tuning thickness is not resolved — you cannot see its top and base as separate events — but it may still be detected as a bright spot whose amplitude tells you it exists. The thinnest bed that can be detected is often a small fraction of the thinnest bed that can be resolved.

This matters for reservoir characterization. A 5 m gas sand below the 25 m resolution limit will not show a clear top-and-base pair on seismic. But it will show an amplitude anomaly whose brightness is a function of its thickness (via tuning) and its impedance contrast (via fluid fill). With calibration from well data, that amplitude anomaly can be inverted for sand thickness. The anomaly is detectable; the sand is not resolvable. Both are useful, and the interpreter needs to know which is which.