What can you really see in seismic?

Module 05  ·  Vertical resolution in practice

Resolution with depth

The λ/4 limit is not one number for a whole survey. It gets worse all the way down, for two reasons at once, and the same bed can be a clean pair of reflections at the top of a section and a single weak event at the bottom of it, with no change in the rock itself.

Two effects act together

Resolution is set by wavelength, λ = V / f, and increasing depth lengthens the wavelength through both terms of that fraction.

Velocity climbs. Rocks compact under their own weight, so the wave speeds up as it goes down. Bigger V on top of the fraction means a longer wavelength.

Frequency falls. The earth absorbs energy, and it takes the high frequencies first. Smaller f underneath means a longer wavelength again. The number describing how much the rock absorbs is called Q; a low Q means strong absorption.

The size of the effect

The two terms multiply, and the thinnest bed that can be resolved typically grows five-fold between the shallow section and four kilometers down. Ten meters becomes fifty.

The cause is the earth rather than the processing or the interpretation, and reprocessing does not fully undo it.

A λ/4 value carried over from a shallow field therefore does not apply to a deep one. The number that matters is λ/4 at the target depth, in the target rock, with the bandwidth that survives to that depth.

The source wavelet

Low Q is a lossy earth — shale, gas sands, near-surface weathering. High Q is closer to competent carbonate or basement, where the source spectrum survives further before it changes shape.

The earth

Velocity is grown smoothly between these two numbers, the way it does over a compacting basin. Set them equal to switch the gradient off and isolate what attenuation alone is doing.

The test bed

Display

From the surface to the probe depth

Drag Inspect this depth and watch every panel move together. Panels 2 to 5 share one two-way time axis, so you can read straight across from the rock to the seismic.

The thickness slider sets the two marked beds only — one at the reference depth, one at your probe depth. Everything else in panel 4 is random background between 15 and 70 m, there so you can watch the whole column lose character, not just the test bed. Panel 4 is drawn in time like the seismic beside it, so the same thickness in meters looks thinner the deeper it sits: 60 m is 54 ms at the reference and 26 ms at 3 s.

1 The pulse, broadening with depth

2 Velocity

3 λ/4 vs your bed

4 The rock

5 The seismic what you get to look at

6 Same bed, two depths

Wavelength at the surface, λ₀ = V₀ / f₀50 m
Surface λ/4 — the shallow limit12.5 m
Probe — two-way time1800 ms
Probe — approximate depth2900 m
Probe — interval velocity3270 m/s
Probe — effective frequency21 Hz
Probe — wavelength λ155 m
Probe — λ/439 m
Bed thickness as a fraction of λ, at probeλ/5.2
Verdict at probeDetectable — visible, not measurable

Try this — and what to watch for

  1. Turn attenuation off. The point: it isolates the velocity effect, so you can see how much of the damage is compaction alone. Push Q to 500, then drag the probe from the top of the section to the bottom. The verdict still degrades. Velocity growth alone stretches λ enough to lose a thin bed by depth, even in a nearly lossless earth. This is the part of the story that is pure geometry, not absorption.
  2. Now turn it back on. The point: this is the other half, and usually the larger half. Drop Q to 20 and repeat the same drag. The bed is lost much shallower. Attenuation compounds the velocity effect instead of replacing it — real sections lose resolution faster than a velocity-only argument would predict.
  3. Raise the source frequency. The point: it shows the limit of what extra source bandwidth can achieve at depth. Raise the peak frequency from 25 Hz to 80 Hz and compare the surface λ/4 stat against the probe λ/4 stat. Surface resolution improves considerably while the probe value barely moves. The high frequencies are the ones the earth removes fastest, so extra source bandwidth improves shallow resolution far more than deep resolution.
  4. Find the crossing. The point: it turns the whole module into one number you can look up for your own target. Set the bed to 15 m and drag the probe until the verdict flips from Resolved to Below detection. Read the two-way time off the stat strip, then look for the same crossing on panel 3, where the teal λ/4 curve crosses the dashed line marking your bed. The two should agree. Panel 3 is the readout stat turned into a curve, so you can see the whole depth range at once instead of one point at a time, and it draws a marker across the panel at the depth where your bed stops being resolvable.
  5. Isolate the velocity term. The point: it separates two causes that are easy to blame on each other. Set the base velocity equal to the surface velocity, so the gradient is zero, and drag the probe. Resolution still gets worse with depth from attenuation alone. Set Q back up near 500 with the flat velocity and the verdict should barely change at all — that is the closest this module gets to an earth with no depth-dependent resolution loss.
  6. Watch panel 6 directly. The point: same rock, same thickness, two depths — the cleanest comparison on the page. With a fairly thin bed and a mid-range Q, compare the reference trace against the probe trace. Both are drawn to the same scale. Same reflection coefficients, same physical thickness, same convolution machinery — only the local wavelet differs. The reference stays two clean kicks; the probe blurs into one, and it is weaker as well as broader, which is why the two share one scale rather than each being stretched to fill its own box.
  7. Compare panels 4 and 5, side by side. The point: it is the gap between the geology and the picture, drawn on one time axis. The rock is on the left, the seismic on the right, on the same time axis. Read straight across at any depth. Near the top, almost every bed in the rock has its own reflection. Deep down, whole groups of beds have collapsed into single events, and some have vanished entirely. That gap between the two panels is the whole subject of this module, and it widens the further down you look.
  8. Read panel 5 as an interpreter would. The point: it is how deep sections actually look, and why they feel vaguer. Look at the background reflectivity above and below the dashed PROBE line, not just at the marked bed. The whole column loses character with depth, not only the highlighted test bed. That washed-out look on the lower part of a real section is usually this effect, not necessarily worse geology.

If you remember nothing else

  • λ/4 is not a fixed number for a survey. It grows with two-way time because both the terms in λ = V/f are moving against you: V goes up, and the earth's absorption pulls f down.
  • The two mechanisms are independent and they add. Velocity growth is pure geometry and would matter even for a lossless earth. Attenuation is a separate, physical loss of high-frequency energy, and it does not need a velocity gradient to hurt you.
  • More source bandwidth mostly buys shallow resolution. The frequencies you add at acquisition are the ones absorbed fastest, so the deep section converges toward the same answer regardless of the source bandwidth.
  • A resolution floor moving up a trace does not mean the geology changed. The same physical bed can cross from resolved to below detection purely by getting deeper, which is why two closely spaced faults or beds can be obvious at 500 ms and invisible at 2500 ms.
Method, assumptions, and where to read more

Interval velocity is grown smoothly between the surface value and the base value you set, using V(t) = V₀ · (Vmax/V₀)^(t / Tmax), where t is two-way time. This is the closed form that falls out of a constant fractional velocity gradient with depth — the usual V₀–k model of refraction seismology — reparameterized by its endpoints so the two sliders stay physically direct. Depth is then the numerical integral of that velocity, halved for one-way travel, and is only meant to be read as an order-of-magnitude figure.

Attenuation follows the standard constant-Q amplitude law: a frequency component f loses amplitude as exp(−π f t / Q) after travel time t. The source wavelet's amplitude spectrum is treated as proportional to f² exp(−(f/f₀)²), which is the shape that gives a Ricker wavelet its peak at f₀. Multiplying the two and solving for the new peak analytically gives the effective frequency used to build the wavelet at every depth in the section — the earth acts as a time-variant low-pass filter, and this is the peak of what survives. The same exponential also sets how much amplitude the reflection keeps, so deep events are both broader and weaker, the way real deep data actually looks.

Bed thickness is fixed in meters and held constant with depth; only its expression on the trace changes, through the local velocity, the local effective frequency, and the local amplitude. The reference bed near the top of the section and the bed at your probe depth are the same construction evaluated at two different times, so panel 6 is a true apples-to-apples comparison. The background reflectivity around them is random, seeded, and regenerated with the button provided; each layer's thickness is drawn in meters and converted to time with the local velocity as the column is built, so it also compacts realistically going down.

This is a 1-D, normal-incidence, single-well cartoon. It leaves out geometric spreading, transmission losses at each interface, multiples, NMO stretch, and the frequency-dependent dispersion that a physically consistent constant-Q medium also produces alongside the amplitude loss modeled here. None of those change the direction of the story, and several of them would only make the deep section look worse than this module shows it.

The λ/4 and λ/8 thresholds and their "Resolved / Detectable / Below detection" labels are the same ones used in the wedge and fault modules, applied here to a wavelength that is itself a function of depth instead of a single fixed number.

Next up

06 · Resolution in map view

Take the horizontal limit from module 04 and point it at something you would actually map: a channel that narrows and splits in two. Watch where it appears to end — and find out that the ending is in the acquisition rather than in the geology.

Open module 06 → All modules
← Horizontal resolution Next: resolution in map view →