Vertical Seismic Resolution
What it is, the λ/4 formula behind it, why it degrades with depth, a free calculator, and the acquisition and processing choices that actually improve it.
What is vertical seismic resolution?
Vertical seismic resolution is the smallest vertical distance between two reflecting interfaces that can still be seen as two separate events on a seismic trace. In practice it answers the question every interpreter asks: how thin a bed can this survey image?
The limit is set by the seismic wavelength at the target, not by the sample rate or the display scale. Two reflections closer together than roughly a quarter of the dominant wavelength merge into one composite wavelet, and the individual top and base can no longer be picked. This threshold is called the Rayleigh resolution limit or, in reservoir work, the tuning thickness.
The λ/4 formula
The seismic resolution formula is simple: wavelength is velocity divided by frequency, and vertical (temporal) resolution is one quarter of that wavelength. This is the λ/4 rule, also written as the Rayleigh criterion:
Two things matter in applying it correctly:
- Use the interval velocity of the bed itself, not the average or RMS velocity down to it. Resolution is a property of the layer being imaged.
- Use the dominant frequency at the target, measured from the data (a spectrum in a window around the horizon), not the frequency the source emitted at the surface. Absorption strips the high end on the way down.
Seismic resolution calculator
Enter the interval velocity and dominant frequency at your target. This vertical seismic resolution calculator returns the wavelength, the λ/4 resolution limit, the λ/8 detection limit, and the equivalent two‑way time of the tuning thickness.
Example presets: shallow clastics 1800 m/s · 60 Hz · mid‑depth reservoir 3000 m/s · 30 Hz · deep carbonate 4500 m/s · 20 Hz
Tuning thickness and the wedge model
The classic way to see thin bed resolution and tuning thickness is a wedge model: a layer that thins from well above λ/4 to zero, overlain and underlain by the same host rock. Convolving it with a wavelet gives the synthetic below.
Three regimes are visible:
- Thick bed (> λ/4): two distinct reflections; thickness can be read directly from their time separation.
- At tuning (≈ λ/4): the side lobes of the top and base wavelets add constructively. Amplitude peaks and the apparent time separation stops shrinking. This is the thinnest bed whose thickness can still be measured.
- Below tuning (< λ/4): the two reflections collapse into one event whose amplitude falls roughly linearly with thickness. The bed is detectable but its thickness must be inferred from amplitude, not time.
Why vertical resolution degrades with depth
Both terms in the formula move the wrong way as depth increases:
The combined effect is large. A shallow target at 1800 m/s and 60 Hz resolves 7.5 m. A deep target at 4500 m/s and 20 Hz resolves 56 m, more than seven times coarser, even though both come from the same survey.
Worked examples
| Setting | Vint (m/s) | fdom (Hz) | λ (m) | λ/4 (m) | λ/8 (m) |
|---|---|---|---|---|---|
| Shallow clastics, high‑res land 3D | 1,800 | 60 | 30 | 7.5 | 3.8 |
| Tertiary sand reservoir, onshore basin | 2,600 | 40 | 65 | 16 | 8 |
| Mid‑depth clastic reservoir | 3,000 | 30 | 100 | 25 | 12.5 |
| Permian platform carbonate | 4,500 | 20 | 225 | 56 | 28 |
| Marine broadband, shallow target | 2,200 | 70 | 31 | 7.9 | 3.9 |
The last row shows why broadband marine acquisition matters: pushing fdom from 40 to 70 Hz nearly halves the resolvable thickness at the same depth.
How to improve vertical seismic resolution
Velocity is fixed by geology. The only lever is dominant frequency at the target, and it is decided mostly in survey design before a single shot is fired:
Acquisition
- Source bandwidth. Vibroseis sweeps extended to 100–120 Hz, low‑dwell sweeps to protect the low end, or small dynamite charges at optimum depth below the weathering layer. Offshore, broadband sources and deep‑towed or variable‑depth streamers suppress the ghost notch.
- Single sensors or small arrays. Long receiver arrays attenuate high frequencies at far offsets through intra‑array statics; point receivers preserve them.
- Group and shot interval. Finer spatial sampling keeps high‑frequency energy from being aliased in the data, which processing would otherwise have to filter out.
- Sample rate. 2 ms keeps 125 Hz of usable bandwidth after the anti‑alias filter; 1 ms is worth it for shallow high‑resolution work.
- Offset range. Near offsets are the least affected by NMO stretch; limiting the stack to a modest Xmax at the target preserves the high end.
Processing and interpretation
- Surface‑consistent deconvolution and Q‑compensation (inverse‑Q filtering) to restore attenuated frequencies.
- Careful statics and velocity analysis: residual misalignment before stack acts as a high‑cut filter.
- Spectral broadening or deterministic wavelet shaping, applied within the data's signal‑to‑noise limits.
- Seismic inversion, spectral decomposition and amplitude‑versus‑thickness calibration against wells to interpret beds below tuning.
Vertical vs horizontal resolution
Vertical and horizontal resolution are controlled by the same wavelength but behave differently. Before migration, lateral resolution is set by the Fresnel zone, rF ≈ √(z · λ / 2), which grows with depth far faster than λ/4 does. After migration, lateral resolution tightens to roughly λ/2 in the ideal case. The bin size of a 3D survey is designed so that spatial sampling never becomes the limiting factor; see the bin size and horizontal resolution tool kits on the main page.
Frequently asked questions
What is vertical seismic resolution?
The minimum vertical separation between two reflectors that can be distinguished as two separate events. The usual limit is one quarter of the dominant wavelength (λ/4), the Rayleigh criterion, also called tuning thickness.
What is the formula for vertical seismic resolution?
Rv = λ/4 = Vint / (4 · fdom). At 3000 m/s and 30 Hz, λ = 100 m and Rv = 25 m.
What is the difference between resolution and detection?
Resolution (λ/4) is the thinnest bed whose top and base can be separated in time. Detection is weaker: beds down to λ/8 or thinner still produce an amplitude anomaly and can be detected, but their thickness cannot be measured from the wavelet shape alone.
Why does vertical resolution get worse with depth?
Velocity increases with compaction, lengthening the wavelength, and high frequencies are absorbed preferentially, lowering the dominant frequency. Both make λ larger, so λ/4 grows from metres at shallow targets to tens of metres at depth.
How can vertical seismic resolution be improved?
Only by raising dominant frequency at the target: broadband sources, point receivers or small arrays, fine group interval and sample rate, Q‑compensation and deconvolution in processing, and inversion or spectral decomposition to interpret below tuning. Velocity cannot be changed.
Does a smaller bin size improve vertical resolution?
No. Bin size controls spatial sampling and horizontal resolution. Vertical resolution depends only on velocity and frequency. A survey with 12.5 m bins and 20 Hz at target has the same vertical resolution as one with 25 m bins and 20 Hz.
Is λ/4 a hard limit?
It is a practical, widely used criterion rather than a physical wall. With high signal‑to‑noise data, well‑known wavelets and inversion, thickness can sometimes be estimated below λ/4; with poor data the effective limit can be worse than λ/4. Survey design should treat λ/4 as the planning target.
Need a survey designed to a resolution target?
We design 2D, 3D and marine acquisition geometries from the geological objective backwards: thinnest bed to resolve → required fdom at target → source, receiver and sampling parameters that can deliver it.
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