geophysics · seismic resolution
Horizontal Resolution (Fresnel Zone Radius)
R_unmig = (V/2)√(t0/f) | R_mig ≈ λ/4 = V/(4f)
click formula to derive ↑
Inputs
ft/s
ms
Hz
Description
Computes the first Fresnel zone radius — the portion of a reflector contributing constructively to a stacked, unmigrated reflection, and the classic measure of horizontal (lateral) seismic resolution — alongside the theoretical resolution limit after ideal 3D migration, which collapses the zone toward a quarter wavelength. Presenting both together lets a practitioner see the resolution actually available on unmigrated/stacked data next to the best-case improvement migration can realistically offer, from the same velocity/time/frequency inputs.
Variables
| Symbol | Unit | Description |
|---|---|---|
| R_u | ft | Unmigrated Fresnel Zone Radius |
| R_m | ft | Ideal Migrated Resolution Limit |
| V | ft/s | Representative velocity above the reflector of interest. |
| t0 | ms | Two-way, zero-offset travel time to the reflector whose lateral resolution is being assessed. |
| f | Hz | Dominant (peak spectral) frequency of the seismic wavelet at the reflector level. |
Assumptions
- Constant (or a single representative average) velocity above the reflector
- Coincident source/receiver (zero-offset) geometry
- A single dominant-frequency wavelet approximation of an inherently broadband source signal
Limitations
- R_mig is a theoretical ideal (full 3D migration) lower bound, not a guaranteed achieved resolution — actual post-migration resolution depends on migration algorithm quality, spatial sampling, aperture, and structural dip
- 2D migration only collapses the Fresnel zone along the line direction, remaining close to full unmigrated width perpendicular to it — sources describing this specific partial-collapse case give inconsistent numeric reduction figures, so this calc discloses the effect qualitatively only and does not compute a 2D-specific value
- Velocity gradients and lateral velocity variation (facies change, salt/carbonate bodies) break the constant-velocity assumption used in both formulas, especially at larger depths
Use Cases
- → Lateral resolvability of nearby features: Assess whether two closely-spaced features (channel margins, a small fault throw) can be distinguished on unmigrated/stacked data versus requiring migration.
- → Justifying reprocessing/remigration: Quantify the theoretical resolution improvement available from better migration (e.g. PSTM to PSDM) to help justify a reprocessing decision.
- → Survey design sanity check: Compare bin spacing and target size against the expected Fresnel zone radius at target depth during survey design review.
Related Calculations
Region Notes
North Sea
Typical exploration-target depths (2.0-2.5 s TWT) with 20-25 Hz dominant frequency and ~3,000 m/s overburden velocity give unmigrated Fresnel radii on the order of 450-550 m, versus an ideal migrated limit near 30-40 m — illustrating why 3D migration is standard practice for fault and stratigraphic delineation in this setting.
Permian Basin
Shallower unconventional targets (1.0-1.5 s TWT) with higher dominant frequencies (30-40 Hz) at ~4,000 m/s overburden velocity give meaningfully smaller unmigrated Fresnel radii than deeper conventional plays, but well-spacing and fault throws are often still finer than even the migrated limit — always compute the specific radius rather than assuming shallow automatically means adequately resolved.
Global
Always state whether a quoted resolution figure is the unmigrated or migrated value — conflating the two significantly overstates what an unmigrated/stacked section can actually resolve.
References
Primary source
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