geophysics · depth conversion
Depth Conversion — Linear Velocity Gradient (V0-k)
Z = (V0/k) × (e^(k×OWT) − 1)
click formula to derive ↑
Inputs
ft/s
s⁻¹
ms
Description
Converts seismic two-way time to depth using Slotnick's (1936) linear velocity-depth gradient model, V(z) = V0 + k·z, integrated to give depth directly from one-way time. Widely used where velocity increases steadily with depth (compaction-driven) and no single average velocity or dense well control is available to constrain a layered model.
Variables
| Symbol | Unit | Description |
|---|---|---|
| Z | ft | Depth |
| V(Z) | ft/s | Velocity at Depth Z |
| V0 | ft/s | Instantaneous velocity at the datum (z=0), from a regression of velocity-depth data over the calibration interval. Sensitive to shallow-section regression noise — do not over-interpret as a standalone geological quantity. |
| k | s⁻¹ | Rate of instantaneous velocity increase with depth (compaction trend), locally regressed from velocity-depth data — never a universal constant. Typical published values fall roughly 0.3–1.2 s⁻¹ in clastic basins. |
| TWT | ms | Two-way, zero-offset (stacked/migrated) travel time pick for the horizon being converted to depth. |
Assumptions
- Velocity increases linearly with depth over the interval being converted — a reasonable compaction-driven approximation in many clastic basins, less so in carbonates or across major unconformities
- V0 and k were calibrated from real velocity data (checkshot, sonic, or Dix-derived) in the area being converted, not assumed from a distant analog
- No major lithology change, unconformity, or overpressure zone within the converted interval that would break the linear trend
Limitations
- Linear velocity functions become non-physical outside the depth range of the data they were fit to — do not extrapolate significantly beyond the calibration interval
- V0 in particular is sensitive to regression noise in the shallow section and should not be over-interpreted as a meaningful geological quantity on its own
- Breaks down across major compaction discontinuities (unconformities, overpressure onset) — use a multi-layer model with a separate V0-k pair per zone in these settings
Use Cases
- → Depth conversion without dense well control: Convert TWT horizons to depth in areas with sparse checkshot coverage, using a regionally-calibrated V0-k pair.
- → Comparison against Vavg method: Cross-check against the single-Vavg time-depth conversion to see how much the linear-gradient assumption changes the converted depth, especially for deeper targets.
- → Synthetic velocity-depth curve generation: Generate a smooth V(z) curve for velocity modeling or as an input trend for well-log-based velocity model calibration.
Related Calculations
Region Notes
Gulf of Mexico
Miocene-Pliocene deepwater shale sections are a classic linear-gradient setting; typical published V0≈1,600-1,800 m/s with k≈0.5-0.7 s⁻¹, though local calibration is always preferred over these regional ranges.
Permian Basin
Onshore Permian stratigraphy includes evaporites and carbonates that break the linear-compaction assumption at specific horizons — best applied zone-by-zone (e.g. clastic intervals only) rather than across the full section.
Global
Always report the calibration depth range alongside any V0-k pair — the same pair applied outside that range is a common source of silently wrong depth conversions.
References
Primary source
Need geoscience support? BauerCalc is just one of the tools we build. If you're looking for independent expertise in well planning, geosteering, reservoir characterization, or opportunity evaluation, visit BauerSubsurface.com.