Average Velocity: Definition, Depth Conversion, and Seismic Tie

Key Takeaways

• Mathematical definition and measurement methods: The average velocity from surface to depth D is defined as V̄ = D / t₁, where t₁ = TWT/2 is the one-way travel time. It can be measured directly from a checkshot survey, in which a downhole geophone is clamped at known depths in the borehole and a seismic source at surface fires a pulse; the travel time from surface to receiver at each depth gives a direct measurement of V̄ to that depth. A vertical seismic profile (VSP) extends the checkshot concept by recording a full trace at each receiver station, capturing both the downgoing and upgoing wavefields to enable formation interval velocity estimation in addition to average velocity. In the absence of checkshots, average velocity is estimated from stacking velocity (normal moveout velocity, Vnmo) using the relationship between NMO velocity and true average velocity established by the Dix interval velocity equation: Vnmo ≈ Vrms in a layered medium, and the true average velocity V̄ is slightly slower than Vrms because the RMS averaging overweights the faster intervals. The difference between Vrms and V̄ is typically 1-4 percent in the WCSB at Montney depths, corresponding to depth errors of 25-100 metres at 2,500-3,000 metres depth if Vrms is used directly for depth conversion without Dix correction.
• Relationship between average velocity, interval velocity, and RMS velocity: The three velocity types describe the same physical quantity (seismic wave propagation speed) at different levels of resolution and mathematical treatment. Interval velocity Vᵢ is the propagation speed within a single geological layer, computed from the Dix equation as Vᵢ(n) = sqrt((Vrms²(n) × t(n) - Vrms²(n-1) × t(n-1)) / (t(n) - t(n-1))), where n is the layer index and t is the one-way time to the layer base. RMS velocity is the root-mean-square of the interval velocities weighted by the interval one-way travel times: Vrms² = Σ(Vᵢ² Δtᵢ) / ΣΔtᵢ. Average velocity is the depth-weighted mean: V̄ = Σ(Vᵢ Δhᵢ) / ΣΔhᵢ = D/t₁. In a medium where velocity increases monotonically with depth (as in most sedimentary basins), Vrms > V̄ > Vₘᵢₙ (the minimum interval velocity), because the RMS operation overweights the high-velocity intervals by squaring. Depth conversion requires V̄, not Vrms; using Vrms directly without Dix correction overestimates depth in a normally compacted sedimentary column. The Dix equation converts between Vrms and interval velocity, and average velocity is then computed as the depth-weighted sum of interval velocities, completing the chain from stacking velocity (observable) to average velocity (needed for depth conversion).
• Depth conversion and well prognosis using average velocity: Depth conversion transforms the seismic section from TWT (milliseconds) to depth (metres) using the relationship D = V̄ × TWT/2, applied either horizon-by-horizon (layer-cake conversion) or using a 3D velocity field derived from the velocity model used in pre-stack depth migration. Layer-cake conversion applies the appropriate average velocity to each horizon independently: the Top Montney A average velocity is computed from the checkshot-calibrated velocity function at that two-way time, and each underlying horizon is converted using its own average velocity, which is generally higher because of the deeper, more compacted rock column above. Well prognosis uses the depth-converted seismic interpretation to predict the depth at which the drill bit will encounter the target formation at the planned well location, giving the drilling engineer the casing setting depths and the formation evaluation team the anticipated formation top depths for wellsite geology. A systematic error in average velocity of 2 percent at Montney depth (approximately 2,500-3,000 metres TWT, corresponding to V̄ of approximately 2,800-3,200 m/s) produces a depth prognosis error of 50-75 metres, which is large relative to the 10-20 metre window available for landing a horizontal well in the target Montney A member. Checkshot surveys in nearby wells, calibrated to the formation tops from well logs, are therefore essential for constraining depth conversion uncertainty to the sub-10 metre level needed for reliable horizontal well landing.
• Lateral variation in average velocity and its geological causes: Average velocity varies laterally across a seismic survey because the geological formations above the target horizon change in lithology, thickness, compaction, fluid content, and temperature. The dominant control on average velocity variation in the WCSB is the thickness and lithology of the shale-dominated Cretaceous section above the Triassic and Devonian targets: where the Cretaceous is thick (basin center), V̄ to the Montney is lower because Cretaceous shales have velocities of 2,200-2,800 m/s; where the Cretaceous is thin or eroded (Peace River Arch area), V̄ is higher because the column contains a higher proportion of Paleozoic carbonates and evaporites at 5,000-6,500 m/s. Gas-charged formations create local low-velocity anomalies (gas causes a significant velocity reduction in unconsolidated sands), which can be exploited as a DHI signal but also create depth conversion artifacts if the gas-velocity anomaly is not accounted for in the velocity model. Permafrost in northern Alberta and BC creates high-velocity near-surface layers (ice-bonded sediments at 3,000-4,000 m/s) that increase V̄ near-surface and must be accounted for in the velocity model to avoid over-estimating the depth to deeper targets. Burial and compaction history affects average velocity through its effect on porosity: over-pressured reservoirs (where fluid pressure exceeds the normal hydrostatic gradient) have anomalously high porosity and low velocity relative to their burial depth, requiring a geo-pressure correction to the velocity model before depth conversion.
• Seismic-to-well tie and average velocity calibration: The seismic-to-well tie is the process of correlating the synthetic seismogram generated from well logs (sonic and density logs convolved with an extracted wavelet) to the actual seismic trace at the well location, establishing which seismic reflection corresponds to which geological formation top. This tie requires converting the well log depths (measured in metres below surface) to two-way travel times using the integrated sonic travel time or the checkshot-measured average velocity at each formation top. If the integrated sonic average velocity at the Top Montney A is 3,020 m/s and the checkshot average velocity at the same depth is 2,985 m/s, the seismic-to-well tie must account for this 1.2 percent sonic-checkshot discrepancy (which arises from borehole effects and formation alteration around the wellbore that affect the sonic log but not the checkshot). The standard approach is to time-shift the synthetic seismogram by the bulk time shift needed to align the strongest tie events, then compute a time-depth transform (the well velocity function) that defines the TWT at each formation top for this specific well. This well velocity function is exported to the seismic interpretation project and used to calibrate the regional average velocity model for depth conversion within the influence radius of the well.