Stacking Velocity

Key Takeaways

• Velocity analysis (semblance analysis) is the standard method for measuring stacking velocities from seismic CMP gathers: the analysis applies NMO correction to each trace in the CMP gather using a systematic grid of trial velocities (typically spanning 1,200 to 6,000 m/s for sedimentary basin exploration targets) and at each trial velocity computes the semblance (a normalized measure of trace-to-trace coherence, ranging from 0 for completely incoherent to 1.0 for perfectly coherent) across all offsets in a short time window sliding downward through the record; the result is displayed as a two-dimensional semblance map with two-way time on the vertical axis and velocity on the horizontal axis, with bright semblance peaks (high coherence) indicating the velocity and time of each significant reflection; the analyst picks the velocity at the semblance peak for each reflection, building a velocity-time function that is interpolated between reflections and applied to the entire seismic line as the stacking velocity; automatic picking of semblance peaks using coherence maximization algorithms is common in 3D seismic processing where manual picking of every CMP location is impractical, but automatic picks require quality control to identify erroneous picks caused by multiples (which produce semblance peaks at lower velocities than primary reflections), cycle-skipping (picking the semblance peak on the wrong cycle of a strong reflector), or noise-driven false peaks in poor-data areas.
• The Dix equation converts stacking velocities (measured from seismic data) to interval velocities (the actual velocity within each layer), enabling depth conversion and geological interpretation of the velocity field: the Dix equation states that the interval velocity in a layer between two reflectors is equal to the square root of [(Vstk2^2 * T2 - Vstk1^2 * T1) / (T2 - T1)], where Vstk1 and Vstk2 are the stacking velocities at the top and bottom of the layer and T1 and T2 are the corresponding two-way times; the interval velocity derived from the Dix equation is the RMS average velocity within the layer, and in thick homogeneous layers it approximates the true average acoustic velocity measurable from sonic logs; errors in the stacking velocity measurements propagate into errors in the Dix interval velocities, and the errors amplify for thin layers (where the difference T2 - T1 is small and noise in Vstk1 and Vstk2 dominates the numerator); in practice, stacking velocity derived interval velocities are calibrated against sonic log measurements at wells to identify systematic biases (caused by anisotropy, multiples contaminating the velocity picks, or NMO stretch effects at large offsets) before they are used for depth conversion or pore pressure prediction.
• Pore pressure prediction from seismic stacking velocities uses the empirical relationship between acoustic velocity and effective stress (the difference between overburden stress and pore pressure) to identify overpressured formations before drilling: in normally pressured formations, compaction causes velocity to increase monotonically with depth as porosity decreases; in overpressured formations (where high pore pressure has retarded compaction), velocity is anomalously low for the burial depth, appearing as a velocity anomaly in the stacking velocity field that can be quantified using the Eaton equation (which relates the ratio of observed velocity to normal-compaction trend velocity to the effective stress ratio and hence to the pore pressure gradient); stacking velocity derived pore pressure prediction is a key input to pre-drill well planning for deepwater wells where overpressure is common, guiding the selection of mud weight, casing design, and blowout preventer ratings; the accuracy of the pore pressure prediction depends on the stacking velocity accuracy, which in turn depends on the velocity analysis quality (fold, offset range, frequency content of the data), the calibration of the Eaton equation constants (which vary between basins and must be established from offset wells with measured pore pressures), and the correction of stacking velocities for anisotropy and lateral velocity variation that would otherwise introduce systematic errors into the pore pressure estimate.
• Anisotropy, dip, and lateral velocity variation cause stacking velocities to differ from RMS velocities, requiring corrections before stacking velocities can be used for quantitative purposes: transverse isotropy with a vertical symmetry axis (VTI, the common form of seismic anisotropy in shales with horizontal bedding) causes NMO moveout to be faster than expected from the true vertical velocity, producing stacking velocities that are higher than the true RMS velocity by a factor controlled by the Thomsen anisotropy parameter eta; in VTI media, the moveout velocity for a horizontal reflector is Vnmo = V0 * sqrt(1 + 2*delta), where V0 is the vertical velocity and delta is the anisotropy parameter; failure to correct for VTI anisotropy in stacking velocity picking leads to overestimates of depth and underestimates of pore pressure from Dix inversion, and AVO gradient errors because the NMO correction at large offsets is imperfect; reflector dip also biases stacking velocities upward (dip moveout, or DMO, correction was developed to remove this bias from the stacking velocity and is applied routinely in modern processing before velocity analysis); lateral velocity variation (caused by lateral facies changes, shallow gas anomalies, or salt bodies near the reflector) causes the reflection hyperbola in the CMP gather to be non-hyperbolic, degrading the semblance peak and biasing the stacking velocity pick; full waveform inversion (FWI) and tomographic velocity model building are modern methods to build accurate velocity models that account for all these effects, but they require dense well control and high-quality data.
• Stacking velocity quality control is essential before any downstream use of the velocity field for depth conversion or pore pressure prediction: the standard QC sequence includes visual inspection of the semblance plots for well-defined peaks (broad or absent peaks indicate poor data quality or too few offsets for velocity discrimination), consistency checks of the picked velocity function with geological expectations (velocity should generally increase with depth with only local reversals in overpressured zones), comparison of Dix interval velocities to sonic log measurements at nearby wells (to identify systematic biases), and examination of the stacked data quality after application of the velocity field (residual moveout on angle stacks after NMO indicates that the stacking velocity was not optimal); in areas with strong multiples (shallow water, carbonates, evaporites), the multiple-generated semblance peaks at lower velocities than the primary reflections are a frequent source of picking errors, and multiple suppression before velocity analysis (using Radon transform demultiple or predictive deconvolution) is necessary to avoid picking multiple velocities as primary velocities; the consequence of using erroneous stacking velocities in depth conversion can be a systematic depth error (too shallow or too deep) that affects all reservoir predictions, potentially resulting in wells that are drilled short of or through the reservoir target.