Velocity Analysis
Velocity analysis, in seismic data processing, is the process of estimating the subsurface seismic wave velocity as a function of depth (or two-way travel time) from the moveout behavior of reflections on seismic gathers, providing the velocity model required for normal moveout (NMO) correction, stacking, and migration that converts the raw field records into an interpretable seismic image; the fundamental observation on which velocity analysis is based is that a reflection from a horizontal reflector at depth z with interval velocity v appears on a common-midpoint (CMP) gather as a hyperbola t^2 = t0^2 + x^2/v_rms^2, where t0 is the zero-offset two-way travel time, x is the source-receiver offset, and v_rms is the root-mean-square velocity from the surface to the reflector; by measuring the curvature (moveout) of the reflection hyperbola at each reflector, the processing geophysicist determines v_rms for that reflector, and by applying the Dix equation (v_int = sqrt((v_rms2^2 x t2 - v_rms1^2 x t1)/(t2 - t1))) to successive reflectors, the interval velocity in each layer between reflectors is calculated; the velocity model derived from velocity analysis controls the quality of NMO correction (incorrect velocities produce over- or under-corrected gathers with residual moveout that degrades stack quality), the accuracy of depth conversion (the transformation of time-migrated seismic sections to depth), and the correctness of amplitude-versus-offset (AVO) analysis (which requires accurate moveout correction to preserve the offset-dependent amplitude variation).
Key Takeaways
- Semblance analysis (also called velocity spectrum analysis) is the standard computational method for velocity analysis in seismic processing: for each CMP gather, the processing software applies NMO corrections for a range of trial velocities (typically 1,400-6,000 m/s in steps of 25-100 m/s) at each two-way time and measures the coherence (semblance) of the NMO-corrected traces across the offset range; semblance is a normalized cross-correlation measure ranging from 0 (no coherence, random noise) to 1 (perfect coherence, all traces identical after NMO correction), and it peaks at the velocity that best flattens the reflection hyperbola; the resulting semblance spectrum (velocity on the x-axis, two-way time on the y-axis, semblance color-coded from low to high) displays as a series of high-semblance peaks at the correct stacking velocities for each reflector; the velocity picker (either a geophysicist using a graphical interface or an automatic algorithm) selects the semblance peak centers as the stacking velocity function for the CMP, with care taken to pick the primary reflector semblance maxima rather than multiples (which produce false semblance peaks at lower velocities), interbed multiples (which produce characteristic parabolic-shaped semblance anomalies), or noise artifacts.
- The distinction between stacking velocity, RMS velocity, and interval velocity is critical for correctly using the velocity analysis output: stacking velocity (the velocity that maximizes semblance for a specific reflection hyperbola at a specific two-way time) is an approximation to v_rms that is strictly equal to v_rms only for horizontally layered isotropic media; in the real subsurface with dipping reflectors, lateral velocity variations, and anisotropy, the stacking velocity deviates from v_rms by amounts that can be significant for depth conversion; v_rms is the root-mean-square of the interval velocities weighted by the two-way travel time in each layer, and it is calculated from the stacking velocities using the assumption of horizontally layered media; interval velocity (the average wave propagation speed in a specific layer between two reflectors) is derived from v_rms using the Dix equation, and is the geologically meaningful quantity that correlates with lithology and pore fluid; interval velocity errors from the Dix equation accumulate with depth (errors in shallow velocities propagate into the Dix calculation for all deeper intervals), making shallow velocity picks particularly important for accurate deep interval velocity determination.
- Velocity analysis spatial sampling determines the lateral resolution of the velocity model: in conventional processing, velocity analysis is performed on a grid of CMP super-gathers (combinations of adjacent CMP gathers averaged to improve semblance statistics) at a lateral spacing of 200-500 meters, then interpolated between analysis locations to create a smooth velocity field; sparse velocity analysis spacing can miss lateral velocity variations from salt bodies, shallow gas pockets, channel fills, and overpressure zones that significantly affect imaging in the areas between analysis locations; high-density velocity analysis (performed at every CMP location rather than on a sparse grid) using automated picking algorithms provides more laterally detailed velocity fields but requires quality control to prevent automated pickers from selecting multiples or noise artifacts rather than primary reflections; in complex geological settings (salt proximity, overthrust belts, highly variable sedimentary fill), the sparse grid velocity analysis of conventional processing is replaced by tomographic velocity model building (which uses all traces rather than just the semblance analysis points) or full-waveform inversion (FWI) that recovers velocity from the full waveform content of the data.
- Anisotropic velocity analysis accounts for the fact that seismic velocity in layered sedimentary rocks is not equal in all directions (VTI anisotropy), causing the NMO moveout of reflections to deviate from the simple hyperbolic form assumed in isotropic velocity analysis: in VTI media, the NMO velocity for P-waves differs from the true vertical velocity (the velocity measured by check-shots or sonic logs) by a factor related to the Thomsen delta parameter (v_NMO = v_vertical x sqrt(1 + 2 x delta)); if anisotropy is not accounted for, the stacking velocities picked from semblance analysis will be biased relative to the true vertical velocity, producing incorrect depth conversion when the NMO velocities are used for time-to-depth transformation without anisotropy correction; anisotropic velocity analysis uses long-offset reflection moveout (which deviates from hyperbolic form at large offsets in anisotropic media) to separately estimate the anisotropy parameters (eta, related to epsilon and delta) in addition to the NMO velocity, providing a more complete velocity characterization for accurate depth conversion and pre-stack inversion.
- Multiple attenuation benefits from accurate velocity discrimination in velocity analysis: water-bottom multiples (seabed reflections that have bounced between the seabed and the reflector multiple times) and interbed multiples have characteristic moveout velocities that are lower than the corresponding primary reflections at the same two-way time, because the multiple has traveled through near-surface low-velocity material multiple times while the primary has only traveled through it once; the velocity discrimination between primaries and multiples appears in the semblance spectrum as two sets of peaks at the same time (or at predictable moveout times for specific multiple orders) but at different velocities; by carefully picking semblance peaks associated with primary reflections and avoiding the lower-velocity multiple peaks, the processor maintains the correct velocity function for primary NMO correction while setting up the velocity difference that is exploited by parabolic Radon transform multiple attenuation (which attenuates energy in the velocity ranges associated with multiples without harming primary reflections in their separate velocity range).
Fast Facts
The semblance coherence measure used in velocity analysis was introduced by Neidell and Taner in a 1971 Geophysics paper that transformed velocity analysis from a manual, interactive process of examining individual gathers into a systematic, automated computation applicable to large seismic datasets. Before semblance analysis, velocity picking was performed by visually examining constant-velocity stacks (CVC stacks, the result of stacking the gather at each of a range of trial velocities and examining which velocity produced the sharpest stack image) at each analysis location, a process that was slow, expensive, and operator-dependent. The semblance spectrum provided a quantitative, reproducible measure of reflection coherence that could be computed automatically and displayed as a picking map, enabling the velocity analysis of the large 3D seismic datasets that became standard in the 1980s and 1990s.
What Is Velocity Analysis?
Velocity analysis is how the seismic processor determines how fast sound travels through the earth at every depth below the survey area. That velocity information is essential for two things: flattening the reflection hyperbolas on the CMP gathers so they can be stacked coherently, and converting the resulting time image into a depth image that can be compared with well data. Without a velocity model, the seismic image cannot be made. With a wrong velocity model, the seismic image is made incorrectly: reflectors appear at the wrong depth, structures are mis-imaged, AVO attributes are distorted. The quality of everything that follows from the seismic data in the exploration or development workflow depends on the quality of the velocity model, and the quality of the velocity model depends on the accuracy of the velocity analysis. A careful velocity picker who distinguishes primary reflections from multiples, accounts for anisotropy, and quality-controls the semblance picks against well velocity data provides the foundation for reliable seismic interpretation. A careless velocity analysis produces a seismic image that looks plausible but places the target reservoir at the wrong depth and in the wrong structural position, sending the drill bit to the wrong location.
Synonyms and Related Terminology
Velocity analysis is also called velocity picking, stacking velocity analysis, or semblance analysis. The resulting output is called the velocity function, the stacking velocity model, or the velocity field. Related terms include NMO correction (normal moveout correction, the application of the velocity-derived time shift to each trace on a CMP gather to flatten reflection hyperbolas and align them for stacking, the primary use of the stacking velocity function determined by velocity analysis), semblance (the normalized coherence measure used in velocity analysis that quantifies how well the traces on a gather align after NMO correction for a given trial velocity, peaking at the correct stacking velocity for each reflector), interval velocity (the average seismic wave velocity in a specific rock layer between two reflector horizons, calculated from successive RMS velocities using the Dix equation, the geologically interpretable velocity quantity that correlates with lithology, porosity, and pore fluid), Dix equation (the formula relating interval velocity in a layer to the RMS velocities above and below the layer, used to convert stacking velocities from velocity analysis into geologically meaningful interval velocities for depth conversion and petrophysical interpretation), and full-waveform inversion (FWI, an advanced velocity model building method that minimizes the difference between observed seismic data and synthetic data computed from a trial velocity model, recovering detailed velocity structure at a resolution approaching the seismic wavelength, used in complex geological settings where semblance-based velocity analysis is inadequate).
Why the Velocity Model Is the Foundation of Every Seismic Interpretation That Follows
Every seismic interpretation decision traces back to the velocity model. Where is the reservoir in depth? The velocity model tells you. Is the structure a real anticline or a velocity pull-up from a shallow fast anomaly? The velocity model reveals it. Does the seismic amplitude change laterally because the lithology changes or because the imaging is affected by a velocity anomaly in the overburden? The velocity model determines which it is. An incorrect velocity model contaminates every interpretation made from the seismic image: the well that is drilled 50 meters above or below the target because the depth conversion was wrong, the trap that appears closed on the seismic but is open when depth-converted with the correct velocities, the AVO anomaly that looks like gas but is an NMO stretch artifact from under-corrected moveout. None of these failures are interpretation errors in the traditional sense. They are velocity analysis failures, upstream of interpretation, that corrupt everything downstream. Velocity analysis is not a processing detail. It is the most consequential technical step between the field records and the interpretable image, and in complex geological environments, it requires the same geological judgment and quality control as any exploration workflow that leads to a drilling decision.