Velocity picking on semblance gathers

You have a CMP gather. You need to find V(t₀). Trying every possible velocity at every time sample is obviously infeasible by hand — but a computer can, cheaply, and show you the result as a semblance panel. The panel is a 2D map of (V, t₀) where a pixel’s brightness is how well that velocity flattens the gather at that time. Bright spots = “this velocity flattens an event here.” Click them in order, and you have V(t₀).

1. The semblance formula

where t_i(V) = √(t₀² + x_i²/V²) is the NMO travel-time at trace i and s_i is the trace amplitude at that time (interpolated). The numerator is the squared stack; the denominator is the sum of squared samples times the number of traces. Ratio is in [0, 1]. Coherent alignment → near 1; noise → near zero.

In production, semblance is computed over a small TIME WINDOW around t₀ (2–5 samples) so the pick includes a few wavelet cycles.

2. The widget

Three panels:

• CMP gather with three hyperbolic events marked by teal-dashed truth curves.
• Semblance panel — V on the horizontal axis, t₀ on the vertical axis going down. Bright spots are the maxima at each of the three true (V, t₀).
• Corrected gather — NMO applied with the piecewise-linear V(t₀) built from your picks, plus a 30 % stretch mute.

Click three times, roughly on the bright spots, and watch the corrected gather flatten. Or click “Auto-pick maxima” and get a best-of-each-row function applied automatically. Each new pick adds to the V(t₀) curve; clicks below or above existing picks just extrapolate.

3. What you see on a real semblance

• Primary reflections produce bright isolated spots at the correct (V, t₀). These are what you want.
• Multiples produce bright spots at lower velocity than the primaries at similar times — they are still hyperbolic, just under-corrected at primary velocity. Pick the upper bright spot, not the lower one.
• Coherent noise (ground roll, direct wave) produces low-velocity streaks along the left edge. Ignore.
• Low-fold patches produce weak, smeared semblance — the picks there are less reliable.

4. Picking strategies

• Top-down, shallow to deep. Start near t₀ = 0 and work down. Shallow picks anchor the function; deep picks respond to the underlying velocity trend.
• Aim high in ambiguity. Between two plausible velocities, pick the higher (primary) one. You can always lower it; over-corrections are harder to spot.
• Check with NMO. Display the gather at each candidate velocity. The best pick is the one whose NMO visibly flattens the event.
• Sparse is fine. You don’t need a pick every 50 ms; 10–20 picks over a 3-s section is normal for land data.

5. What automated pickers do

Automated velocity pickers scan the semblance for local maxima subject to constraints: monotonic V with depth (usually), minimum separation between picks, minimum semblance threshold. They save a lot of time on clean data. In complex geology they miss — picking multiples as primaries, over-smoothing through a rapid V change, or drifting into noise. A processor reviews every automated pick.

6. From picks to a velocity model

A picked V(t₀) at one CMP is one 1D profile. 3D velocity analysis picks V(t₀) at a grid of CMPs and interpolates between them — producing a V(x, y, t₀) volume. That volume is what goes into NMO, migration, and inversion.

Where this goes next

§3.4 breaks the hyperbolic assumption. Real earth is often anisotropic — in shale layers especially — and the exact move-out equation picks up a non-hyperbolic term controlled by a parameter called η. When you pick a single V_NMO for an anisotropic layer, you systematically mis-image deep reflectors.

References

• Taner, M. T., Koehler, F. (1969). Velocity spectra — digital computer derivation and applications of velocity functions. Geophysics, 34, 859.
• Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.
• Dix, C. H. (1955). Seismic velocities from surface measurements. Geophysics, 20, 68.
• Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge UP.