Velocity picking on semblance gathers

Part 3, Velocity Analysis & NMO

Learning objectives

  • Define semblance and read a (V, t₀) semblance panel
  • Click through a velocity function on a real-looking gather and see NMO update live
  • Recognize the common picking pitfalls: multiples, low-velocity noise, mispick aliasing
  • Appreciate how automated pickers agree with hand-picked functions in easy cases and disagree in hard ones
  • Build a supergather and read a velocity error on CMP-absolute-offset vs CMP-signed-offset sort order

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

S(V,t0)=(∑isi(ti(V)))2N⋅∑isi(ti(V))2S(V, t_0) = \frac{\left(\sum_i s_i(t_i(V))\right)^{2}}{N \cdot \sum_i s_i(t_i(V))^{2}}

where ti(V) = √(t02 + xi2/V2) is the NMO travel-time at trace i and si 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.

Velocity analysis via semblancevelocitytimeCMP AFTER NMOSemblance is amplitude coherency over the gather - peaks at correct velocity

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. Supergathers and sort order

A single CMP rarely carries every offset you want, and the offsets it does carry are often sparse. So for velocity analysis you build a supergather: combine the traces from a handful of neighboring CMPs into one gather so the full offset range is densely, and redundantly, sampled. Duplicate offsets are welcome, they stack down random noise on the semblance. Where the velocity must be exact (pre-drill pore-pressure prediction along a planned well path, say), you keep the supergather tight, only CMPs next to the well, so you do not blur a real lateral velocity change.

How you sort the traces inside that supergather changes what a velocity error looks like:

  • CMP, absolute offset. Order traces by |offset|, from zero outward, regardless of whether each was shot ahead of or behind the midpoint. The display is monotonic and tidy: a velocity error reads as a one-sided bend, the event drooping below t0 at far offset (velocity too high) or rising above it (too low), and you can read off the offset where the bend begins.
  • CMP, signed offset. Order from the farthest positive offset (ahead of the midpoint), through zero, to the farthest negative offset (behind it). Now an on- or off-velocity event is symmetric: flat when the velocity is right, a full smile or frown when it is not.

On the signed display the smile/frown of §3.2 applies directly: a frown (far offsets still below t0) is an under-correction, the velocity is too high, lower it; a smile (far offsets pulled above t0) is an over-correction, the velocity is too low, raise it. The counter-intuitive part is the direction, and it is worth pinning down: because the NMO shift scales as 1/V2, a slower velocity applies a larger correction, so it is the slow velocity that over-shoots into a smile. This is the mirror image of the post-migration convention, where a smile means the velocity was too high (over-migration); the two are exactly opposite, see §5.2.

Read the two sides separately near faults. When a midpoint sits on a fault, one side of the spread can image the footwall and the other the hanging wall, two different velocity histories at the same t0. A change that moves only the near traces, only the far traces, or only one side of a signed gather is a clue that you are picking across a fault. Cross-check the stacked section so every pick lands on the correct side of the fault for that time.

5. 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.

6. 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.

7. 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.

**The one sentence to remember**

Semblance turns the velocity-picking problem into a click-through-bright-spots exercise; the bright spots are where the gather flattens, and the piecewise-linear function through them is your V(t₀).

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.

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