Noise characterization on a shot gather

Part 1 — Acquisition & the data we process

Learning objectives

Distinguish the six most common events on a shot gather by their slope, curvature, and frequency content
Recognize which noises are coherent (structured) and which are random, and why that matters for attenuation strategy
Predict where each noise attenuator (f-k filter, Radon, bandpass, SRME) fits in the processing flow
Identify noise on a real shot gather by eye before choosing which tool to apply

A raw shot gather is not pure signal with a sprinkle of noise. It is a superposition of many events, only some of which you want. The job of noise characterization is to recognize each event from its signature and choose the right attenuator. Attempt that without looking first and you will attenuate signal.

1. The classic events

A typical land or marine gather contains, at minimum:

Primary reflections. Hyperbolic in (time, offset), velocity = medium velocity. This is the signal.
Direct arrival. Linear, traveling directly from source to receivers near the surface.
Ground roll (land) / swell noise (marine). Low-frequency, very slow surface-wave energy in a pronounced cone at low offsets.
Refracted head waves. Linear, fast, from first-break refractors deeper in the section. Essential data for statics, not for imaging.
Multiples. Hyperbolic reflections that have bounced more than once — same shape family as primaries but later and at lower apparent velocity after NMO.
Ambient random noise. Uncorrelated Gaussian that stacking easily dispatches.

The widget below lets you toggle each event on the same synthetic gather. Take a minute to switch things on and off one at a time — train your eye to recognize each pattern before it appears over signal on a real dataset.

2. What makes each signature unique

All the coherent events have a signature in the (time, offset) plane that maps to a distinct region of the (frequency, wavenumber) domain. That is the trick f-k filtering uses: separate events by their slope and curvature.

Apparent velocity of a linear event on a shot gather is vₐ = Δx / Δt (the reciprocal of the event’s slope). It is the speed at which the event moves across the receiver array, not necessarily a subsurface velocity.

- **Ground roll** — tiny apparent velocity (300–1000 m/s), low frequency (5–15 Hz). In f-k, it sits in a fan with very steep slopes. Filter: *f-k fan reject*, or adaptive surface-wave attenuation if amplitude is extreme. - **Direct arrival** — intermediate apparent velocity, broadband. Filter: top-mute before processing; its frequency content is fine, but its amplitude at near offset ruins everything. - **Refracted head wave** — very high apparent velocity (3–50 km/s depending on refractor). Filter: top-mute; but keep an unmuted copy for refraction statics. - **Multiples** — hyperbolic like primaries, but their NMO velocity is slower (less earth seen before the wavelet arrives). Filter: Radon de-multiple, SRME, or adaptive subtraction (all in Part 4). - **Random noise** — uncorrelated, uniform in f-k. Filter: stacking, median filters, or random-noise attenuators.

3. Coherent vs random is the key distinction

Every attenuator is designed around one of two assumptions:

Noise is random — attenuate by averaging (stacking, median filtering). Gains grow as √N from §0.8.
Noise is coherent but has a different signature from signal in some domain (f-k, τ-p, offset-dependence, angle). Attenuate by transforming into that domain and muting.

If you treat coherent noise as random, your stack hides it but leaves it lurking — producing coherent amplitude artifacts on the stacked section that look like events. If you treat random noise as coherent, you cannot find a domain where it is well-separated from signal; you simply waste effort.

4. A noise checklist for any new dataset

Display a full-amplitude shot gather with a strong low-cut bandpass for visibility.
Note each coherent event and estimate its apparent velocity.
Estimate the dominant frequency of each event (or do an f-k analysis).
For every coherent event, name the processing step that will attenuate it.
Estimate the amplitude of the random ambient; the ratio to primary amplitude tells you how much fold you need.

5. Why this matters for processing

Every denoising step in every seismic flow takes one of two forms:

\text{signal}_{\text{out}} = \text{signal}_{\text{in}} + (\text{noise}_{\text{in}} - \text{noise}_{\text{estimated}})

\text{signal}_{\text{out}} = F(\text{signal}_{\text{in}} + \text{noise}_{\text{in}})

where the second form is a transform-domain filter that mutes the estimated noise and leaves the signal. Either way, the algorithm starts with a noise model — and the model comes from knowing the data, which is exactly what this section trains.

**The one sentence to remember**

Every noise has a signature: slope, curvature, frequency content. Learn to recognize them on a gather before you reach for the attenuator — otherwise you are guessing, and denoising is an expensive way to guess.

Where this goes next

Section §1.5 closes Part 1 with survey design sanity: how source and receiver spacing, spread geometry, fold, offset range, and azimuth distribution decide which processing problems you can even attempt and which you cannot.

References

Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.
Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge UP.
Claerbout, J. F. (1976). Fundamentals of Geophysical Data Processing. McGraw-Hill.
Oppenheim, A. V., Schafer, R. W. (2009). Discrete-Time Signal Processing (3rd ed.). Prentice Hall.