Noise taxonomy

“Noise” is one word for many physical phenomena, and each is fought differently. Your task in the figure is to find, at each of four sites, which family owns the octaves the reflections need, and whether that family is random or coherent, because that decides the remedy.

The figure opens on the remote land line at 6 Hz, where ground roll holds over 99 % of the noise and buries the reflections by 45 dB; there the reflections win only from 18 to 75 Hz. Every site has such a band, and the families at its two edges decide the receivers and the array.

The five families

• Instrument noise: the self-noise of the sensor and the recorder, thermal noise in the coil and the electronics among it. On the record it is close to white and independent from trace to trace. It is the floor, visible only where nothing else is loud, above the reflections’ band.
• Ambient noise: on a towed streamer, swell noise, the cable shaken by the waves: strong below about 10 to 15 Hz, patchy along the streamer and growing with the sea state. On land, wind shaking the geophones and the vegetation, and distant traffic. True microseisms, driven by ocean waves, lie lower still, near 0.1 to 0.3 Hz (periods of 3 to 10 s), below the seismic band. Ambient noise is random, though correlated over tens of metres.
• Ground roll: Rayleigh waves that the source itself sends along the free surface. Slow (a few hundred to about 1000 m/s), low in frequency (roughly 3 to 20 Hz), dispersive and strong: surface waves spread as $x^{-1/2}$ where body waves spread as $1/r$, so on a raw land record ground roll can stand 30 dB or more above the reflections. At the seabed its counterpart is the slower Scholte wave. It is coherent from trace to trace, which is what arrays and f-k filters exploit.
• Cultural bursts: traffic, machinery, footsteps and hammering near the line. Brief, large and scattered in time and place, with broad spectra, so they are edited or despiked out rather than filtered by frequency.
• Harmonic lines: steady sinusoids. On land, induction from power lines at the mains frequency (50 Hz in most of the world, 60 Hz in the Americas) and its odd harmonics; at sea, a vessel’s propeller blade rate (the shaft rate times the number of blades) and its overtones. Each is a narrow spike in the spectrum, removed by a notch or by subtracting the estimated harmonic.

Random or coherent

For the remedy, the classification that matters is random against coherent. Random noise (instrument, ambient, bursts) is unrelated between traces far enough apart: between shots, or between receivers beyond its correlation length, which for instrument noise is zero and for ambient noise is tens of metres. Summing $N$ such traces with the reflections in step raises the amplitude signal-to-noise ratio by up to $\\sqrt{N}$. Bursts are random too, but large and rare, so one burst can dominate a sum; they are better edited out before the stack than averaged. Coherent noise (ground roll, lines) repeats with its own moveout or its own frequency, and is removed by exploiting that structure. A second axis is where the noise comes from: ground roll is made by the source, so a stronger source raises it as much as the reflections; the other families are there with or without a shot.

Why this shapes acquisition

A group of $N$ geophones summed into one trace works against both kinds, in different ways. Against random noise it gains up to $\\sqrt{N}$ in amplitude, like a stack, the full gain only where its geophones are spaced beyond the noise’s correlation length. Against ground roll it is a spatial filter: when the group spans about one ground-roll wavelength $\\lambda = c/f$, the ground roll’s phase turns through a full cycle across it and cancels, while reflections arriving almost vertically add in step. At sea, a deeper tow moves the streamer away from the swell; dual-sensor streamers, which record pressure and vertical particle velocity, remove the receiver ghost and can therefore be towed deeper, which is how they gain on swell noise. A node on the seabed avoids swell and flow noise altogether, much of the reason ocean-bottom surveys deliver usable low frequencies, but it records Scholte waves instead. Every receiver choice is a bet against a particular family, so survey design starts by naming the family that owns the octaves the target needs.

References

• Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press.
• Yilmaz, Ö. (2001). Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data (2 vols.). SEG Investigations in Geophysics 10.
• Pritchett, W. C. (1990). Acquiring Better Seismic Data. Chapman & Hall.
• Elboth, T., Reif, B. A. P., Andreassen, Ø. (2009). Flow and swell noise in marine seismic data. Geophysics, 74(2), Q17-Q25.
• Longuet-Higgins, M. S. (1950). A theory of the origin of microseisms. Philosophical Transactions of the Royal Society A, 243, 1-35.