# Dictionary:Alias

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FIG. F-11. f,k plot. (a) The region passed by array, frequency, and velocity filters is cross-hatched. Radial lines through the origin represent constant apparent velocity Va (Va=f/k=ω/κ). (b) Data beyond the Nyquist wavenumber fN (determined by discrete spatial sampling) wraps around (aliases) and may get mixed up with the signal. In wraparound, data to the right of +kN continues rightward from –kN, where KN is the Nyquist wavenumber.

(ā’ lē ∂s) 1. Ambiguity resulting from the sampling process. Where there are fewer than two samples per cycle, an input signal at one frequency yields the same sample values as (and hence appears to be) another frequency (the sampling theorem). Half of the frequency of sampling is called the folding frequency or Nyquist frequency, fN. The frequency fN + Δf appears to be the smaller frequency, fN – Δf. The two frequencies, fN + Δf and fN – Δf, are aliases of each other.

FIG. A-8. Aliasing of 200 Hz (dashed line) as 50 Hz (solid line). Both 50 and 200 Hz waves give the same sample values when sampled at 250 Hz (4 ms sampling).

See Figure A-8.

To avoid aliasing, frequencies above the Nyquist frequency must be removed by an alias filter (q.v.) (also called an antialias filter) before sampling. Aliasing is an inherent property of all sampling systems and it applies to (e.g.) sampling at discrete time intervals, as with digital seismic recording, to the sampling which is done by the separate elements of geophone and source arrays (spatial sampling), and to sampling such as is done in gravity surveys where the potential field is measured only at discrete stations, etc.

2. The wraparound (q.v.) consequent to a Fourier analysis over a limited range such as occurs with the 2D Fourier transform in the f-k domain (q.v.) and is illustrated in Figure F-11. See Sheriff and Geldart[1].

Analogy: A variant of what has been explained by former SEG President, Dr. Larry Lines:

‘Take, for example, a car driving through a school zone versus a car driving down an interstate highway. In the case of the school zone, the car is driving slowly enough that you, as a bystander, are able to register the spin of its rims with your eyes. In the case of the car driving fast down the highway, however, your eyes do not ‘sample’ the spinning of the rims quickly enough. This has the effect of making the rims appear to be spinning more slowly. In other words, the frequency of the rotation appears to be lower than it actually is due to under-sampling.’

## References

1. Sheriff, R. E; Geldart, L. P (August 1995). Exploration Seismology, 2nd Ed. Cambridge Univ. Press. p. 282–282, 451–452. ISBN 9780521468268.