Vibration-coherent noise removal

The shear probe, like nearly all other velocity sensors, measures the velocity of the fluid relative to the platform that holds the probe. Thus, platform vibrations induce a signal that is due to platform motions and does not represent environmental shear.

The algorithm described by Goodman et al (2006) is often used to remove vibration-induced components from shear-probe spectra. This algorithm estimates the transfer functions that relate the vibration (or acceleration) signals to the shear-probe signals. Like all transfer function estimates, the algorithm relies on the coherency between the shear-probe and vibration signals in order to achieve a statistically significant estimate of the transfer functions among these signals.

Focusing on one specific direction, one specific shear probe, one can simply:

- compute the coherence squared [math]\displaystyle{ \Gamma^2(f) }[/math] between the observed velocity or shear frequency spectrum [math]\displaystyle{ E_{\mathrm{obs}}(f) }[/math] and the vibration frequency spectrum [math]\displaystyle{ E_{\mathrm{vib}}(f) }[/math].

- and remove the vibration-coherent content of the shear spectrum using [math]\displaystyle{ E_{\mathrm{clean}}(f)=E_{\mathrm{obs}}(f)(1-\Gamma^2(f)) }[/math]

The statistical significance increases with increasing number of fft-segments used to make a spectral estimate. However, this removal biases the spectrum of shear low, in a wavenumber-independent manner, and must be corrected .

A desire to achieve a high spatial resolution of [math]\displaystyle{ \varepsilon }[/math]-estimates by using short lengths of data with few fft-segments conflicts with the need to achieve good statistical reliability of the transfer function and, thus, the correction for vibration induced signals.

References

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