Vibration-coherent noise removal: Difference between revisions
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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 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 [[The_Goodman_algorithm|algorithm]] described by Goodman et al (2006)<ref> Goodman, L., Levine, E. R., & Lueck, R. G. (2006). On measuring the terms of the turbulent kinetic energy budget from an AUV. Journal of Atmospheric and Oceanic Technology, 23(7), 977-990. </ref> is often used to remove vibration-induced components from shear-probe spectra. | ||
The algorithm described by Goodman et al (2006)<ref> Goodman, L., Levine, E. R., & Lueck, R. G. (2006). On measuring the terms of the turbulent kinetic energy budget from an AUV. Journal of Atmospheric and Oceanic Technology, 23(7), 977-990. </ref> 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. | 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. | 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>\Gamma^2(f)</math> between the observed velocity or shear frequency spectrum <math>E_{\mathrm{obs}}(f)</math> and the vibration frequency spectrum <math>E_{\mathrm{vib}}(f)</math>. | |||
- and remove the vibration-coherent content of the shear spectrum using <math>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 [[The_bias_induced_by_the_Goodman_algorithm|biases the spectrum of shear low]], in a wavenumber-independent manner, and must be corrected <ref> Lueck, R. G., 2022: The bias in coherent-noise removal. Journal of Atmospheric and Oceanic Technology –, submitted, doi:--.</ref>. | |||
A desire to achieve a high spatial resolution of <math>\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== | ==References== | ||
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return to [[Flow chart for shear probes]] | return to [[Flow chart for shear probes]] | ||
[[Category:Shear probes]] | |||
Latest revision as of 19:49, 6 June 2024
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)[1] 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 [2].
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
- ↑ Goodman, L., Levine, E. R., & Lueck, R. G. (2006). On measuring the terms of the turbulent kinetic energy budget from an AUV. Journal of Atmospheric and Oceanic Technology, 23(7), 977-990.
- ↑ Lueck, R. G., 2022: The bias in coherent-noise removal. Journal of Atmospheric and Oceanic Technology –, submitted, doi:--.
return to Flow chart for shear probes
