Field calibration

Calibration of infrasound detectors (consisting of a microbarometer and a WNRS) is of great importance to the detection and parameterization of infrasound sources (Gabrielson, 2011; Demeyer et al., 2023; Green et al., 2021; Kristoffersen et al., 2023). The methods pioneered by Gabrielson (2011) is recommended. This method of calibration involves the co-localization of a reference sensor (without any WNRS) near the barycentre of the detector-under-test (microbarometer + WNRS).

This reference sensor must be previously calibrated either in a calibration laboratory or on site by the use of a portable calibration system, such as the device called SMIT (for Système de Métrologie Infrasonore de Terrain) developed by the CEA . This system is composed of a portable infrasound dynamic pressure generator, a geophysical field digitizer, a calibrated reference sensor, and the on-board electronics necessary for measurement and processing of the results. Coupled with a laptop computer, the system allows the calibration of any type of geophysical infrasound sensor at the location where the measurement will be performed in the field.

Given that the detector and the reference sensor are observing the same pressure field, the autospectra () and cross-spectral densities (), and the measured pressure at the reference sensor,   are used to determine the pressure at the detector-under-test, :

where the * denotes the complex conjugate.

To ensure that the response is determined for signals, which are observed by both the detector-under-test and the reference sensor, the magnitude-squared coherence (MSC) is considered. The MSC is shown to be

and only time intervals and frequencies where is greater than 0.98 are considered.

In addition, the method proposed by Charbit et al. (2015), which includes sub-dividing the signal into six different frequency bands, is used. By using these bands, more appropriate data window lengths are used for each frequency, which allows for better signal stationarity at all frequencies. It should be noted that these are the frequencies bands used for the 20 Hz sampling frequency measurements. Welch's method (Welch, 1967) is applied to each segment, such that each segment is sub-divided into 15 sub-windows with 50% overlap.

The next method for removal of the `dip' artefact is through the use of the Kramers-Kronig (K-K) relations (Kramers, 1927; Kronig, 1926; Kristoffersen et al., 2023), which use the relationship between the real and imaginary parts of a complex gain. The relations, using the Hilbert transform, are as follows (Bechhoefer, 2011; Hu 1989):

where denotes the Cauchy principal value that excludes the singular point around ,  is frequency, is a complex function of frequency (for our purposes the detector gain), and  and  denote the real and imaginary parts of the complex number, respectively. . Since the gain (like any complex number) can be written in terms of the amplitude and phase, , it is shown that the gain can be written in terms of the phase, as

where is the magnitude of the gain as the frequency approaches infinity. For these relations to be valid, the phase must converge towards 0 as the frequency approaches ∞ (Bechhoefer, 2011; Gabrielson, 2019). Since the calibration phase (for a normally operating WNRS) is close to 0 over the entire IMS band, the amplitude is determined by truncating the frequency near approximately 1 Hz.

These methods to remove the `dip' artefact each have their advantages and disadvantages. For the across-array coherence, it can provide quite accurate amplitude and phase measurements when there are sufficient infrasound signals present in the desired frequency range. However, when there are fewer ambient signals, the results become less reliable. For the K-K relations, there is no need to eliminate points as with the across-array coherence, but any errors in the phase cause errors in the amplitude estimations.

Potential Stimuli

Ambient sources are typically used. Very large baffled speakers (size of a truck trailer) and propane burners have been used, but not as part of this project.

Practical Considerations

It is important that the reference be co-located with the bary-centre of the WNRS to avoid high frequency phase errors, and low frequency phase errors associated with the partial coherence of the wind-noise. Either, a single reference sensor which is located to within a few cm’s of the bary-centre of the sensor-under-test (SUT), or two reference sensors (or two inlets to a single reference sensor) with an average position that is within a few cm’s of the SUT. Even distances of one metre will result in low-frequency phase errors.

The duration needed to acquire sufficient data for the Gabrielson calibration differs greatly from station to station. For low-noise (low-wind) conditions that may be typical at a forested-continental station (e.g. IS26), as little as a day or two is enough. However, at a high-noise (high-wind) station, such as one that has little terrain or vegetation to moderate wind, several weeks or a month may be needed to identify enough sufficiently low-noise time-windows to generate a sensor response, given that the reference sensor is not fitted with a wind-noise reduction system.

Measurement Uncertainty

The amplitude uncertainties for the Gabrielson method will vary depending on the station and wind conditions, but are typically about a few percent, while the phase uncertainties may be around a few (1-5) degrees.

Comment on CTBTO ‘5%’ operational tolerances and acceptance criteria

In terms of the amplitude, the 5% operational tolerance is acceptable. However, the phase tolerance is, perhaps, more important than the amplitude, as phase errors can lead to back azimuth and trace velocity biases. These biases are also highly frequency dependant. Therefore, at high frequency (>1 Hz) even large errors of 10 degrees do not have a substantial impact on wave parameter determination. However, at 0.02 Hz, even errors as small as 1 degree can have substantial impact on the back azimuth (10°) and speed (100 m/s) errors, depending on the size and configuration of the infrasound station.

References

Gabrielson, T. B. (2011). In situ calibration of atmospheric-infrasound sensors including the effects of wind-noise-reduction pipe systems. The Journal of the Acoustical Society of America, 130(3), 1154-1163.

Demeyer et al., 2023 Reference needed

Green, D. N., Nippress, A., Bowers, D., & Selby, N. D. (2021). Identifying suitable time periods for infrasound measurement system response estimation using across-array coherence. Geophysical Journal International, 226(2), 1159-1173.

Kristoffersen et al., 2023Reference needed

Charbit, M., Doury, B. & Marty, J., 2015. Evaluation of infrasound insitu calibration method on a 3-month measurement campaign, in 2015 Infrasound TechnologyWorkshop of the Provisional Technical Secretariat of the Comprehensive Nuclear-Test-Ban Treaty Organisation, Vienna International Centre, Vienna.

Welch, P. (1967). The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Transactions on audio and electroacoustics, 15(2), 70-73.

Kramers, 1927Reference needed

Kronig, 1926;Reference needed

Bechhoefer, 2011Reference needed

Hu 1989Reference needed

Gabrielson, 2019Reference needed