Field calibration

Before the station is originally installed or upgraded, the manufacturer's provided data is verified to be substantially in agreement with the nominal response data by an initial calibration. The system is then calibrated in operational conditions to verify that its measured response is within the tolerances specified by the manufacturer and IMS specifications. The outcome of this initial calibration is used as a baseline for certification purposes and for future calibrations. The determination of the sensor self-noise in the presence of low background signals (self-noise test) is part of the initial calibration.

A seismological station comprises three essential components: a seismometer to detect ground motion, a recording system which digitizes data with precise time-stamping, and a communication system interface. The seismometer itself is the sensor which records the analogue signal, whereas the data acquisition system (e.g. pre-amplifier, digitizer) converts the analogue signal to digital data with timing, state of health and authentication information. The system is thereby the whole recording unit consisting of the seismometer and the acquisition system.

The operational manuals for IMS stations necessitate regular calibrations of these stations. Thereby, the full frequency response of the operational system is determined and compared against the initial calibration results. Seismological stations are equipped with an internal or external calibration unit to conduct electrical calibrations which results can be compared to a previously established reference at the time of station certification or revalidation (initial calibration). Yet, electrical calibration faces a number of challenges such as maintenance issues, high costs, and, above all, lack of traceability. Further, the implementation of the method differs from one station to another and for different sensor types.

Non-feedback seismometers are calibrated with full frequency response at least four times per year, and feedback seismometers are calibrated with full frequency response at least once per year. The calibrations are performed at one sensor at a time to ensure data availability.

On-site calibrations are performed as full frequency response calibrations, that means that the instrument characteristics are measured at all frequencies (up to Nyquist frequency). They are performed as electrical calibrations with the frequencies being excited either by sine waves or by random binary signals. Additionally, station operators may perform single or small sample frequency calibrations between yearly full frequency response calibrations.

As far as the question of how often the field sensors need to be calibrated is concerned, several approaches are possible, depending on available transfer standards per array/station as well as on accessibility of the station. An on-site calibration at least once a year, comparable to the currently performed electrical calibration would be the minimum recommendation to check for instrument drifts, varying behaviour or failures. Note that for a single calibration period, suitable time with enough coherent signal need to be chosen. Furthermore, a continuous installation of a reference sensor is on option (comparable to IMS infrasound station). This offers the possibility to observe any changes over the year with regard to environmental factors, or to check for any failures of the station seismometer.

Other things that should be taken into account should be whether the station sensors are already installed or not. If the station sensors are not installed, a huddle test, that is running two or more instrument as close to each other as possible on the same pier (e.g. Sleeman et al., 2006), together with the reference(s) is a good choice. Otherwise, if the station is already running, the references should be installed at the station directly. However, if more references are to be distributed in a larger array, they could be first installed in a huddle test to check for any possible changes due to transportation. A very important step for the traceable field calibration is the regular calibration of all parts of the systems that also includes the digitizers/data loggers and pre-amplifiers. The data logger's zero-frequency calibration can be determined by applying a precisely-known voltage to the digitizer's input terminals and measuring the resulting output digital counts. This can be done once a year during the maintenance visits at the station as the digitizers have to be checked anyway.
 Note that these are all solely suggestions and the actual realization depends on the conditions at the station or sensor to be calibrated.

Calibration with calibration coil:

The application of a so-called electrical calibration method is common for in-situ calibrations in the field. It is applied to obtain parameters for an analytical representation of the response function (e.g. in form of a finite numbers of poles and zeros) and assumes the form of the function to be known. Such methods make use of the equivalence between ground motions and external forces on the seismic mass. This is done by applying an external electromagnetic excitation of the seismic mass through built-in calibration coils, using a signal generator for example, and observing the system’s response to the excited signal. This procedure is a purely electrical measurement, and requires the proportionality factor between the current in the coil and the equivalent ground motion to be known (e.g. Wielandt 2012; Larsonnier et al. 2014).

In addition, this electrical excitation of the seismometer can also be performed remotely by the control system of the associated digitizer. This is particularly advantageous if the seismometer is installed in a vault, a cave or is otherwise difficult to access (Larsonnier et al. 2014).

For the electrical calibration with calibration coils there are different excitation methods, each of them offering advantages: The steady-state method, which applies sinusoidal signals at various frequencies across the system’s passband, the transient method using impulse signals, and the random signal method employing arbitrary broadband signals.

1. Steady-state calibration with sinewaves:

The output of a linear system is also sinusoidal if the input is sinusoidal. Further, the absolute value of the transfer function corresponds to the ratio of the input and output signal amplitudes, which can be numerically analysed (if being digitally recorded) by sine-wave fitting to extract amplitudes and phases for one frequency at a time, which makes it very time consuming (Berger et al. 1979; Wielandt 2012). The accuracy of this method depends, among others, on the accuracy of the measured input and output signals (Peterson et al. 1980). Other relevant parameters such as the eigenfrequency or the damping can for example be determined graphically using standard curves (Wielandt 2012), but this simple method is not very precise.

2. Transient calibration with impulse and step signals:

A step or impulse signal can be generated by switching on and off a current trough the calibration coil. This is a simple, but not very accurate calibration procedure (Wielandt, 2012). However, care must be taken that, when using impulse signals, the peak signal does not exceed the dynamic range of the system; therefore, only low-level impulses can be applied. Compared to that, step signals can be applied at higher levels. Nevertheless, most power is confined to low frequencies. The broadband character of the impulse signals can be advantageous (Berger et al. 1979).

3. Calibration with arbitrary signals:

Using arbitrary signals, the shape of the sensor’s frequency response can be determined. Berger et al. (1979) suggest the usage of a random binary signal or broadband white noise as input to the calibration coil. These types of signals have broadband power and can be used at high levels. Compared to the above-mentioned methods with predetermined signals, here both the input and output signals are recorded. This procedure provides the added benefit of eliminating the transfer function of the recorder from the analysis. The frequency response is obtained by calculating the cross-spectrum between the input and output signals and fitting a perturbed model of the sensor’s response to it (Berger et al. 1979; Fels and Berger 1994). Noise effects such as ground or electronic noise are reduced by using cross-spectral methods. Yet, by this method only the shape of the frequency response is determined, but not the overall sensitivity of the seismometer (e.g. Davis et al. 2005).

Electrical calibration can also be applied for sensors without calibration coils (such as geophones). The excitation signal is sent through the signal coil instead. In addition to the signal generated by ground motion, an undesired ohmic voltage is produced by that, which can be compensated in e.g. a bridge circuit or numerically. Another approach suggests recording the sensor’s response to the interruption of a known direct current sent through the signal coil

A general introduction to electrical seismometer calibration using calibration coils can be found in Wielandt (2012), and detailed descriptions and guidelines can be found in e.g. Hutt et al. (2009).

Calibration with seismic stimuli:

As stated above, calibration or adjustment with calibration coils, only leads to a determination of the shape of the frequency response. Other important parameters such as the absolute sensitivity or absolute gain remain unknown. Additionally, not all ground motion sensors possess calibration coils; therefore, other excitation mechanisms and in-situ calibration methods must be considered.

A common approach suggested by several studies is the calibration of an unknown sensor against a known one using seismic stimuli recorded by these closely located sensors. This approach is a so-called relative calibration which can be applied on-site under certain circumstances. Seismic excitation signals that have been used for this so far include mainly continuous recordings of ambient ground noise, microseisms, or the Earth’s tides.

Aiming at the determination of the full frequency response of a fully operational seismometer in its natural environment without any interruption of the recordings, these comparison methods provide the basic approach for an absolute and also a traceable calibration.

Under the assumption that both co-located sensors record the same coherent ground motion and that one sensor has a known absolute frequency response, the response of the unknown sensor can be determined including the sensor’s sensitivity and absolute gain. Prerequisite is that the recorded signals are coherent between the sensors and well above the instrumental self-noise (e.g. electronic noise) and background seismic noise levels, the latter being station depend. Therefore, other seismic stimuli, either natural or anthropogenic may be used.

For this approach, it is assumed that the convolutional model is valid for the recorded seismograms, that means that the spectrum of the measured seismogram S(ω) is given by the product of the seismometer’s response function I(ω), the response function of the recording system A(ω) and the true spectrum of the ground motion E(ω):

\(S_i(\omega) = I_i(\omega)\,A_i(\omega)\, E(\omega) ,\)

where i stands for the corresponding seismometer. Presuming that both sensors measure the same ground motion, the transfer function Z(ω) between the sensors is given as:

\(Z(\omega) = \frac{I_\mathrm{SUT}(\omega)}{I_\mathrm{Ref}(\omega)} = \frac{S_\mathrm{SUT}(\omega) A_\mathrm{Ref}(\omega)}{S_\mathrm{Ref}(\omega)A_\mathrm{SUT}(\omega)} .\)

The subscripts denote the reference and seismometer under test, respectively. The transfer or gain function Z(ω) connecting the output of both sensors is directly related to the spectral ratio of the signals recorded by them and independent of the ground motion. For the response function of the unknown sensor, it follows accordingly:

\(\hat I_\mathrm{SUT}(\omega) = \hat Z(\omega)\cdot I_\mathrm{Ref}(\omega)\)

The determination of the estimated transfer \(\hat Z(\omega)\) between the sensors is done for example by calculation of spectral ratios (e.g. Pavlis & Vernon 1994).

References

Wielandt, E. (2012). Seismic sensors and their calibration. In New manual of seismological observatory practice 2 (NMSOP-2) (pp. 1-51). Deutsches GeoForschungsZentrum GFZ.

Larsonnier, F., Nief, G., Dupont, P., & Millier, P. (2014). Seismometer calibration: comparison between a relative electrical method and a vibration exciter based absolute method. In Proc. of IMEKO TC3, TC5, TC22 Int Conferences.

Berger, J., Carr Agnew, D., Parker, R. L., & Farrell, W. E. (1979). Seismic system calibration: 2. Cross-spectral calibration using random binary signals. Bulletin of the Seismological Society of America, 69(1), 271-288.

Peterson, J., Hutt, C. R., & Holcomb, L. G. (1980). Test and calibration of the seismic research observatory (No. 80-187). US Geological Survey.

Fels, J. F., & Berger, J. (1994). Parametric analysis and calibration of the STS-1 seismometer of the IRIS/IDA seismographic network. Bulletin of the Seismological Society of America, 84(5), 1580-1592.

Davis, P., Ishii, M., & Masters, G. (2005). An assessment of the accuracy of GSN sensor response information. Seismological Research Letters, 76(6), 678-683.

Hutt, C. R., Evans, J. R., Followill, F., Nigbor, R. L., & Wielandt, E. (2009). Guidelines for standardized testing of broadband seismometers and accelerometers. US Geol. Surv. Open-File Rept, 1295, 62.

Pavlis, G. L., & Vernon, F. L. (1994). Calibration of seismometers using ground noise.Bulletin of the seismological society of America, 84(4), 1243-1255.

Sleeman, R., van Wettum, A., & Trampert, J. (2006). Three-channel  correlation analysis: A new technique to measure instrumental noise of  digitizers and seismic sensors. Bulletin of the Seismological Society of America, 96(1), 258-271.