About metrology

When making a measurement of a physical parameter like seismic velocity or infrasound pressure, the result is expected to be physically meaningful. This is achieved by linking the measurement to an authentic realisation of the parameter that is defined via base quantities such as mass, length, time and voltage. These base quantities are in turn linked to fundamental physical constants and quantum phenomena. The end-to-end linking of a measurand to fundamental quantities is known as measurement traceability. 

These considerations are the subject of Metrology – the science of measurement, which has an important role in all fields of science and technology [JCMG 2012]. 

Using fundamental phenomena as the basis of all physical measurement means that global equivalence of measurement data can be assured, and that the same set of units can be used to make quantitative statements of measurements. The International System of Units (abbreviated to SI from Système International), also known as the metric system, is the recognised measurement system used in industry, science and everyday trade and commerce, in nearly every part of the world. The SI is founded on seven universal constants underpinning seven base units [ISO 2022], that in turn provide measurement traceability and a coherent basis for every derived physical parameter.

Metrology considerations begin with primary measurement standards; the definitive realisation of a particular quantity that underpins all subsequent measurements of that quantity. The link between the primary measurement standard and the fundamental physical phenomena is a specialist task usually undertaken by a team of experts at a National Metrology Institute (NMI). Primary standards for sound pressure and acceleration have long been established, but historically have not extended down to the frequency ranges where the IMS seismic, infrasonic, and hydroacoustic technologies operate.

Details of new primary standards developed within the SI, supporting IMS seismic, infrasound and hydroacoustic measurements are provided in this Good Practice Guide. 

Measurement traceability is vital for measurements to be physically meaningful. Imagine a vendor selling cloth by the metre, but using his arms to measure out the lengths. Clearly, there is no guarantee here of the actual quantity provided. In this almost trivial example the actual length may, or may not matter too much, but it is easy to see how the measurement traceability concept becomes invaluable when engineering precision, or safety-critical information is required. 

Global consistency in measurement is also important. Since the basis for the SI is a set of unchanging physical constants, periodic traceable calibration provides a means of compensating for instability in the measurement device, for example temporal drift, and allows any such drift between calibrations to be estimated. Data of this type is important for quality assurance, which in turn contributes to the overall trustworthiness of the data. Finally, the matter of compatibility between measurements has obvious benefits when components from different supply chains are used together. However in the context of a global sensor network, compatibility in the data across the network also relies on traceable calibration. Regardless of the method used to calibrate a particular field sensor, if that method is ultimately traceable to a primary standard within the SI, then the data produced by that sensor can be considered equivalent to any other sensor that also has a traceable calibration, no matter where or when these data are obtained. By extension, measurement traceability provides for transparency and impartiality in acquired data. 

Calibration may provide a means of quantifying data, but without measurement traceability, all of the wider benefits are lost.  

All sensors used for seismo-acoustic monitoring respond to dynamic signals. However, these sensors might also exhibit a response to static stimuli such as ambient pressure or the acceleration due to gravity. Thus, as the stimulus frequency tends to zero, as in the frequency ranges of interest in IMS applications, it is not unreasonable to expect that the dynamic sensitivity of the sensor tends towards the static sensitivity. That said, there are models of seismometer that have an integral electronic high-pass filter with a very low corner frequency, which effectively reduces the static sensitivity to zero. 

Electronic filters aside, this raises the question of whether a calibration with a static stimulus (which we will refer to as static calibration) can suffice. 

The short answer, from a perspective of metrological correctness is “no, it cannot”. Static and dynamic quantities are not the same, even though they share the same SI units. For example, the definitions of  pressure [ISO 2019] and sound pressure [ISO 2020]are distinct and different. A static calibration therefore refers to a different quantity of interest. 

The distinguishing factor is that dynamic quantities are subject to time variations and in the case of seismo-acoustic quantifies, these variations are oscillatory and have an associated frequency (or frequencies). Likewise, the transduction mechanism within a sensor is subjected to the same time variations. The mechanical or acoustical impedance of the transduction mechanism, typically represented by stiffness, inertia and dissipative elements, will govern the dynamic response of the sensor. For seismic sensors in particular, the overall sensor construction and mounting can also influence the dynamic response.  

In the static case, only the acting stiffness is relevant once equilibrium has been reached, but in a dynamic environment the other elements will also have an influence. These result in the sensitivity of the sensor being a function of frequency, characterised by the frequency response. The impedance parameters also impart a transient response to the sensor, so it is important to ensure that the sensitivity relates to the steady-state response. 

The downsides of dynamic calibration is that in general, the methods are inherently more demanding and typically have higher measurement uncertainty than static calibration. These factors can lead to static calibration methods appearing more attractive. Remember though, that the static stimulus is a different quantity to that of interests, so the calibration becomes an approximate to the true sensitivity of the sensor to the actual quantity to be measured. The approximation therefore needs to be validated and the underlying assumptions justified. Ultimately this process is likely to require assessment with dynamic stimuli and the associated measurement uncertainty factored into the overall assessment. 

The frequency response of the sensor is also an essential characteristic that must be accounted for. If a static calibration approach supplemented with a frequency response estimation is used, the method and/or model for connecting the two is important, and measurement uncertainty aspects of all parts of the process must be accounted for. 

With these additional considerations, the appeal of static calibration quickly diminishes. That, plus the fact that measurement traceability is not established for the quantity of interest, means that the static calibration approaches cannot recommended. 

The final important concept in metrology is measurement uncertainty. The Guide to the Expression of Measurement Uncertainty [JGMG 2008, JCMG 2009] (a documents adopted by all global authorities on measurement and standardisation) begins by saying “When reporting the result of a measurement of a physical quantity, it is obligatory that some quantitative indication of the quality of the result be given so that those who use it can assess its reliability”. This is acknowledgement that no measurement is perfect, not even the primary measurement standard mentioned earlier. 

Measurement uncertainty is a statement of confidence that the measured value represents the true value of a parameter within the bounds of the measurement uncertainty. Therefore, the measurement uncertainty should be expected to increase with the desired level of conference, and it does. The concept is essential for comparing data from more than one measurement, including measurements made in different places, at different times or by different people. 

The process of estimating measurement uncertainty is beyond the scope of this document, but is elaborated in detail in the official document noted above. There are many guides to be found online. 

One important point to note, is that in a multi-step process such as establishing measurement traceability, the measurement uncertainty from one step is inherited by the next step. At each step additional components of uncertainty specific to the action, will add to the inherited measurement uncertainty. This is known as uncertainty propagation, and means that measurement uncertainty grows with each step in the process, each making a contribution to the measurement uncertainty in the final piece of information sought.  

References

International Organization for Standardization. ISO 80000-1:2022. Quantities and units - Part 1: General. 2022

International Organization for Standardization. ISO 80000-1:2022. Quantities and units - Part 4: Mechanics (item 4-14.1). 2019

International Organization for Standardization. ISO 80000-1:2022. Quantities and units - Part 8: Acoustics (item 8-2.2). 2020

Joint Committee for Guides in Metrology. JCMG 200: Ed. 3. International vocabulary of metrology – Basic and general concepts and associated terms (VIM). 2012

Joint Committee for Guides in Metrology. JCMG 100: Evaluation of measurement data — Guide to the expression of uncertainty in measurement. 2008

Joint Committee for Guides in Metrology. JCMG 104: Evaluation of measurement data — An introduction to the “Guide to the expression of uncertainty in measurement” and related documents. 2009