The demand from industry to produce accurate acceleration measurements down to ever lower frequencies and with ever lower noise is increasing. Different vibration transducers are used today for many different purposes within this area, like detection and warning for earthquakes, detection of nuclear testing, and monitoring of the environment. Accelerometers for such purposes must be calibrated in order to yield trustworthy results and provide traceability to the SI-system accordingly. For these calibrations to be feasible, suitable ultra low-noise accelerometers and/or signal processing functions are needed. <br />Here we present two digital signal processing (DSP) functions designed to measure ultra low-noise acceleration in calibration systems. The DSP functions use dual channel signal analysis on signals from two accelerometers measuring the same stimuli and use the coherence between the two signals to reduce noise. Simulations show that the two DSP functions are estimating calibration signals better than the standard analysis. <br />The results presented here are intended to be used in key comparison studies of accelerometer calibration systems, and may help extend current general low frequency range from e.g. 100 mHz down to ultra-low frequencies of around 10mHz, possibly using somewhat same instrumentation.

&lt;p&gt;Infra-AUV is a new EU project that will establish primary measurements standards for low frequency phenomena across the fields of airborne and underwater acoustics and vibration (seismology). Combining expertise from the national measurement institutes and geophysical monitoring station operators, it will develop both high-precision laboratory-based methods of calibration and methods suitable for field use. Infra-AUV will also address requirements for reference sensors that link laboratory calibration capabilities to field requirements for measurement traceability.&lt;/p&gt;&lt;p&gt;To establish standards in the three technical areas, a variety of calibration principles will be employed, including extension of existing techniques such as reciprocity and optical interferometry, and development of new methods. There will also be an investigation of the potential for in-situ calibration methods, including use of both artificially generated and naturally occurring stimuli such as microseisms and microbaroms. The influence of calibration uncertainties on the determination of the measurands required by the monitoring networks will also be studied.&lt;/p&gt;&lt;p&gt;The project was strongly motivated by the CTBTO strategy to drive new metrology capability to underpin IMS data. The intention is to maintain interaction with stakeholders, not only in connection with the IMS, but with the broad range of users of low frequency acoustic and vibration data.&amp;#160;&lt;/p&gt;

&lt;p&gt;At present, seismometers are not traceably calibrated. This means that their output sensitivity is not determined in a way that is traceable to the International Systems of Units (SI). The European research project &lt;em&gt;19ENV03 &lt;/em&gt;&lt;em&gt;Infra-AUV&lt;/em&gt;, which is part of the EMPIR programme, develops methods and procedures to enable such traceable calibrations.&lt;/p&gt; &lt;p&gt;In contrast to many other sensors, seismometers are operated stationary in their typical measurement application, i.e., they must not be moved after their deployment. Conventional calibration approaches which involve a laboratory calibration of the seismometer to be calibrated are therefore not feasible. For this reason, a new concept currently developed by different European partners within the &lt;em&gt;Infra-AUV&lt;/em&gt; project proposes an on-site calibration scheme.&lt;/p&gt; &lt;p&gt;For the on-site calibration, a reference seismometer is traceably calibrated to the SI in a laboratory. This reference is then used on-site to provide a secondary calibration of other seismometers, e.g. in a seismic station, using natural excitation sources [Schwardt et al., 2022, DOI: 10.1007/s10712-022-09713-4].&lt;/p&gt; &lt;p&gt;The calibration of reference seismometers in the laboratory is carried out as a primary calibration. This means that the measured quantity (the velocity-proportional voltage output) is compared to a different quantity, in this case to a dynamic displacement measurement traced back to the units length and time, which can be measured very precisely by laser interferometry. In this calibration, the seismometer is excited with low-frequency mechanical vibrations generated by electrodynamic exciters. These calibrations must be performed for the horizontal and vertical axes. The frequency range of interest is from 20 Hz down to 0.01 Hz, depending on the seismometer under test. Either mono-frequency sinusoidal excitations of different frequencies are applied subsequently, or multiple frequencies are excited simultaneously using a multi-sine approach. The magnitudes and phases of both measured signals, the interferometric reference and the seismometer under test, are determined by using sine approximation algorithms or by applying a discrete Fourier transform (DFT).&lt;/p&gt; &lt;p&gt;The results of the laboratory calibration, the transfer function of the reference seismometer, can then be derived from the ratios of the measured magnitudes and the differences of the phase angles for the different excitation frequencies. In addition, the associated measurement uncertainties are estimated and are part of the calibration result. Influences that may change the sensitivity of a seismometer, e.g., temperature effects, electromagnetic sensitivity, or ground stiffness need to be analysed and additionally taken into account for the uncertainty estimation.&lt;/p&gt; &lt;p&gt;For the uncertainty of the on-site calibration, differences between the laboratory and the on-site environment also need to be taken into account. This includes, for example, aspects like typically different temperatures or different ground materials.&lt;/p&gt;

Primary calibration of accelerometers by laser interferometry has been performed for more than 50 years. It was made possible by the advent of the commercial He-Ne lasers in the 1960ties. During the last 20 years the progress in digital signal treatment has made it available for most interested laboratories.However, these huge progresses have merely reduced but not removed some basic problems.• The quality and basic parameters of the exciter systems • The influence from the mechanical setup on the accelerometer and thereby on the measurement results. This paper describes several topics and considerations found relevant for primary calibration of accelerometers, following recent international intercomparisons and progress in the calibration grade vibration exciter system design.

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