Uncertainty assessment of the array derived rotation measurements

Analyzing the rotational motions of the seismic wavefield is useful for a multitude of applications ranging from the wavefield decomposition to geological structure estimation or source inversion (Igel et al. 2015, Sollberger et al. 2020). Despite the recent progress in performance (Bernauer et al. 2018), portable rotation sensors are not yet able to measure the seismic background noise in quiet environment. Parallel to the construction of high performance observatory sensors (Igel et al. 2021), several experimentations have shown that seismic rotation motions can be derived from the recordings of classical three translational component (3C) seismometers when arranged in a dense seismic array (Spudich et al. 1995, Suryanto et al. 2006) . Even if these Array Derived Rotation (ADR) measurements can theoretically estimate the seismic rotation background noise, the accuracy of this kind of indirect measurements can be strongly affected by the quality and the variability in the sensors response or installation conditions across the seismic array (Donner et al. 2017). This work proposes to quantify, as a function of the array aperture and wavefield properties (frequency and wavelength), the uncertainty of the ADR measurements due to uncertainty or lack of detailed knowledge in the precise locations of sensors, orientations and instrumental response, along with the effects of some incoherent disturbing noises across the seismic sensor array. This approach has been applied to the ADR measurements performed with the (3C) dense seismic array deployed at the Low Noise Inter-Disciplinary Underground Science & Technology laboratory (LSBB), Rustrel, France. This analysis shows that a particular attention has to be paid, beyond the standard practices accepted for most seismic arrays, concerning the sensors’ setting up in order to reach uncertainty lower than 10% on the derived rotation measurements.