Scaling P and S wave translational to array-derived rocking motions: An empirical estimation of local wave propagation direction and velocity in rock site conditions

Abstract

We analyze the rotational motions of 484 earthquakes in the $M_{\text{L}}-$0.7 to $M_{\text{L}}$1.8 range that were induced by the 2018 geothermal stimulation in the Helsinki, Finland, metropolitan area, located in the cratonic Fennoscandian Shield environment. The rotational motions of $P$ and $SV$ waves in the 2 Hz–15 Hz frequency band are calculated from translational geophone array seismograms recorded in a 1.4 km–4.9 km epicentral distance range. We observe maximum peak rocking rates of $1.7\times 10^{-4}$ mrad/s for the $P$ wave and $6.5\times 10^{-4}$ mrad/s for the $SV$ wave. We show that the ratio of the computed peak rocking rates to the observed peak vertical acceleration yields a good approximation of the local apparent wave velocity. For this, the rotational motions are obtained in the local coordinate system that minimizes rotation about the radial axis. This analysis indicates variations in the back-azimuth from the great-circle direction which are associated with structural subsurface heterogeneities. Our comparison with results from synthetic waveforms and results from a delay-and-sum plane wave beamforming analysis demonstrate the effectiveness of the employed seismogeodetic method to compute rotational ground motion from geophone arrays, and the effectiveness of the scaling analysis for local wave velocity estimates. The obtained average magnitude dependent rocking rate relationships for $P$ and $SV$ waves are important reference observations for building predictive models for rocking motions in a hard rock environment. The obtained empirical translational-to-rocking scaling relation for the $P$ wave can contribute to the development of full-waveform scaling relations.