Reconstruction of Clipped Time-History Records, with Application to Ground Motions from the 1992 ML 5.8 Roermond, Netherlands, Earthquake

Abstract Analog-to-digital conversion of time-history data can lead to amplitude truncation (known as clipping) in cases in which a signal exceeds the full-scale range of the digitizer. When digitizers are configured, it is necessary to balance two competing requirements: maximizing instruments’ full-scale range for recording large amplitudes, while ensuring weak signals are recorded with sufficient resolution. An example of this trade-off is seen when recording earthquake ground motions, which span several orders of magnitude: from weak-motion teleseisms or local microseismicity, through to large-magnitude earthquakes. This can lead to clipped records in which strong ground motions saturate instruments configured to record weak signals. To address this problem, we present a new approach: nonstationary clipped waveform restoration, CWRΔt. The approach is capable of reconstructing even severely clipped waveforms, truncated at as low as 10% of true peak motion. The approach is based on “Projection onto Convex Sets” and builds upon the stationary and deterministic CWR method of Zhang et al. (2016). A key advantage of the method presented herein lies with the characterization of temporal uncertainties that can be propagated into other domains such as Fourier, power spectral density, or damped pseudospectral amplitude. We benchmark the method against artificially clipped ground-motion records from the European Engineering Strong-Motion database. A significant improvement is demonstrated with respect to the original CWR method. Clipped records from the 1992 ML 5.8 Roermond, Netherlands, earthquake are then reconstructed. This key event in northwestern Europe stands as the region’s largest instrumentally recorded earthquake, but from which the majority of records have, until now, been unusable. We successfully verify the CWRΔt approach against ground-truth records through comparison with collocated clipped/unclipped records from high- and low-gain instruments at three sites. Finally, we apply the method to clipped records in the epicentral region, providing the tool to develop a key data set for engineering seismology in Europe. The proposed method has a multitude of applications beyond seismology, being generalizable to any time-history data.