Restoration of clipped seismic waveforms using projection onto convex sets method

The seismic waveforms would be clipped when the amplitude exceeds the upper-limit dynamic range of seismometer. Clipped waveforms are typically assumed not useful and seldom used in waveform-based research. Here, we assume the clipped components of the waveform share the same frequency content with the un-clipped components. We leverage this similarity to convert clipped waveforms to true waveforms by iteratively reconstructing the frequency spectrum using the projection onto convex sets method. Using artificially clipped data we find that statistically the restoration error is ~1% and ~5% when clipped at 70% and 40% peak amplitude, respectively. We verify our method using real data recorded at co-located seismometers that have different gain controls, one set to record large amplitudes on scale and the other set to record low amplitudes on scale. Using our restoration method we recover 87 out of 93 clipped broadband records from the 2013 Mw6.6 Lushan earthquake. Estimating that we recover 20 clipped waveforms for each M5.0+ earthquake, so for the ~1,500 M5.0+ events that occur each year we could restore ~30,000 clipped waveforms each year, which would greatly enhance useable waveform data archives. These restored waveform data would also improve the azimuthal station coverage and spatial footprint.