Estimating Lab-Quake Source Parameters: Spectral Inversion from a Calibrated Acoustic System

Laboratory acoustic emissions (AEs) serve as small-scale analogues to earthquakes, offering fundamental insights into seismic processes. To ensure accurate physical interpretations of AEs, rigorous calibration of the acoustic system is essential. In this paper, we present an empirical calibration technique that quantifies sensor response, instrumentation effects, and path characteristics into a single entity termed instrument apparatus response. Using a controlled seismic source with different steel balls, we retrieve the instrument apparatus response in the frequency domain under typical experimental conditions for various piezoelectric sensors (PZTs) arranged to simulate a three-component seismic station. Removing these responses from the raw AE spectra allows us to obtain calibrated AE source spectra, which are then effectively used to constrain the seismic AE source parameters. We apply this calibration method to acoustic emissions (AEs) generated during unstable stick-slip behavior of a quartz gouge in double direct shear experiments. The calibrated AEs range in magnitude from -7.1 to -6.4 and exhibit stress drops between 0.075 MPa and 4.29 MPa, consistent with earthquake scaling relation. This result highlights the strong similarities between AEs generated from frictional gouge experiments and natural earthquakes. Through this acoustic emission calibration, we gain physical insights into the seismic sources of laboratory AEs, enhancing our understanding of seismic rupture processes in fault gouge experiments.