Reconciling Ground Motions and Stress Drops for Induced Earthquakes in the Western Canada Sedimentary Basin

A regional ground-motion prediction equation (GMPE) is defined for earthquakes in the western Canada sedimentary basin. The stress parameter model that is input to the GMPE, which controls high-frequency amplitudes, is developed based on an empirical Green's function (EGF) study in the same region (Holmgren et al., 2019). The GMPE is developed using the generic GMPE approach of denier and Atkinson (2015a,b); regional parameters, including attenuation and site response, are calibrated using a database of response spectra. The ground-motion database comprises 726 records from 92 earthquakes with magnitudes 2.3-4.4, at distances to 200 km; most events are believed to be related to hydraulic fracturing. To investigate discrepancies between the values of GMPE stress parameter and EGF stress drop for individual earthquakes, stress parameters are computed for each event by fitting the GMPE to observed response spectra. There is a large scatter in the EGF versus GMPE stress estimates, even though the GMPE estimates were implicitly calibrated to equal the EGF values on average. The discrepancies can be attributed to two methodological factors. First, the EGF approach removes the site and path terms through spectral division, whereas the GMPE approach relies on an average regional model as determined from regression of the source and path attenuation. The use of an average regional model results in greater uncertainty, in particular, due to directivity effects (which are better accommodated in the EGF approach). Second, the EGF approach is performed in the Fourier domain, whereas the GMPE fitting is done in the response spectral domain. We conclude that EGF stress-drop models provide useful constraints for GMPE development, when used in combination with calibration to a ground-motion database.