An important issue in ground motion and hazard analysis for induced earthquakes is the variability of ground‐motion amplitudes (sigma). We investigate the contributions of uncertainty in source parameters to sigma using ground‐motion recordings from 38 earthquakes in central United States (CUS) having moment magnitudes from 3.0 to 4.3. We optimize the location and magnitude of events with respect to a ground‐motion prediction equation (GMPE) that has zero bias on average. We define the ground‐motion center (GMC) as the location and magnitude that results in the lowest total standard deviation (sigma) with respect to the GMPE. An iterative grid‐search technique is used to find each event’s GMC, alternating between searching for the optimum epicenter of the GMPE and the optimum moment magnitude; the best location and magnitude, from a ground‐motion perspective, is that which minimizes the residuals.
The value of sigma is more sensitive to revisions in magnitude than to those in location. Changes in the event magnitude, which raise or lower the entire GMPE curve to better match the cloud of data for the event, impact the between‐event component of sigma significantly. Changes in the event location impact the within‐event component of sigma but are less significant because of the contributions of site variability. By defining the sigma value based on the GMC locations and magnitudes, we can avoid double‐counting uncertainties in source parameters (location, magnitude, and stress drop) in the characterization of sigma. We conclude that after optimizing the location and magnitude of the events, the total sigma (averaged over selected frequencies) for records within 70 km is 0.24 log10 units for the vertical component (0.28 log10 units for the geometric mean of the horizontal components), which is much lower than the value of 0.39 (or 0.38 for the horizontal) that was calculated before optimizing the source parameters.