LOCATING EARTHQUAKES USING A DISTANCE-WEIGHTED VELOCITY-INDEPENDENT METHOD

Arrival-Order-Location methods can be used to locate epicenters in regions where seismic velocities are poorly constrained or unknown. An epicenter can be found that minimizes, for every combination of three stations (triad),

(r_b- r_a)/(r_c- r_a) - (t_b- t_a)/(t_c- t_a)

where r_a,b,c,d... are the epicentral distances to stations a,b,c... and t_a,b,c,d... are the arrival times (same phase) at stations a,b,c... such that t_a < t_b < t_c < t_d .....etc. Weighting these residuals according to inverse-epicentral distance and averaging over all possible station triads (at least four stations are required) produces reliable epicenter locations without a priori velocity information. Velocities can be calculated a posteriori using the determined epicentral distances to all pairs of stations and the observed arrival times according to V_ab = (r_b- r_a)/(t_b- t_a). Since this location technique assumes that all arrivals are of the same type (and therefore travel at the same velocity), the distribution of calculated velocities can be used as a measure of uncertainty (i.e., a proxy for the traveltime residual used in traditional location methods).

This approach was applied to 14 mid-continent earthquakes and the resulting epicenters were compared to those published by the USGS. In 78% of these events, the distance-weighted velocity-independent technique produced a narrower range of calculated seismic velocities than did the published epicenters. Because the method is two-dimensional, it works best when focal depths are small relative to array dimensions.