Effects of earthquake mislocation on estimates of velocity structure

Abstract Recently, there have been several attempts at imaging slab structure using teleseismically observed travel times. These times are a function of both event location and velocity structure. Teleseismically determined epicenters of subduction zone earthquakes, which can occasionally be checked by comparison with accurately determined epicenters using local seismographs, are systematically incorrect by as much as 40 km. Observed travel-time residuals are calculated with respect to this incorrect location. Theoretical residuals, on the other hand, are usually calculated by initiating ray tracing at the teleseismically determined hypocenter. In comparing the theoretical and observed times, we make two errors. First, ray tracing should be initiated at the true location of the earthquake, not at the location determined from teleseismic observations. Obviously, this can rarely be done, but fortunately this source of error produces only subtle differences in the theoretical residuals. The second, much more significant, error results from the fact that the observed residuals are calculated with respect to a location that differs from the actual source, whereas, the theoretical residuals are calculated with respect to the same location used to initiate ray tracing. This inconsistent handling of event locations produces profound differences in residuals which, unless accounted for in the velocity determination, could result in velocity estimates that are severely biased. To demonstrate this, we analyze travel-time residuals from a small thrust earthquake in the central Aleutians, which produced impulsive teleseismic arrivals. Times from the local Adak array provide tight constraints on its absolute location. The ISC location, which is constrained primarily by teleseismic times, is 40 km north of the local-array location. We compute residuals from the observed arrival times with respect to the local-array and the teleseismic locations. The residual distribution computed at the local-array location is dominated by large (average of 2 s), negative residuals to the north, as expected for a high-velocity slab dipping to the north. On the other hand, the residual distribution computed at the teleseismic location has negative residuals averaging less than 0.5 s to the north and larger amplitude negative residuals to the south. Theoretical times are calculated by initiating ray tracing within a thermal model of the Aleutian slab at the local-array location. When theoretical residuals are calculated with respect to the location used to initiate ray tracing, these times agree well with observed times at the local array location. The correlation coefficient is 0.84. However, the correlation between these synthetic times and observed times at the teleseismic location drops to 0.04. This latter comparison is often used in the literature, and can lead to biased estimates of velocity structure. The former comparison is only possible when absolute event locations are known. We suggest a technique to correct for this bias. The procedure of calculating travel-time residuals with respect to the hypocenter determined by least-squares minimization of the residuals is equivalent to applying a specific high-pass linear filter to the residuals mapped on the unit focal sphere. In nearly all teleseismic problems this filter has been applied to the data. To make a self-consistent analysis we should also apply this filter to the synthetic times. The correlation between filtered data and filtered synthetic for the Aleutian event is 0.51.