Constraints on earthquake epicentres independent of seismic velocity models

SUMMARY We investigate the constraints that may be placed on earthquake epicentres without assuming a model for seismic wave speed variation within the Earth. This allows location improvements achieved using 1‐D or 3‐D models to be put into perspective. A simple, arrival order misfit criterion is proposed that may be used in standard location schemes. The arrival order misfit criterion does not use a seismic velocity model but simply assumes that the traveltime curve for a particular phase is monotonic with distance. Greater robustness is achieved by including a contribution from every possible pairing of stations and the effect of timing inconsistencies reduced by smoothing. An expression is found that relates the smoothing parameter to the number of observations. A typical event is studied in detail to demonstrate the properties of the misfit function. A pathological case is shown that illustrates that, like other location methods, the arrival order misfit is susceptible to poor station distribution. 25 ground truth and 5000 other teleseismically observed events are relocated and the arrival order locations compared to those found using a least‐squares approach and a 1‐D earth model. The arrival order misfit is found to be surprisingly accurate when more than 50 observations are used and may be useful in obtaining a model independent epicentre estimate in regions of poorly known velocity structure or the starting point for another location scheme.