Introduction

In a 1D earth, given a sufficient network of stations, times and epicentres are orthogonal so that unbiased epicentres can be estimated independently of the travel times; this is clear because if the P arrival times at a circle of stations are constant, the epicentre must be in the centre of the circle whatever the travel time. Networks of stations are not so well distributed in practice but epicentre estimates are still insensitive to travel-time tables, so that given the origin time of at least one earthquake, obtained from observations very close to the epicentre, corrections to travel times can be found by averaging the O–C residuals in a series of small distance ranges. Epicentres can then be revised using the updated travel-time tables. This method of ‘successive approximation’, where the tables and then the epicentres are repeatedly revised until corrections become small enough to neglect, is that used by Jeffreys and Bullen (1940).

The travel-time analysis carried out by Herrin et al. (1968) to derive the 1968 Tables and that of Kennett and Engdahl (1991) to derive the iasp91 Tables also use successive approximation. Herrin et al. (1968) estimate station effects but, just as distance corrections are found by grouping residuals in distance ranges and averaging, so station effects are found by grouping residuals by station and averaging. Kennett and Engdahl (1991) do not allow for station effects.