S U M M A R YNew empirical traveltime curves for the major seismic phases have been derived from the catalogues of the International Seismological Centre by relocating events by using P readings, depth phases and the iasp91 traveltimes, and then re-associating phase picks. A smoothed set of traveltime tables is extracted by a robust procedure which gives estimates of the variance of the traveltimes for each phase branch. This set of smoothed empirical times is then used to construct a range of radial velocity profiles, which are assessed against a number of different measures of the level of fit between the empirical times and the predictions of the models. These measures are constructed from weighted sums of L2 misfits for individual phases. The weights are chosen to provide a measure of the probable reliability of the picks for the different phases.A preferred model, ak1.?5, is proposed which gives a significantly better fit to a broad range of phases than is provided by the iusp9I and sp6 models. The differences in velocity between ak135 and these models are generally quite small except at the boundary of the inner core, where reduced velocity gradients are needed to achieve satisfactory performance for PKP differential time data.The potential resolution of velocity structure has been assessed with the aid of a non-linear search procedure in which 5000 models have been generated in bounds about ak135. Misfit calculations are performed for each of the phases in the empirical traveltime sets, and the models are then sorted using different overall measures of misfit. The best 100 models for each criterion are displayed in a model density plot which indicates the consistency of the different models. The interaction of information from different phases can be analysed by comparing the different misfit measures. Structure in the mantle is well resolved except at the base, and ak135 provides a good representation of core velocities.

S U M M A R Y Over the last three years, a major international effort has been made by the Sub-Commission on Earthquake Algorithms of the International Association of Seismology and the Physics of the Earth's Interior (IASPEI) to generate new global traveltime tables for seismic phases to update the tables of Jeffreys & Bullen (1940). The new tables are specifically designed for convenient computational use, with high-accuracy interpolation in both depth and range. The new imp91 traveltime tables are derived from a radially stratified velocity model which has been constructed so that the times for the major seismic phases are consistent with the reported times for events in the catalogue of the International Seismological Centre (ISC) for the period 1964-1987. The baseline for the P-wave traveltimes in the imp91 model has been adjusted to provide only a small bias in origin time for well-constrained events at the main nuclear testing sites around the world.For P-waves at teleseismic distances, the new tables are about 0.7s slower than the 1968 P-tables (Herrin 1968) and on average about 1.8-1.9s faster than the Jeffreys & Bullen (1940) tables. For S-waves the teleseismic times lie between those of the JB tables and the results of Randall (1971).Because the times for all phases are derived from the same velocity model, there is complete consistency between the traveltimes for different phases at different focal depths. The calculation scheme adopted for the new imp91 tables is that proposed by Buland & Chapman (1983). Tables of delay time as a function of slowness are stored for each traveltime branch, and interpolated using a specially designed tau spline which takes care of square-root singularities in the derivative of the traveltime curve at certain critical slownesses. With this representation, once the source depth is specified, it is straightforward to find the traveltime explicitly for a given epicentral distance. The computational cost is no higher than a conventional look-up table, but there is increased accuracy in constructing the traveltimes for a source at arbitrary depth. A further advantage over standard tables is that exactly the same procedure can be used for each phase. For a given source depth, it is therefore possible to generate very rapidly a comprehensive list of traveltimes and associated derivatives for the main seismic phases which could be observed at a given epicentral distance.

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