In this study a method is presented for determining the in situ elastic wave velocities of slabs simultaneously with the relative relocations of earthquakes. The method is an extended arrival time difference (ATD) scheme that incorporates a realistic model. Several assumptions are made about the characteristics of ray paths in and around the slab in order to take advantage of the realism of the model without completely sacrificing the simplicity inherent in the ATD technique. The errors introduced by these approximate rays are estimated by comparing them with more exact rays calculated with a three-dimensional ray-tracing routine. In general, the comparisons suggest that these errors are usually much less than 0.1 s. The inverse method is tested on the same set of hypothetical data. The results of these tests show that the parameters that influence the arrival time differences the most are the amplitude of the slowness anomaly within the slab and the azimuths and takeoff angles for rays leaving the master event.

The arrival time differences are relatively insensitive to the other parameters describing the slab (strike, dip, half width, and the position of the master event), which implies that the scheme is fairly insensitive to the particular choice of analytic function to describe the slowness variation within the slab. Convergence of the inverse routine is rapid in the tests; usually less than five iterations are required before a stable solution is reached. It appears that coupling between solutions for slab parameters and ray directions is insignificant. Unlike the standard ATD approach, solutions for hypocenters and velocities are not directly coupled in this scheme, although well-located events are required to insure that the hypocenters are not unduly biased by variations in structure. Once the velocity structure of the slab is determined, that information can be used routinely by this scheme to relocate less well-recorded events. This method was applied to arrival time data from earthquakes located between 200 and 600 km depth in the Izu-Bonin subduction zone. Structure in the 200-300 km depth range could not be resolved, and results in the 500--600 km depth range proved to be too sensitive to noise. Data from events between 27 ¿N and 31 ¿N show that P wave velocities within the slab from 400 to 500 km depth are 4--6% higher than those of the ambient mantle. Between 300 and 400 km depth the slab structure varies regionally. North of about 32.5 ¿N the P wave velocity within the slab is 3--4% higher than ambient from 180 to 375 km depth. In contrast, the velocities south of 32.5 ¿N increase from 6--7% higher than ambient in the 375-410 km depth range to 8--10% higher in the 325-375 km depth range and appear to be 9% higher than ambient in the 270-325 km depth range. The determination of the high velocities in this region between 325 and 375 km depth proved to be independent of the selection of data and of the choice of starting model. Above 325 km depth, however, the velocity determinations are somewhat dependent on the choice of starting model. As a result of this dependence, no upper bound on the depth of the high velocities could be resolved.

A plausible explanation for the exceptionally high P wave velocities within the slab south of 32.5 ¿N is that the olivine-spinel phase change boundary is elevated in this part of the slab, while north of 32.5 ¿N it is not significantly elevated. It is not known if the phase change is elevated south of 31 ¿N, but the velocities between 400 and 500 km depth in this region imply that it is not depressed. The high-velocity zone south of 32.5 ¿N lies in an area that marks the beginning of a seismic gap, increasing in breadth to the south, between deep and shallow seismicity. The dip of the slab also becomes gradually steeper to the south of this region. In contrast, the lower velocities north of 32.5 ¿N occur in a region where the seismicity is fairly continuous and is aligned along a shallow dipping plane. If the seismic gap south of 32.5 ¿N represents a region of high velocity, then the increasingly vertical dip of the slab in the south could be due to a substantial gravitational force provided by the excess mass extending above the ambient olivine-spinel phase boundary. The decreasing width of the gap to the north suggests that the evolution of the Izu-Bonin seismic zone has been governed by a propagating instability from the south.