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with magnitudes of 5% to the 3D grid nodes. Synthetic data were calculated for the checkerboard model. Then we added random errors to the synthetic data and inverted them with the same algorithm that we used for the observed data. The inverted image of the checkerboard suggests where the resolution is good and where it is poor. The checkerboard resolution tests and other synthetic tests we conducted showed that both the high-velocity Tonga slab and the low-velocity back arc and mantle wedge were reliably resolved and that there was no trade-off between them. 12. Y. Tatsumi, J. Geophys. Res. 94, 4697 (1 989); J. H. Davies and D. J. Stevenson, ibid. 97, 2037 (1992). 13. Y. Zhang and T. Tanimoto, Nature 355,45 (1 992); T. Tanimoto and D. J. Stevenson, J. Geophys. Res. 99, 4549 (1 994) 14. Y. Shen and D. W. Forsvth, J. Geo~hys. Res. 100, 221 1 (1 995). 15. Y. Xu and D. Wiens, ibid., in press. To invert regional wave forms we used a nonlinear inversion method that adopts a reflectivity formalism (28) to compute the partial derivatives. This method allows the entire regional distance (400-to 1500-km range) wave form to be inverted from P wave arrival to surface waves at frequencies between 0.01 and 0.055 Hz. Broadband seismograms from earthquakes of 10 to 240 km deep that propagate almost entirely within one of the tectonic regions of the southwest Pacific were used in the wave form inversion. Parameter variances and resolution tests suggest that the results are well constrained to depths of about 200 km. The S wave velocities from the wave form inversion and the P wave velocities from the tomography would not necessarily show the same structure. The larger total heterogeneity from the wave form inversion may result from a greater effect of partial melt beneath the Lau back arc on S wave velocity than on P wave velocity (9, 29).

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