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Notes: Seismic traveltime data are used to determine and assess a weighted least-squares model of the 3-D P-velocity structure of the Earth's mantle. A total of 682090 summary rays constructed from over three million ISC traveltime observations are used to constrain velocity perturbations in 12496 6° by 6° cells. An iterative block LU decomposition procedure, applied on the massively parallel Connection Machine 2 (CM-2), is used to compute a formal weighted least-squares model of P-velocity variations as well as the full resolution and covariance matrices. It is found that the shallow mantle beneath the continents of the northern hemisphere is well resolved. However, the majority of mid-oceanic features, such as spreading ridges and hot spots, are not well constrained. As a function of depth, the resolution is highest in the upper to mid-mantle, due to variations in ray coverage. Primarily because of ray geometry, single blocks are not resolved below 1870 km. The estimates of spatial resolution, constructed from the complete resolution matrix, are useful in judging whether subducting lithosphere extends into the lower mantle. The results indicate that possible extensions of subduction zones in the northern hemisphere are imaged reliably down to at least 1470 km. However, areas beneath most subduction zones in the southern hemisphere are averaged over scale lengths of 800 km or more below a depth of 1070 km. Velocity estimates for the mid to lower mantle beneath Hawaii are the result of averaging over 1900 km or more. Generally, vertical and lateral averaging of 600 to 1000 km is occurring in the depth range 2270 to 2670 km. P-wave velocity values in the region just above the Core-Mantle Boundary (CMB) are large-scale spatial averages (1500 km or more) and individual cells are poorly resolved. The model parameter standard error remains moderate throughout the lower mantle due to smaller traveltime errors associated with rays that bottom in this region. These standard errors reach no more than 0.3 per cent of the Jeffreys-Bullen average velocity. The greatest standard errors, 0.9 per cent of the average velocity, are found in the upper mantle underlying the Pacific basin. These large parameter errors are due primarily to the poor ray coverage in the Pacific coupled with the large arrival-time uncertainties for P recordings in the epicentral distance range 0° to 20°.