Using the arrival times of 10 distinct phases from the International Seismological Center catalogue (P, S, PP, PcP, SS, ScS, PKPab, PKPbc, PKPdf, SKSac) and two sets of differential times (SS - S410S and SS - S660S), we estimate the P and S velocity structure of the whole Earth (mantle, outer core, and inner core), boundary topography of four interfaces within the Earth, hypocentral relocation parameters, and station corrections. The entire catalogue is relocated and reassociated using the radial velocity model ak135. Both P and S phases are used in the relocation of over 41,000 events. In depth, isotropic velocity variations within the Earth are parameterized by 22 layers. Lateral variations in shear and compressional velocity within the layers are represented by one of two grids. In the mantle, each layer is subdivided into 4560 equal-volume cells, of dimension 3¿ ¿ 3¿ at the equator. However, in the outer and inner core, the cell size is increased to 6¿ ¿ 6¿. This change in grid spacing accounts for decreasing cell volumes with depth and variations in sampling between the mantle and core. Previous attempts using a fine grid throughout the Earth resulted in poor resolution of core structure. With the current grid, the resolution of velocity heterogeneity in the mantle and outer core is comparable. In the upper and midmantle, the well-resolved cells lie beneath Eurasia and a narrow zone surrounding the mantle beneath the Pacific basin. In the lowest mantle, the resolution decreases significantly. An examination of the averaging kernels associated with six locations near the base of the mantle reveals the significant lateral and vertical averaging inherent in estimates of compressional velocity. In well-sampled regions of the outer core, we are able to resolve compressional velocity variations in our 6¿ ¿ 6¿ cells. However, velocity variations in the inner core are poorly constrained at the scale of our blocks. In well-sampled regions of the mantle and outer core model, parameter standard deviations remain below 0.25%. For much of the inner core, the standard deviations are quite large, exceeding 0.5%. Narrow, high-velocity anomalies are imaged in the upper mantle, associated with subduction zones. In a number of locations, such as beneath the Americas, these features extend well into the lower mantle. In the outer core, heterogeneity is generally lower in magnitude, of the order of 0.5%. The most notable feature in the outer core is a systematic shift to slightly higher velocity. In addition, we find a roughly symmetric distribution of heterogeneity at the base of the outer core. Compressional velocities are generally higher in the equatorial regions and lower at the poles.