This paper reviews the development in global seismic tomography at Harvard during the last 25 years within the context of more general developments in this field. The first attempt at detecting the very long wavelength anomalies in the lower mantle (Dziewonski et al., 1977) was successful, in the sense that the main findings - including the correlation of the velocity and gravity anomalies in the lower mantle - have been confirmed by later studies using more data and higher resolution. The principal reason for the success of this extremely low resolution study is that the power spectrum of the Earth's heterogeneities is very red, so that there is a substantial and detectable signal even in first three harmonic orders. This has been demonstrated for the upper mantle by Masters et al. (1982), with a much better signal-to-noise ratio, for the strong degree-2 harmonic in the upper mantle. They determined that the most likely source of this signal is in the transition zone. The current stage of seismic tomography began in 1984 with the publication of toro papers: one on the structure of the lower mantle (P-velocities, Dziewonski, 1984) and upper mantle (S-velocities, Woodhouse and Dziewonski,' 1984). Even though the degrees of expansion (6 and 8, respectively) were relatively low by the current standards, because of the topology of the power spectra of the heterogeneities, they captured all the important large-scale structures. Most dramatic progress occurred during the year 1986, where for the first time we have derived the whole mantle S-velocity model (Woodhouse and Dziewonski, 1986), measured the topography of the core-mantle boundary (Morelli and Dziewonski, 1987), obtained even-degree structure from normal mode splitting (Giardini et al., 1987), which was fully compatible with the structure derived from the P-wave residuals (Morelli and Dziewonski, 1986), and established the existence of anisotropy in the inner core using both travel time data (Morelli ei at, 1986) and normal mode splitting (Woodhouse er al., 1986). The maps of lateral heterogeneity have led us to point out the correlation between the location of fast velocity anomalies in the mid-mantle and the possible traces of the slabs subducted during the last 100 million years (Woodhouse and Dziewonski, 1989). The current issues deal with the attempts to achieve higher resolution not only in the spatial domain but also the parameter domain, namely: resolution of anisotropy Ekstrom and Dziewonski have shown that there are significant lateral variations in the radial anisotropy particularly associated with the Pacific plate, which at a depth of 125 km is comparable in amplitude with isotropic variations, primarily due to cooling of the lithosphere. Boschi and Dziewonski (2000) demonstrated that introduction of radial anisotropy in the mantle, particularly the lower mantle, explains the core travel times equally well as the outer core heterogeneity There is significant progress in improving the resolution of the properties of the transition zone, including the topography of the 400 and 660 km discontinuities. The future developments in global tomography should include more detailed regional studies using permanent and movable arrays. The U.S. Array project, currently being considered for funding, is an example of an initiative which should allow a gradual transition from resolution of the global (lambda approximate to 2000 km) to continental (lambda approximate to 400 km) and, eventually, to regional scale (lambda approximate to 70 km, and perhaps better with the "flexible" experiments) structures.
