The data from the International Seismological Centre bulletins for the years 1964--1979 are used to derive a three-dimensional model of lateral variations of the P velocity in the lower mantle. Unlike previous studies, in which such perturbations were represented by a blocklike parameterization, we seek the solution in the form Δ&ngr;(r, &thgr;, ϕ) =&Sgr;k=0K &Sgr;l=0L &Sgr;m=0l fk(r) (kAlm cos mϕ +kBlm sin mϕ)plm (cos &thgr;). Some 500,000 travel time residuals for teleseismic distances from 5000 earthquakes are used in an iterative procedure to derive the coefficients A and B, the maximum K and L used are 4 and 6, respectively. In each iteration, in addition to solving for the three-dimensional structure, we also relocate all the earthquakes, perturb the average travel time curve, and determine station corrections for over 1000 stations. Particular attention is given to the problem of weighting the individual observations in order to avoid, as much as possible, the bias due to the uneven distribution of sources and receivers. The resulting model shows a high level of perturbation just below the 670-km discontinuity and just above the core-mantle boundary, where the maximum perturbations reach 1--1.5% of the average velocity even for this highly smoothed model. At a depth of 2000 km the rms perturbations are some 3 to 4 times lower than at either of the two boundaries. The model predicts well the large-scale pattern of observed travel time residuals for various source regions except for the distinct effects of the subduction zones. The most striking large-scale three-dimensional feature of the model is a ring of high velocities circumscribing the Pacific basin within a depth range from 100 km to the core-mantle boundary. If the proportionality between perturbations in the velocity and temperature is assumed, the derived pattern of anomalities could be consistent with a two boundary layer model of convection in the lower mantle. Some caution, however, should be exercised in interpreting the results near the 670-km discontinuity, where the resolving power of our data set is limited by the lack of adequate control of the upper mantle structure. At the same time, a significant global increase in the level of perturbations in the lowermost mantle is established beyond question. The results of Dziewonski et al. (1977) on the correlation between the ''equivalent geoid'' and the observed geoid for the angular order numbers 2 and 3 is confirmed, but there is no significant correlation for degrees from 4 to 6. These calculations are made for the rigid earth. Richards and Hager (this issue) show that introduction of finite viscosity can change the sign of a geoid anomaly. In addition, recent studies of lateral variations in the shear velocity reveal the presence of large-scale anomalies in the upper mantle. Thus, while the inferences made here with respect to the origin of the gravest orders of the geopotential field are not conclusive, they point the way in which results from seismology can be used to address some of the basic questions of geodynamics.