A method of tomographic inversion to obtain three-dimensional velocity perturbations in the Earth's whole mantle has been developed, and applied to more than two million P-wave arrival time data reported by International Seismology Center (ISC). The model is parameterized with 32,768 blocks; the divisions in latitude, longitude, and radius are 32, 64, and 16, respectively. Horizontal cell size is 5.6° × 5.6°. The layer thicknesses vary with depth; 29 km just below the surface and 334 km just above the core-mantle boundary. Starting from a spherically symmetric Earth model, we obtained a three-dimensional model using the following iterative procedures. First, we relocated all the events; second, we backprojected the residual into the whole mantle; third, we refined the spherically symmetric Earth model. The solutions have been converged in five iterations. We adopted the following techniques in the backprojection procedure. The first order smoothness was introduced as a damping, which makes the solution independent of the starting model and its apparent fluctuation minimal. The basic equations for delay times and smoothness are solved using the conjugate gradient method, an iterative method which guarantees the convergence of solution into the exact least squares solution. The weight on the smoothness, i.e., the damping factor, was objectively determined by a simplified cross validation technique. The final solution was obtained as an average of the ten solutions, each of which was derived from one tenth of the total data set. The reliability of the solution is examined in two ways: (1) mapping the resolution given by the reconstruction of checkerboard patterns, and (2) mapping the variance given from the gaussian noise input. This is the first result which delineates the whole mantle structure with its reliability mapping. The longest wavelength anomalies of the lower mantle are similar to those of previous studies by Dziewonski (1984) and Hager and Clayton (1989). However, the shorter wavelength patterns have many discrepancies. The fast anomalies of the uppermost mantle beneath the shield and the slow anomalies beneath the active tectonic regions are clearly seen. We also revealed the l = 2 pattern at the transition zone reported by the previous surface wave and free oscillation studies. The most striking feature is that of the fast anomalies lying along the extension of the large subducting plate up to depths of about 1000 km or more. The resolving powers in these regions are generally good. © 1990.
