The progress achieved during the last four or so years in seismic tomography of the mantle has created favorable conditions to attempt a major effort in delineating aspherical properties of the Earth from region D" to the inner core. We can now be confident that our current models are adequate to strip the long wavelength effect of lateral heterogeneity in the outermost 2700 km. We propose to use travel time (primarily ISC data base) and waveform data.