Multimode Love and Rayleigh wave data related to the Pacific Ocean and to North America are inverted using two sets of parameters: 1) the isotropic P and S velocities plus the density and 2), five elastic parameters describing a transversely isotropic medium, plus the density. It is found that the assumption of isotropy leads to very unrealistic upper-mantle models while much more realistic models are obtained under the assumption of transverse isotropy. The lateral variations in density between the Pacific Ocean and North America are then less than 1.5% and, in both regions, a large density gradient is well resolved at a depth near 360 km.