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A correct anisotropic velocity model is critical for seismic imaging. We investigate here the possible advantages of inverting simultaneously for reflected and diving waves using P-waves recorded at the surface. Simple tests in 1-D and 2-D VTI (Vertical Transversely Isotropic) models with spatially varying Vp and e show that reflected energy alone only provides partial information on the sub-surface properties after travel time tomography. However, both the velocity profile Vp, the depth interfaces and e can be well inverted by combining the two types of waves in the 1-D and 2-D examples investigated here.