Seismic Tomography of the Earth's Mantle

The analysis of information contained in seismograms is the most promis­ ing tool for retrieving the three-dimensional structure of the Earth's mantle and thereby improving our understanding of its dynamics. The procedure through which three-dimensional images of different parts of the Earth's interior arc obtained by inversion of a set of observables measured on the surface of the Earth is commonly termed "tomography," by analogy with the medical procedure with which it shares many aspects of methodology but with much less favorable experimental conditions. Ideally, one would like to be able to model entire seismograms, over a wide frequency band, for a large number of uniformly distributed sources and stations in order to obtain an optimal illumination of the inhomogeneities appropriate for tomographic inversion. In practice, a number of difficulties and limitations arise. Onc is the nonuniform distribution of sources and receivers: Seis­ micity is concentrated at plate boundaries, and the distribution of con­ tinental and island areas leaves large portions of the oceans unin­ strumented. Another difficulty is our limited ability to accurately forward model the effects of wave propagation in a realistic Earth, which presents departures from a spherically symmetric referencc model of both elastic/anc1astic and isotropic/anisotropic nature. This is why, until now, the simplest kind of tomography (travel time tomography) has prevailed, relying on simplifying assumptions concerning the interaction of asphericity with propagating seismic waves. Ray theory and the laws of geometrical optics in their