Matrix autoregressive analysis of free-oscillation coupling and splitting

The study of the splitting and coupling of free oscillations can potentiall y provide some unique information about the Earth-in particular about how d ensity varies laterally relative to sheer velocity and bulk sound speed. Mo de splitting has been studied for many years but it is clear that the time is ripe to revisit this field. Tn particular, the rapid expansion of the gl obal seismic network and the occurrence of many large (and deep) earthquake s in the past few years means that mode-splitting analyses are capable of m uch higher precision than in the past. Some studies have already argued tha t 3-D density can be recovered (and that density variations are negatively correlated with shear velocity in the lower mantle). This result is controv ersial and we present some experiments that indicate that claims of density recovery with the current mode data set are premature. However, we believe that, with expanded data sets and new analysis techniques, the precision n eeded to recover the 3-D density structure of the Earth and its 3-D anelast ic structure is now within our reach.