3-D multiobservable probabilistic inversion for the compositional and thermal structure of the lithosphere and upper mantle. I: a priori petrological information and geophysical observables

Traditional inversion techniques applied to the problem of characterizing the thermal and compositional structure of the upper mantle are not well suited to deal with the nonlinearity of the problem, the trade-off between temperature and compositional effects on wave velocities, the nonuniqueness of the compositional space, and the dissimilar sensitivities of physical parameters to temperature and composition. Probabilistic inversions, on the other hand, offer a powerful formalism to cope with all these difficulties, while allowing for an adequate treatment of the intrinsic uncertainties associated with both data and physical theories. This paper presents a detailed analysis of the two most important elements controlling the outputs of probabilistic (Bayesian) inversions for temperature and composition of the Earth's mantle, namely the a priori information on model parameters,p(m), and the likelihood function, L(m). The former is mainly controlled by our current understanding of lithosphere and mantle composition, while the latter conveys information on the observed data, their uncertainties, and the physical theories used to relate model parameters to observed data.