Abstract

Over the last three decades a vast number of tomographic images has been produced, but the quantitative assessment of their accuracy and uniqueness has only just started. A relatively recent technique in this direction has been made by (Trampert et al., 2004) using probabilistic tomography. It is based on a
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full model space search, the Neighbourhood Algorithm (NA), with which to solve the inverse problem. This provides a representation of seismic constraints as probability density functions (pdfs) from which one can easily calculate the most likely model and its associated uncertainty. Since a full model space search quickly limits the dimension of the explorable parameter space, an essential condition to apply the NA is to have a small number of unknowns. Probabilistic tomography has been applied to invert surface waves and normal-modes. The aim of this thesis was to incorporate body wave data to increase the depth resolution in the lowermost mantle. The first step, therefore, was to establish a formalism which allows us to treat body waves as surface waves and free oscillations and, thus, separate the inverse problem into its lateral and radial components. In a spherically layered Earth using the path-average approximation, body wave delay times can be inverted in two steps. The first step is the construction of vertical travel-time residual maps as a function of ray parameter. The second step is their depth inversion, less well constrained than the first step but characterized by a small number of parameters and, hence, suitable to be solved by the NA. Such a procedure, called path-average approach, works well for long wavelength structure for the forward and inverse problem. Combing a body wave dataset characterized by a good resolution between 2441 and 2891 km and the advantages of the path-average approach, we provided a new insight into the lowermost mantle based on lateral variations of P-, S-seismic velocities and the corresponding seismologically observed ratio without an explicit depth inversion for seismic wave velocities variation. Following a robust statistical approach, we are able to link these seismic heterogeneities to mineral physics and provide evidence for the existence of post-perovskite near the core-mantle boundary. In the framework of probabilistic tomography, applying the path-average approach we inverted body wave vertical travel-time residual maps, normal-mode splitting functions and surface wave phase velocity maps locally for depth using the NA. We constructed a shear wave, compressional wave, bulk sound speeds and density perturbation model with associated uncertainty. The estimation of the correlation between parameters and the RMS amplitude of seismic variations clearly indicates a thermal and chemical nature of heterogeneity in the lower mantle. Furthermore, our models fully confirm the conclusions achieved by the model of Resovsky & Trampert (2003), produced without body waves. One strength of probabilistic tomography is the possibility to convert easily the pdfs of seismic velocities and density perturbations into pdfs of thermal and compositional anomalies. We constructed a model of temperature, iron and perovskite variations combining mineral physics data with the shear, bulk sound wave-speeds and density variation models described above.
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