Simultaneous Inversion of Normal Mode Splitting Coefficients for Vs, Vp and ρ Using the Neighbourhood Algorithm.

Unlike travel times or waveform data, normal mode data are directly sensitive to the density of the Earth. However, the sensitivity kernels for density are much smaller than those for velocities, so the controversy about the possibility of resolution of the mantle's density is still vivid, especially since the publication of model SPRD6 (Ishii and Tromp, 1999) whose high density structures corresponding with the "plumes" under Pacific and Africa would have important consequences on deep mantle dynamics. Several authors ( Resovsky and Ritzwoller, 1999, 2002, Romanowicz, 2001, Kuo and Romanowicz, 2002) pointed out significant trade-offs between velocity and density structure and the controversy is still going. However the inversion procedures used in previous studies, with the exception of Resovsky and Ritzwoller (2002), all rely on least-squares inversions and require the use of a starting model, the choice of which is critical for the reliability of the results. Unlike such a simple inversion scheme the result of which is one "best" model, stochastic methods sample the parameter space, and their result is a set of models whose statistical properties reflect the likehood function. Here, in order to investigate the resolution of density in the lower mantle, we apply the Neighbourhood Algorithm (Sambridge, 1999a) which uses forward modeling to sample the parameter space preferentially where the fit is better. Our dataset consists of the ensemble of mantle-sensitive normal mode splitting coefficients currently available. We parametrize the models in depth using cubic spline functions and limit our study to lateral variations of degree 2. We present the results of the first stage, which samples the parameter space and gives qualitative results on the domain of best-fitting models. We also present preliminary results of the second (the appraising) stage of the algorithm (Sambridge, 1999b) which uses bayesian integrals to retrieve quantitative information (resolution matrix, covariance) from the set of models obtained in the first stage.