Rosaria Tondi

Seismic travel time inversion for 3D structures regularized with Sobolev norms

Asymptotic ray methods are commonly used for forward modelling in seismology and seismic exploration, but rays propagating through heterogeneous media exhibit chaotic behaviour. This means that we can observe a sensitive dependence on initial ray conditions and thus, for long times, the exponential amplification of very small perturbations. The degree of chaos in the model, which may be quantified in terms of the average Lyapunov exponent for all the rays in the model, can be approximated by the square root of the Sobolev norm of order 2 of the corresponding model parameters. In this paper, we present a new inversion technique which considers the Sobolev norm as the regularization term of the ill-conditioned seismic inverse problem. We show that in this way we can control the divergence of rays in our model during the iterations and obtain stable solutions with a negligible dependence on the chosen discretization. The robustness and limitations of the algorithm are illustrated by numerical examples produced with a real heterogeneous 3D structure. The sensitivity of the algorithm to non-Gaussian distribution of noise is also tested.

Deep and Shallow Solid-Earth Structures Reconstructed with Sequential Integrated Inversion (SII) of Seismic and Gravity Data

In this paper, the possibility of using simultaneously seismic and gravity data, for the reconstruction of solid-Earth structures, has been investigated through the use of an algorithm which allows joint efficient and reliable optimisation of compressional velocity and mass density parameters, We view the measured data as a realisation of a stochastic process generated by the physical parameters to be sought and we construct a “probability density function” which includes three kinds of information: information derived from gravity measurements; information derived from seismic travel time inversion and information on the physical correlation among density and velocity parameters. We show that combining data has a beneficial effect on the inversion since: it makes the problem more stable and as a consequence, providing that the quality of data is sufficiently high, enables more accurate and reliable reconstruction of the unknown parameters. In this context, we look forward the GOCE mission, which promises high spatial resolution (100–200 km) and accurate (1–2 mGals) gravity data.