Exploration of Monte Carlo Transdimensional Methods for Anisotropic Seismic Imaging

Seismic imaging, exploiting seismic waves' travel-time measurements, allows for the reconstruction of the three-dimensional variability of the seismic propagation velocities, illuminating the heterogeneities in the elastic and density structure of our planet. In this context, seismic anisotropy refers to the phenomenon in which seismic velocities manifest a dependence on the direction of propagation and polarization of the waves. Anisotropic anomalies are associated with different source mechanisms depending on the environment. In the upper-mantle, seismic anisotropy is mostly due to the preferential crystallographic orientation of inherently anisotropic minerals, caused by deformation processes; in the crust, seismic anisotropy mainly originates from fluid-filled cracks oriented by the stress minimum-compression directions. Including anisotropic anomalies in seismic imaging allows for 1) a more realistic representation of the seismic velocities, reducing the generation of artifacts; 2) reconstructing information on the deformation processes in the upper-mantle, and fluid distribution/stress geometry in crustal environments. Despite this, the isotropic approximation - which ignores any directional effect in the velocity anomalies - persists today as a common choice. The reason is that the heterogeneous distribution of seismic data makes the simultaneous reconstruction of isotropic and anisotropic anomalies particularly challenging, mainly because of the heavy non-uniqueness of the solution. In this thesis project, innovative methods for anisotropic seismic imaging are developed to directly address the problems of non-uniqueness and uncertainty quantification. Adopting probabilistic sampling algorithms, solution models compatible with the data within the uncertainties are sampled to explore the variability of the seismic anomalies reconstructed; the manifestation of consistent structures among several sampled models and highly variable features allow for uncertainty quantification. To adapt to the heterogeneous distribution of data information, solution models are parameterized using irregular meshes with variable complexity and configurations among different samples. The developed method is validated using synthetic experiments with anisotropic models representative of active geodynamical environments. The simultaneous inversion of different types of simulated data is tested to reconstruct the anomalies that characterize the target models, showing statistical metrics to explore non-uniqueness and quantify uncertainties. The validated method is applied to the anisotropic inversion of P-wave travel-time data in two crustal environments, with the aim of reconstructing the patterns of fluid-filled cracks and the geometry of the forces; low-uncertainty anomalies are isolated for the interpretation using the probabilistic approach. In the first application to the Etna volcano, the isotropic and anisotropic anomalies are interpreted with a radial pattern of dikes between 6 and 16 km depth surrounding a region hypothesized to be a magmatic storage; the geometry of inferred minimum-compression directions is explained proposing a state of pressurization for the magmatic storage. In the second application to the Val d'Agri (southern Apennines) seismogenic zone, the inversion evidences isotropic anomalies consistent with the geological-structural context of the region. The anisotropic anomalies illuminate regions of fluid accumulation in aligned cracks and minimum-compression directions. The comparison between the stress inferred from the anisotropic anomalies and numerical simulations shows excellent agreement, highlighting the role of subsurface lateral density heterogeneities in stress reorientation and further supporting the validity of anisotropic imaging in the Earth's crust as a means to reconstruct the geometry of stress.