Imaging upper-mantle anisotropy with joint body-surface wave trans-dimensional inference

In the Earth's upper-mantle, the isotropic (i.e., directional-invariant) symmetry of elastic wave velocities is typically broken by crystal-scale mechanisms, such as crystallographic-preferred orientation of anisotropic minerals (e.g., olivine) in regions subject to significant strain (e.g., subduction zones, mantle plumes, ridges...). The resulting anisotropic (i.e., directional-dependent) elastic properties are manifested in the seismic observations at the surface (e.g., travel-times), making them primary carriers of information related to the geodynamic processes occurring in the Earth’s mantle. However, the seismic tomography problem is notoriously under-determined (i.e., infinite solutions), due to limitations in the distribution of data at the Earth’s surface, and this condition is even exacerbated when simplifying imaging assumptions, such as isotropy, are replaced by more realistic anisotropic approximations that increase the degrees of freedom of the inverse problem.

Reconstructing seismic anisotropy is a challenging inference problem, where uncertainty estimation plays a crucial role in the separation of robustly inferred features and anomalies resulting from misinterpreted trade-offs with isotropic structure. In this context, the high non-linearity of the problem hampers uncertainty assessment when regularized iterative linearized methods (e.g., LSQR) are used.

In this study we show how to setup a joint inversion of multiple observables, such as body-wave delay times and Rayleigh-wave station-station differential phase travel-times, to constrain upper-mantle structure. Rayleigh and body waves illuminate - respectively - the shallower and the deeper sections of the imaging domain, leading to a cross-constrain for mantle anisotropy and isotropic structure. We implement a trans-dimensional probabilistic sampling algorithm to populate an ensemble of likely hexagonal anisotropic mantle models describing the observations within the uncertainties. Probabilistic sampling allows a greater exploration of the model space, with the possibility to evaluate uncertainty and trade-off metrics. To test the inference method, we make use of synthetic seismograms simulated with SPECFEM through geodynamic models of the Earth's mantle.