Adrian Marin Mag, Christophe Zaroli, Paula Koelemeijer

Seismic tomography is routinely used to image the Earth’s interior using seismic data. However, in practice, data limitations lead to discretised inversions or the use of regularisations, which complicates tomographic model interpretations. In contrast, Backus-Gilbert methods make it possible to infer properties of the true Earth, providing useful insights into the internal structure of our planet. Here, we show how in the absence of data uncertainties the Backus-Gilbert-based SOLA method can be utilised as a deterministic linear inference (DLI) method to derive a new method: SOLA-DLI. SOLA-DLI enables us to interpret results through the target kernels, rather than the imperfect resolving kernels. This also allows us to build families of models, rather than just properties. These advantages are illustrated in this contribution using three case studies. In the first, we illustrate how properties such as various local averages and gradients can be obtained, including associated bounds on these properties and resolution information. Our second case study shows how trade-offs between physical parameters are naturally included in SOLA-DLI, which is particularly relevant to inferences of Earth structure using normal- mode data. Using our final case study, we demonstrate that SOLA-DLI can be utilised to obtain the coefficients of basis function expansions, which leads to discretised models with specific advantages compared to classical least-squares solutions. This publication is accompanied by a SOLA-DLI software package that allows the interested reader to reproduce our results and to utilise the method for their own research.