Reducing the computational cost of seismic waveform modelling is a major challenge towards a more accurate imaging of the deep Earth. With this aim in mind, Masson and Romanowicz (2017) proposed a methodology (“Box tomography”) in the framework of regional tomography, that allows us to couple full 3D solvers outside and inside the target region in order to take into account teleseismic wavefields recorded at stations located beyond the boundaries of the target region. Since this methodology allows one to compute seismograms to higher frequency at reasonable computational cost, one can aim to image the target region at a finer scale. It also allows to include core phases in the context of regional tomography without having a target region that extends all the way to the Core-Mantle Boundary. We show preliminary results of an application of this method to imaging the deep structure under the Yellowstone hotspot down to 20 seconds period. Previous regional traveltime tomography inversion studies showed different velocity anomaly structures in this area, sometimes extending all the way down to the CMB (Nelson and Grand, 2018), sometimes being much shallower (Obreski et al. 2010). Those apparently contradictory results attest to the difficulty of constraining the morphology of the Yellowstone plume. Here, we use data from 332 stations inside and 100 stations outside the box, that have been chosen in order to enhance and optimize the azimuthal coverage. We selected 54 events located around the target region with magnitudes between 5.2 and 7, ensuring an optimal illumination of the target region. By using the framework of Full Waveform Inversion, we are able to use all of the information contained in a seismogram towards producing a better constrained model of the Yellowstone area. We also show benchmarks tests for proving the accuracy of the box tomography methodology.