The development of dense networks of broad-band seismographs makes teleseismic data amenable to full-waveform inversion (FWI) methods for high-resolution lithospheric imaging. Compared to scattered-field migration, FWI seeks to involve the full seismic wavefield in the inversion. We present a parametric analysis of 2-D frequency-domain FWI in the framework of lithospheric imaging from teleseismic data to identify the main factors that impact on the quality of the reconstructed compressional (P)-wave and shear (S)-wave speed models. Compared to controlled-source seismology, the main adaptation of FWI to teleseismic configuration consists of the implementation with a scattered-filed formulation of plane-wave sources that impinge on the base of the lithospheric target located below the receiver network at an arbitrary incidence angle. Seismic modelling is performed with a hp-adaptive discontinuous Galerkin method on unstructured triangular mesh. A quasi-Newton inversion algorithm provides an approximate accounting for the Hessian operator, which contributes to reduce the footprint of the coarse acquisition geometry in the imaging. A versatile algorithm to compute the gradient of the misfit function with the adjoint-state method allows for abstraction between the forward-problem operators and the meshes that are during seismic modelling and inversion, respectively. An approximate correction for obliquity is derived for future application to real teleseismic data under the two-dimension approximation. Comparisons between the characteristic scales involved in exploration geophysics and in teleseismic seismology suggest that the resolution gain provided by full waveform technologies should be of the same order of magnitude for both applications. We first show the importance of the surface-reflected wavefield to dramatically improve the resolving power of FWI by combining tomography-like and migration-like imaging through the incorporation of the forward-scattered and the backscattered wavefields in the inversion. The resolution of FWI is assessed through checkerboard tests and confirms a resolution of the order of the wavelength for both the P and S speeds, when the full wavefield is incorporated in the inversion. Secondly, we show that computationally efficient strategies, which consist of decimating the number of frequency components involved in the inversion, do not apply to teleseismic acquisitions, because the scattering-angle bandwidth sampled by plane-wave sources can be narrow and coarsely sampled, compared to that provided by dense profiles of point sources in exploration seismology. The waveform inversion is less sensitive to the band of incidence angles spanned by the plane-wave sources and to the sampling of this band. However, the deficit of vertically propagating plane waves hampers the vertical resolution of planar layers. Aliasing artefacts created by coarse arrays of receivers are illustrated. We show how taking into account the Hessian in the inversion and the suitable management of frequencies in the inversion help to mitigate these artefacts. Acceptable reconstructions are shown for both the P- and S-wave speeds for a receiver spacing of up to 20 km in the 0.1-0.4 Hz frequency range. Building a reliable initial model for FWI is a highly non-linear problem in exploration seismology. We show how the low-frequency content of the teleseismic sources allow us to build accurate P- and S-wave speed models starting from simple vertical-gradient velocity models. All of these results are derived using a 2-D realistic synthetic experiment that was performed with noise-free data. Most of conclusions of this parametric study should apply in three dimensions. The impact of noise and the footprint of other experimental parameters such as the estimation of the temporal plane-wave signature and the estimation of the incidence angle of the impinging plane waves, need however to be assessed in the future.