Accurately monitoring and predicting the evolution of the West Antarctic Ice Sheet via secular changes in the Earth's gravity field requires knowledge of the underlying upper mantle viscosity structure. Published seismic models show the West Antarctic lithosphere to be ∼70-100 km thick and underlain by a low velocity zone extending to at least ∼200 km. Mantle viscosity is dependent on factors including temperature, grain size, the hydrogen content of olivine, the presence of partial melt and applied stress. As seismic wave propagation is particularly sensitive to thermal variations, seismic velocity provides a means of gauging mantle temperature. In 2012, a magnitude 5.6 intraplate earthquake in Marie Byrd Land was recorded on an array of POLENET-ANET seismometers deployed across West Antarctica. We modelled the waveforms recorded by six of the seismic stations in order to determine realistic estimates of temperature and lithology for the lithospheric mantle beneath Marie Byrd Land and the central West Antarctic Rift System. Published mantle xenolith and magnetotelluric data provided constraints on grain size and hydrogen content, respectively, for viscosity modelling. Considering tectonically-plausible stresses, we estimate that the viscosity of the lithospheric mantle beneath Marie Byrd Land and the central West Antarctic Rift System ranges from ∼1020-1022 Pa s. To extend our analysis to the sublithospheric seismic low velocity zone, we used a published shear wave model. We calculated that the velocity reduction observed between the base of the lithosphere (∼4.4-4.7 km/s) and the centre of the low velocity zone (∼4.2-4.3 km/s) beneath West Antarctica could be caused by a 0.1-0.3% melt fraction or a one order of magnitude reduction in grain size. However, the grain size reduction is inconsistent with our viscosity modelling constraints, suggesting that partial melt more feasibly explains the origin of the low velocity zone. Considering plausible asthenospheric stresses, we estimate the viscosity of the seismic low velocity zone beneath West Antarctica to be ∼1018-1019 Pa s. It has been shown elsewhere that the inclusion of a low viscosity layer of order 1019 Pa s in Fennoscandian models of glacial isostatic adjustment reduces disparities between predicted surface uplift rates and corresponding field observations. The incorporation of a low viscosity layer reflecting the seismic low velocity zone in Antarctic glacial isostatic adjustment models might similarly lessen the misfit with observed uplift rates.