After school in Twickenham Murray gained a BSc degree with first class honours in Physics and Computer Science from the University of Wales, Aberystwyth. In 1990 she was awarded a PhD in geophysics from the University of Cambridge’s Scott Polar Research Institute.
In 1993 Murray was appointed Lecturer in Physical Geography at the University of Leeds, being promoted to Reader in Glaciology in 2002 and Professor of Glaciology at Leeds in 2004. In 2005 she was appointed Professor of Glaciology at Swansea University where she heads up the Swansea Glaciological Group. 
From 2004 she has been Leverhulme Research Fellow studying "Basal conditions on Rutford Ice Stream, Antarctica". A leading member of the International Glaciological Society Murray is unusual that her medal cited discoveries at both poles. September 2007 marked the launch of the GLIMPSE Project, a 5 year project headed by Murray to determine the controls on thinning at the margin of the Greenland Ice Sheet. GLIMPSE is funded by a Leverhulme Trust Research Leadership Award granted to Murray in mid-2007.
- Atkinson, P., Jiskoot, H., Massari, R. and Murray, T. Generalised Linear Modelling applications in geomorphology. Earth Surface Processes and Landforms Technical and Software Bulletin, 23, 1185-1195, 1998.
- Barrand, N.E. and Murray, T. (In review) Multivariate controls on the incidence of glacier surging in the Karakoram Himalaya. Arctic, Antarctic and Alpine Research, submitted October 2005.
- Fowler, A. C., Murray, T. and Ng, F.S.L. Thermal regulation of glacier surging. Journal of Glaciology, 47(159), 527-538, 2001.
- Jiskoot, H., Pedersen, A.K. and Murray, T. Multi-model photogrammetric analysis of the 1990s surge of Sortebræ, East Greenland. Journal of Glaciology, 47(159), 677-687, 2001.
- Lockwood, R.A., Murray, T., Stuart, G.W. and Scudder, L. Locating leaks from water supply pipes using the passive acoustic method, Journal of Water Supply: Research and Technology, 54(8), 519-530, 2005.
- Luckman, A., Murray, T. and Strozzi, T. Surface flow evolution throughout a glacier surge measured by satellite radar interferometry, Geophysical Research Letters, 29(23), 2095, 10.1029/2001GL014570, 2002.
- Murray, T. Assessing the paradigm shift: deformable glacier beds. Quaternary Science Reviews, 16(9): 995-1016, 1997.
- Pritchard, H., Murray, T., Strozzi, T., Barr, S. and Luckman, A. Glacier surge-related topographic change derived from Synthetic Aperture Radar interferometry, Journal of Glaciology, 49(166), 381-390, 2003.
- James, T.D., Murray, T., Barrand, N.E. and Barr, S.L., Extracting photogrammetric ground control from lidar DEMs for change detection, Photogrammetric Record. 21(116): 310-326, 2006.
- Kohler, J., James, T.D., Murray, T., Nuth, C., Brandt, O., Barrand, N.E., Aas, H.F. and Luckman, A.J. (2007). Acceleration in thinning rate on western Svalbard glaciers, Geophysical Research Letters, 34(L18502): doi:10.1029/2007GL030681.