In 1996 he was awarded the RAOU's John Hobbs Medal for outstanding contributions to Australian ornithology as an amateur. In 2009 he was awarded an Honorary DSc by the University of Sydney.
From the 1990s Murray has been part of a research team studying the movements of albatrosses, especially wandering albatrosses, Diomedea exulans. Some papers resulting from this collaborative research are:
Nicholls, David; Murray, Durno; Battam, Harry; Robertson, Graham; Moors, Philip; Butcher, Eric; & Hildebrandt, Michael. (1995). Satellite tracking of the Wandering Albatross, Diomedea exulans, around Australia and in the Indian Ocean. EMU 95: 223–230.
Nicholls, D.G.; Murray, M.D.; Butcher, E.; & Moors, P. (1997). Weather systems determine the non-breeding distribution of Wandering Albatrosses over southern oceans. EMU 97: 240–244.
Nicholls, D.G.; Murray, M.D.; Butcher, E.C.; & Moors, P.J. (2000). Time spent in Exclusive Economic Zones of southern oceans by non-breeding Wandering Albatrosses (Diomedea spp.): implications for national responsibilities for conservation. EMU 100: 318–323.
Murray, M.D.; Nicholls, D.G.; Butcher, E.C.; & Moors, P. (2002). How Wandering Albatrosses use weather systems to fly long distances. 1. An analytical method and its application to flights in the Tasman Sea. EMU 102: 377–385.
Murray, M. D.; Nicholls, D. G.; Butcher, E.; & Moors, P.J. (2003). How Wandering Albatrosses use weather systems to fly long distances. 2. The use of eastward-moving cold fronts from Antarctic lows to travel westwards across the Indian Ocean. EMU 103: 59–65.
Murray, M.D.; Nicholls, D.G.; Butcher, E.C.; Moors, P.; Walker, K.; & Elliott, G. (2003). How Wandering Albatrosses use weather systems to fly long distances. 3. The contributions of Antarctic lows to eastward, southward and northward flight. EMU 103: 111–120.
BirdLife International. (2004). Tracking ocean wanderers: the global distribution of albatrosses and petrels. Results from the Global Procellariiform Tracking Workshop, 1–5 September 2003, Gordon's Bay, South Africa. BirdLife International: Cambridge, UK. ISBN0-946888-55-8
Robin, Libby. (2001). The Flight of the Emu: a hundred years of Australian ornithology 1901-2001. Carlton, Vic. Melbourne University Press. ISBN0-522-84987-3