One of the big inspiration for At the Mountains of Madness was Admiral Byrd's first Antarctic expedition from 1928 to 1930, from which Lovecraft drew many details that he would transplant onto the Miskatonic University Expedition. Byrd wrote a 100-page piece for National Geographic Magazine, which was published in August 1930 as The Conquest of Antarctica By Air. It's listed in Beyond the Mountains of Madness on page 14 under 'More Reading'.
Issues are available on eBay all the time, starting at around a mere $6 (my copy is from there). But you can also download it as a 172-page PDF, which although lacking in resolution, will give you a way to read Byrd's extensive details on the expedition without adding yet another book to your library.