Basically you take waves that are transiting the area of interest and do transforms on them to ascertain the structure underground. Dave Hitz of NetApp used to joke these guys have great compression algorithm, they can convert a terabyte of data into 1 bit (oil/no-oil).

One of the challenges is that the algorithms are running in a volume of space, so 'nearest neigbor' in terms of samples has more than 8 vectors.

In the early 2000's they would stream their raw data off tape cartridges into a beowulf type cluster, process it, and then store the post processed (and smaller) data to storage arrays. Then that post processed data would go through its own round of processing. One of their challenges was that they ended up duplicating the data on multiple nodes because they needed it for their algorithm and it was too slow to fetch it across the network.

A single system image with a TB of memory would let them go back to some of their old mainframe algorithms which, I'm told, were much easier to maintain.