This project used seismic and well bore data to reconstruct parts of subterraneous geology.  In Saudi Arabia, I am told that, much of the oil is in geologies that used to be rivers and streams.  

Where, then, are these things? 

It is possible to drill horizontally!

Tools used:  

1. Combinatorial Morse Theory 

2. Minimal surface algorithms by John Sullivan. 

Other applications of this technology:

1.  Detection of membranes in lungs from MRI Data

2.  ...