Get into Seismic, a couple of acquistion engineers in my crew have electrica/electronic degree. Basically what we do is record reflected waves bouncing of the earth's layers that orignates from a high energy source and record the data using highly sensitve hydrophones. The hydrophones are located in streamers that are towed behind the seismic vessel and can be as long as 12km. Obviously this is just the tip of the iceberg of what seismic engineers do but it does help tremendously if you have an electrical background. You'll have to be familiar with terms like sampling rates, nyquist frequencies, anti-aliasing filters, scsi, IEEE 32... just to give an example. However you will be working mostly on a Seismic vessel and not on an oil rig.. but I guess that still counts as being offshore. The pay is good and you typically only spend 5 weeks offshore. It does allow for extensive international travel as the vessel will always be moving around to it's next survey job.