The Great Static is not explained much, only mentioned specifically by Doctor Dala, Doctor Borous, and Doctor Klein, and Doctor 0 is the only one that mentions it but does not give it a name. So let's take a quick look at what exactly they say regarding the matter - maybe we'll be able to figure out just what the Great Static is.
After asking Dala "This used to be a mountain?" she will respond with this: "Yes, Big MT was quite big indeed until the Great Static. Then the top of the mountain was used as part of a detonation experiment (aka, an explosion). This cleared additional space in the Crater, however, allowing us more real estate to build upon."
So, already, we know what the Great Static is, by just using one comment. Klein and Borous mention it once each with no significance, so we'll need to look at 0's comment next.
After asking 0 to tell you about "the facility", he will respond with the following: "Big MT used to be a mountain. Then there was a... slight mishap. Now it's a crater - the Dome used to be buried, now it's exposed to the sky. [He pauses.] Don't get me wrong. Makes the sky light up like a planetarium at night. All those spectra... so soothing."
By 0's testimony, a "slight mishap" occurred, causing the Dome to be "exposed to the sky", which it is in 2281. Doctor Mobius is the one who we get our final clue from, surprisingly, and it's not through initial dialogue, either.
Over the intercom, while traveling through Big MT, Mobius may randomly broadcast the following statement: "Klein... remember the time you forgot to carry the 2 and nearly blew up the Y-0 Research Center? Oh, wait, you did! [He pauses.] Or was that me?"
Now, it is not known for sure that this explosion at Y-0 was the Great Static, but it is entirely possible. Maybe one day we can dig a bit deeper. Let me know if you find anything useful. I want to make sure that last bit is correct. I know for a fact, however, that the Great Static was the catastrophe that caused the upper half of the mountain to explore and expose The Think Tank.