Macbook Air 2012 crash with glitching screen

Hi all, I turn myself to you as a last resort for an annoying issue with my Mid-2012 Macbook Air. Recently my Macbook started crashing at random intervals. The symptoms are always nearly the same: computer freezes, screen has these glitching squares and the computer restarts after a few seconds. To me this seems like a crash, but since it happened both under small and high workloads, regardless of the application I was using, I started to keep a log. I was not able to find any way to predict when the computer would crash. The battery level didn’t make a difference, the workload neither, the angle of the screen (I though maybe a bad connection with the GPU) made no difference either. 

Extra remarks: The crashes seem to happen at shorter intervals as time goes by. Sometimes there is a distortion of the audio as the crash occurs (a loud crackling noise), but this happens only one out of ten times.

Because I want to continue using my MacBook, which for the rest functions absolutely fine and fits my needs, I was hoping to get some insight from you. Thank you in advance!

Things I tried so far: 

• I replaced the battery with a fresh one two weeks ago, this made no difference to the problem.
• I reset the PRAM and SMC, no difference
• I updated the computer, no difference
• I have Windows installed on my PC and the crashes happen there, too.
• Wiped the computer clean and reinstalled everything using Time Machine, no difference.
• …

Attached you will find a picture of the screen after a crash.