Devil's Advocate position here: Ride it.
The fracture is completely circumferential around the seat tube. If there is no evidence of the fracture propagating off in another direction along the tube or into the seat stays, there is no down-side to riding the bike except 1) the saddle is somewhat rotationally unstable (though not completely, because of the rough interfaces between the two parts) and 2) you can't lift the bike by the saddle without the seatpost coming out.
This part of the frame, especially at the front of the seat tube where it joins the top tube, is under a lot of tensile stress. Even more so with a heavier rider. Trying to re-construct the frame by any combination of welding or adding tubing elements is likely to be unsuccessful, as outlined by several posts above.
The seatpost can't drop into the seat tube as long as the clamp is tight. The tendency of the saddle to rotate while riding is minimal, because of the rough interface. The saddle can be somewhat stabilized by constructing one or more "stays" connecting the seatpost clamp to some part of the frame. It's not ideal, but it's not dangerous. Of course, you should be vigilant about watching for fractures elsewhere on the frame, but this is a particularly high-stress area.
Here's my reason for this suggestion (note that it's only a suggestion!):
I had the same exact frame failure on a folding bike after about 7,000 miles. This was a bike (Dahon Mu XL) with a very long seatpost. I'm not a lightweight rider, so I reasoned that welding would not be a good fix, and that a new frame would be likely to fail in the same way. So I opted to continue riding the bike, but with the addition of two stays connecting the seatpost clamp to the frame's rack mounts. The bike now has 12,600 miles on it and no further frame cracks have appeared. You can see the fractured stub of the seat tube and the stays in the image below.
Leaving Devil's Advocate Mode!
Stabilized Seat Tube Fracture