It kind of depends on what you mean by structure. Buildings would not survive. The great perimids would look like odd hills after this stuff.
Moon is x impacts per day * 365 days * 500 million / 37.9 million square kilometers = 4815 days worth of bombardment per km squared. Each day represents 2800 kg so each square meter gets hit with ~ 13.5 kg if stuff going 17,000 m/s.
1/2 Mass * velocity squared. 13.5 kg * 17,000^2 = 1950750000j or 1/2 a ton of TNT per square meter. Except the force is conctrated in one direction so it’s closer to 1 to 3 tons of TNT for every single square meter.
Now it’s diffent because these impacts don’t happen at the same time. But they also don’t happen from a single direction so taller structure would be hit along their surface.
(Edit: this was written to respond to your original comment about the Sears tower, not the one that you have up now which is about ancient egyptian physics or something. I'm too lazy to type up another response. I'll just leave it at "you're wrong" and depart)
> But if you put say the sears tower there 500 million years ago it would not be recognizable as a structure
That's just not true. Look at the Apollo 11 photos. Those exposed rocks are 3+ billion years old (six times older than the timescale we're talking about) and they're certainly not covered in a mound of dust. A 500m-scale structure on the moon would absolutely still be standing, absent really really bad luck.
Look at the size of those rocks. Fist sized chunks of rubble are not a structure. After the surface solidified it was continuously bombarded and broken into tiny fragments. That same thing would happen to buildings on those time scales.
Picture a cooling pile of molten rock that’s solidified, now you can’t pick that up. You can only pick up fragments that are blown apart and looking at those pictures their are plenty of fragments you need to dig to find the solid rock.
Additionally, useful surface structures probably would be made in part of lightweight materials transported from Earth; a useful base would likely be largely subsurface. There's no particular reason why an entrance to such a base need be durable or monumental, or even directly visible with human eyes (or artificial aids thereto) from many kilometres above (let alone from Earth).
Apart from radio beacons and similar navigational aids, there's good reason to think a predecessor terrestrial spacefaring civilization would see very differently from mammals closely related to humans.
(Along those lines, one can imagine a predecessor Earth civilization whose leading species is comfortable in a temperature or pressure that humans could not tolerate, and that their comfortable working conditions would drive the location and composition of a lunar base for them. Even our own species had (and has) mountain-dwelling civilizations in environments challenging to subtropical coastal people. If they had been in the Space Race, mountain-dwellers might have had some advantages in needing to haul around less atmosphere (being comfortable with a higher cabin altitude), and they're the same species as the first Americans and Soviets in space.)
Moon is x impacts per day * 365 days * 500 million / 37.9 million square kilometers = 4815 days worth of bombardment per km squared. Each day represents 2800 kg so each square meter gets hit with ~ 13.5 kg if stuff going 17,000 m/s.
1/2 Mass * velocity squared. 13.5 kg * 17,000^2 = 1950750000j or 1/2 a ton of TNT per square meter. Except the force is conctrated in one direction so it’s closer to 1 to 3 tons of TNT for every single square meter.
Now it’s diffent because these impacts don’t happen at the same time. But they also don’t happen from a single direction so taller structure would be hit along their surface.