According to NASA, there are at least four different kinds of moonquakes:

• deep moonquakes (~700 km below the surface, probably caused by tidal in origin)
• meteorites impact vibrations
• thermal quakes (the frigid lunar crust expands sunlight returns after the two week lunar night)
• shallow moonquakes (20 or 30 kilometers below the surface)

Little is known about the causes, or the distribution, of shallow moonquakes. One possible explanation is that relatively young craters may slump. Neal and his colleagues are proposing that a network of 12 seismometers be placed around the moon to gather data; this would be part of the larger plan to find safe lunar bases.

So, who was first to work on the problem of moonquake-proof habitats? Robert Heinlein is a good candidate: he made some suggestions in his 1948 story Gentlemen, Be Seated, which takes place on the Moon as a new colony is expanding. First, he identifies the problem:

"Every engineering job has its own hazards," he insisted, "and its advantages, too. Our men don't get malaria and they don't have to watch out for rattlesnakes..."

"Okay, okay," I interrupted, "so the place is safe... So you keep unnecessary airlocks. Why?"

He hesitated before he answered, "Quakes."

Quakes. Earthquakes-moonquakes, I mean.
(Read more about moonquake-proof habitats)

One solution that is offered is that of extra airlocks; by compartmentalizing your walkway or habitat, you can cut your losses. The second suggestion is that of flexible joints:

"Show him a flexible joint," Knowles directed. "Coming up." We paused half-way down the tunnel and Konski pointed to a ring segment that ran completely around the tubular tunnel. "We put in a flex joint every hundred feet. It's glass cloth, gasketed onto the two steel sections it joins. Gives the tunnel a certain amount of springiness."
(Read more about moonquake-proof habitats)

As a final suggestion, to be used during emergencies when relatively small leaks might result from quakes (or other causes), Heinlein suggests the use of "tag-alongs:"

There were perhaps a dozen bladder-like objects in the tunnel, the size and shape of toy balloons. They seemed to displace exactly their own weight of air; they floated without displaying much tendency to rise or settle. Konski batted one out of his way and answered me before I could ask.

"This piece of tunnel was pressurized today," he told me.

"These tag-alongs search out stray leaks. They're sticky inside. They get sucked up against a leak, break, and the goo gets sucked in, freezes and seals the leak."
(Read more about tag-alongs)

And beyond the Moon? One of the seismometers carried to Mars by the U.S. Viking landers during the mid-1970's remained operational. Only one possible marsquake was detected in 546 Martian days. The Mars Global Surveyor spacecraft detected what appeared to be changes to the Martian surface; Michael Meyer, chief scientist for the mission, speculated that the changes might have been caused by marsquakes.