One is that there were once two moons orbiting Earth and they merged in the very early days of the Moon's formation, researchers said.
Another idea is that a large body, perhaps a young dwarf planet, found itself in an orbit around the Sun that put it on a collision course with the Moon.
This latter giant impact idea would have happened somewhat later than a merging-moons scenario and after the Moon had formed a solid crust, said Meng Hua Zhu, from Macau University of Science and Technology.
Signs of such an impact should be visible in the structure of the lunar crust today.
"The detailed gravity data obtained by GRAIL has given new insight into the structure of the lunar crust underneath the surface," Zhu said.
The new findings from GRAIL gave Zhu's team of researchers a clearer target to aim for with the computer simulations they used to test different early-Moon impact scenarios.
The researchers ran 360 computer simulations of giant impacts with the Moon to find out whether such an event millions of years ago could reproduce the crust of today's Moon as detected by GRAIL.
They found the best fit for today's asymmetrical Moon is a large body, about 780 kilometers in diameter, smacking into the nearside of the Moon at 22,500 kilometers per hour.
That would be the equivalent of an object a bit smaller than the dwarf planet Ceres moving at a speed about one-quarter as fast as the meteor pebbles and sand grains that burn up as "shooting stars" in Earth's atmosphere.
Another good fit for the impact combinations the team modelled is a slightly smaller, 720-kilometre diameter, object hitting at a mildly faster 24,500 kilometers per hour.
Under both these scenarios, the model shows the impact would have thrown up vast amounts of material that would fall back on the Moon's surface, burying the primordial crust on the farside in 5 to 10 kilometers of debris.
That is the added layer of crust detected on the farside by GRAIL, according to Zhu.
The new study suggests the impactor was not likely an early second moon of Earth's. Whatever the impactor was -- an asteroid or a dwarf planet -- it was probably on its own orbit around the Sun when it encountered the Moon, said Zhu.
The giant impact model also provides a good explanation for the unexplained differences in isotopes of potassium, phosphorus and rare-earth elements like tungsten-182 between the surfaces of the Earth and Moon, the researchers said.
These elements could have come from the giant impact, which would have added that material to the Moon after its formation, according to the study.