For the sake of their study, which was recently published in Nature Communications, Asphaug and Nayak used computer modeling to simulate how other meteoric impacts could have created these crater patterns, which they theorized were formed when the resulting ejecta circled back and impacted the surface in other locations.
As Dr. Asphaug told Universe Today via email, their work was the result of a meeting of minds that spawned an interesting theory:
"Dr. Nayak had been studying with Prof. Francis Nimmo (of UCSC), the idea that ejecta could swap between the Martian moons. So Mikey and I met up to talk about that, and the possibility that Phobos could sweep up its own ejecta. Originally I had been thinking that seismic events (triggered by impacts) might cause Phobos to shed material tidally, since it's inside the Roche limit, and that this material would thin out into rings that would be reaccreted by Phobos. That still might happen, but for the prominent catenae the answer turned out to be much simpler (after a lot of painstaking computations) - that crater ejecta is faster than Phobos' escape velocity, but much slower than Mars orbital velocity, and much of it gets swept up after several co-orbits about Mars, forming these patterns."
"Dr. Nayak had been studying with Prof. Francis Nimmo (of UCSC), the idea that ejecta could swap between the Martian moons. So Mikey and I met up to talk about that, and the possibility that Phobos could sweep up its own ejecta. Originally I had been thinking that seismic events (triggered by impacts) might cause Phobos to shed material tidally, since it's inside the Roche limit, and that this material would thin out into rings that would be reaccreted by Phobos. That still might happen, but for the prominent catenae the answer turned out to be much simpler (after a lot of painstaking computations) - that crater ejecta is faster than Phobos' escape velocity, but much slower than Mars orbital velocity, and much of it gets swept up after several co-orbits about Mars, forming these patterns."