"Was it just recycled, near-surface material or was there any evidence of fresh lava coming out?"
Mr Rosenberg said the size of the material and how far it travelled would also give them an idea of how energetic the eruption was.
"It will also allow us to estimate some hazard zones. It's all part of understanding what Monday's eruption was all about."
Mr Rosenberg said both White Island, 51km north of Opotiki in Bay of Plenty, and Mt Tongariro were at low levels of activity today, with small earthquakes continuing.
"White Island continues to produce the plume that sometimes contains a bit more ash than other times," he said.
"Tongariro is about the same. People would have seen some very nice steam plumes this morning."
Mr Rosenberg said the plume's visibility was the result of calm weather and cold air allowing the steam to rise.
Gas readings taken during flights over the central North Island volcano this morning showed the presence of magma under the mountain at an unknown depth.
GNS Science volcanologist Craig Miller said the tests showed another larger magmatic explosion could take place.
It was a now "waiting game" to find out whether that would happen, he said.
"What is does confirm is there is a magmatic source at depth. Whether the magma is going to stay at those unknown depths or whether it's coming to the surface is the question."
If no magma was detected in this morning's tests, it would have meant another eruption was unlikely, Mr Miller said.
He said magma rising to the surface could be preceded by earthquakes or an "inflation" of the volcano.
"Now there is a vent established it is easier for magma to rise. We would hope we would get warning."
Any larger eruption at Mt Tongariro was likely to be on a relatively small scale, similar to eruptions at Mt Ngauruhoe in the 1970s, he said.
Analysis by Massey University of ashfall taken from Mt Tongariro earlier this week found moderate levels of the potentially toxic chemical fluorine.
Today's tests will shed more light on the eruption.
It will take several days for rocks collected from Mt Tongariro today to be crushed and analysed.
The White Island eruption this week was the first ash emission there since 2001.
Scientists flew over White Island yesterday to monitor the volcano and collect air samples.