The severe dryness of the lunar surface should make this possible for orbiting radar. To provide deep radar imaging, the antenna diameter must be four times the radar wavelength being used. That's a lot of mass to put into orbit along with the ancillary equipment.
Billings suggests a way out.
Readings from a number of smaller antennas in an interferometer array can substitute, synthesizing an image. It will be tricky to do this in orbit, and an intercontinental interferometer is an option. Using a 7-meter wavelength, you'd have a 250 meter resolution and a penetration of 70 meters, good enough to detect a convincing sample, given that many tubes are likely to be larger than this. However, a considerable amount of power will be needed if the signal returning to Earth is to be detectable. Computer algorithms needed to sift signal from noise are getting better.