There have been many studies on hfunderground antennae, most from a military/civil defense aspect. The cheapest yet most effective will likely be made from solid center insulator coax like rg8, with the shield removed, the farther the earth is from the wire the less loss so insulator thickness comes into play but keep in mind these studies more or less were looking at transmit and receive characteristics, not reception alone. Also note that being below ground causes the velocity factor to be altered from normal, so less "antenna" is required to meet a specific freq characteristic if that is desired.
As you likely suspect, the deeper it's buried the more losses increase. A few inches is good for emp resistance, the shallower the better if all you care about is being able to mow over it, some folks just pin a insulated wire to the ground and let the thatch grow over it, no burial needed. Kinda like those dog fences.
I've a arrl antenna handbook that has excerpts from a fedgov study where various hf antennas were utilised deep inside an abandoned mine, and the results were promising. In the same article was noted a great signal increase on 80m for a vehicle traveling thru a deep rock canyon, apparently the canyon acted as a slot antenna. Neat stuff!
https://apps.dtic.mil/dtic/tr/fulltext/u2/783274.pdf