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I'm more curious about the technology behind this survey. How do they do it? What's the range? How high can you be and get a decent result?
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Probably from an four seater airplane about 1 km to 1.5 km above the ground
Your questions depend on a lot of factors. Modern lidar systems usually work with a “return” system (no official name). Imagine you shoot with two lasers at the wall in front of you. One laser travels to the wall and back to you. Another laser has to pass a membrane (or a piece of paper - or leaves of a tree!) so you get two signals back: one deflected by the wall right behind the membrane and one of the membrane itself. Creating the difference you get an overview of what the treetops look like as well as what the ground underneath looks like. You can have an arbitrary amount of return values, more make things more complicated though.

The range depends on wavelength and wattage. In theory you can go up to a few thousand metres, usually you work around 200-1000 m when going airborne. Terrestrial you usually go for less than a hundred meters to have a high point density as well. This also kind of answers the last question: if you go higher, your point density will be lower. In some cases it might make sense, especially if you’re looking at mainly flat surfaces (still, depends on the use case) but in rough terrain you want to digitise you might want to chose a higher point density to replicate real world features more precisely.

Why does one laser go to the wall and the other hit a leaf? Is the idea that you point them at different places?
The laser, depending on the wavelength, is able to penetrate things. In the case of aerial laser scanning it is able to penetrate leaves but not the ground.
Maybe I do not fully understand, what is requested but I think am missing something.

I thought one would like to have a ground profile, _without_ the trees. If one laser penetrates the leaves (and not the ground), why the complicated setup with to laser signals and calculating the difference. The second penetrating would be sufficient.

My bad with explaining. The two laser example was to try to give an easy example and I ended up confusing everyone I guess. You have a single laser (for each wavelength usually). The laser shoots and is being returned (leaf). The same impulse is being returned again but from another surface at a marginally later point in time (the ground). If you would visualise that with common LIDAR software, you would have two points on the same trajectory: one at e.g. 20 m height above zero (ground) and one at 30 m above zero (leaf). You only have a single laser available that penetrates leaves but not ground. I hope that makes it more understandable. English is not my first language as well, so in case you want me to explain something again, I can try again or look up resources in English!
Lidar effectively turns to tradeoffs at different plane heights. You may also be interested in Synthetic Apature Radar which is a satellite technology that is very powerful but takes some knowledge to test the right things and understand the outputs
“The Lost City of the Monkey God” is an absolutely fantastic read if you’re interested in the usage of LiDAR for archeological discovery.
Pfft. Those Olmec and them Maya sure were built on ceremony. Very ceremonious people, excruciatingly. All about ceremony.

Every archeological find seems to be about some type of ceremony.

I wonder where they slept, ate, exercised, hunted, cooked, stored their goods, made their trades, and schooled their young though. Ceremoniously, no doubt.