Is there a meaningful concept of a mountain having a footprint area?

Question

Is there a meaningful way to delimit a mountain as an area with a sharp boundary? Looked as as a 2D shape on the datum it would be a footprint of the mountain similar to a building footprint, while as a region cut out of the surface it would delimit the surface of the mountain from surface that is not port of the mountain.

Obviously there's going to be some degree to which this is arbitrary but it seems like some function of slope, aspect, elevation etc ought to be able to produce some meaningful partition of the earth's surface. I would like to know if any concept like this is used at all, how it's defined, and how well it corresponds with the intuitive sense of one point being part of a mountain, another point being part of a different mountain, and a third point not being part of any mountain. If it's just completely unworkable despite the intuitive appeal, then a reasonable explanation of why is an acceptable answer.

Answer 1

The mountain you see is only a part of the story. From a geological view all mountains have roots, in which the weight of the mountain depresses the upper crust into the lower crust (occasionally with gravity inversion, as in salt diapirs), and the overall crust is depressed into the upper mantle. This results in a regional gravity anomaly which could be regarded as one form of the mountain footprint. That is, a map of the deviation of the mountain's 'Bouguer anomaly', away from the regional gravitational envelope. But that's just a geophysical perspective. You could doubtless develop comparable 'footprint definitions' from a hydrologic or geomorphologic perspective.