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Isostatic depression is normally associated with glaciation, but can other geologic processes result in similar behavior of the lithosphere? Especially, can the weight of a volcano cause the surrounding lithosphere to sink.

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Yes, they can. Hawaiian Trough is a good example. The impact on thin oceanic crust is naturally larger/faster than on stiff continental crust.

Generally the lithosphere will always respond to load, even if it's sediments, ice or water. The process also works the other way, exhumation by erosion ease the load and cause uplift.

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Absolutely. Lithospheric flexure due to volcanic edifice emplacement is well-documented. Not only do you get isostatic depression near the volcano, but further afield you actually can have uplift due to a "hinging" sort of effect. Lithospheric flexure drives the growth of underwater coral atolls through subsidence at a recently emplaced volcano (coral forms at a fixed depth beneath sea level), but later can lift the same coral above sea level due to far-field volcanic emplacement, turning the underwater atoll into an island. See the seminal work on this by McNutt & Menard (1978).

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