Where do magma chambers exist? Is it necessary that they exist in the asthenosphere where the circumstances of temperature and pressure are suitable for the rocks to be molten? Or they exist in places of shallow depth?
Magma chambers can exist at a range of depths from very deep to very shallow. Only requirement that is really necessary is that there be enough pressure from overlying rock strata to keep the magma chamber from reaching the surface and erupting/exploding. Volcanoes typically represent a slow leak of molten magma. Even large Volcanic eruptions will only expel a fraction of the magma available.
There are several important geological factors that will control the size. location, and depth of a magma chamber:
- Magma buoyancy: Density of the magma (Dissolved gases/liquid and chemical composition vs density of the surrounding host rock.
- Integrity of the overlying host rock: tectonic settings, fault and fracture patterns, how seismically active is the local region.
- Rate of melting: dependent upon source rock composition, heat flow, depth of source material.
Back in the early 1990s, Japanese researchers imagined magma plumes near the lower mantle / outer core boundary.
Here is an article discussion shallow and deep Magma sources for the kilauea, Hawaii. As this article suggests, magma can originate at depth and migrate upward and supply shallow chambers.
Facts on the Yellowstone volcanic complex.