Melt migration in deformable media

Extraction of melt from partial melts in the Earth's interior requires both permeability and deformability of the solid matrix. With the aid of simple macroscopic analogs, including laboratory experiments, we show how creep deformation of the matrix can be incorporated in Darcy's Law, leading to a quantitative assessment of how matrix compaction governs melt extraction. The most striking consequence of the resulting theory is the prediction of magmons: well-preserved, solitary waves of enhanced partial melt with wavelengths ~ kilometer. These vertically propagating waves might exist in the Earth's mantle, causing episodicity in space and time of volcanic activity. However, geophysical and geochemical evidence remain elusive.