Seismic waves decay as they radiate away from their sources, partly for geometric reasons because their energy is distributed on an expanding wave front, and partly because their energy is absorbed by the material they travel through. The energy absorbtion depends on the material properties. When the temperature approaches the melting temperature the absorption increases. Molten material does not support S-waves at all and P-waves are highly attenuated. Molten volumes such as the Earth´s core or volcanic magma chambers cast an S-wave shadow and P-waves are delayed by them. If S-waves traverse a crustal volume it can be concluded that it does not contain a sizeable magma chamber. Shallow-level magma chambers have been confirmed by these methods beneath the volcanoes Krafla and Katla. Conversely, it can be shown that a significant magma chamber does not exist beneath Hekla at shallowerlevel than 10-14 km.
Figure from the paper by Heidi Soosalu and PállEinarsson (2004) showing the raypaths of S-waves in the crust beneath Hekla. It can be concluded that a magma chamber does not presently exist in the depth range 4-10 km beneath the volcano.
Recent publications of the Institute of Earth Sciences on this topic:
Soosalu, H., P. Einarsson (2004). Seismic constraints on magma chambers at Hekla and Torfajökull volcanoes, Iceland. Bull. Volcanol., 66, 276-286, DOI: 10.1007/s00445-003-0310-1.
Ólafur Guðmundsson, Bryndís Brandsdóttir, William H. Menke and Guðmundur E. Sigvaldason. The crustal magma chamber of the Katla volcano in south Iceland revealed by seismic undershooting. Geophys. J. Int., 119, 277-296, 1994.
Bryndís Brandsdóttir and William H. Menke (1992). Thin low-velocity zone within the Krafla caldera, NE-Iceland attributed to a small magma chamber. Geophys. Res. Lett., 19, 2381-2384.