Elastic energy release in great earthquakes and eruptions - Gudmundsson, Agust (Frontiers in Earth Science, 2014)
The sizes of earthquakes are measured using well-defined, measurable quantities such as seismic moment and released (transformed) elastic energy. No similar measures exist for the sizes of volcanic eruptions, making it difficult to compare the energies released in earthquakes and eruptions. Here I provide a new measure of the elastic energy (the potential mechanical energy) associated with magma chamber rupture and contraction (shrinkage) during an eruption. For earthquakes and eruptions, elastic energy derives from two sources: (1) the strain energy stored in the volcano/fault zone before rupture, and (2) the external applied load (force, pressure, stress, displacement) on the volcano/fault zone. From thermodynamic considerations it follows that the elastic energy released or transformed (dU) during an eruption is directly proportional to the excess pressure (pe) in the magma chamber at the time of rupture multiplied by the volume decrease (-dVc) of the chamber, so that . This formula can be used as a basis for a new eruption magnitude scale, based on elastic energy released, which can be related to the moment-magnitude scale for earthquakes. For very large eruptions (>100 km3), the volume of the feeder-dike is negligible, so that the decrease in chamber volume during an eruption corresponds roughly to the associated volume of erupted materials , so that the elastic energy is . Using a typical excess pressures of 5 MPa, it is shown that the largest known eruptions on Earth, such as the explosive La Garita Caldera eruption (27-28 million years ago) and largest single (effusive) Colombia River basalt lava flows (15-16 million years ago), both of which have estimated volumes of about 5000 km3, released elastic energy of the order of 10EJ. For comparison, the seismic moment of the largest earthquake ever recorded, the M9.5 1960 Chile earthquake, is estimated at 100 ZJ and the associated elastic energy release at 10EJ.