Elastic energy release in great earthquakes and eruptions

*Correspondence: Agust Gudmundsson, Department of Earth Sciences, Royal Holloway University of London, Queen’s Building, Egham TW20 0EX, UK e-mail: rock.fractures@ googlemail.com The sizes of earthquakes are measured using well-defined, measurable quantities such as seismic moment and released or 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 dU = −pedVc. 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. Then the decrease in chamber volume during the eruption corresponds roughly to the associated volume of erupted materials Ver and the elastic energy is Uer = peVer . 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 1019 J. For comparison, the seismic moment of the largest earthquake ever recorded, the M9.5 1960 Chile earthquake, is estimated at 1023 J and the associated elastic energy release at 1019 J. Thus, the largest eruptions release elastic energy of the same order of magnitude as the largest earthquakes, suggesting that 1019 J may be close to the maximum elastic energy that is available for driving earthquakes and volcanic eruptions.