Source mechanisms of volcanic explosion earthquakes: single force and implosive sources

Volcanic explosion earthquakes accompanying explosive eruptions are viewed as representing an abrupt release of pressurized magma beneath a volcano through a vent. I examine the source mechanisms of explosion earthquakes assuming two extreme cases of magma property. When magma is assumed to be a perfect gas which migrates upward isentropically through a vent acting as a nozzle, the seismic source is expressed as a single force. On the other hand, when magma flow is assumed to be incompressible, an implosive source is dominant. Both source models predict that the seismic magnitude is proportional to the cross-sectional area of the vent. I investigate observed seismic magnitudes for different volcanoes based on data in published papers and reports. The results show that the seismic magnitude of the largest event for each volcano is essentially proportional to the cross-sectional area of the vent for vent radii ranging from 10 to 600 m. The consistency found between the theoretical prediction and the observed relation suggests that the vent area plays a substantial role in the magnitude of explosion earthquakes. I further estimate that initial pressures in the reservoir are of the order of a few MPa, with a one order of magnitude uncertainty based on the single force model. I also apply the implosive source model to the observed seismic magnitudes and estimate the product of bulk modulus of magma and flow velocity to be 10¹⁰–10¹¹ J/m² s.