Source parameters of the volcanic eruption earthquakes at Mount Tokachi, Hokkaido, Japan, and a magma ascending model

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Abstract
We estimate the source parameters of the eruption earthquakes observed at Mount Tokachi, Hokkaido, Japan, in 1989, on the basis of the single force model. By fitting the theoretical source spectra with the observed ones, the peak amplitude of force and the source duration were estimated to be 107–1010 N, and 0.5–0.8 s, respectively. For the explosion earthquakes, which have the largest magnitudes among the eruption earthquakes, the peak amplitude of force is proportional to the square of source duration suggesting constant temperature inside the magma just beneath a crater. For small eruption earthquakes, which are small events accompanying weaker eruptions (not explosive), the source duration has a constant value independent of the peak amplitude of force; this suggests that the temperature inside the magma is proportional to the square of radius of the magma body. To give a physical explanation of the empirical relations of source parameters, we present a magma ascending model as a source of eruption earthquakes; a spherical batch of gas‐rich magma vertically migrates from a deep‐seated magma reservoir to the surface and is cooled by heat conduction. When the magma reaches the ground surface, it erupts and causes an eruption earthquake. This model predicts that the ascending magma has a same temperature at the surface when the magma radius exceeds a “critical magma radius” (CMR) which is determined from the physical properties of the magma or volcano. On the other hand, when the magma radius is less than CMR, the temperature increases with the radius. The value of CMR for Mount Tokachi is estimated at about 10 m. Comparing the empirical relations derived from seismic analysis with the magma ascending model, we conclude that the radius of an ascending batch of magma plays an important role in the generation of eruption earthquakes. The magma batch whose radius is larger than CMR causes an explosion earthquake, and the magma smaller than CMR causes a small eruption earthquake.

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