A Numerical Simulation of Magma Motion and Seismic Wave Radiation Associated with a Volcanic Eruption

We apply the finite difference method to calculate the magma motions and seismic wave radiation associated with a volcanic eruption. Our model consists of a cylindrical reservoir and narrow cylindrical conduit embedded in a homogeneous crust. A lid caps the vent and a plug blocks the flow of magma between the chamber and conduit. The magma reservoir is overpressurized prior to the eruption. The sudden removal of the plug triggers the transfer of magma from the chamber to the conduit, and an eruption occurs when the pressure at the conduit orifice exceeds the strength of the lid capping the vent. The exit pressure remains fixed to the atmospheric pressure throughout the eruption. Magma dynamics is expressed by the equations of mass and momentum conservations in a compressible fluid, in which the vesiculation process associated with depressurization is accounted for by a constitutive law relating pressure and density. Seismic waves are calculated from the equations of elastodynamics. The fluid and solid are dynamically coupled by applying the continuity of wall velocities and normal stresses across the conduit and reservoir boundaries. Free slip is allowed at the fluid-solid boundary. Our numerical simulations show that (1) the removal of the plug generates a compression wave which propagates up the conduit, and a rarefaction wave which propagates into the chamber; (2) a high-amplitude pressure pulse occurs at the lid when the magma impinges the lid, causing the failure of the lid; (3) the magma reservoir gradually deflates, and (4) superimposed on the reservoir deflation are decaying long-period oscillations caused by acoustic resonance in the reservoir. Magma motions are detected as (1) seismic signals prior to an eruption; (2) large-amplitude Rayleigh waves excited by the rupture of the lid; and (3) a gradual subsidence of the crust and (4) periodic oscillations of the seismic waves. These characteristics of the simulated seismic wave field are often observed at volcanoes such as Sakurajima, Tokachi, and Popocatepetl. The strength of the lid plays an important role in shaping up seismic waveforms associated with Vulcanian eruptions.