A numerical simulation of magma motion, crustal deformation, and seismic radiation associated with volcanic eruptions



The finite difference method is used to calculate the magma dynamics, seismic radiation, and crustal deformation associated with a volcanic eruption. The model geometry consists of a cylindrical reservoir and narrow cylindrical conduit embedded in a homogeneous crust. We consider two models of eruption. In the first model, a lid caps the vent and the magma is overpressurized prior to the eruption. The eruption is triggered by the instantaneous removal of the lid, at which point the exit pressure becomes equal to the atmospheric pressure. In the second model, a plug at the reservoir outlet allows pressurization of only the magmatic fluid in the reservoir before the eruption. Magma transfer between the reservoir and conduit is triggered by the instantaneous removal of the plug, and the eruption occurs when the pressure at the conduit orifice exceeds the material strength of the lid capping the vent. In both models, magma dynamics are expressed by the equations of mass and momentum conservation in a compressible fluid, in which fluid expansion associated with depressurization is accounted for by a constitutive law relating pressure and density. Crustal motions 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. Both models predict the gradual depletion of the magma reservoir, which causes crustal deformation observed as a long-duration dilatational signal. Superimposed on this very-long-period (VLP) signal generated by mass transport are long-period (LP) oscillations of the magma reservoir and conduit excited by the acoustic resonance of the reservoir–conduit system during the eruption. The volume of the reservoir, vent size, and magma properties control the duration of VLP waves and dominant periods of LP oscillations. The second model predicts that when the magmatic fluid reaches the vent, a high-pressure pulse occurs at this location in accordance with the basic theory of compressible fluid dynamics. This abrupt pressure increase just beneath the vent is consistent with observed seismograms in which pulse-like Rayleigh waves excited by a shallow source are dominant. The strength of the lid plays an important role in the character of the seismograms and in defining the type of eruption observed.