ALBERT

Description: In the last decades, the development of the surface and satellite geodetic and geophysical observations brought a new insights into the seismic cycle, documenting new features of inter-, co-, and post-seismic processes. In particular since 2002 satellite mission GRACE provides monthly models of the global gravity field with unprecedented accuracy showing temporal variations of the Earth's gravity field, including those caused by mass redistribution associated with earthquake processes. When combined with GPS measurements, these new data have allowed to assess the relative importance of afterslip and viscoelastic relaxation after the Sumatra 26.12.2004 earthquake. Indeed the observed post-seismic crustal displacements were fitted well by a viscoelastic relaxation model assuming Burgers body rheology for the asthenosphere (60–220 km deep) with a transient viscosity as low as 4  x 10 17 Pas and constant ~10 19 Pas steady state viscosity in the 60–660-km depth range. However, even the low-viscosity asthenosphere provides the amplitude of strain which gravity effect does not exceed 50 per cent of the GRACE gravity variations, thus additional localized slip of about 1 m was suggested at downdip extension of the coseismic rupture. Post-seismic slip at coseismic rupture or its downdip extension has been suggested by several authors but the mechanism of the post-seismic fault propagation has never been investigated numerically. Depth and size of localized slip area as well as rate and time decay during the post-seismic stage were either assigned a priory or estimated by fitting real geodesy or gravity data. In this paper we investigate post-seismic rupture propagation by modelling two consequent stages. First, we run a long-term, geodynamic simulation to self-consistently produce the initial stress and temperature distribution. At the second stage, we simulate a seismic cycle using results of the first step as initial conditions. The second short-term simulation involves three substeps, including additional stress accumulation after part of the subduction channel was locked; spontaneous coseismic slip; formation and development of damage zones producing afterslip. During the last substep post-seismic stress leads to gradual ~1 m slip localized at three faults around ~100-km downdip extension of the coseismic rupture. We used the displacement field caused by the slip to calculate pressure and density variations and to simulate gravity field variations. Wavelength of calculated gravity anomaly fits well to that of the real data and its amplitude provides about 60 per cent of the observed GRACE anomaly. Importantly, the surface displacements caused by the estimated afterslip are much smaller than those registered by GPS networks. As a result cumulative effect of Burgers rheology viscoelastic relaxation (which explains measured GPS displacements and about a half of gravity variations) plus post-seismic slip predicted by damage rheology model (which causes much smaller surface displacements but provides another half of the GRACE gravity variations) fits well to both sets of the real data. Hence, the presented numerical modelling based on damage rheology supports the process of post-seismic downdip rupture propagation previously hypothesized from the GRACE gravity data.

Description: SUMMARY A new mathematical and numerical model is presented for the propagation of a pressure- and buoyancy-driven dyke filled with volatile-saturated magma and a gas cap at its upper part. The model accounts for coupling between conduit flow of a bubbly magma, gas filtration through the magma, gas accumulation in a gas cap and elastic deformation and fracturing of the host rock. All these processes allow studying different regimes of dyke propagation. The rate of propagation of dykes is controlled by the rate of the fracturing at the tip and by the flow rate of magma inside the dyke. When high energy is needed to fracture the host rock and magma viscosity is low, the rate of propagation is controlled by the rate of fracturing (fracture-controlled regime). When the energy to fracture the host rock is low, propagation is controlled by the magma flow rate (magma-controlled regime). We study the transition between these regimes for the case of a constant magma vesicularity and constant mass of gas in the cap. Under these conditions, the propagation of the dyke is self-similar. In the fracture-controlled regime the propagation rate only weakly depends on the amount of the gas in the gas cap, whereas at the magma-controlled regime it is significantly enhanced with increase the mass of gas at the cap. The gas pressure in the cap opens the dyke in front of the magma and allows magma flow rates that are significantly higher than predicted by models that ignore the gas cap. The maximum propagation rate is obtained at the transition between the fracture- and magma-controlled regimes. If the gas mass in the gas cap is high enough, a gas pocket can separate from the magma as a distinct unconnected pocket and propagate as a gas-filled crack at a constant velocity. Pressure decreases during ascent leads to higher vesicularity and faster gas filtration through the magma and into a gas cap. Gradual increase of the mass of gas in the cap is important in accelerating the propagation rate of dykes.

Description: SUMMARY A new mathematical and numerical model is presented for the propagation of a pressure- and buoyancy-driven dyke filled with volatile-saturated magma and a gas cap at its upper part. The model accounts for coupling between conduit flow of a bubbly magma, gas filtration through the magma, gas accumulation in a gas cap and elastic deformation and fracturing of the host rock. All these processes allow studying different regimes of dyke propagation. The rate of propagation of dykes is controlled by the rate of the fracturing at the tip and by the flow rate of magma inside the dyke. When high energy is needed to fracture the host rock and magma viscosity is low, the rate of propagation is controlled by the rate of fracturing (fracture-controlled regime). When the energy to fracture the host rock is low, propagation is controlled by the magma flow rate (magma-controlled regime). We study the transition between these regimes for the case of a constant magma vesicularity and constant mass of gas in the cap. Under these conditions, the propagation of the dyke is self-similar. In the fracture-controlled regime the propagation rate only weakly depends on the amount of the gas in the gas cap, whereas at the magma-controlled regime it is significantly enhanced with increase the mass of gas at the cap. The gas pressure in the cap opens the dyke in front of the magma and allows magma flow rates that are significantly higher than predicted by models that ignore the gas cap. The maximum propagation rate is obtained at the transition between the fracture- and magma-controlled regimes. If the gas mass in the gas cap is high enough, a gas pocket can separate from the magma as a distinct unconnected pocket and propagate as a gas-filled crack at a constant velocity. Pressure decreases during ascent leads to higher vesicularity and faster gas filtration through the magma and into a gas cap. Gradual increase of the mass of gas in the cap is important in accelerating the propagation rate of dykes.

Description: SUMMARY We study the interaction of acoustic pressure waves with an expanding bubbly magma. The expansion of magma is the result of bubble growth during or following magma decompression and leads to two competing processes that affect pressure waves. On the one hand, growth in vesicularity leads to increased damping and decreased wave amplitudes, and on the other hand, a decrease in the effective bulk modulus of the bubbly mixture reduces wave velocity, which in turn, reduces damping and may lead to wave amplification. The additional acoustic energy originates from the chemical energy released during bubble growth. We examine this phenomenon analytically to identify conditions under which amplification of pressure waves is possible. These conditions are further examined numerically to shed light on the frequency and phase dependencies in relation to the interaction of waves and growing bubbles. Amplification is possible at low frequencies and when the growth rate of bubbles reaches an optimum value for which the wave velocity decreases sufficiently to overcome the increased damping of the vesicular material. We examine two amplification phase-dependent effects: (1) a tensile-phase effect in which the inserted wave adds to the process of bubble growth, utilizing the energy associated with the gas overpressure in the bubble and therefore converting a large proportion of this energy into additional acoustic energy, and (2) a compressive-phase effect in which the pressure wave works against the growing bubbles and a large amount of its acoustic energy is dissipated during the first cycle, but later enough energy is gained to amplify the second cycle. These two effects provide additional new possible mechanisms for the amplification phase seen in Long-Period (LP) and Very-Long-Period (VLP) seismic signals originating in magma-filled cracks.