Michele Dragoni

Displacement and stress produced by a pressurized, spherical magma chamber, surrounded by a viscoelastic shell

Abstract Theoretical arguments and petrological observation indicate that magma chambers are surrounded by a thermal metamorphic shell. Owing to their higher temperature, the rocks of this shell have mechanical behaviour different from that of the cooler, more distant crustal rocks. This situation is represented by a model in which a spherical magma chamber is surrounded by a viscoelastic shell. The shell is elastic dilatational and Maxwell deviatoric; outside, the medium is elastic. Displacement and stress fields outside the magma chamber are calculated analytically, assuming that the chamber is internally pressurized, with different source functions. The model illustrates some time-dependent effects which are a result of the presence of the viscoelastic shell: amplification of displacement in the surrounding medium, relaxation of shear stress within the shell and stress concentration outside it. These phenomena may be relevant to the interpretation of some aspects of the ground deformation and induced seismicity, which were observed in the Campi Flegrei volcanic area, Italy, during the period 1982–1984.

Downslope flow models of a Bingham liquid: Implications for lava flows

It is widely recognized that lavas behave as Bingham liquids, which are characterized by a yield stress σϒ and a plastic viscosity η. We consider two models describing downslope flows of a Bingham liquid with different aspect ratios A (= flow height/flow width): model 1 with A ⪡ 1 and model 2 with A ≈ 1. Sufficiently uphill with respect to the front, such flows can be considered as laminar and locally isothermal. For both models, we obtain analytically the steady-state solution of the Navier-Stokes equations and the constitutive equation for a Bingham liquid. We study the flow height and velocity as functions of flow rate, rheological parameters and ground slope. It is found that such flows remain in the Newtonian regime at low yield stresses (σϒ ⪅ 103dyne/cm2), but the transition to the Bingham regime also depends on flow rate and occurs at higher values of σϒ for higher flow rates: for instance, a high aspect ratio flow (model 2) is still very close to the Newtonian regime at σϒ = 104 dyne/cm2, if the flow rate is greater than 105 g/s. In the Bingham regime, flow heights are generally greater and flow velocities are smaller than in the Newtonian regime; moreover, flow heights are independent of flow rate, so that a change in flow rate results exclusively in a velocity change. After assuming a specific temperature dependence of σϒ and η between the solidus and the liquidus temperatures of an ideal Bingham liquid (1000°C and 1200 °C respectively), flow heights and velocities are examined as functions of temperature along the flow. Several effects observed in lava flows are predicted by these models and allow a more quantitative insight into the behaviour of lava flows.

A dynamical model of lava flows cooling by radiation

The behaviour of a lava flow is reproduced by a two-dimensional model of a Bingham liquid flowing down a uniform slope. Such a liquid is described by two rheological parameters, yield stress and viscosity, both of which are strongly temperature-dependent. Assuming a flow rate and an initial temperature of the liquid at the eruption vent, the temperature decrease due to heat radiation and the consequent change in the rheological parameters are computed along the flow. Both full thermal mixing and thermal unmixing are considered. The equations of motion are solved analytically in the approximation of a slow downslope change of the flow parameters. Flow height and velocity are obtained as functions of the distance from the eruption vent; the time required for a liquid element to reach a certain distance from the vent is also computed. The gross features of observed lava flows are reproduced by the model which allows us to estimate the sensitivity of flow dynamics to changes in the initial conditions, ground slope and rheological parameters. A pronounced increase in the rate of height increase and velocity decrease is found when the flow enters the Bingham regime. The results confirm the observation according to which lava flows show an initial rapid advance, followed by a marked deceleration, while the final length of a flow is such that the Graetz number is in the order of a few hundreds.

The effect of crystallization on the rheology and dynamics of lava flows

Abstract The dynamics of a lava flow is studied by a two-dimensional model describing a viscous fluid with Bingham rheology, flowing down a slope. The temperature in the flow is calculated assuming that heat is transferred through the plug by conduction and is lost by radiation to the atmosphere at the top of the flow. Taken into account is that the increasing crystallization takes place in the flow as a consequence of cooling. The lava viscosity and yield stress are expressed as a function of crystallization degree as well as of temperature: in particular it is assumed that yield stress reaches a maximum value above the solidus temperature, according to experimental data. Dynamical variables, such as velocity and thickness of the flow, are calculated for different values of the maximum crystallization degree and the flow rate. The model shows how the lava flow dynamics is affected by cooling and crystallization. The cooling of the flow is controlled by the increase of yield stress, which produces a thicker plug and makes the heat loss slower. The increasing crystallization has two opposing effects on viscosity: it produces an increase of viscosity, but at the same time produces an increase of yield stress and hence reduces the heat loss and keeps the internal temperature high. As a consequence, lava flows are significantly affected by the dependence of yield stress on temperature and scarcely by the maximum crystallization degree.

A model for the formation of lava tubes by roofing over a channel

The formation of lava tubes is a common phenomenon on some basaltic volcanoes, such as Etna. A model for tube formation by roofing of a channel is proposed and involves first describing lava as a Bingham liquid flowing down a slope. It is further assumed that lava flows in a channel with rectangular cross section: as a result of heat loss into the atmosphere, a crust is gradually formed on the upper surface of the flow and this crust eventually welds to the channel levees. We assume that a lava tube is formed when such a crust is sufficiently thick to resist the drag of the underlying flow and to sustain itself under its own weight. The minimum thickness of the crust satisfying such conditions depends on the tensile strength and shear strength of the crust itself. Assuming that the growth of the crust produces a downflow linear increase of the shear stress at the interface between flowing lava and the crust, the distance is evaluated between the eruption vent and the point where the tube is formed. The model predicts that if the flow rate is constant, the thickness of the flow increases as the crust fragments grow and weld to each other, and the velocity of the crust decreases to zero. Once the lava tube is formed, the initial flow rate can be achieved by a flow thickness smaller than the vertical size of the tube, with the same viscous dissipation: this may explain why under steady state conditions, the lava level inside a tube is frequently lower than the roof of the tube itself.

A three‐dimensional Bingham model for channeled lava flows

We propose a three-dimensional (3-D) Bingham model for channeled lava flow. Unlike from the 3-D Newtonian models, this model can be applied also far from the vent where the Bingham rheology cannot be neglected as a consequence of the lava cooling. We assume the lava to be an isothermal Bingham liquid flowing in a rectangular channel down a constant slope. The flow velocity is calculated by solving semianalytically the steady state Navier-Stokes equation together with the 3-D Bingham constitutive equation. The flow vorticity is evaluated and used to define the plug shape and position for different flows: a completely filled conduit, a partially filled conduit, and an open channel. Each component of the flow vorticity vector satisfies the Laplace equation and has been evaluated by using the relaxation method. The mass flow rate is evaluated for different values of the yield stress; it appears that the Bingham rheology causes a significant reduction in flow rate as the yield stress increases. For the highest yield stress values the plug in the center of the flow welds with the plugs in the flow corners, suggesting a possible rheological mechanism for the lava tube formation.

Longitudinal deformation of a lava flow : the influence of Bingham rheology

Abstract The behaviour of a lava flow is reproduced by a two-dimensional model of a Bingham liquid flowing down a slope. The liquid is described by two parameters, viscosity and yield stress, both strongly temperature dependent. Assuming liquidus temperature at the eruption vent, the temperature decrease due to the heat loss by radiation produces changes in the rheological parameters and, consequently, in velocity, strain and strain rate along the flow. Velocity, compressive strain, strain rate and stress along the flow direction are computed as functions of the distance from the vent and of time, for different kinds of lava flows (basic and acidic) and are compared with corresponding results for a Newtonian liquid. The model shows that, in connection with the pronounced velocity decrease occurring at a certain distance from the vent, the compressive strain, strain rate and stress also show a strong variation. A greater compressive strain is, in fact, induced in a Bingham flow cooling by radiation, than in a Newtonian flow. This behaviour may explain the presence of folds which are commonly observed at the surface of cooled lava flows.

Evaluation of stresses in two geodynamically different areas: Stable foreland and extensional backarc

Areas which are geodynamically different have different behaviors both in their thermal regime and seismic activity. A stable area has a geotherm which can be considered as standard, extensional and compressional areas have, respectively, high and low temperature gradients. The Italian region includes different geodynamical areas and all such situations are present. We consider the Apulian platform as an example of a stable area and the Tuscany-Latium as an example of an extensional area. For both of them the present geotherms are calculated, taking into account, for the Tuscany-Latium, its thermal history. Assuming that each region is subject to a constant strain rate, the stresses are calculated as functions of depth and time. The rheological behavior is assumed to be linear viscoelastic, with viscosity dependent on temperature and elastic parameters dependent on lithology. The geothermal profile and the rheological structure of the lithosphere remarkably affect the processes of stress accumulation which control the distribution of seismic activity. The abrupt decrease of the temperature gradient at the Moho produces considerably higher stress values with respect to the case of uniform gradient, thus favoring subcrustal seismicity. In the case of a standard temperature gradient, subcrustal seismicity is predicted and a gap in seismicity, indicating a soft intracrustal layer, exists if there is a discontinuity in rheology. By contrast, in the case of a high-temperature gradient, subcrustal seismicity is not to be expected, even in the presence of a discontinuity in rheology, since subcrustal temperatures are already too high to permit a sufficient stress accumluation.

Rheological consequences of the lithospheric thermal structure in the Fennoscandian Shield

Abstract The surface heat-flow density of the Fennoscandian Shield, after removing the disturbances due to palaeoclimatic changes, shows a remarkable contrast from the Archaean terrains to the Late Proterozoic provinces which derive from tectonic reactivation and reheating of older materials. This involves lateral variations in the rheological behaviour of the lithosphere. On the basis of seismic structural data and assumptions about the petrological composition and flow parameters of steady-state dislocation creep, strength profiles and lateral viscosity variations have been deduced for several sites. In the northern and northeastern parts of the shield, where the Moho temperature and mantle heat-flow density are typically cratonic, the rheological thickness of the lithosphere, given by the depth at which the strength is reduced to 1 MPa, ranges from 120 to 140 km. In the southwestern shield, were enhanced Moho temperatures and mantle heat-flow density occur, the rheological thickness is reduced to 60–80 km. The depth of the brittle-ductile transition in the upper crust, above which most earthquakes occur, varies on average from 30 km in the northeast to 18 km in the southwest. The limiting temperature of the brittle uppermost layer on average is 365 ± 70°C. The essentially aseismic behaviour of the mantle agrees with the subcrustal predominating ductile deformations predicted by the models. The average lithospheric strength falls within the range 70–200 MPa, typical of the older stable areas. The viscosity of the upper mantle, at a reference depth level of 60 km, ranges from 10 21 to 10 24 Pa s and increases with the geological age, being maximum beneath the Archaean nucleus.

Asperity distribution of the 1964 Great Alaska earthquake and its relation to subsequent seismicity in the region

Abstract The 1964 Alaska earthquake was the second largest seismic events in the 20th century. The aim of this work is the use of surface deformation data to determine asperity and slip distributions on the fault plane of the Alaska earthquake: these distributions are calculated by a Monte Carlo method. To this aim, we decompose the fault plane in a large number of small square asperity units with a side of 25 km; this allows us to obtain plane surfaces with an irregular shape. In the first stage, each asperity unit is allowed to slip a constant amount or not to slip at all, providing the geometry of the dislocation surface that best reproduces the observed displacements. To this purpose, a large number of slip distributions have been tried by the use of the Monte Carlo method. The slip amplitude is the same for all the asperities and is equal to the average fault slip inferred from the seismic moment. In the second stage, we evaluate the slip distribution in the dislocation area determined by the Monte Carlo inversion: in this case, we allow unit cells to undergo different values of slip in order to refine the initial dislocation model. The results confirm the previous finding that the slip distribution of the great Alaska earthquake was essentially made of two dislocation areas with a higher slip, the Prince William Sound and the Kodiak asperities. Analysis of the post-1964 seismicity in the rupture region shows a strong correlation between the larger earthquakes (Mw≥6) and the distribution of locked asperities following the 1964 event, which can be considered as an independent test of the validity of the model. We do not find slip values higher than 25 m for any of the patches, and we determine two separate high-slip zones: one correspondent to the Prince William Sound asperity, and one (∼18 m slip) to the Kodiak asperity. The slip distribution connected with the 1964 shock appears to be consistent with the following seismicity in the region.