Bulletin of Volcanology

, Volume 74, Issue 4, pp 873–880

Magma convection and mixing dynamics as a source of Ultra-Long-Period oscillations


    • Istituto Nazionale di Geofisica e VulcanologiaSezione di Pisa
  • Paolo Papale
    • Istituto Nazionale di Geofisica e VulcanologiaSezione di Pisa
  • Melissa Vassalli
    • School of Geological SciencesUniversity College Dublin
  • Gilberto Saccorotti
    • Istituto Nazionale di Geofisica e VulcanologiaSezione di Pisa
  • Chiara P. Montagna
    • Istituto Nazionale di Geofisica e VulcanologiaSezione di Pisa
  • Andrea Cassioli
    • Dipartimento di Sistemi e InformaticaUniversità di Firenze
  • Salvatore Giudice
    • Istituto Nazionale di Geofisica e VulcanologiaSezione di Pisa
  • Enzo Boschi
    • Istituto Nazionale di Geofisica e Vulcanologia
Research Article

DOI: 10.1007/s00445-011-0570-0

Cite this article as:
Longo, A., Papale, P., Vassalli, M. et al. Bull Volcanol (2012) 74: 873. doi:10.1007/s00445-011-0570-0


Many volcanic eruptions are shortly preceded by injection of new magma into a pre-existing, shallow (<10 km) magma chamber, causing convection and mixing between the incoming and resident magmas. These processes may trigger dyke propagation and further magma rise, inducing long-term (days to months) volcano deformation, seismic swarms, gravity anomalies, and changes in the composition of volcanic plumes and fumaroles, eventually culminating in an eruption. Although new magma injection into shallow magma chambers can lead to hazardous event, such injection is still not systematically detected and recognized. Here, we present the results of numerical simulations of magma convection and mixing in geometrically complex magmatic systems, and describe the multiparametric dynamics associated with buoyant magma injection. Our results reveal unexpected pressure trends and pressure oscillations in the Ultra-Long-Period (ULP) range of minutes, related to the generation of discrete plumes of rising magma. Very long pressure oscillation wavelengths translate into comparably ULP ground displacements with amplitudes of order 10−4–10−2 m. Thus, new magma injection into magma chambers beneath volcanoes can be revealed by ULP ground displacement measured at the surface.


Magma dynamicsMagma convectionMagma mixingULP ground displacement


Various volcanic eruptions have been shortly preceded by injection of new magma into a magma storage region at shallow depth (<10 km), triggering mixing and convection a few hours to weeks before eruption onset (e.g., Bateman 1995; Folch and Marti 1998; Snyder 2000). Early recognition of signals from monitoring networks, diagnostic of ongoing magma convection and mixing in shallow magmatic systems, is therefore critical for developing reliable early-warning systems and forecasting of short-term volcanic hazard.

Although it is a critical precursor of hazardous events, shallow magma chamber replenishment cannot be directly observed. Analysis of records from volcano monitoring networks can in principle reveal such replenishment, but to-date there is no established method for identifying the signal of magma injection.

Recent progress in volcano monitoring worldwide is providing unprecedented observation of small amplitude ground oscillations with Ultra-Long-Periods (ULP) of hundreds of seconds, preceding and accompanying visible volcanic activity (Voight et al. 2006; Houlì and Montagner 2007; Sanderson et al. 2010). There is a general consensus on the relevance and potential usefulness of such signals for understanding the underground magma dynamics and forecasting the short-term volcanic hazard. However, the lack of a generally accepted theoretical background describing the generation of ULP signals at active volcanoes represents a severe limitation to both their interpretation and use into civil protection-oriented procedures. This work provides that theoretical background, showing through numerical simulations that magma convection and mixing dynamics following the arrival of new magma at shallow depths produce ULP ground displacements observable at the surface.

Numerical modeling

The numerical simulations of magma reservoirs and country rocks solve magma fluid dynamics and rock solid dynamics, with appropriate conditions at the magma–rocks interface. The fluid dynamics simulations need robust, stabilized methods to solve the strongly nonlinear system of conservation equations closed with constitutive equations for the physical properties of the fluid. In this work, simulations are performed with GALES (Longo et al. 2006), a stabilized finite element parallel C++ code solving mass, momentum, and energy equations for multicomponent homogeneous gas–liquid (± crystals) mixtures. Code validation analysis includes several cases from the classical engineering literature, corresponding to a variety of subsonic to supersonic, one-component to multicomponent gas–liquid flow regimes.

The multicomponent nature of GALES allows modeling magma dynamics as they result from the mixing of compositionally diverse magmas. Magma properties and gas–liquid phase distribution, gas composition, and liquid–gas density and viscosity, are computed as a function of the local P-T-X conditions, by employing composition-dependent modeling and parameterizations (Papale 2001; Papale et al. 2006; Giordano et al. 2008). Non-Newtonian behavior of multiphase magma at high strain rates, which can be relevant during the rapid ascent of magma along volcanic conduits and fissures (Caricchi et al. 2007; Costa et al. 2009; Giordano et al. 2010), is not accounted for.

Determining the time–space-dependent ground displacement requires modeling the magma–rocks boundary conditions and the mechanical response of rocks, the latter depending on heterogeneous rock properties, presence and distribution of faults, interfaces, fluids, and volcano topography (e.g., O’Brien and Bean 2004). A first-order analysis performed here assumes magma–rock one-way coupling and adopts the Green’s functions formulation for a homogeneous, infinite medium (Aki and Richards 2002). In this process, we consider as point sources the fluid dynamics computational grid nodes located at the reservoir walls. As source time functions, we use the respective temporal evolutions of magmatic forces computed from pressures and stresses provided at those nodes by the numerical simulations of magma convection and mixing dynamics. Ground displacement at a series of virtual receivers is finally obtained by integrating, over all sources, the Green’s functions associated with individual sources. Such a one-way coupling and homogeneous rocks assumption are a-posteriori justified by the extremely long wavelength, of the order of hundreds of kilometers, associated with ULP pressure oscillations.

Numerical simulations

Numerical simulations are performed with reference to the two volcanoes Etna and Campi Flegrei in Southern Italy. These volcanoes offer a large literature on eruptive styles and magma compositions, along with recent reconstructions of the present state of the magmatic system and characteristics of country rocks. A range of magma compositions (reported in Table 1) from basalt (Etna) and basalt to shoshonite (Campi Flegrei) is involved. The employed total volatile contents (Spilliaert et al. 2006; Mangiacapra et al. 2008) span the range 1.5–3.5 wt.% for H2O and 0.5–2 wt.% for CO2. Larger volatile contents are carried by the magma coming from depth, according to open-system degassing at shallow volcanic depths (Wallace and Anderson 2000). Deep magmas are therefore expected to be buoyant in shallower, partially degassed magmas (Longo et al. 2006), giving origin to processes governed by magma convection and mixing.
Table 1

Composition of magmas employed in the numerical simulations


Mount Etna

Mount Etna

Campi Flegrei

Campi Flegrei


Shallow (basalt)

Deep (basalt)

Shallow (shoshonite)

Deep (basalt)
























































Numbers are wt%. FeO is total iron as reduced component

Data from Andronico et al. (2005), Mangiacapra et al. (2008), and references therein. H2OT and CO2T indicate total water and carbon dioxide, respectively, including the amount dissolved in the liquid and that exsolved in the co-existing gas phase

The magmatic simulation domains and initial conditions are shown in Fig. 1, and represent a 2D, Cartesian, simplified picture consistent with the bulk knowledge from geochemical, petrological, seismological, and geodetical studies (Carbone et al. 2006; Spilliaert et al. 2006; Aiuppa et al. 2007; Corsaro et al. 2007; Lokmer et al. 2008; Mangiacapra et al. 2008; Patanè et al. 2008; Zollo et al. 2008; Arienzo et al. 2010; Di Renzo et al. 2011). Common elements in the two domains are the presence of one or more chambers as well as of a feeding dyke and the existence of an initial gravitationally unstable interface between two compositionally different magmas.
Fig. 1

System definition, and initial and boundary conditions for the numerical simulations. Note the difference in scale of the two domains. a Mount Etna case, compositions from the 2002–2003 eruption. The width of the two shallow dykes is 10 m. b Campi Flegrei case. Compositions are a shoshonite (shallow magma) and a basalt (deep magma). Compositions for the Mount Etna and Campi Flegrei simulations are reported in Table 1. Total volatile contents are reported in Fig. 1. Temperatures are 1,400 K (Etna) and 1,433 K (Campi Flegrei)

The two domains significantly differ in terms of their size, geometrical complexity, depth/pressure range, employed magma compositions and corresponding physicochemical properties, and for the resulting density contrast at the interface between the two magma types (see Fig. 1). An overpressure corresponding to 1 MPa is imposed as boundary condition at system bottom in the Etna case to include a forcing component to natural convection as due to thrust from deep magma. The Campi Flegrei case corresponds instead to pure natural convection (no overpressure at system bottom).

In order to reduce the computational challenges, the present simulations assume constant magma temperature and neglect dispersed solid phases (crystals). Initial conditions are determined by lithostatic load at system roof (average rock density 2,500 kg/m3), zero velocity everywhere, magma-static pressure distribution and corresponding gas–liquid partition computed with non-ideal composition-dependent modeling (Papale et al. 2006), also employed in run time to provide the gas–liquid partition of volatile species H2O and CO2 as a function of local pressure, temperature, and composition. Free inflow/outflow of magma is allowed at domain bottom and no slip conditions are assumed at solid boundaries.

Magma mixing is accounted for by weighting the local properties on those of the end-member magmas based on local proportions. This approximates mechanical mingling, appropriate for the relatively short time scale of the simulations (order of hour) and grid size range (from 0.2 to 10 m, resulting in order 105 computational elements in each simulation). A time resolution of 0.01 s is employed, after having verified numerical stability in a preliminary set of test simulations.

Continuity of pressure and stress is taken as the boundary condition along the nonmoving magma–rock interface. Physical properties of rocks are homogeneous averages that describe the volcanic edifices within the range of considered depth (<10 km, vp = 3,000 m/s; vp/vs = 1/√3, ρ = 2,500 kg/m3).

The real characteristics of the magmatic systems and volcanic edifices, although scarcely known in further detail, are expected to be substantially more complex. The simulations therefore should be regarded as a first-order characterization of the processes and dynamics associated with the arrival of buoyant magma into a pre-existing reservoir at constant fluid system domain volume.


The numerical results pertaining to magma dynamics are summarized in the color plots of Fig. 2. Movies showing the time–space distribution of composition, pressure, and gas volume fraction are provided as Online Resources 16. Total simulated times correspond to nearly 30 (Etna) and 170 (Campi Flegrei) min of real time.
Fig. 2

Simulated dynamics at three different times. a–c Mount Etna case, d–f Campi Flegrei case. The color plots representing the evolution of magma composition refer to the areas identified by the boxes on the left. Note (from comparison with Fig. 1) that the scale of the two domains is very different. Movies showing the time evolution of composition, pressure, and gas volume fraction for both the Mount Etna and Campi Flegrei cases are given in Online Resources from 1 to 6

Initially, the interface between the two magma types is perturbed by buoyancy and, for Mount Etna, by pressure forces. After about 20 s (Etna) and 70 s (Campi Flegrei) a plume of buoyant magma starts to develop. The density difference between the head of the plume and the surrounding magma progressively increases as the plume moves up towards regions characterized by lower pressure. As a consequence, plume buoyancy progressively increases, enhancing plume expansion and acceleration. The vertical motion of the rising plume is disturbed by the formation of a series of vortexes that favor further magma mixing. Subsequent plumes give origin to small buoyant magma batches interacting with each other, further enhancing mixing between the incoming magma and the magma originally residing in the chamber.

In the Etna case, plume rise and expansion cause magma pressure increase in the chamber up to a maximum of 1.5 MPa after about 60 s (Fig. 3). Sinking of dense magma into the feeding dyke, favored by chamber pressure increase, reduces the mass in the chamber and consequently the local pressure. Intense mixing of volatile-rich and volatile-poor magmas takes place in the feeding dyke, where compression by the sinking magma results in magma pressure increase. As a consequence of mixing at dyke level, no pure deep magma component enters the chamber after a very short initial phase. Alternating phases dominated by buoyancy and sinking at chamber inlet result in ULP pressure fluctuations with a period of about 110 s and amplitude decreasing with time (Fig. 3). The progressive substitution of the original denser magma by lighter buoyant magma leads to overall chamber pressure decrease, by a maximum of −2 MPa after about 25 min.
Fig. 3

Pressure variations as a function of time. The location of the reported pressure variations is indicated by the red points in the left schemes of Fig. 1. a Mount Etna case, b Campi Flegrei case. In both panels, the upper diagram shows the difference between the local pressure at current time and at time zero, while the bottom diagram shows the same quantity after subtraction of a detrending function (red curve in the upper diagrams)

The simulation pertaining to Campi Flegrei (Figs. 2 and 3) shows similar general dynamics, with discrete buoyant batches of volatile-rich, lighter-mixed magma rising and expanding into the chamber, where further mixing with the resident magma takes place. The pressure change after the first 30 min is about 1 order of magnitude smaller than in the Etna case, likely due to much larger chamber size therefore more mass of new magma required to cause comparable pressure changes. However, once a substantial pressure increase is produced, ULP oscillations appear, this time with longer period of about 330 s. The amplitude of pressure oscillations is 1 order of magnitude lower than for the Etna case, with no damping emerging up to the maximum simulated time. The overall pressure change in the chamber is about −0.5 MPa, about 1/4 of that for the Etna case in less than 1/6 time. A trend towards overall pressure decrease emerges, superimposed to an extremely long-period oscillation over a time scale comparable with that of the simulation. Over the nearly 3 h of simulated time a volatile-rich mixture of basalt and shoshonite accumulates close to the chamber roof, giving origin to a stratified reservoir.

The elastodynamic simulations reveal that the computed ULP pressure oscillations, originated by the ingression of buoyant magma in the magma chamber, translate into comparably ULP ground displacement dynamics with amplitudes of millimeter (Campi Flegrei) to micrometer order (Etna). Figure 4 shows such ground oscillations, as they would be recorded by instruments having cutoff periods of 500, 200, and 50 s. It must be recalled in fact that any instrument measuring ground displacement can only record movements occurring over a certain frequency range, acting therefore as a filter. A cutoff period of 50 s characterizes most classical broadband seismometers, whereas oscillations with longer periods can be detected by dilatometer, Global Positioning System (GPS), or tiltmeter networks (e.g., Lay and Wallace 1995). Accordingly, Fig. 4 shows that ULP ground movements like those predicted by the present modeling could not be detected by classical broadband seismometers (although more recent seismometers extend their working range up to 100–200 s periods; Havskov and Alguacil 2004), while they are in principle visible in the records from other instruments, especially borehole dilatometers characterized by high signal-to-noise ratio.
Fig. 4

Computed time series of ground displacements (topographic effects neglected). Left panels Mount Etna case. From top to bottom, high-pass filtering at corner periods of 500, 200, and 50 s. The data were detrended before filtering, demeaned and tapered using a Tukey window to alleviate border effects. The synthetic recordings are from a virtual receiver located on a flat surface 2.5 km east of the surface projection of the central chamber point. Right panels Campi Flegrei case, same as above with virtual receiver located 4 km east of the chamber axis

Discussion and conclusions

The simulation results show that the evolution of the magmatic pressure depends nonlinearly on the characteristics of the simulated system, varying from point to point in response to both general and local dynamics. Pressure variations over the simulation time scale do not constitute the focus of this work, since their evaluation requires longer computing times. We note however that in both simulation cases presented here, and over the maximum simulated times, the overall pressure in the shallow system decreases as a consequence of partial replacement by lighter magma. This is true even for the Etna case, for which a 1 MPa overpressure at system bottom has been imposed in the simulations as a forcing component to magma flow.

Pressure decrease is a counterintuitive consequence of new magma injection and appears to relate to reduced overall magma density in the constant volume chamber. The density decrease in fact reduces both the hydrostatic and thermodynamic pressure contributions, the former related to the weight of the magmatic column above any given point, the latter related to an equation of state for the multiphase multicomponent magma. The density decrease is in turn a consequence of injection of lighter magma and sinking of denser magma towards deeper system regions. Gas exsolution and expansion upon ascent through the shallow chamber at one hand tends to increase pressure (and consequently favors dense magma sinking into the feeding dyke) at the other hand contributes further to overall density decrease.

It is relevant to note that an elastic response of reservoir walls, not included in the fluid dynamics simulations, may act as a buffer, reducing the extent of overall pressure change without however changing its sign. We stress however that pressure decrease at shallow level is not proposed here as an unavoidable consequence of magma chamber recharge by buoyant magma. In fact, the above described processes controlled by light magma injection and dense magma sinking are highly nonlinear and a general pressure balance cannot be established on the basis of only two simulations performed here. It is well possible that other system conditions (e.g., different geometries, different compositions involved, different efficiency of magma exchange at dyke level, etc.) may result in different pressure trends. This subject forms part of ongoing investigation that will be presented elsewhere.

The most remarkable feature and the outstanding result emerging from the present simulations is represented by ULP pressure oscillations accompanying magma convection and mixing (see Fig. 3 and Online Resources 717 for pressure oscillations computed at several different points in the computational domain). Such oscillations are a consequence of the complex dynamics characterized by buoyant plume ascent and expansion, local vortex formation, and dense magma sinking. The patterns of ULP pressure oscillations are different from point to point in the magmatic domain, depending in a complex way on both global and local dynamics. Although desirable, a parameterization of the different contributes that concur to determine the period of pressure oscillations is not possible at the moment, since it requires a substantially larger number of simulations in a comparably large range of system conditions.

When integrated along the entire boundaries of the simulated domain and transported to the Earth’s surface, complex patterns of ground motion dominated by ULP frequencies emerge (Fig. 4). Although heterogeneities in country rocks have been neglected in the present analysis, they are not expected to affect significantly the patterns of ground motion over the frequency of the computed ULP displacements. Oscillating ground motion with a period of, say, 100 s corresponds in fact to wavelengths of order 100 km. Heterogeneities over a spatial scale of 1 km or less have therefore negligible effects at such wavelengths.

The above discussion may suggest that ULP pressure oscillations in the magmatic body translate into ground oscillations with same or similar waveforms. However, even when looking at the 500 s low pass-filtered ground displacement waveforms in the upper diagrams of Fig. 4, that is not the case. The computed ground displacement waveforms are in fact substantially more complex than the pressure oscillations that generate them. The reason for such complex relationships rests in the fact that ground displacement waveforms result from the interactions between pressure waves generated from many sources and having different waveforms; even more importantly, pressure waves are generated at different times along the fluid–solid domain boundary, as a response to the internal time–space-dependent dynamics affecting the magmatic body. The general conclusion is therefore that spatially extended magmatic bodies undergoing pressure fluctuations and representing a source for ground displacements should not be regarded as lumped bodies undergoing overall pressure increase or decrease. A corollary is that full-waveform inversion of ground displacement signals, if it neglects the time–space-dependent magma dynamics as do inversions performed at volcanoes, could lead to misleading results, since those waveforms critically depend on the internal dynamics of the fluid system.

ULP ground oscillations are proposed here as a diagnostic product of deep magma convection. Due to either intrinsic technological limitation or coarse sampling rates, ULP ground displacements with frequency range 10−2–10−3 Hz like those from the present simulations are still seldom measured at real volcanoes. In the large majority of cases, in fact, the employed instruments do not cover such a frequency range (Scarpa 2001) or do not have enough temporal resolution. This is true at Mount Etna and Campi Flegrei where broadband seismic instruments have a cutoff frequency corresponding to about 40 s and long baseline tiltmeter data are recovered with a frequency of one every 10 min (Mount Etna; Bonaccorso et al. 2002; Cannata et al. 2009) or have just been set up and are still in the experimental phase (Campi Flegrei; R. Scarpa, personal communication). The resolving capability of GPS networks is of order several millimeters or larger (Bonaccorso et al. 2002), still too low to detect ground oscillations with amplitude comparable to that emerging from the present simulations. Additionally, GPS data are commonly averaged over hours or tens of hours to obtain a picture of the long-term volcano deformation (Bonaccorso et al. 2002).

Identification of sustained oscillations with small amplitude like those emerging from numerical modeling, requires on the one hand the deployment of near-field advanced instrumentation represented by arrays of very broadband seismometers, borehole strain meters, long baseline tiltmeters, and GPS networks; on the other hand, it needs the development and application of sophisticated data analyses able to separate the contributions of the spatially coherent signals from those due to noise. Although systematic collection and analysis of signals in the frequency range 10−2–10−3 Hz is still not carried out (Scarpa 2001), recent advances in volcano monitoring, and particularly the deployment of very broadband instruments at a growing number of volcanoes throughout the world, are increasingly revealing ULP ground oscillations. At Soufrière Hills, Montserrat (West Indies), dilatometric data show oscillations with periods around 103 s, following phases of dome collapse (Voight et al. 2006). ULP ground motion with periods in the range 30–600 s was recorded at Santiaguito volcano, Guatemala, during a 3.5 days broadband survey (Sanderson et al. 2010). Ground oscillations in the frequency range 10−2–10−3 Hz were measured at Piton de la Fournaise volcano, Réunion Island, and interpreted as due to pressure oscillations in a shallow magma chamber as a consequence of injection of magma of deeper provenance (Houlì and Montagner 2007).

The numerical simulations presented here show that convection dynamics taking place in magma reservoirs are expected to produce pressure oscillations and ground motion in the ULP frequency range. This paper provides therefore the physical background for the interpretation of emerging ULP signals at active volcanoes, at the same time offering a strong motivation for reexamining the existing seismic, strain, tilt, and high-rate GPS records worldwide for the presence of ULP signals. The results of highly nonlinear magmatic processes simulated here, and the records from the most recent and advanced broadband instruments deployed at volcanoes, concur to demonstrate that new and vital information on the underground volcano dynamics can be gained through extensive and systematic exploration of the ultralow frequency domain of geophysical signals.


This work has been performed in the frame of Projects FIRB RBAU01M72W and RBPR05B2ZJ; and Projects INGV-DPC 2004–2006 V3_2, and 2007–2009 V1 and V4.

Supplementary material

445_2011_570_MOESM1_ESM.avi (5.3 mb)
Supplementary Movie 1This movie shows magma composition for the Mount Etna case. Initial compositions are made of 90 wt.% of the corresponding component and 10 wt.% of the other component, to avoid numerical shifts to component fractions >1 or <0. The zero on the depth scale corresponds to sea level (AVI 5,412 kb)
445_2011_570_MOESM2_ESM.avi (5.5 mb)
Supplementary Movie 2This movie shows overpressure for the Mount Etna case. Overpressure is given by pressure at local time–space minus the pressure at same place and time zero. The zero on the depth scale corresponds to sea level (AVI 5,645 kb)
445_2011_570_MOESM3_ESM.avi (5.3 mb)
Supplementary Movie 3This movie shows gas volume fraction for the Mount Etna case. Calculated gas volume and multiphase magma densities at magma interface and time zero are 10 vol.% and 2,250 kg/m3 (shallow magma), and 35 vol.% and 1,700 kg/m3 (deep magma). The zero on the depth scale corresponds to sea level (AVI 5,433 kb)
445_2011_570_MOESM4_ESM.avi (5 mb)
Supplementary Movie 4This movie shows composition for the Campi Flegrei case. Initial compositions are made of 90 wt.% of the corresponding component and 10 wt.% of the other component, to avoid numerical shifts to component fractions >1 or <0. The depth scale on the left refers to meters below sea level (AVI 5,157 kb)
445_2011_570_MOESM5_ESM.avi (2.3 mb)
Supplementary Movie 5This movie shows overpressure for the Campi Flegrei case. Overpressure is given by pressure at local time–space minus the pressure at same place and time zero. The depth scale on the left refers to meters below sea level (AVI 2,308 kb)
445_2011_570_MOESM6_ESM.avi (2.2 mb)
Supplementary Movie 6This movie shows gas volume fraction for the Campi Flegrei case. Calculated gas volume fractions and multiphase magma densities at magma interface and time zero are 3.5 vol.% and 2,400 kg/m3 (shoshonite), and 7.5 vol.% and 2,350 kg/m3 (basalt). The depth scale on the left indicates meters below sea level (AVI 2,284 kb)
445_2011_570_MOESM7_ESM.doc (13.5 mb)
ESM 1(DOC 13,835 kb)

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