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

## Authors

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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

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## Abstract

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.

### Keywords

Magma dynamicsMagma convectionMagma mixingULP ground displacement## Introduction

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

_{2}O and 0.5–2 wt.% for CO

_{2}. 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.

Composition of magmas employed in the numerical simulations

Simulation | Mount Etna | Mount Etna | Campi Flegrei | Campi Flegrei |
---|---|---|---|---|

Magma | Shallow (basalt) | Deep (basalt) | Shallow (shoshonite) | Deep (basalt) |

SiO | 48.4 | 47.9 | 52.5 | 47.6 |

TiO | 1.67 | 1.69 | 0.85 | 1.24 |

Al | 17.8 | 16.9 | 17.6 | 15.5 |

FeO* | 10.2 | 10.5 | 7.62 | 8.3 |

MnO | 0.18 | 0.17 | 0.12 | 0.14 |

MgO | 5.53 | 6.56 | 3.60 | 10.0 |

CaO | 10.2 | 11.1 | 7.93 | 11.1 |

Na | 3.87 | 3.31 | 3.43 | 2.88 |

K | 2.11 | 1.93 | 4.28 | 1.49 |

H | 1.5 | 3.5 | 2.0 | 3.5 |

CO | 0.5 | 2.0 | 1.0 | 2.0 |

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/m^{3}), 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 H_{2}O and CO_{2} 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 10^{5} 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, *v*_{p} = 3,000 m/s; *v*_{p}/*v*_{s} = 1/√3, *ρ* = 2,500 kg/m^{3}).

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.

## Results

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.

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.

## 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 7–17 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 10^{3} 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.

## Acknowledgments

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.