Can geophysical modelling predict the end of the Soufrière eruption?

D Elsworth, G Mattioli, J Taron, B Voight and R Herd, Implications of magma transfer between multiple reservoirs on eruption cycling. Science (2008) 322: 246-248.

Science is about data and models. First you collect a mass of data. Then you spend anything up to a lifetime trying to devise a model that satisfactorily explains your facts. If you doubt the word “lifetime”, remember Charles Darwin and evolution. But the goals of science models are well worth the effort put into devising them because, if correct, they bring some order into the apparent chaos of a mass of data and may lead to the predictions about the future of a phenomenon.

The prolonged eruption of Montserrat’s Soufrière Hills volcano (SHV) has produced many data sets with unparalleled detail and continuity. In turn, these data sets have encourage people to generate many models about aspects of how the volcano has behaved so far, and therefore might do in the future. The instances when the eruption has shown cyclic activity have especially fascinated modellers. For example, lava domes on SHV and other explosive volcanoes often have periods of repetitive cyclic ground deformation, degassing, seismicity (earthquakes), lava extrusion and explosive eruptions -- the cycles taking hours to days. Lensky, Sparks, Navon and Lyakhovsky have recently (2008) modelled these distinctive cycles in terms of a cyclic “dance” between the resistance of a rigid frozen lava plug capping the lava conduit, bubbly magma beneath this cap and gas-bearing magma deeper in the volcano that can foam as soon as the pressure above it drops.

The long-term cyclic behaviour of SHV since 1995 has recently attracted the attention of a team of modellers based on both sides of the Atlantic (USA, UK) and Australia. The volcano has alternated between 2-3 year periods of extruding lava on and around its summit (with or without explosions, dome collapses etc) and quiet periods for 1.5-2 years, when it just sits there innocently and invites foolhardy islanders and tourists to try to approach it too closely.

What causes this cyclic behaviour? Elsworth and his colleagues recently published their ideas in the eminent journal Science. Their starting point was two sets of data: (1) estimates of the volume of lava extruded (peacefully as domes or violently in explosions) at the SHV summit; (2) the movements of GPS monitoring stations all over Montserrat during the same period.

The GPS (Global Positioning System) stations on the island in 2003-5 are shown on Figure 1. They were all, of course, the sorts of ultra-accurate instruments that can record positions to within 1 mm or so.

Fig. 1.  Sites of GPS stations on Montserrat in 2003-5. The red triangles are long-term stations and the blue diamonds are temporary ones. The arrows at some stations show how they moved horizontally during that period (note scale below).

The volcano was quiet during that period, with no lava extrusion. But meanwhile the GPS data show that the magma reservoirs below were continuously inflating, like a balloon under a blanket. Put some ink marks on the top of the balloon and blow it up. You will see the marks move both away from each other and upwards, as the balloon inflates. This means that the GPS data (Fig. 2) show that the volcano inflates during quiet (no lava/explosions) periods and deflates when surface lava extrusion is active.

Fig. 2.  The top panel shows the cumulative erupted magma throughout the eruption. The lower two panels show vertical movements at two of the GPS stations during the same period. The volcano clearly slowly “breathes”!

The next point that Elsworth and his colleagues had to fix for their modelling was the number of magma reservoirs beneath the volcano. The GPS data alone cannot give a firm answer to this question but other published studies can help. During the early years of the eruption, research into seismic (earthquake) signals from beneath the volcano agreed with other lines of enquiry, such as the compositions of minerals in the erupted andesites and also in samples of powdered rock heated experimentally to various temperatures at various pressures. All this evidence pointed to a single large (about 4 km³) magma reservoir only about 5 km below the summit of SHV.

Next the focus of research on the erupted rocks turned to the small (up to a few cm) scattered “dark blobs” seen in many samples. Although the lava surrounding them is andesite, the chemical composition of the blobs is basalt (lower SiO₂ and higher MgO than andesite; see Topic 1 of this website – “General introduction: the science view”). Basalts are relatively hot magmas that trickle into the base of the Earth’s crust beneath volcanoes such as SHV, having formed by “wet” melting in the mantle above the subduction zone underlying the Lesser Antilles. In the long term they develop, by fractional crystallisation, into andesite (see section 1) but they also play a short-term role, by reheating reservoirs of earlier semi-crystalline andesite and thus triggering eruptions. The growing consensus of opinion is that this magma-mixing reservoir at SHV is deeper that the main andesite one, at about 10-12 km depth. More recent geophysical data also fit this view.

The “magmatic plumbing” beneath SHV used by Elsworth and his colleagues for their modelling is shown in Fig. 3.

Fig. 3  “Magmatic plumbing” used by Elsworth and his colleagues in their modelling calculations. Don’t be confused by the umpteen symbols referring to equations in the article. The essentials of this diagram are listed in the text below.

The two magma reservoirs are drawn spherical because there is no detailed evidence yet of their real shapes. The magma reservoirs are labelled I (shallow) and II (deep). The connections between the reservoirs (and also both from the Earth’s mantle below and up to the surface above) are considered to be narrow enough to contain little magma, compared with the main reservoirs. Two long arrows from the upper magma reservoirs point to two GPS stations (1 and 2). Small arrows above each of these show how the slight surface bulging caused by magma pumping into reservoirs several km below cause the surface of Montserrat to move slightly upwards and away from SHV (and then to return when the magma leaves the reservoir). Obviously similar arrows can be drawn from the deeper reservoir to GPS stations 1 and 2.

The stage at SHV is now set for the geophysical modellers to do their mathematical magic. The mathematical direction Elsworth and his colleagues took is called inversion, where you measure effects of a process and use maths to figure out what caused these effects. Inversion can be thought about simply by imagining a bomb going off somewhere in a village. Ask villagers which direction they heard the explosion come from and draw all these directions as lines on a map of the area. The crater will be where the lines all converge. Now repeat the experiment with an earthquake somewhere beneath an area dotted with seismometers, each recording the arrival of the earthquake shock waves at different times. A seismologist can then use inversion maths to pinpoint the source of the earthquake.

For the SHV “magmatic plumbing” Elsworth and his colleagues take the accumulated records of the volumes of magma erupted, and the gyrations of the island-wide GPS stations over 12 years, and calculate the volumes of magma (as rates of flow in metres per second) moving in and out of both reservoirs throughout the eruption. At this point you may ask; “Fascinating stuff but so what?” Most of the detailed conclusions, such as those shown on Fig. 4, are indeed strictly for “magmatic plumbers” (who may be Jo in the USA but more likely Andrzej in the UK!) to think about but the one that really matters to all Montserratians is shown in Fig. 5.

Fig. 5.  The graph that matters!  Again hard to follow but the dotted line shows how an elastic pressurised body (e.g. a balloon) would shrink as it deflated (very slowly!). The lower (deeper) magma reservoir is doing this stepwise. E=eruption; P=pause. For this model the diameter of the “pipe” (conduit) between the two reservoirs is only 30 metres. It is probable that the new Gages Vent – source of the vicious 28 July 2008 explosive eruption – is much the same diameter below the surface.

It appears that, although the upper (shallower) reservoir is the direct source of all the erupting lava, this has not changed significantly in volume (~4 km³) over the 12 years of the eruption (to 2007). Therefore it is the lower (deeper) reservoir that fuels the activity. For instance, the lower reservoir continues to receive magma from below at a steady rate of about 1 cubic metre per second, whether or not there was/is surface eruption. Furthermore, during the last twelve years the lower magma reservoir has been steadily shrinking. Projecting this process into the future, Elsworth and his colleagues estimate that about 95% of the magma that is going to come out of SHV during this long eruption has now done so.

Of course these conclusions may not be gospel. It will take the labours of other equally well qualified groups of geophysicists and mathematicians to check every detail of the present model and its possible errors or alternatives. That is how science slowly progresses. But, for the moment, let us take the results of the model at their face value. Does this mean that the end of the eruption is nigh? It is extremely tempting to jump to this conclusion but the trap is to assume that, because about 95% of the magma volume has been erupted, therefore only about 5% of the time of the eruption remains. Oh that volcanoes were so simple! The eruption might end even sooner, if some critical part of the magmatic plumbing freezes, or later, if that last 5% takes its time oozing or blasting out. We shall see; watch the MVO website!

In 2010 this group of researchers updated their work in a short report that re-estimated the depth of the shallow magma reservoir at about 5 km depth and the deeper one at about 17 km depth. The deeper one appears to change volume about 20 times faster than the shallower one and therefore dominates in the fuelling of the eruption.