This geo-factsheet by Jasper Sodha won the annual Pepys Cockerell Prize

Volcanic eruptions are notoriously hard to predict, let alone model. When they erupt, they can cause catastrophic devastation to livelihoods dependent on them. This factsheet looks at the ways that eruptions can be predicted and modelled; an imperfect yet vital science.

Volcanic monitoring is essentially a mass data collection exercise from varying sources. Seismology, geodesy, petrology, and geochemical observations from land and above, are critical in formulating an idea of a volcano’s (in)activity. Increased seismic activity relative to background levels, is a key indicator of magma propagating upwards from deep reservoirs to shallower holdings. Prior to eruptions, seismographs may detect swarms of high-frequency, small earthquakes before a period of calm which varies in length from months to minutes. Finally, there is a gradual increase in tremors, indicating surface ruptures. Long-term generalisations of unrest can be made easily, but short-term, life-saving precursors are harder to come by, as this table shows:

Year of Eruption	Precursor Time (Minutes)
1970	25
1980	23
1991	30
2000	79

There have been 21 eruptions since a dense seismograph network was installed in Iceland (1973). Warnings were issued to 14 (67%) of them. 4 were not detected until after eruption and 3 more were not detected until after human observation. It is clear that seismicity struggles to consistently predict and prepare for imminent eruptions, potentially failing 33% of the time. There are many problems, with few solutions:

• Seismographs don’t register earthquakes if the crust is not near its failure limit when magma flows through it.
• Seismographs must be accessible; however, humans, cars and even horses can affect readings. Therefore, spikes need to be recorded on multiple seismographs to confirm an earthquake.
• Pinpointing an earthquake is difficult. Costly networks of seismographs are required, as it is easier to locate earthquakes relatively, not individually, enabling accuracies within 100m. Seismographs measure in the North, East and Vertical components to provide a better picture.
• Seismographs typically record multiple frequencies to distinguish between tele-seismic (0.5-2 Hz) events and local (2-4 Hz) events.
• The modelled location can be distorted by the velocity model used for Primary and Secondary waves.

Volcanic geodesy is arguably even more vital in monitoring volcanoes. Geodesy studies the changing size and shape of specific parts of the Earth. Geodetic measurements help volcanologists understand how magma is flowing in the roots of the volcano’s plumbing system. Think of a volcano like a balloon. As new magma enters the system there is a detectable expansion on the surface. Magma flowing out results in a deflation. This process was visible prior to Mt St Helens (1980), where the northern flanks ballooned upwards and outwards at rates of 1m per day. Normally, however, changes are so minute that observations require specialist equipment on land and from above:

• Gravity Measurements
• Tilt and Strain via Levelling
• GNSS (Global Navigation and Systems Satellite) Geodesy
• InSAR (Interferometric Analysis of Synthetic Aperture Radio)

Gravity measurements can be carried out by relative or absolute gravimeters, showing changes or absolute values. Gravity measurements are accelerations but are so small that they are measured in microGals (10^-8m/s²). As magma flows out, there is reduced mass and thus, gravity readings decrease. This technique was used to help work out the density of the magma in Kilauea’s lava lake. This then provided understanding of gaseous and explosive levels. Gravity measurements should not be used alone, as magmatic vesiculation and water table movements can give erroneous data.

Instead, optical levelling with fixed reference points, can be used to infer ground tilt and strain. It is important to ensure that levelling benchmarks are fixed into solid bedrock, minimising error. However, tiltmeters are more accurate than levelling, eradicating human error, as sensors at each end of a tube, continuously measure changing water levels. To calculate tilt, the change in water height is divided by the length of the tube, giving a result measured in microradians. 1mrad = 1mm height change for every 1km in distance.

The measurements required in volcanic geodesy have extremely small magnitudes. Therefore, observations from satellites cannot use smartphone GPS, which is only accurate to 3m. Satellites are effectively timing devices, measuring how long it takes for their pseudo random code signal to be received, accurate to 1/100^th of the length of the pseudo random code. This time is then multiplied by the speed of the wave (speed of light) to calculate a distance. By using multiple satellites, an intersection point can be found, pinpointing a location; requiring 3 satellites for the intersection and 1 to describe the location of those satellites. Using 20 satellites, we can be accurate to about 1m.

However, this is still not sufficient for volcanic geodesy, so to achieve mm-level accuracy, the actual carrier wave (instead of the pseudo-random code) of one of the two frequencies emitted by the satellite is used, giving us 2mm accuracy. This technique is called GNSS geodesy. However, changing atmospheric pressure in the atmosphere, water vapour in the troposphere, and the ions in the ionosphere (where The Northern Lights occur), can drastically change the speed of the waves, which aren’t the same as in empty space; the speed of an Electromagnetic Wave (≈ 3×10⁸ m/s). Therefore, both frequencies (L1 and L2) of the carrier wave are used, alongside water vapour models to help minimise residual error, providing mm-level accuracy for measuring the changing direction of benchmarks set in bed rock. In Iceland, Glacio-Isostatic adjustments may need to be made to combat the effects of glacial melting. Continental drift of benchmarks also needs to be accounted for by using the ITRF (International Terrestrial Reference Frame), which describes the average plate movement per annum. This is particularly difficult in deformation zones such as in Iceland. This diagram shows how stations move; recorded via GNSS.

InSAR is the other common technique for measuring deformation from above. Radar pulses are emitted and reflected off the Earth’s surface; the echo recorded. The amplitude of each pixel in a SAR image gives the strength of the radar reflection. The phase of each pixel measures the angle of reflection, indicating vertical and lateral terrain shift, with a value between 0 and 1 full wave cycle (2prad). This method of observation is only useful with two images of the same area at different times. These images are cross-referenced and the difference between each pixel’s phase is mapped, creating an interferogram. This gives the change in distance from the satellite to the ground. The images consist of coloured bands (fringes) equal to a relative change of half the satellite’s radar wavelength. A fringe acts as a contour line of equal line-of-sight change, much like isobars or isotherms:

Interferograms are complicated, as the satellite’s direction, orientation and ascent, can completely invert an otherwise identical interferogram. InSAR gives a holistic view of deformation instead of individual data points (GNSS). However, InSAR does not provide real time data.

All of this crustal deformation data can be used to calculate the depth and volume of magmatic processes occurring in the volcano’s roots. There are different models that volcanologists use. The most basic is the Mogi model, requiring only 4 parameters. It assumes that the pressure source causing deformation is spherical and operates in an elastic half-space. However, this is rarely the case. More often, models with 8 parameters are used to map ground deformation resulting from magmatic dikes and sills (Okada Dislocation Models), and spheroids (Yang Model):

To make these models more accurate to account for the Earth’s non-uniform surface and changing material properties, the data is inverted to find the optimum combination of parameters. Mathematical calculations are carried out to ultimately give a c² variable. The lower the c², the better the model’s parameters are in fitting the recorded data.

Volcanic gas is another important measure of activity. Direct sampling in Giggenbach bottles is difficult and dangerous but provides insight for the largest range of gases. Meanwhile multi-gas stations are hard to initially set up close to the gas source, but automatically measure for the most common components (H₂O, CO₂ and SO₂). Satellites use spectroscopy to measure volcanic gases but can currently only measure for SO₂ due to its absence from background measurements and abundant quantities. Furthermore, atmospheric conditions must be optimal (no clouds) when satellites pass over the gas source. Satellites excel, however, in monitoring ash clouds; which are dangerous to aviation. Eyjafjallajökull’s 2010 eruption halted Europe’s air traffic. 100,000 flights were cancelled. Multiple monitoring methods are required for reliable results. Despite numerous techniques, there are many factors whose effects cannot be modelled. These include the dangerous results of different magma melts mixing, the influence of water (Hawaii, 2018), how magma rheology affects laminar flow, and how the free gas phase affects the magma’s explosiveness. Volcanic monitoring is a complicated, flawed and imperfect science. However, new and improved equipment is continuously being developed, with projects such as the Krafla Magma Testbed designed to help volcanologists better understand these captivating forces of nature. At the moment, long-term predictions can be made but precise timings are non-existent. Short-term warnings are improving and must continue to do so, to prevent catastrophic loss of life.

Left: A Giggenbach bottle taking gas samples at fumaroles in Yellowstone National Park. (Credit: Lowenstern, Jacob B. Public domain)

Centre-Top: A GNSS antenna on the southern flank of Kilauea, Hawaii. It is positioned above a permanently set and drilled brass disc (benchmark). (Credit: USGS Photo by Sarah Conway)

Centre-Bottom: A seismograph. The lines produced form a seismogram. The greater the line’s amplitude (height), the higher the earthquake was on the Richter Scale. The Richter Scale is logarithmic so magnitude 5 earthquake is 100 times greater than a magnitude 3 earthquake. (Credit: Yamaguchi)

Right: A tiltmeter on Mauna Loa, Hawaii, measuring small changes in the profile of the volcano’s slopes. (Credit: USGS)

(Featured Image: © Jasper Sodha)