Download Chapter 1 Volcanic Processes as a Source of Statistical Data

Chapter 1
Volcanic Processes as a Source
of Statistical Data
Heidy M Mader
There are currently about 1500 active volcanoes on Earth (Tilling 1989).
Eruptive activity presents many different styles, ranging from highly explosive eruptions through to non-explosive or effusive behaviour, which vary
greatly in the hazard that they pose. Currently, millions of people are at
risk from volcanic hazards. The average annual death toll due to volcanic
hazards is rising because more people are living in close proximity to active
volcanoes. Our understanding of the physical processes and parameters involved in the generation and evolution of volcanic flows is now advanced, and
sophisticated process-oriented numerical models exist that describe eruptive
processes well. There are 100’s to 1000’s of eruptions each year on Earth
and many volcanoes are monitored around the clock by dedicated observatories. Thus, volcanology is rich in statistical data and statistical modelling
is an emergent and rapidly-growing area of interest. This volume is aimed at
presenting the current state of statistical modelling within volcanology. The
purpose of this chapter is to give a general introduction to volcanic eruption
processes, data, and modelling as well as an overview of the volume as a
whole.
The volume is restricted to terrestrial volcanism (i.e. on land) and in
the absence of large volumes of water, such as groundwater, sea or lake
water, or snow. For a review of ‘phreatomagmatic’ volcanism, which results
from the interaction of magma and water, see Zimanowski (1998).
1
1.1
Spatial And Temporal Distributions
Volcanoes occur where molten rock, or ‘magma’, reaches the Earth’s surface.
A cursory glance at Figure 1.1 shows that the distribution of the world’s
volcanoes is not random; most of them are located along the edges of the
tectonic plates that make up the Earth’s lithosphere. In fact, about twothirds of the world’s active subaerial volcanoes are located in the plate
margins that surround the Pacific Ocean forming the so-called ‘Ring of
Fire’. At these margins, two plates converge and the oceanic plate sinks, or
‘subducts’, into the mantle below the continental plate (Figure 1.2). Hence
these subduction zones are also called ‘convergent’ or ‘destructive’ plate
margins. The descending plate is dehydrated and the escaping fluids (mainly
water) rise into the overlying mantle wedge thereby lowering the solidus (the
temperature at which a solid begins to melt) of the Earth’s mantle. Melting
occurs producing water-rich magmas that rise to the surface.
Decompression of material as it rises from depth is an alternative mechanism that causes melting. This occurs along the ‘divergent’, ‘constructive’
plate margins, indicated by the mid-ocean ridges (e.g. Iceland), where the
tectonic plates are created by upwelling of material. Decompression is also
the melting mechanism at localized, intraplate ‘hot-spots’ (e.g. Hawaii),
where it is hypothesized that material is rising in the form of a localized
plume in response to convective processes deep in the mantle.
Significant data also exist on the temporal distributions of volcanic
eruptions on a global scale. Figure 1.3 shows the record of historicallyrecorded eruptions with magnitude greater than 4M for the last 2000 years.
This is a stochastic dataset that suffers from the problem that recording
is likely to be less reliable, especially for smaller magnitude eruptions, as
one goes back in time. Coles and Sparks (this volume) apply extreme value
methods to this dataset, that take into account historical bias in recording,
to show how one might obtain quantitative estimates of the likelihood of
future extreme volcanic events.
Similar spatial and temporal data exist on more local scales. Our ability to produce reliable stochastic analyses of such data can be extremely
important. For example, Connor et al. (2000) investigate the likelihood of
a volcanic eruption at the location of a proposed high-level nuclear waste
repository in the volcanically-active Yucca Mountain region of Nevada,
USA. In this volume Connor et al., Jaquet, Varley et al. and Weller et al.
present studies of stochastic forecasting for spatial and temporal eruptive
behaviour. Their chapters, along with that of Coles and Sparks, demonstrate that probabilistic predictions of long-term activity depend heavily on
our understanding of the spatial and temporal controls on volcanoes and
volcanic eruption behaviour. Such models are greatly enhanced by strong
2
links between physical and statistical models. It is essential then to acquire
some knowledge of the underlying physical processes operating in volcanic
eruptions.
1.2
Explosive Versus Effusive Activity
Figure 1.4 shows schematically the generic architecture of a terrestrial volcano and the range of surface flows that might occur as a consequence of an
eruption. Magma rises from some source region, usually located at the base
of the Earth’s crust or in the upper mantle, and ponds at depth within the
volcanic edifice in a magma chamber (geologic studies of eroded volcanoes
reveal chamber volumes 1 − 106 km3 with the top at a few km depth or
more) which is connected to the vent by a conduit (usually of order 1 to 100
m in diameter). The magma consists of a pure liquid silicate melt containing dissolved volatiles (primarily H2 O vapour with lesser amounts of CO2
and S) and possibly crystals or fragments of older rock. Magma chamber
dynamics is complex. Bubble and crystal nucleation and growth occur and
convective flows, due to both thermal and compositional density gradients,
are possible in magma chambers (e.g. Huppert and Woods 2002; Woods
and Huppert 2003).
To understand what gives rise to a volcanic eruption, we need to consider the process of bubble nucleation and growth within magmas. The
amount of volatiles that can be dissolved in the magma is a function of
pressure. The pressure at depth is generated by the weight of the overlying
rock and an overpressure due to the input/output magma budget within the
volcanic edifice. If the pressure is such that an appreciable volatile supersaturation is reached, then bubbles will nucleate above that depth (which
could be either in the magma chamber or in the conduit). The chapter
by Diez (this volume) explores simple models of magma ascent and flow
in conduits and the impact of these processes on eruption columns in the
atmosphere.
Nucleation can occur prior to an eruption, such that a population of
pre-existing bubbles exists at the onset of an eruption. Alternatively, nucleation can be initiated by an unloading event, for example a landslide at
the surface, that leads to the propagation of a decompression wave down
through the volcanic edifice. Once formed, the bubble nuclei grow by diffusion of more dissolved volatiles into the bubbles from the surrounding melt
and by decompression as the bubbly magma expands up the conduit. It
is this process of exsolution or ‘degassing’, possibly in addition to continued input of fresh magma from depth, that drives terrestrial eruptions by
causing the growth of a gas phase internally within the magma at depth.
The different eruption styles reflect the physico-chemical conditions and
3
processes experienced by the magma during its transit from the chamber to
deposition at the surface.
1.2.1
Explosive Eruptions
Explosive eruptions (Figures 1.4 (a) and 1.5) are often associated with magmas that have a high silica (SiO2 ) content, such as rhyolites. These magmas
tend to have high water contents (typically 6% to 8% by weight) and so a
high potential expansion of the magma on degassing. Rhyolites also tend
to have high viscosities (typically 108 to 1010 Pas when fully degassed) and
low gas diffusivities. Thus, the mobility of the gas phase is low. A sudden
decompression event imposed on a rhyolite tends to result in widespread
bubble nucleation and the magma column expands maximally as very little gas can escape from the highly viscous magma. The gas expansion in
an explosive eruption is sufficiently violent that at some depth (the fragmentation surface) the magma is torn apart or fragmented into many small
pieces called pyroclasts. Fragmentation marks the transition from a bubbly
flow, where the continuous phase is a liquid, to a flow of vesicular (bubbly)
pyroclasts carried upwards by a hot gas. The mixture is erupted into the
atmosphere in the form of a momentum-controlled jet (exit velocities 100’s
ms−1 ; total mass discharged 1011 − 1014 kg, equivalent to 0.1 − 150 km3 of
dense rock, at discharge rates of 103 − 105 m3 s−1 ).
What happens at the surface depends critically on the buoyancy of the
gas-pyroclast mixture. If the bulk density of the mixture is less than atmospheric on eruption the material will rise as a convecting, buoyant plume
called a Plinian eruption column (heights of 25 km or more) (Figure 1.5
(a)). The plume will continue to rise until it reaches its height of neutral
buoyancy. At this height it spreads out laterally to form an umbrella cloud
from which pyroclastic material rains down on the surrounding area or can
be transported around the globe. On the other hand, if the bulk density of
the gas-pyroclast mixture is greater than atmospheric pressure on eruption,
the column will collapse (Figure 1.5 (b)) and flow down the side of the
volcano as a pyroclastic flow (Figures 1.5 (c) and (d)).
Pyroclastic flows are amongst the most devastating and lethal volcanic
events for populations close to volcanoes, primarily because of their extreme
mobility; they can reach speeds of 100’s kmh−1 and can travel as much as
100 km or more from the source vent. An example of the fearsome impact of
these flows occurred on the Caribbean island of Martinique in 1902 when a
pyroclastic flow was generated by an explosion of Mount Pelée volcano and
descended on the city of St Pierre, killing some 29,000 people in a matter of
about two minutes; the detonations leading to the flow were heard at 07:50
and the clock of the Military Hospital was found with its hands stopped
4
at 07:52. The cause of death as a result of these flows is primarily due
to suffocation by the dust rather than the effects of temperature (of order
1000 ◦ C). There were only two survivors left in St Pierre. One of these was
Augustus Ciparis, who was a prisoner in the town jail. His cell was below
ground level and had a small grating above the door but no window, thereby
providing effective protection from the dust of the flow. He was found four
days after the flow had passed, still locked in his cell and badly burnt and
shocked. In common with many of the dead at St Pierre, Ciparis’ clothes
were unscathed; the temperature in the flow was intense but short-lived and
the heat generated was enough to burn skin but not to ignite fabric.
1.2.2
Effusive Eruptions
At the other end of the spectrum is effusive activity (Figures 1.4 (b) and (c)
and 1.6). Effusive eruptions tend to occur in magmas with low silica (SiO2 )
content, such as basalts. Basalts have low water contents (typically just a
few weight %), low viscosities (typically 102 to 103 Pas when fully degassed)
and high diffusivities. In these magmas, fewer nuclei are formed and rapid
diffusion into them leads to large bubbles that can rise up through the
low-viscosity magma, often collecting more bubbles as they go (Figure 1.6
(c)). Thus, much of the gas escapes from the magma, thereby reducing the
driving force for a major explosion. Typical activity can range from slow
bubbling in vent-bound lava lakes through to intense lava ‘fire fountains’
(Figure 1.6 (a)) that can feed lava flows (Figure 1.6 (b)). The ease of gas
segregation can allow metre-sized bubbles to be formed that ascend from
depth as gas slugs and burst at the surface (Figure 1.6 (c)). Lava flows
typically have discharge rates in the range 1 − 103 m3 s−1 and total volumes
of 10−2 − 20 km3 .
Lava dome eruptions (Figures 1.4 (c) and 1.6 (d)) are perhaps the
least explosive form of volcanic activity. These eruptions are characterized
by slow extrusion (1-100 m3 s−1 ) of high-viscosity lava such that a dome is
formed over the vent (up to 1 km high and several kilometres across). The
viscosity of the lava is high because the magmas are typically somewhere
between basalts and rhyolites in composition, extensive degassing has taken
place during ascent causing a major increase in the viscosity of the melt
(Section 1.3.3), and extensive crystal growth caused by undercooling may
also have occurred.
The management of volcanic eruption scenarios is often complicated
by the fact that volcanic activity can display dramatic changes in eruption
style. For example, it is common for slow, steady lava-dome eruptions to
be interrupted suddenly (and repeatedly) by violent explosions. In some
cases, such as on Montserrat, a cyclic pattern emerges. This condition has
5
been studied by Sparks (1997) and Voight et al. (1999). Gas exsolution and
crystallisation during the slow, extrusive phase increase magma viscosity.
This produces a stiff plug of magma which inhibits flow of magma up the
conduit. As a result, high pressures start to evolve, especially at the top
of the conduit. Eventually, these pressures are sufficient to drive the plug
from the conduit. Pressure is released in an explosive event. A fresh batch
of magma ascends and a new cycle commences. Connor et al. (2003),
developed a log-logistic probability model of repose intervals that attempted
to account for these competing processes in the conduit.
1.3
Pre-Eruptive Physical Processes
Processes that occur within the conduit during or immediately preceding
an eruption are arguably of prime importance for a number of reasons: they
are inextricably linked to eruption precursors that are (or could be) used
for forecasting; they provide the initial conditions for the surface flows; and
they control the sudden, dangerous switches in eruption styles. We will
now consider some of these subsurface processes in a little more detail so
that we can later consider how they relate to data collected during volcano
monitoring.
1.3.1
Nucleation and Growth of Bubbles and Crystals
Bubble nucleation and growth provide the primary driving force in most
eruptions. But how do bubbles nucleate? Imagine a system with a liquid
and gas in contact at a constant pressure. At ‘saturation’, gas and liquid are in equilibrium, the amount of gas dissolved in the liquid is stable.
For bubbles to nucleate, the pressure must be dropped until a certain ‘supersaturation’ ∆P is reached. We distinguish between ‘homogeneous’ and
‘heterogeneous’ nucleation (see Figure 1.7) (Hurwitz and Navon, 1994). Homogeneous nucleation occurs in the absence of solid surfaces (Figure 1.7 (a)).
The supersaturation required for homogeneous nucleation in a rhyolite (i.e.
the high silica, highly explosive type of magma) is high (∆P ≥ 120 − 350
MPa). The supersaturation required for heterogeneous nucleation on crystals (or other solid surfaces) is generally much lower (∆P ≥ 5 − 25 MPa)
(Figure 1.7(b)).
Whether bubbles nucleate on crystals at all and what the supersaturation is depends on the wetting characteristics of the crystals. A melt that
strongly adheres to, or ‘wets’, a crystal will not allow an intervening gas
phase to displace it. The supersaturation is a function of the melt-vapour
surface tension, the Helmholtz free energy for creating a curved surface, and
the strength of wetting, which can be determined from the contact angle
6
θ at the intersection of the three phases (Figure 1.7 (c)). When θ = 0◦ ,
the melt completely coats the crystal, wetting is strong, nucleation is homogeneous and requires a high supersaturation, i.e. ∆P is a maximum.
When θ = 180◦ , the gas completely coats the crystal, there is no wetting,
nucleation is heterogeneous and occurs at low supersaturation, i.e. ∆P is
a minimum. The composition of the magma and the crystals has a strong
effect on the supersaturation needed to initiate nucleation.
Mangan et al. (2004) have recently reported that in dacitic magmas
(which have a silica content that is intermediate between rhyolite and basalt)
homogeneous nucleation occurs at the low supersaturations more commonly
associated with heterogeneous nucleation (∆P = 35 ± 5 MPa). As a result,
nucleation occurs early in dacitic melts, there is more time for bubble coalescence and other processes related to gas loss, and the likelihood of effusive or only moderately explosive eruptions is increased. This explains why
the most explosive eruptions are most commonly associated with rhyolitic
magma; only this type of magma has the capacity to generate the necessary
high supersaturations.
Once bubbles have nucleated they grow by decompression, as the material expands up the conduit, and by diffusion of more volatiles from the
melt. The gas concentration in the bubbles is lower than in the surrounding
melt and so the volatiles in the melt surrounding the bubbles will diffuse
towards the bubble. This process is described by the diffusion equation
∂C
∂t
= D∇2 C,
∇2 =
where
∂2
∂2
∂2
+
+
,
∂x2 ∂y 2 ∂z 2
(1.1)
(1.2)
C is the concentration, t is time, and D is the diffusivity. The diffusivity
D is a measure of the rate at which the molecules of a particular volatile
species move down a concentration gradient in a particular medium.
Crystallisation of a silicate melt during magma intrusion or eruption
may result from either a decrease in temperature or a change in the concentration of one of its components. Cooling is not the main driving force for
crystallization of ascending water-saturated magmas, which may be nearly
isothermal over most of the eruption sequence. Rather crystallization is
more commonly induced by an increase in the liquidus (the temperature at
which the solid and liquid are in equilibrium) as H2 O is lost from the melt
by decompression. Figure 1.8 shows the schematic model of Métrich and
Rutherford (1998) in which crystallization is driven by decompression and
H2 O loss in a basaltic magma which contains 2.5 wt% H2 O at the outset.
The model supposes equilibrium and a decompression rate slow enough to
allow nucleation and crystal growth.
7
1.3.2
Open-System Degassing
It was stated earlier that rhyolites typically contain high water contents
(dissolved as water vapour), that the water is not very mobile, and that
degassing is rapid during eruptions, i.e. the water cannot escape during an
eruption. This leads to highly explosive activity. Nevertheless, rhyolitic volcanoes often erupt effusive lava flows and domes which are comparatively
free of volatiles. One possible explanation of this paradox is that these
‘dry’ lavas derive from dry magma at depth. This is not compatible with
information from Fe-Ti oxide geothermometry and observations of mineral
assemblages. For example, it is often observed that effusively-erupted rhyolitic lavas contain just ∼ 0.1 wt% H2 O and that they also contain hornblende crystals. However, at least 3 wt% H2 O is necessary to stabilise the
hornblende crystals at the temperatures indicated from Fe-Ti oxide geothermometry. The implication is that the magmas were much wetter at depth
and that the water must have escaped prior to the eruption, i.e. that the
system was ‘open’ in some way.
The generally accepted explanation for this paradox is provided by
the ‘permeable foam’ model of Eichelberger (1995) (see Figure 1.9). The
timescale necessary for a bubble to diffuse across the conduit is too long to
explain the observed gas loss. Eichelberger (1995) proposed that the pores
must be connected and form a permeable network that enhances gas escape
from the magma, both laterally and vertically. In this way, the diffusion
length-scale is substantially shortened. Volatiles only have to diffuse to the
nearest bubble that is connected to the permeable network, and can then
flow out of the system. Thus, the style of volcanic eruptions, extremely
explosive Plinian eruption columns or comparatively gentle dome-building
eruptions, depends on both the initial physical properties of the magma and
processes that alter these properties during magma ascent.
1.3.3
Magma Rheology
The viscosity of magma is a key parameter in all considerations of flow
behaviour below the fragmentation level. For a simple definition of viscosity
consider Figure 1.10 (a). In this arrangement, fluid is contained in the gap
between two flat plates with the two horizontal cartesian coordinates as
shown and the third coordinate x3 perpendicular to the page. A stress
(force per area of plate) is applied to the upper plate to make it move. The
fluid in the gap responds by flowing. This stress force is described by the
following equation
∂u1
τ12 = η
,
(1.3)
∂x2
8
where τ12 is the stress in the x1 direction perpendicular to the x2 direction.
The flow velocity is in the x1 direction and changes in the x2 direction, so
the partial derivative gives the spatial velocity gradient and describes the
deformation rate or ‘strain rate’ of the fluid in the gap. η is the viscosity
and is a measure of the internal resistance to flow. In the special case where
η is independent of the strain rate, i.e. a graph of stress as a function of
strain rate produces a straight line, the viscosity is called ‘Newtonian’.
The viscosity of pure silicate melts (i.e. magmas that contain no bubbles or crystals) can be considered Newtonian for a wide range of flow conditions. However, the viscosity varies strongly as a function of temperature
and dissolved volatile content. The effect of water content on the viscosity of the melt is of particular importance to conduit flow dynamics (see
Figure 1.10 (b)). This is a consequence of the polymeric nature of silicate
melts, which consist of long chains or rings of Si–O tetrahedra. As water is
added to such a melt, the effect is to break-up these chains thereby lowering
the viscosity. Conversely, during an eruption, water is lost from the melt to
the bubbles, and the viscosity can rise by many orders of magnitude.
Whilst the viscosity increase during an eruption is by far the dominant
rheological effect, it is important not to neglect the effect of the multiple
phases. During bubble formation, a melt undergoes a transition from a
single phase to a two-phase bubbly flow (or possibly from a two-phase liquidcrystal mixture to a three-phase flow). This structural change also has a
rheological effect, which has recently been investigated by Llewellin et al.
(2002) and Rust and Manga (2002). Adding bubbles to a Newtonian liquid
causes the mixture to become shear-thinning, i.e. the viscosity drops as the
strain-rate increases. Also, the surface tension at the bubble walls provides
a restoring force. This introduces a component of elasticity into unsteady
flows, i.e. the bubbly flows are ‘viscoelastic’. By increasing the gas content
of the flow the viscosity of the mixture tends to reduce, except for slow,
steady flow (spherical bubbles with no elastic recovery).
1.3.4
Fragmentation and the Gas-Particle Flow Regime
The final major change in flow regime that can occur within the conduit is
that of fragmentation. Prior to fragmentation, the fluid consists of a continuous liquid phase (the silicate melt) that contains growing bubbles (and
possibly crystals). If degassing is sufficiently rapid and widespread then
at some height in the conduit the continuous liquid phase is disrupted. A
suspension of hot, discrete, bubbly magma fragments, the ‘pyroclasts’, in a
continuous gas phase is created. Fragmentation is the defining characteristic of explosive eruptions (see Figure 1.4 (a); i.e. the presence or absence of
fragmentation is used to distinguish between explosive and effusive volcan9
ism.
Figure 1.11 shows a flowchart that describes the processes leading up
to fragmentation. A pressure decrease initiates degassing. Bubbles nucleate and start to grow. This causes two important changes. Firstly, water
is lost from the melt into bubbles. This causes the viscosity of the melt
surrounding the bubbles to increase dramatically (Figure 1.10 (b)). The
viscosity increase is maximal just at the bubble walls as here the dehydration is the greatest. Secondly, the growth of the bubbles causes an overall
density decrease. If the conduit is open and in the absence of significant
gas loss from the magma, the mixture expands, causing a huge increase in
the flow velocity (i.e. an acceleration) and hence strain-rate. The combined
effect of the increased viscosity and strain rate is that the stress at the
bubble walls becomes very great (remember that τ = η γ̇ Figure 1.10 (a)).
Fragmentation occurs when the stress at the bubble walls exceeds a critical
strength condition. Several mathematical fragmentation criteria have been
proposed by Papale (1999), Zhang (1999), and Melnik (2000).
Above the fragmentation level, the continuous phase is no longer magma
but gas. The frictional and viscous forces are much reduced and the flow
becomes turbulent. By the time the flow reaches the vent, it has typically
accelerated sufficiently to reach the local speed of sound. It is a standard
fluid dynamical result that flow in an enclosed channel, such as a conduit,
cannot exceed the local speed of sound. Such flows are termed ‘choked’.
Thus, whilst the flow pressure at the vent (usually well in excess of atmospheric pressure) is a consequence of the dynamics of the flow, the choked
flow condition provides a strong constraint on the flow velocity.
1.4
Data From Volcano Monitoring
The previous section discusses some primary physical processes that occur
prior to or during an eruption. More in-depth information about conduit
processes is needed in order to forecast the nature of volcanic eruptions.
However, these below-ground processes are not accessible to direct observation. This section considers the range of observations of volcanic behaviour
that are possible. A wealth of data are routinely collected by volcano observatories all over the world. These data are, in effect, proxies for sub-surface
processes and provide a rich source of statistical data. Proper statistical
treatment of these data will assist us in drawing accurate inferences about
the processes occurring at depth that control eruptive style and duration.
10
1.4.1
Seismic Monitoring
Seismological data are measurements of ground vibrations due to earthquakes and volcanic tremor. Seismic monitoring is one of the most common
forms of ‘volcano-watching’. Seismometers, being fairly cheap and easy to
install, have been used for more than a century to collect seismic data near
volcanoes. This seismic monitoring has demonstrated conclusively that volcanic eruptions are most often preceded by some form of seismic unrest.
Seismic activity appears to be one of the best methods currently available for forecast eruptions, at least on timescales of a few days to weeks.
Numerous successful hazard assessments have relied primarily on seismic
data; for example, many thousands of lives were saved in the 1990’s as a
result of evacuations of Pinatubo and Mayon volcanoes following seismic
precursors to the eruptions.
The study of seismic traces and time-series is complex. The method
relies on first monitoring the background seismicity. Observers look for
changes in this background trace that might herald an eruption. Historically, the interpretation of seismic data has been more of an art than a
science. The staff at a particular volcano observatory become familiar with
‘their’ volcano, possibly over very long acquaintance, and come to understand what type of outcome to expect from changes in seismic behaviour,
without necessarily being able to link the observations to specific processes
at depth. Neuberg, in his chapter, provides an examination of seismic monitoring and modelling using time-series data analysis techniques.
Rigorous statistical methods of analysis are being increasingly used and
examples are given in the chapters by Alasonati (discrete wavelet transformations and hidden Markov models), Hellweg and Seidl (contingency tables), Jaquet et al. (variogram analysis) and Palacios et al. (the GutenbergRichter law). Recently, there have been attempts to model the physical
processes to reproduce the seismic signals and hence explain their origin.
Models fall into two camps (Neuberg, this volume). Chouet (1985) proposed that the seismic wave field is produced by resonating cracks filled
with bubbly magma. By contrast, Neuberg et al. (1998) postulate that
the wave field results from excitation of a volcanic conduit filled with a
gas-melt mixture with depth-dependent properties. These models are the
first to consider the fundamental processes, and produce synthetic seismic
signals that can be compared to natural signals.
1.4.2
Ground Deformation
Prior to an eruption, there is an increase in pressure at depth. This causes
the volcanic edifice to swell. Therefore, studies of ground deformation are
one of the most useful indicators of existing volcanic activity and an im11
pending volcanic eruption. Ground deformation is measured by conventional surveying techniques, GPS (global positioning system), SAR (synthetic aperture radar) interferometry by satellite, or tiltmeters that can be
installed either on the flanks of a volcano or in a borehole. These techniques
aim to obtain repeated measurements of relative vertical height and/or horizontal distance. Changes in ground deformation often indicate an alteration
in sub-surface activity.
Interpreting the data and so making reliable forecasts is problematic.
The paper by Mogi (1958) was the first attempt to infer sub-surface processes from surface deformation. He modelled the magma chamber as a
sphere within an semi-infinite, elastic medium with a flat surface. He calculated the topographic change of the flat surface due to a pressure change
in the sphere. Mogi successfully applied this theory to Sakurajima volcano,
Japan, and Kilauea volcano, Hawaii. His theory has been extended to allow
for more realistic topographies and magma chamber shapes. That these
theories manage to predict general ground deformation as well as they do,
given that volcanoes are not strictly elastic bodies, is perhaps surprising.
Brittle fracture occurs at volcanoes often indicated by an abrupt occurrence of ground deformation at the onset of an eruption. This contrasts
with ground deformation being modelled as a gradual, precursive, change.
1.4.3
Gas Monitoring
Volatile degassing provides the primary driving force for explosive eruptions. The quantity of volatiles dissolved in magma prior to an eruption
determines to a large part whether an eruption will be explosive or not.
Since volatiles play such an important role, studies of gas emissions at volcanoes are used to provide insights into the sources of magmas, how magmas
move up through the volcanic system, the impact of hydrothermal systems,
and eruptive styles.
Volcanic gases are released through ‘fumaroles’ and hot springs located
on the flanks of volcanoes. The gases can be sampled directly by hand,
by ground-based UV (ultraviolet) or IR (infrared) spectrometers, or more
recently by space-based TOMS (total ozone mapping spectrometer) which
measures sulphur dioxide erupted by volcanoes into the stratosphere.
1.4.4
Other Monitoring Data
A host of other types of data are collected on active volcanoes. It is beyond the scope of this chapter to describe them all in detail. Commonly
collected data include, gravity, magnetic, electrical and thermal measurements. Visual observations are made of plume heights, flow propagation
12
(e.g. runout, speed, direction) eruption style and duration. Observations
of the volcanic rocks left behind by volcanism are also important in establishing physicochemical properties and so providing important constraints
on modelling.
1.5
Modelling Approaches
During the past few decades, an important focus of physical volcanological
research has been the numerical modelling of flow processes. The goal of
process modelling is to understand the fundamental controls that drive the
dynamics of volcanic eruptions. Ultimately, these models may provide a
forecasting tool. Models now exist for a wide range of different flow processes. A new generation of physically and mathematically sophisticated
models often include 2 or (pseudo) 3 dimensions, independent sets of equations for different phases, unsteady flow conditions, and complex descriptions of key physical parameters (e.g. viscosity, diffusivity, equation of state,
solubility laws etc.). These models capture the primary features of the dynamics of the sub-surface flows in the magma chamber and conduit and
the surface flows in Plinian eruption columns and pyroclastic flows. Several
examples of such modelling are presented in this volume.
Sparks and Melnik present a model of magma flow up a volcanic conduit, whereas Neuberg discusses the wave field produced by excitation of
a conduit filled with a melt-bubble mixture. These models produce synthetic time series that can be compared against natural time series. A key
feature of synthetic time series models is that they provide insight into the
statistical structure of observed volcano time series. Likewise, the potential
exists to validate (or calibrate) these models by comparing (or matching)
the statistics of the natural time series with those of the synthetic time
series. The chapters by Alasonati et al., Jaquet et al., Nason, and Young
review contrasting statistical approaches for analysing such time series data.
The chapter by Bonadonna considers probabilistic forecasting of fallout from Plinian eruption columns. Her approach uses a process-based
numerical model that allows for atmospheric diffusion, wind transport, and
particle fall with stochastic sampling of inputs to produce a probability map
of tephra accumulation.
As the complexity of models increases, so do the computational difficulties associated with implementing them. The chapters by Connor and
Connor, and Diez address some of these issues. Diez describes computational approaches for implementing a coupled conduit flow and eruption
column model. Connor and Connor discuss data inversion using parallel
computing techniques. Parallel computing is increasingly used in probabilistic modelling, such as that presented by Bonadonna, where the full
13
parameter-space of a complex process-oriented model has to be explored.
The inversion technique presented by Connor and Connor optimizes a nonlinear model to estimate eruption parameters using geologic observations
(in their case, measurements of a tephra deposit).
So far this chapter has recognized volcanic hazards as physico-chemical
processes having the potential to cause loss of life or damage to property
and infrastructure. Hazard management and mitigation involves determining the risk associated with these hazards, i.e. the probability and extent to
which a particular hazardous event will cause loss of life or damage to property or infrastructure. The distinction between hazard and risk is critical
to any sensible decision- or policy-making process.
Determining risk requires scientists to draw together many disparate
strands of information. These include data from monitoring, calculated
outputs from process-oriented models, and the formal incorporation of expert opinion. Outputs from such compilations include probabilistic event
trees and hazard maps, both of which attempt to identify and evaluate
risk and define regions for possible evacuation and exclusion. The chapters
by Aspinall, Marzocchi et al., and Bonnadonna discuss approaches to this
problem.
1.6
Concluding Remarks
This chapter summarises our current understanding and ability to model
the fundamental processes operating during volcanic eruptions. Predicting
these processes will allow us to manage volcanic emergencies more effectively. The processes are inherently stochastic, so predictions need to be
probabilistic.
Years of direct observation and monitoring of individual volcanoes has
produced a wealth of data which can be analysed statistically. These analyses will ultimately link monitoring observations with unobserved processes
at depth, infer significance from change, and help volcanologists assign probabilities to expected outcomes.
This volume provides a snapshot of statistical ideas and methods that
are currently of interest within volcanology. The following chapters describe
applications of statistical methods to specific volcanological problems, and
cultivate didactic links between process-oriented volcanology and statistical
modelling.
Further Reading
For general reviews of eruption processes and models see the volumes edited by
Gilbert and Sparks (1998) and Freundt and Rosi (1998). Monitoring and hazard
14
mitigation are covered by the volumes edited by Scarpa and Tilling (1996) and
McGuire, Kilburn and Murray (1995). An excellent general text covering many
aspects of volcanology, including monitoring and hazard assessment but excluding
statistics, is the Encyclopaedia of Volcanology edited by Sigurdsson et al. (2000).
Acknowledgements
This chapter has benefited from comments by my co-editors Stuart Coles and
Chuck Connor. My attendance at the “Statistics in Volcanology” workshop was
sponsored as part of the Environmental Mathematics and Statistics Programme
funded jointly by NERC/EPSRC, UK.
15
Bibliography
[1] Blower, J.D., Keating, J.P., Mader, H. M. & Phillips, J. C. 2002. The
evolution of bubble size distributions in volcanic eruptions. Journal
of Volcanology and Geothermal Research, 120, 1-23.
[2] Chouet, B. 1985. Excitation of a buried magmatic pipe: A seismic
source model for volcanic tremor. Journal of Geophysical Research
90(B2), 1881-1893.
[3] Connor, C.B., Stamatakos, J.A., Ferrill, D.A., Hill, B.E., Ofoegbu,
G.O., Conway, M.F., Sagar, B. & Trapp, J. 2000. Geologic factors
controlling patterns of small-volume basaltic volcanism: Application
to a volcanic hazards assessment at Yucca Mountain, Nevada. Journal
of Geophysical Research 105(1), 417-432.
[4] Connor, C.B., Sparks, R.S.J., Mason, R.M., Bonadonna, C. & Young,
S.R. 2003. Exploring links between physical and probabilistic models
of volcanic eruptions: The Soufrière Hills Volcano, Montserrat. Geophysical Research Letters, 30(13), 1701, doi:10.1029/2003GL017384.
[5] Eichelberger, J.C. 1995. Silicic volcanism: Ascent of viscous magmas
from crustal reservoirs. Annual Reviews of Earth and Planetary Science, 23, 41-63.
[6] Gilbert, J.S. & Sparks, R.S.J. (eds) 1998. The physics of explosive
volcanic eruptions. Geological Society, London, Special Publications,
145.
[7] Freundt, A. & Rosi, M. (eds) 1998. From magma to tephra: Modelling
physical processes of explosive volcanic eruptions. Developments in
Volcanology, 4, Elsevier.
[8] Huppert, H.E. & Woods, A.W. 2002. The role of volatiles in magma
chamber dynamics. Nature, 420(6915), 493-495.
16
[9] Hurwitz, S. & Navon, O. 1994. Bubble nucleation in rhyolitic melts:
Experiments at high pressure, temperature and water content. Earth
and Planetary Science Letters, 122, 267-280.
[10] Llewellin, E.W. , Mader, H.M. & Wilson, S.D.R. 2002. The rheology
of a bubbly liquid. Proceedings of the Royal Society of London, Series
A 458, 987-1016.
[11] Mangan, M.T., Sisson, T.W. and Hankins, W.B. 2004. Decompression experiments identify kinetic controls on explosive
silicic eruptions. Geophysical Research Letters, 31, L08605,
doi:190.1029/2004GL019509.
[12] McGuire, W.J., Kilburn, C.R.J. & Murray, J. (eds) 1995. Monitoring
active volcanoes. UCL Press, London.
[13] Melnik, O. 2000. Dynamics of two-phase conduit flow of high-viscosity
gas-saturated magma: Large variations of sustained explosive eruption intensity. Bulletin of Volcanology, 62(3), 153-170.
[14] Métrich, N. & Rutherford, M.J. 1998. Low pressure crystallization
paths of H2 O-saturated basaltic-hawaiitic melts from Mt Etna: Implications for open-system degassing of basaltic volcanoes. Geochimia
Cosmochima Acta, 62, 1195-1205.
[15] Mogi, K. 1958. Relations between the eruptions of various volcanoes
and the deformation of the ground surfaces between them. Bulletin of
the Earthquake Research Institute (University of Tokyo), 36, 99-134.
[16] Murase, T. 1962. Viscosity and related properties of volcanic rocks at
800 ◦ C to 1400 ◦ C. Hokkaido University Faculty of Science Journal
Series, 7(1), 487-584.
[17] Neuberg, J., Baptie, B., Luckett, R. & Stewart, R. 1998. Results from
the broad-band seismic network on Montserrat. Geophysical Research
Letters, 25(19), 3661-3664.
[18] Papale, P. 1999. Strain-induced magma fragmentation in explosive
eruptions. Nature, 397(6718), 425-428.
[19] Rust, A.C. & Manga, M. 2002. Effects of bubble deformation on the
viscosity of dilute suspensions. Journal of Non-Newtonian Rheology,
104, 53-63.
[20] Scarpa, R. and& Tilling, R.I. (eds) 1996. Monitoring and mitigation
of volcanic hazards. Springer, Berlin/Heidelberg.
17
[21] Sigurdsson, H., Houghton, B., NcNutt, S.R., Rymer, H. and Stix, J.
(eds) 2000. Encyclopaedia of Volcanoes. Academic Press.
[22] Simkin, T. & Siebert, L. 1994. Volcanoes of the World, 2nd Edition.
Geoscience Press, Tucson.
[23] Sparks, R.S.J. 1997. Causes and consequences of pressurisation in lava
dome eruptions. Earth and Planetary Science Letters, 150(3-4), 177189.
[24] Tilling, R.I. 1989. Volcanic hazards and their mitigation - Progress
and problems. Reviews of Geophysics, 27(2), 237-269.
[25] Voight, B. et al. 1999. Magma flow instability and cyclic activity
at Soufrière Hills Volcano, Montserrat, British West Indies. Science,
283(5405), 1138-1142.
[26] Woods, A.W. & Huppert, H.E. 2003. On magma chamber evolution during slow effusive eruption. Journal of Geophysical Research,
108(B8), 2403, doi:10.1029/2002JB002019.
[27] Zimanowski, B. 1998. Phreatomagmatic explosions. In: Freundt, A. &
Rosi, M. (eds) From magma to tephra: Modelling physical processes of
explosive volcanic eruptions. Elsevier, Developments in Volcanology,
4, chapter 2, 225-53.
[28] Zhang, Y. X. 1999. A criterion for the fragmentation of bubbly magma
based on brittle failure theory. Nature, 402(6762), 648-650.
18
60˚
“Ring of Fire”
30˚
0˚
-30˚
-60˚
270˚
315˚
0˚
45˚
90˚
135˚
180˚
225˚
270˚
Figure 1.1: The spatial distribution of volcanoes (dots) relative to tectonic
plates (dotted-lines). Locations of volcanoes active in the Holocene (last
10,000 years). (Ex: Simkin and Seibert, 1994)
Oceanic-continental convergence
Figure 1.2: Melt generation in subduction zones, e.g. the ‘Ring of Fire’
shown in Fig. 1.1. The lithosphere and the asthenosphere are layers of the
upper mantle. Courtesy: USGS.
19
7.0 7.5
6.5
6.0
5.5
Magnitude
5.0
4.5
4.0
0
500
1000
1500
2000
Year
Figure 1.3: Historical record of eruptions with magnitude greater than 4M.
The magnitude of an eruption is given by M = logm − 7 where m is the
mass released in kg. (Ex: Coles and Sparks, this volume)
umbrella cloud
fire fountain
Plinian
eruption
column
lava
dome
pyroclastic
flow
fragmentation
bubbly flow
(crystal growth?)
increasing
pressure
bubbly flow
(crystal growth?)
nucleation
magma chamber
increasing
pressure
nucleation
magma chamber
(a)
magma input from depth
lava
flow
lava
lake
(b)
magma input from depth
bubbly flow
(crystal growth?)
increasing
pressure
nucleation
magma chamber
(c)
magma input from depth
Figure 1.4: Sketches of the basic physical process for (a) explosive eruptions,
(b) effusive eruptions, and (c) lava dome eruptions.
20
(a)
(b)
(c)
(d)
Figure 1.5: Explosive eruptions. (a) Plinian eruption column. Lascar
volcano, Chile, 1993. (b) Collapsing eruption column, Soufrière volcano,
Montserrat, 20th October 1997. Courtesy: E. Calder. (c) and (d) Pyroclastic flow towards Shimbara city, Unzen volcano, Japan, 24th June 1993.
Note size of houses for scale. Courtesy: Volcanological Society of Japan.
21
(a)
(b)
(c)
(d)
Figure 1.6: Effusive eruptions. (a) Fire fountain on Pu’u ’O’o, Kilauea, 2nd
June 1986. Note helicopter in white circle for scale. Courtesy: C. Heliker,
USGS. (b) Lava fountain feeding lava flows, Fernandina, Galápagos, 1978.
Courtesy: Tom Simkin, Smithsonian Institution (photo by Marc Orbach).
(c) Large bubble ∼ 5 m across on lava pond, Mauna Ulu, 1969. Courtesy:
J. B. Judd, USGS. (d) Lava dome, Mt St Helens, USA, 13th September
1984. Courtesy: L. Topinka, USGS.
bubble
q
crystal
melt
(a)
(c)
(b)
Figure 1.7: Nucleation processes. (a) Homogeneous bubble nucleation in the
absence of solid surfaces. (b) Heterogeneous bubble nucleation on crystals.
(c) Heterogeneous nucleation dominates for contact angles θ > 68◦
22
Summit
craters
0
Melt
composition
wt%
Fraction (wt%)
of solid
.8 .6
.4
.2
0
ol. + cpx. + plag. + mgt.
0
0
1
2
3
4
200
-740 m
ol. + cpx.
400
600
-2200 m
ol.
800
Basaltic magma
with 2.5 wt% H²0
1000
K²0
H²0
PH²0
Figure 1.8: Crystallisation processes. In the sketch on the left, a basaltic
magma containing 2.5 wt% H2 O at 2200 m depth rises up an inclined conduit to erupt on the flank of a volcano. The graphs on the right show the
increase in the crystal content and magma composition as the material rises
up the conduit. As the magma rises, water is steadily lost due to decompression. The liquidus increases and different crystals are nucleated at different
depths. The solid fraction of crystals increases and the chemical composition of the remaining melt (see K2 O curve) is changed. Specific crystals
identified are: ol = olivine, cpx = clinopyroxene, plag = plagioclase, mgt =
magnetite. (Ex: Métrich and Rutherford, 1998)
23
(a)
(b)
Figure 1.9: The ‘permeable foam’ model. (a) Volatiles escape by diffusing
towards bubbles that are connected to a permeable network. (b) Flow
through the network can be lateral (volatiles escape via cracks and fissures
in the conduit walls), or vertical, (volatiles escape via the vent).
24
stress=force/area
= τ12 [Pa]
u1+du1
dx2
u1
velocity gradient du1/dx2 [s-1]
= strainrate [s-1]
x2
x1
(a)
1011
Viscosity [Pa s]
109
107
105
103
800°C
1000°C
1200°C
1400°C
101
2
4
6
8
10
12
H2O content [wt%]
(b)
Figure 1.10: The viscosity of magmas. (a) Flow of a viscous fluid between a
fixed (bottom) and a moving (top) plate. The strain-rate is identical to the
spatial velocity gradient. (b) The Newtonian viscosity of rhyolitic magmas
as a function of temperature and gas content. Note the logarithmic y-axis.
(Ex: Murase, 1962)
25
density
decrease
velocity
increase
strainrate
increase
fragmentation
pressure
decrease
gas volume fraction
increase & dissolved
water decrease
viscosity
increase
Figure 1.11: Flowchart of processes leading to fragmentation. Courtesy: P.
Papale.
26