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The geometric difference between non-feeders and feeder
dikes
Nobuo Geshia, Shigekazu Kusumotob, Agust Gudmundssonc
a Geological Survey of Japan, AIST, 1-1-1 Higashi, Tsukuba,
Ibaraki, 305-8567, Japan b Graduate School of Science and
Engineering for Research, University of Toyama, 3190 Gofuku,
Toyama-shi, Toyama, 930-8555, Japan c Department of Earth Sciences,
Queen's Building, Royal Holloway University of London, Egham,
Surrey, TW20 0EX, UK
ABSTRACT Feeder-dikes bring magma to the surface; non-feeders
become arrested and never reach the surface. The differences, if
any, between these dike types remain largely
unexplored because, in the field, it is normally unknown if a
particular dike is a feeder or non-feeder. Here present
measurements of feeder and non-feeder dikes
exposed from depths of more than 200 m to the surface in the
walls of the AD 2000 caldera collapse of the Miyakejima Volcano,
Japan. A typical feeder thickness reaches a maximum of 2-4 m at the
surface, decreases rapidly to about 1 m at depth of 20 - 40 m, and
then remains constant to the bottom of the exposure. By contrast, a
typical non-feeder thickness reaches a maximum of 1.5-2 m at 15 -
45 m below the tip, and then decreases slowly with depth to 0.5-1 m
at the bottom of the exposure. We propose that free-surface effects
and magmatic overpressure (driving pressure) changes during the
eruption cause the overall shape of a feeder to differ from that of
a non-feeder.
Keywords: dike emplacement, magma pressure, rock properties,
crustal stresses, surface deformation, volcanic hazard
Geology, 38, 195198, 2010
INTRODUCTION Most volcanic unrest periods do not result in an
eruption (Newhall and Dzurisin,
1988). Even those unrest periods where a magma-filled fracture,
a dike, is known to have been injected from a magma chamber do not
normally result in an eruption
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(Pollard et al., 1983; Bonafede and Rivalta, 1999; Gudmundsson,
2003). Since dikes (including inclined sheets) supply magma to all
fissure eruptions, understanding the conditions that either stop
(arrest) the dike tip or allow it to reach the surface are of
fundamental importance for understanding unrest periods and for
assessing volcanic hazards and risks.
There have been some geometric studies of feeder dikes close to
craters (Gudmundsson, 2003; Gudmundsson et al., 1999), but no
systematic studies of thickness variations of feeders and
non-feeders in highly active volcanoes, primarily because the most
active parts of volcanic edifices lack suitable outcrops of dikes.
The Miyakejima Volcano is probably unique because the caldera
collapse in A.D. 2000 (Geshi et al., 2002) generated a 200-450 m
high, subvertical outcrop that is ideal for detailed geometric
measurements of non-feeders and feeders.
Here we report the first results on the dikes in this outcrop.
The focus is on (1) detailed measurements of the thickness
variation of feeders and non-feeders as a function of depth and
host-rock properties, (2) the overall geometric difference between
the feeders and non-feeders, and (3) a general conceptual model to
explain the difference.
DIKES IN THE CALDERA WALL The Miyakejima Volcano, a basaltic -
andesitic stratovolcano on the volcanic front of
Izu - Mariana subduction zone (Fig. 1A), is one of the most
active volcanoes in Japan. There have been repeated flank fissure
eruptions through a radial dike system in the volcano, with smaller
summit eruptions, for at least the past 10 ka (Fig. 1B) (Tsukui et
al., 2005). The summit, a basaltic stratocone built primarily
between 10-3 ka, collapsed at around 2.5 ka. The resulting caldera
was subsequently buried by an intracaldera cone until about 1 ka.
The A.D. 2000 caldera, 1.7 km across and about 450 m deep, dissects
both the earlier stratocone and the later intracaldera cone (Fig.
1B; Geshi et al., 2002; Geshi, 2009).
We observed165 dikes in the caldera wall, some of which can be
traced vertically for up to 350 m (Fig. 2). The average dike
thickness from all the measurements is 1.3 m, whereas the maximum
measured dike thickness is 9.9 m. Some dikes in the caldera
wall
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show en echelon arrangement of segments, but most are offset in
an irregular manner (Fig. 2). Most of the dikes strike radially
from the central vent area which was destroyed during the caldera
formation. The dike frequency is highest in the northwestern sector
of the caldera walls, where the 10-2.5 ka deposits are exposed.
The dikes in the caldera wall are of two types; feeders and
non-feeders (Fig. 2). All the non-feeders terminate either by
tapering away inside layers or ending bluntly at layer contacts,
indicating that the dike segments seen in the caldera wall did not
reach to the surface. Some 95% of dike-segments in the caldera wall
are non-feeders although it is impossible to know if segments of
the non-feeders reached the ground surface away from outcrop. The
number of non-feeders exposed in the caldera wall (>100),
however, is much greater than that of surface eruption fissures
(
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dike segmentation, cross-cutting younger dikes, hydrothermal
alteration, brecciation by the caldera collapse, and debris cover.
The representative five non-feeder dikes and three feeder dikes are
shown in Figure 3.
For a typical non-feeder, the thickness increases from the tip
to a maximum of 1.5-2.1 m at 15-45 m below the tip, and then
decreases slowly with depth to 0.5-1 m at the bottom of the
exposure (Fig. 3). Below the maximum, the rate of decrease of dike
thickness is typically about 0.5 m/100 m. For example, the
non-feeder dike 90-04 (Fig. 3) increases its thickness to 2.1 m at
45 m below the tip, and then decreases its thickness to 0.8 m at a
depth of 180 m. The thickness of segmented dikes locally changes at
the segment boundary but generally decreases with the depth (Fig.
3).
For feeder-dikes, the thickness distribution is very different
(Fig. 3). Typically, the thickness reaches a maximum of 2-4 m at
the surface, decreases rapidly to about 1 m at depth of 20-40 m,
and then remains constant to the bottom of the exposure. For
example, the thickness of the feeder to the 1535 fissure eruption
(Fig. 3) peaks at 3.5 m at the base of its spatter cone. Then it
first decreases rapidly to about 1.0 m at a depth of 30 m and then
remains essentially constant to the bottom of the exposure at 100
m.
FACTORS CONTROLLING DIKE THICKNESS One remarkable feature of the
non-feeder dikes is the general and gradual thickness
decrease below the maximum at a few tens of meters below the
tip. We suggest that this thickness decrease is primarily related
to the decreasing magmatic overpressure (driving pressure) and
increasing host-rock Youngs modulus with depth. This follows, in a
simple way, from the following equation (Sneddon and Lowengrub,
1969):
b
ELvPo
212 (1)
where b is the thickness (strictly, the maximum thickness) of
the dike, Po is the magmatic overpressure (the pressure in excess
of the normal stress on the dike at the point of thickness
measurement), is Poisson's ratio and E Young's modulus of the host
rock at the point of measurement. L is the dike controlling
dimension, that is, the smaller of the dip and strike dimensions of
the dike.
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Eq. (1) has been used by many workers as a simple model for
dikes and sills (Delaney and Pollard, 1981; Gudmundsson, 1990;
Poland et al., 2008). For E = 1GPa (compliant, near-surface rocks)
and = 0.25 (Bell, 2000), the average magmatic overpressures of the
non-feeders 90-01, 90-02, 90-03, and 90-04 are 7-12 MPa. These
values are similar to those obtained by many other workers (Delaney
and Pollard, 1981; Gudmundsson, 1990; Poland et al., 2008).
The magmatic overpressure or driving pressure is given by
(Gudmundsson, 1990): demro pghP (2)
where r is the density of the host rock, m is the density of the
magma, g is the acceleration due to gravity, h is the dip dimension
or height of the dike (positive upward from the source chamber) at
the point of thickness measurement, pe is the excess magmatic
pressure in the source chamber before rupture and dike injection
(normally equal to the in situ tensile strength of the rock), and d
is the stress difference between the vertical and the horizontal
compressive stress at the point of dike-thickness measurement.
Since most dikes are pure extension fractures, d is generally equal
to the difference between the minimum and maximum principal
compressive stresses at the point of measurement.
From Eqs. (1,2) it follows that the overpressure of a
propagating dike increases with increasing dip dimension (height)
of the dike above its source chamber so long as the average density
of the host rock layers is greater than the magma density. When Po
increases, it follows from Eq. (1) that, other things being equal,
the dike thickness increases. Thus, the thickness of a dike
normally decreases, and its strike dimension increases, that is,
the dike becomes thinner and longer along strike, with increasing
depth below the point of maximum overpressure (Gudmundsson, 1990),
in agreement with the present measurements (Fig. 3).
Gas expansion may decrease the density of basaltic magma at very
shallow levels in the volcano. Initial water contents of the
basaltic magmas of Miyakejima are estimated at 2 wt% (Kuritani et
al., 2003) and the magmas already contained bubbles when they
intruded into the volcanic edifice. Thus, even if the density of
the rock layers through
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which the dike propagates decreases toward the surface, so does
the magma density. Consequently, the buoyancy term in Eq. (2)
results in the dike overpressure and, from Eq. (1), thickness may
increase down to a few tens of meters below the surface. Below this
depth, however, the overpressure generally decreases as the dike
height h above its source chamber decreases. Also, as a result of
compaction of the porous and poorly-consolidated pyroclastics in
the volcano, Youngs modulus generally increases with the depth.
Thus, from Eq. (1), an average increase in Young's modulus and
decrease in overpressure results in the dike thickness decreasing
with depth below its maximum.
In addition to the general thickness trends, there are
irregular, local thickness variations in both dike types (Fig. 3).
There is, for example, an abrupt thickness increase in dike 110-01,
a local "bulge", at 75-85 m below the dike tip where the dike
dissects poorly-consolidated scoriaceous tuff. Similar
dike-thickness variations have been observed, for example, in
layered sedimentary rocks (Baer, 1991).
This irregularity in thickness is, we propose, primarily related
to abrupt changes in the physical properties, primarily Young's
modulus, of the rock layers that the dikes dissect. Although
Young's modulus generally increases with depth, as explained above,
it may vary abruptly between compliant or soft poorly-consolidated
pyroclastic layers and stiff lava flows and welded layers. The
difference in stiffness between these layers may easily reach a
factor of ten, and occasionally a factor of 100 (Bell, 2000).
DISCUSSION AND CONCLUSIONS The essentially constant thickness of
a typical feeder dike, except for its near-surface
part, suggests the buoyancy of the magmas was gradually lost
during the eruption, and that the magma reached a
stress-equilibrium with the host rock at the end of eruption. We
attribute the rapid dike-thickness increase toward the surface in
the uppermost 20-40 m to two factors. One is the elastic
free-surface effect (Isida, 1955; Pollard et al., 1983; Gray,
1992), which effectively means that due to lack of constraints at
the free surface (as half the elastic space is "removed"), on
meeting the surface the fracture (here the dike) tends to open up.
The second factor is erosion of the dike walls due to thermal and
dynamic effects (Bruce and Huppert, 1989).
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Feeders propagate and grow as non-feeders before they reach the
surface. Therefore, the geometric difference between these types of
dike, as described above, is primarily a reflection of the feeders
reaching the surface. A non-feeder largely keeps its original
emplacement geometry, whereas once a feeder reaches the surface its
magmatic overpressure gradually falls, during the course of the
eruption, and its thickness decreases to balance the horizontal
stress in the host rock.
In conclusion, this study shows that there are significant
differences between the overall geometries of feeder-dikes and
non-feeders, indicating that the non-feeders reflect the overall
shapes of magma-filled fracture before eruption whereas the feeders
reflect the overall shapes at the end of eruptions. The magmatic
pressure within a typical feeder seems to equilibrate with the host
rock during the eruption so that, except in the near-surface part,
its thickness becomes relatively constant. Thus, the feeder
thickness does not reflect the emplacement conditions, but rather
the conditions at the end of the eruption. This is in stark
contrast with a typical non-feeder which largely keeps its original
thickness. Thus, the geometry of an exposed non-feeder is an
indication of its magmatic overpressure, a controlling factor in
the mechanics of dike emplacement.
ACKNOWLEDGMENTS The authors thank Hiroshi Shinohara and Teruki
Oikawa for helpful suggestions,
Valerio Acocella, Mike Poland, Alessandro Tibaldi, and Sandra J
Wyld for helpful review comments, and the Japan Meteorological
Agency (Miyake Observatory) and the local government of Miyake
Village for support during the field surveys.
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control of basaltic fissure eruptions: Nature,
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porous
sedimentary rocks: Journal of Geophysical Research, v. 96, p.
11,911-11,929. Bonafede, M. and Rivalta, E., 1999, The tensile
dislocation problem in a layered elastic
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medium: Geophysical Journal International, v. 136, p. 341-356.
Delaney, P.T., and Pollard, D.D., 1981, Deformation of host rocks
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during growth of minette dikes and breccia bearing intrusions
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Gray, T.G.F., 1992, Handbook of Crack Opening Data: Abington
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Gudmundsson, A., 1990, Emplacement of dikes, sills and crustal
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Sneddon, I.N., M. Lowengrub, 1969, Crack Problems in the
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English Abstract)
Figure 1. A) Locality map of Miyakejima Volcano. B) Outline of
the caldera formed during the 2000 eruption and the radial trends
of major eruption fissures (broken lines).
Figure 2. A) Part of the dike swarm in the northwestern part of
the caldera wall (a.s.l. means "above sea level"). The blue arrows
indicate dike 90-01 and pink arrows indicate dike 90-04. B) Feeder
dike to the AD 1535 scoria cone, with a thick tip indicated by the
upper arrow and its thin lowermost exposed part by the lower arrow.
The thickness variations of these dikes are presented in Fig.
3..
Figure 3. Variation in thicknesses of 5 non-feeders and 3
feeder-dykes. Notice the widely different overall geometries of the
dikes, as well as the abrupt local thickness changes in many of
them. Horizontal broken lines show segment boundaries (S.B.).
Host-rock lithology is shown in the diagram for dike 110-01,
showing a local bulge in tuff layer.
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The difference between feeders and non-feeder dikes, Geology,
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