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Dyke apertures record stress
accumulation during sustained
Samuel T. Thiele1,2*, Alexander R. Cruden1, Steven Micklethwaite1, Andrew P. Bunger3,4 &
The feedback between dyke and sill intrusions and the evolution of stresses within volcanic systems
is poorly understood, despite its importance for magma transport and volcano instability. Long-lived
ocean island volcanoes are crosscut by thousands of dykes, which must be accommodated through
a combination of ank slip and visco-elastic deformation. Flank slip is dominant in some volcanoes
(e.g., Kilauea), but how intrusions are accommodated in other volcanic systems remains unknown.
Here we apply digital mapping techniques to collect > 400,000 orientation and aperture measurements
from 519 sheet intrusions within Volcán Taburiente (La Palma, Canary Islands, Spain) and investigate
their emplacement and accommodation. We show that vertically ascending dykes were deected
to propagate laterally as they approached the surface of the volcano, forming a radial dyke swarm,
and propose a visco-elastic model for their accommodation. Our model reproduces the measured
dyke-aperture distribution and predicts that stress accumulates within densely intruded regions of
the volcano, blocking subsequent dykes and causing eruptive activity to migrate. These results have
signicant implications for the organisation of magma transport within volcanic edices, and the
evolution and stability of long-lived volcanic systems.
Magma plumbing systems comprise temporally and spatially interconnected dykes, sills and magma chambers
that exert fundamental controls on volcanic behaviour1. ey inuence and reect edice processes, and so
provide a record of volcano dynamics and long-term evolution that is essential for the development of predictive
models. Dierent volcanoes exhibit a range of magma plumbing styles due to variations in geological setting.
For example, the mechanical properties of the volcanic basement, and exure of the underlying lithosphere,
can exert a rst-order control on stresses within and beneath volcanic edices, and hence the organisation of
their magma plumbing systems2,3. Similarly, magma plumbing systems have been suggested to be inuenced
by topographic stresses4–6, upli due to the emplacement of magma at depth7,8, edice instability3,9,10, remote
tectonic stresses11,12 and basement structures13.
In this contribution we investigate the mechanisms that control and accommodate dyke injections in the shal-
low plumbing system of Volcán Taburiente, which forms the northern part of La Palma (Canary Islands; Fig.1).
is area is of interest as many thousands of intrusions1,11,14 are exceptionally well exposed along spectacular
cli sections, and because these intrusions may record the self-organisation of a radial magma plumbing system
into a discrete ri zone15. e eventual collapse of the edice aer ca. 400 kyr of activity16 could also be linked
to this plumbing system reorganisation.
Geological setting. e Canary Islands are constructed on slow moving (< 2cm/year) Jurassic oceanic
crust west of the coast of Morocco. As a result, volcanic islands in this region tend to be long-lived compared
to e.g., Hawaiian volcanoes, due to lower plate-velocities, and they undergo limited subsidence because of the
stiness of the underlying oceanic crust17. e intraplate setting of the Canary Islands and their distance from
Atlantic mid-ocean ridge spreading centres also results in low horizontal dierential stresses compared to other
USA. *email: email@example.com
Scientic Reports | (2020) 10:17335 |
It is broadly accepted that magmatism at La Palma (and the other Canary Islands) results from an upwelling
mantle plume that triggers mantle melting through decompression and the addition of heat17. However, magma
production rates are much lower than at other hotspots17,19, and as a result many of the islands (including La
Palma) do not appear to host long-lived shallow magma reservoirs. is hypothesis is supported by pyroxene
phenocryst and melt inclusion geobarometry20,21 and geophysical observations from eruptions at the neighbour-
ing El Hierro in 201122.
Instead, eruptions on La Palma appear to be fed by magma that accumulated and crystallised pyroxene and
olivine within deep, long-lived reservoirs in the upper mantle (~ 20–30 + km depth) before being emplaced for a
much shorter period of time (weeks to months) in the uppermost mantle or lower crust (10–15km depth), and
nally migrating upwards along rapidly propagating dykes to erupt (Fig.1).
As is typical of ocean island volcanoes, each of the Canary Islands is constructed from several distinct volcanic
edices. La Palma consists of an uplied Pliocene seamount (~ 4–2Ma) overlain by a succession of sub-aerial
edices: Garaa (~ 2–1.2Ma), Taburiente (1.2–0.56Ma), Bejenado (0.56–0.49Ma), and Cumbre Vieja (0.56Ma
to present)16. Lavas and pyroclastic products from Volcán Taburiente cover most of the north of the island, with
Garaa and seamount complex rocks exposed only along the bottom of deeply incised ravines. e southern part
of the island is formed by the currently active Cumbre Vieja volcano, a N–S oriented ridge lined with Holocene
scoria cones and lava ows16.
Each of these volcanic edices are separated by signicant erosional unconformities, generally related to large
edice collapse events15. e Garaa edice is thought to have collapsed to the south-west at ~ 1.2Ma, forming
a large depression that was rapidly lled by Volcán Taburiente11,17. From ~ 0.8Ma Taburiente volcanism appears
to have migrated southwards, extending the edice’s southern ank and forming an elongate, N-S oriented
ridge. is ridge collapsed towards the west at ~ 0.56Ma, aer which post-collapse volcanism rapidly formed
the Bejenado edice16. However volcanism continued to migrate southwards, leaving the collapse escarpment
(now dened by the Cumbre Nueva ridge15) unlled and forming the currently active Cumbre Vieja edice in
the south of the island.
Dykes in the shallow parts of the Taburiente edice have radial orientations1,11,14, indicating that the least
compressive stress σ3 is oriented circumferentially around a central point. Circumferential orientations of σ3
can be caused by a source of pressure at the swarm centre (e.g., a magma chamber) or by a radially decreasing
topographic load (as is typically imposed by a volcanic edice), although topographic stresses tend to dominate
at shallow depths23. Similar radial dyke swarms have been reported from Mt Somma/Vesuvio (Italy)24, Summer
Coon (USA)25, Oki-Dozen (Japan)26 and Lyttleton (New Zealand)27.
While dykes that are injected into elongate ri zones such as those in Hawaii can be accommodated by lateral
ank displacement28, the accommodation mechanism for radial swarms is less clear. With this in mind, we pre-
sent data on the orientation and thickness of dykes within the Volcán Taburiente, quantify the bulk-strain they
induced, and consider their inuence on intra-edice stresses and the evolution of the magma plumbing system.
Orientation and thickness. Erosion of the Cumbre Nueva collapse scarp has incised deep into Volcán
Taburiente to form an arcuate series of ~ 1km high clis known as Caldera Taburiente15,29 (Fig.1). We have
taken advantage of this landscape to map the spectacularly exposed shallow magma plumbing system in unprec-
edented detail using 14 unmanned aerial vehicle (UAV) surveys conducted over ~ 2–50 hectare areas. Emerging
Figure1. Location and prominent topographic features of La Palma, Canary Islands. Schematic cross section
A–A′ through Volcán Taburiente is based on various geobarometry studies20,21. Deection of dykes in the upper
parts of the edice to propagate laterally is inferred from results of this study. Map created using QGIS 2.18
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three-dimensional (3-D) digital mapping techniques30,31 were then applied to extract > 400,000 orientation and
thickness measurements from 519 sheet intrusions.
As expected, these measurements highlight the generally radial orientations of the intrusions. We constrain
the focal point of the radial dyke swarm using strike measurements and a maximum likelihood estimator (see
Supplementary Method), which delineates an area in the southern part of Caldera Taburiente ~ 1.5km north of
Bejenado (see Supplementary Fig.S1). Surveys from the northern side of the Caldera (Las Pareditas, Risco Liso,
Hoyo Verde and Los Cantos) also suggest a population of thicker and somewhat shallower dipping intrusions
striking NW and crosscut by the radial dykes (see Supplementary Figs.S1, S2).
Many sheet intrusions in Caldera Taburiente have geometries that suggest they propagated laterally. ese
include basal terminations, step-overs and broken bridge structures with shallow dipping axes (see Supplemen-
tary Fig.S2). Field observations of stretched vesicles and striated chilled margins associated with strongly aligned
plagioclase ow fabrics32 indicate ow lineations that plunge gently (0°–40°) both towards and away from the
dyke swarm focal point (see Supplementary Fig.S1). As such, we interpret that dykes ascending vertically from
below Volcán Taburiente were deected to propagate laterally and radially as they approached the surface (Fig.1).
A large range of thicknesses were measured for both dykes (dip > 45°) and inclined sheets (dips < 45°, includ-
ing true sills). Measurements from dykes have a mode thickness of ~ 0.6m and a long-tailed distribution, extend-
ing to ~ 5m (Fig.2a). To avoid biases due to measurements near dyke tips, a ‘maximum aperture’ dataset was
created by removing measurements below the 75th percentile and those above the 90th percentile (assumed to
reect erroneous measurements or abnormally thick dyke sections). For clarity, we use the term ‘thickness’ to
describe the collection of all measurements and ‘aperture’ to refer to the estimates of each intrusion’s maximum
thickness. e aperture measurements have a mode of ~ 1m and a long-tailed distribution similar to the thick-
ness data (Fig.2a).
e thickness and aperture of inclined sheets are similar to the dykes, although they tend towards higher
values (Fig.2a) with modes of ~ 0.6 and 1.25m respectively. Unlike the dykes, however, the aperture distribution
of inclined sheets contains anomalously thick subpopulations (> 30m thick, e.g. Supplementary Fig.S2). is
irregularity could be because fewer inclined sheets were sampled, but might also suggest that the apertures of
sills and other shallow-dipping intrusions are limited by dierent factors to dykes.
A striking relationship can be observed between intrusion altitude, a rough proxy for its depth of formation,
and thickness. Below ~ 1400m above sea level, the intrusions have a median thickness of ~ 1m, but by ~ 1800m
this has increased to nearly 2m, where it appears to plateau (Fig.2b). Based on a paleo-altitude estimate
of ~ 2500m around the rim of present-day Caldera Taburiente (the current elevation of its highest point), and
assuming that most of the dykes formed when the edice was similar to its current size, this region of increasing
dyke thickness corresponds to below surface paleo-depths of ~ 1100 to 700m. Above ~ 1800m altitude (< 700m
paleo-depth) the frequency of > 2.5m thick dykes also appears to increase (Fig.2b).
Excess magma pressure. e ratio between dyke aperture and length has been used by several authors to
estimate excess pressure driving dyke emplacement26,33–35, where excess pressure is the dierence between total
magma pressure and the normal stress resisting initial dyke opening. We have applied this method to our dataset
by selecting 52 dykes that are exposed in their entirety in the UAV surveys, such that their tip-to-tip ‘span’ could
be measured. Assuming the dykes propagated sub-horizontally, as suggested previously, these span measure-
ments were projected onto a vertical plane to give measurements of the dyke height (h). Excess pressure (Pexcess)
was then estimated using the aperture (a) measurements; assuming that the dykes are much longer than they are
Figure2. Kernel density estimates (a) describing the thickness and aperture (dened as the 75th to 90th
percentiles of thickness measurements for each dyke) of all dykes (i, ii) and inclined sheets (iii, iv). ickness
measurements were also divided into 50m high bins (b) based on their elevation and the interquartile range
(red lines), median (black line) and a kernel density estimate of the underlying distribution (grey) plotted. is
shows a clear increase in thickness between ~ 1400 and 1800m above sea level. No clear trend in thickness can
be seen above this altitude, although unusually thick dykes appear to become more common.
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high and vertical pressure variations are negligible, Pexcess can be related to a and h using the plane-strain solution
to a pressurised elliptical crack33,35:
is excess pressure estimate will vary proportionally to the elastic properties of the volcanic edice. e
bulk Young’s modulus (E) is rather dicult to ascertain, and in this context presumably depends on the ratio
of compliant pyroclastic material to sti basalt ows. Values of 1 to 5 GPa have been used by previous authors
for studies on basaltic volcanoes25,33,34, and hence we evaluate excess pressure over this range. Poisson’s ratio (v)
was kept xed at 0.25.
e results (Fig.3) show substantial variation in estimated excess pressure, probably because (1) propagation
directions may not have been strictly horizontal, meaning the dyke ‘height’ will be under- or over-estimated, (2)
solidied apertures may not represent the fracture aperture during dyke propagation, and (3) a range of actual
magma pressure is likely. Regardless of these limitations, the results indicate excess pressures of ~ 10 to 60MPa,
similar to estimates from other studies25,33,34.
Induced strain. e continuity of exposure in Caldera Taburiente allowed us to estimate the vertical and
tangential strain induced by the intrusions in Volcán Taburiente, using a cylindrical coordinate system with its
origin at the previously described maximum likelihood radial centre. Tangential strain estimates range between
1 and 10%, with maximum values observed in the north of the caldera (Fig.4a). An increased number of intru-
sions in this area is noticeable both in the eld and in aerial imagery, suggesting that these results are reasonable.
Vertical strain (Fig.4b) follows a similar but weaker trend, suggesting relatively modest endogenous growth
from shallow intrusions (1–2%). e large spike in the 90th percentile of estimated vertical strain at the Hoyo
Verde site results from a single very thick (> 30m) inclined sheet (Supplementary Fig.S2), and is probably only
a local eect.
Strain accommodation mechanisms. is strain must have been accommodated by a combination
of (1) accumulated elastic stresses in the edice, (2) ductile and plastic deformation such as compaction and
faulting, and/or (3) ank movement along a basal detachment or ductile layer. Mechanisms (1) and (2) can be
combined in a Maxwell visco-elastic model that estimates the edice stresses that result from intrusions in the
absence of a basal detachment and associated ank slip.
First, we dene a polar coordinate system with r and θ corresponding to the radial distance and rotation
(strike direction) relative to the focal point of the dykes, respectively (Supplementary Fig.S3). Assuming that
radial and vertical stresses are transmitted to the volcano’s free surface (σr = σz = 0), stress caused by the injection
of the radial dykes (σθ) will be uniaxial in the circumferential direction. To avoid unreasonably large strains near
the centre of the dyke swarm, we also assume that ascending dykes are deected towards areas of lowest stress and
so, as an ensemble, induce approximately constant circumferential stress. us, the rate of dyke-injections (fd)
varies in proportion with 2πr such that the rate of circumferential strain (ε̇θ) is spatially uniform (Supplementary
Fig.S3). is is convenient as it makes our choice of r arbitrary (we use 5km). Similar accommodation-stress
induced migration of volcanism has been demonstrated by Derrien and Taisne36, who simulated repeated dyke
injection into an analogue volcano.
Based on these assumptions, we can relate ε̇θ with σθ and the edice’s bulk properties (shear modulus G and
viscosity µ) using the Maxwell visco-elastic constitutive equation (see Supplementary Method for derivation):
Figure3. Height and aperture of the 52 dykes for which measurements could be obtained (a), coloured using
overpressure estimates calculated using Eq.(1) and a Young’s modulus (E) and Poisson’s ratio (v) of 2.5 GPa and
0.25 respectively. e top 25% of estimates were considered to be outliers (unlled circles) as they result from
dykes with unusually small length-aperture ratios. Kernel density estimates of the calculated excess pressure
using dierent Young’s moduli highlight signicant uncertainty and/or variation (b), although they suggest that
typical values between 10 and 60MPa seems plausible. Note that outliers (top 25% of calculated excess pressure)
were excluded during the kernel density estimation.
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Strain rate ε̇θ can be related to the frequency fd at which dykes intrude across a given circumference (dened
by radius r) and their aperture a, rewriting Eq.(2) as:
Using Eq.(1), we can also relate dyke apertures to the excess magma pressure, which we here dene as some
initial excess pressure P0 minus the accumulated accommodation stresses σθ. Substituting into Eq.(3) and re-
arranging into a conventional form for a rst-order, linear ordinary dierential equation we get:
is dierential equation (Eq.(6)) can be solved analytically to give the accommodation stress as a function
of time t (assuming that the initial σθ = 0), namely:
Values for G and v and µ are somewhat constrained by the literature25,33,34, although uncertainties exist due
to their scale-dependence and the highly fractured and heterolithic nature of volcanic materials. Based on the
abundance of compliant breccia and pyroclastic materials in Volcán Taburiente, we have chosen to use a Young’s
modulus of 2 GPa and Poisson’s ratio of 0.25, which corresponds to a shear modulus of 0.8 GPa. Viscosity is
less well constrained, but is generally thought to be on the order of 1022–1023 Pas for basaltic rocks at shallow
depths and low temperatures9. We tried a range of µ between 1 × 1022 and 5 × 1022 Pas (Supplementary Fig.S3).
e model is insensitive to Poisson’s ratio.
e remaining variables in Eq.(1) (P0, fd and h) can be related directly to the observed dyke aperture distri-
bution and nal bulk strain. P0 is related to the largest observed aperture using Eq.(1), and given we are using
E = 2 GPa, our eld observations (Fig.3) suggest that it should be 60–70MPa. All three terms can also be related
directly to the observed nal strain, the accommodation stress asymptote, and hence the mode of the aperture
distribution (see the Supplementary Method for more details). us, we can estimate these terms by tting them
to our measurements of dyke aperture and spacing (see Supplementary Fig.S3).
Finally, we perturbed the overpressure at each timestep (using a numerical solution to Eq.(4)) such that
it followed a normal distribution with a mean of P0 and a standard deviation that was optimised (along with
Figure4. Map showing the median (solid line), 10th and 90th percentiles (dotted lines) of tangential (a) and
vertical (b) strain estimated using 1m spaced scan lines extracted from each digital outcrop model. ese show
a general tangential strain of ~ 2–4% through much of the caldera and substantially higher values (6–10%) in the
north. A similar pattern is observed for vertical strain, although the net vertical extension is much less (~ 1–2%).
Data from Los Andenes has been omitted from this analysis due to the limited number of intrusions at that site.
Note the dierence in the strain plot scale between (a,b).
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P0, fd and h, as previously described) to t the observed aperture distribution. Overpressure was modelled as a
stochastic variable to account for natural variations in the yield stress at which the source magma chamber fails
during each dyking event37 and variations in magma buoyancy and viscosity.
e estimated apertures (Fig.5) show a close t to our observations, and the optimised parameters are geo-
logically reasonable with the exception of dyke height (53m), which is signicantly less than we would expect.
Using an elastic modulus of 2 GPa in Eq.(1) and excess pressures of 65–80MPa, > 100m high dykes would be
10s of metres thick, which has not been observed.
is discrepancy can be explained if h instead represents an eective elastic height, which is signicantly less
than the actual height of large dykes due to (1) partial closure prior to solidication, and (2) bonding between
either side of the fracture due to unbroken rock bridges (which are commonly observed on La Palma and else-
where as ‘step-overs’; Supplementary Fig.S2). Unbroken rock-bridges tying together nominal fracture surfaces
are commonly observed in laboratory experiments examining uid-driven rock fracture; a striking example is
shown in Fig.24 of Hampton etal.38. However, the quantitative impact of these rock-bridges on fracture aperture
remains an unresolved topic of ongoing research.
Because petrological constraints indicate magma is not stored at shallow depths below La Palma20,21, we suggest
the Taburiente dykes are radial because of topographic stresses rather than a shallow pressure source. e tempo-
ral progression of dyke orientations from NW striking towards radial observed from deeper parts of the edice
(Supplementary Fig.S1) is also consistent with deection due to increasing edice load. Early intrusions would
have formed in a NW orientation because of a combination of NNW-oriented regional maximum horizontal
stress, post-collapse stress modication39 and topography associated with the Garaa volcano. As the Taburiente
edice grew (probably quite rapidly16), topographic stresses progressively came to dominate regional stresses,
favouring more radial dyke orientations.
Due to the topographic source of radial stress in Volcán Taburiente, dykes need not have propagated away
from the dyke swarm focal point. Indeed, this is unlikely given, (1) the lack of evidence for shallow storage,
and (2) the variable plunge-directions of observed ow indicators. Instead, we suggest that dykes ascending
through the crust re-oriented into radial orientations as they entered the region below Volcán Taburiente where
topographic stresses became dominant. In our conceptual model (Fig.1), dykes propagate laterally as they are
deected away from regions of elevated topographic stress40, and possibly also due to decreasing buoyancy at shal-
low depths, forming blade-shaped intrusions (e.g. Supplementary Fig.S2). Similar interactions between ascend-
ing dykes and topographic loads have been suggested based on numerical models5 and eld observations12,25.
e inverse correlation between dyke thickness and depth results from a shi in the balance between conn-
ing pressure (resisting fracture opening) and internal magma pressure, although a decrease in host-rock elastic
modulus at shallow depths could also play a role. We suggest that the distinct range of paleo-depths (1.1–0.7km)
over which the increase in aperture occurs could be explained by the transition from supercritical to gaseous H2O
at pressures of ~ 22 MPa41 (depths ~ 750–900m). It is also plausible that less overpressured dykes are arrested or
deected before they reach the upper levels of the edice, and hence shallower dykes tend to be thicker.
Based on the distribution of preserved eruptive centres, it has been suggested16 that the northern anks of
Volcán Taburiente were formed by two diuse ri-zones trending NE and NW. Including the collapsed Cumbre
Nueva ridge in the south, this would give the Taburiente edice a ‘three-pointed-star’ type geometry that has
long been proposed as typical for the Canary Islands7. However, based on our strain estimates (Fig.4), we nd
no evidence for a concentration of dykes along the NE or NW margins of the Caldera.
Figure5. A numerical solution to the previously described Maxwell accommodation model using the elastic
parameters described in the text, randomly varying magma pressure sampled from a normal distribution, and
calibrated using Powell minimization to t observed aperture data. e optimised parameters (µ = 3.0 × 1022,
Fd = 2.1 days/ka, h = 53m and P = Ν(µ = 66, σ = 8.8) MPa) give results that closely match the observations. e
nal bulk strain of 5.5% and equilibrium excess pressure of 17.5MPa were not used to calibrate the model, and
match eld estimates (Figs.3, 4) excellently. Note, however, that this is probably not a unique solution and so
there may be other parameter combinations that reproduce the observed aperture data equally well.
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Instead, our data suggests that even though dykes in the Taburiente magma plumbing system are radial,
N–S orientations are favoured, causing denser dyke swarms and larger (~ 8% vs ~ 3%) extensional strain in the
Hoyo Verde and Los Cantos areas. Measurements of dykes crosscutting the seamount complex also suggest a
dominant N–S trend14. It seems plausible that this orientation was favoured from early in the growth of Volcán
Taburiente due to NNW–SSE oriented regional horizontal stress11 and topographic loads associated with the
Garaa edice and its subsequent collapse. Abundant proximal pyroclastic deposits exposed immediately above
the basal unconformity of Volcán Taburiente at Los Cantos support this hypothesis, as they suggest signicant
early volcanic activity in the north of the Caldera.
e location of the focal point of the radial dykes provides an additional constraint on the geometry of Volcán
Taburiente, as it should lie at the centre of the topographic stress eld and hence below the edice paleo-summit.
Its position in the south of Caldera Taburiente suggests a more elongate edice than is indicated by modern-day
topography. We therefore conclude that our dyke orientation measurements and the strain induced by their
emplacement are best explained by a somewhat elongated Taburiente edice. is topography would further
encourage the emplacement of N–S dykes4, helping to explain the strain localisation observed in the north of
Caldera Taburiente and the late-stage growth of the N–S oriented Cumbre Nueva ridge.
Combining these interpretations of Volcán Taburiente’s shallow magma plumbing system with our Maxwell
visco-elastic model for radial dyke accommodation, we propose that a combination of topographic and remote
tectonic stresses governed dyke-propagation paths, while dyke induced strain was accommodated visco-elasti-
cally. Accommodation stresses associated with this visco-elastic deformation will have caused stress to evolve
towards an isotropic state within heavily intruded portions of the edice. Subsequent dykes would have been
deected away from these regions of high stress6,36, causing volcanic activity to migrate. In our model (Fig.5)
the accommodation stress reaches a maximum at about the same time that eruptive activity began to focus on
the southern ank of Volcán Taburiente, forming the Cumbre Nueva ridge. We propose that this shi in activity
occurred as dykes were deected southwards by a ‘stress-plug’ formed near the centre of the radial dyke swarm
(below the summit of Volcán Taburiente), noting that escape to the north would have been blocked by stresses
related to the older Garaa edice16.
e transition from radial to focused dyking below the Cumbre Nueva ridge can thus be explained by accom-
modation stresses blocking dyke ascent below the summit of Volcán Taburiente and regional tectonic stress
favouring N–S oriented dykes. If widespread, this process of stress-plug development followed by lateral escape
may help to explain the apparent self-organisation of many volcanic systems into elongate volcanic ridges or ri
zones. e competition between stress plug development due to intrusive activity and counteracting topographic
stress changes due to eruptive activity and/or edice instability could also be a signicant control on the evolu-
tion of magma plumbing systems and distribution of associated volcanism.
e close t between eld measurements and the apertures predicted by our Maxwell visco-elastic model
highlight the inuence of accommodation stress on dyke apertures. Volcanic systems typically have long-tailed
dyke aperture distributions, which have previously been interpreted to reect the distribution of magma cham-
ber failure pressures33. Our results show that this need not be the case. Instead, the build-up of accommodation
stress can also cause long-tailed dyke aperture distributions, regardless of the distribution of source overpres-
sures. ese eects must be considered should aperture data be used to estimate source properties33,37,42, as these
methods typically assume lithostatic stress.
We conclude that the stresses induced by successive intrusions accumulate in volcanic edices and inuence
dyke propagation paths and apertures. e stress eld within heavily intruded regions may be signicantly dif-
ferent to that predicted by a lithostatic model, because dyke-induced deformation increases horizontal stress
magnitude and in doing so reduces the dierential stress. Stress plug development by this mechanism may be
an important and widespread control on the spatio-temporal distribution of volcanism in long-lived volcanic
Digital mapping. To circumvent limited access to steep and unstable exposures within Caldera Taburiente,
14 unmanned aerial vehicle (UAV) surveys were conducted over ~ 2–50 hectare areas. Survey sites were chosen
to capture a representative distribution of the available exposure within Caldera Taburiente and a range of dif-
ferent depths. Imagery was collected using a DJI Phantom 4 Pro and its integrated camera (20–megapixel CMOS
sensor) along horizontal ight lines ~ 30–60m from the cli faces using horizontal and ~ 30 degree downward
oriented viewing angles and vertical and horizontal overlaps of ~ 80%. ese image sets were then reconstructed
using a structure-from-motion multi-view-stereo (SfM-MVS) workow30,43 to create a database of 3-D digital
outcrop point cloud models at ground sampling distances of ~ 2–5cm. Specic details of each of the surveys
is included in the Supplementary Method and the dataset can be downloaded from https ://doi.org/10.26180
/5d688 c17f2 ed2.
e upper and lower surfaces of 519 intrusions within these models were then digitised from the high-reso-
lution 3-D point clouds using the Compass plugin in Cloud Compare31. Continuous exposure within the survey
areas means that all intrusions > 20cm thick could be identied, allowing the number and spacing of intrusions
in each survey area to be characterised. Structure-normal estimates (SNEs)30 constraining dyke orientation and
true thickness were also generated at each point along the intrusion contacts. ese were manually vetted to
remove invalid results in non-planar sections of the dyke or where data quality was poor30, aer which 12 million
SNEs from ~ 400,000 locations remained, covering ~ 60% of the 66km of digitised dyke margins.
Strain estimation. Dykes in each survey were divided into horizontal scan-lines spaced at intervals of 1m
vertically to investigate the bulk-strain associated with their emplacement. Assuming Mode I opening, the dila-
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tion vector of each dyke along a scan line was calculated from the SNEs by multiplying the structure normal vec-
tor by the dyke thickness. ese opening vectors were summed along each scan line, and the resultant expressed
in radial and tangential components based on the maximum likelihood radial centre. e same method was used
to estimate vertical strain at each location, although in this case vertical scan lines were used and both dykes and
inclined sheets were included.
Visco-elastic modelling. Python code for our visco-elastic modelling and the generation of Supplemen-
tary Fig.S3 and Fig.5 is included in the Supplementary Method, along with the derivation of our Maxwell
constitutive equation (Eq.(2)).
e digital outcrop models and associated structural measurements analysed during this study are available on
the FigShare repository, https ://doi.org/10.26180 /5d688 c17f2 ed2. e python code used to perform our analyses
is included in the Supplementary Information les.
Received: 1 November 2019; Accepted: 2 September 2020
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magmatic sheet-intrusion swarms and long-lived conduits. In Volcanic and Igneous Plumbing Systems (ed. Burchardt, S.) 89–112
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e authors gratefully acknowledge the sta at Parque Nacional Caldera de Taburiente for their generous support
and hospitality during collection of the eld data presented in this study. We would also like to thank JC Car-
racedo for a splendid introduction to the Canary Islands during the early stages of this work. ST was supported by
a Westpac Future Leaders Scholarship and Australian Postgraduate Award. APB wishes to acknowledge support
provided by the U.S. National Science Foundation under Grant No. 1645246. ARC is supported by Australian
Research Council Discovery Grant DP190102422. We also wish to acknowledge insightful and constructive
reviews by two anonymous reviewers.
S.T., S.M. and A.C. developed the ideas presented in this paper and collected the eld data. S.T., A.B. and J.K.
developed the Maxwell accommodation model. S.T. performed the analyses and wrote the python code to
produce Figs.2, 3, 4 and 5. All authors helped interpret the results and their implications, and contributed to
manuscript preparation and writing.
e authors declare no competing interests.
Supplementary information is available for this paper at https ://doi.org/10.1038/s4159 8-020-74361 -w.
Correspondence and requests for materials should be addressed to S.T.T.
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