Fractal Analysis of Enclaves as a New Tool for Estimating Rheological Properties of Magmas During Mixing: The Case of Montaa Reventada (Tenerife, Canary Islands)

Abstract

The volcanic unit of Montaña Reventada on the island of Tenerife (Canary Islands, Spain) is an example of magma mingling and mixing in which the eruptive process was triggered by an intrusion of basanite into a phonolite magma chamber. The eruption started with emplacement of a basanitic scoria deposit followed by emplacement of a phonolitic lava flow characterized by the presence of mafic enclaves. These enclaves represent approximately 1 % of the outcrop and are basanitic, phono-tephritic and tephri-phonolitic in composition. The morphology of each enclave is different, varying from rounded to complex finger-like structures usually with cuspate terminations. In this study we quantified textural heterogeneity related to the enclaves generated by the mixing process and thus provided a new perspective on the 1100 Ad Montaña Reventada eruption. The textural study was performed by use of fractal geometry methods and the results show that the logarithm of the viscosity ratio between the phonolitic magma and the enclaves ranges between 0.39 and 0.81, with a mode at 0.49. This enables us to infer the water content is 2–2.5 wt% for the phonolitic magma and 1.5–2 wt% for the basanitic magma and the enclaves.

Full text

Fractal Analysis of Enclaves as a New Tool for Estimating Rheological Properties of Magmas
During Mixing: The Case of Montan
˜a Reventada (Tenerife, Canary Islands)
HELENA ALBERT,
1
DIEGO PERUGINI,
2
and JOAN MARTI
´
3
Abstract—The volcanic unit of Montan
˜a Reventada on the
island of Tenerife (Canary Islands, Spain) is an example of magma
mingling and mixing in which the eruptive process was triggered
by an intrusion of basanite into a phonolite magma chamber. The
eruption started with emplacement of a basanitic scoria deposit
followed by emplacement of a phonolitic lava flow characterized
by the presence of mafic enclaves. These enclaves represent
approximately 1 % of the outcrop and are basanitic, phono-te-
phritic and tephri-phonolitic in composition. The morphology of
each enclave is different, varying from rounded to complex finger-
like structures usually with cuspate terminations. In this study we
quantified textural heterogeneity related to the enclaves generated
by the mixing process and thus provided a new perspective on the
1100 ADMontan
˜a Reventada eruption. The textural study was
performed by use of fractal geometry methods and the results show
that the logarithm of the viscosity ratio between the phonolitic
magma and the enclaves ranges between 0.39 and 0.81, with a
mode at 0.49. This enables us to infer the water content is
2–2.5 wt% for the phonolitic magma and 1.5–2 wt% for the ba-
sanitic magma and the enclaves.
Key words: Magma mixing, Fractal analysis, Tenerife, Vis-
cosity, Water content, Basanite.
1. Introduction
Fractal geometry has recently been used in several
studies to study mixing processes. In these studies
magma mixing is described as a chaotic process
(FLINDERS and CLEMENS,1996;PERUGINI et al., 2002,
2003a,2006;P
ERUGINI and POLI,2000;POLI and PE-
RUGINI,2002), which implies that study of magma
mixing can be kinematically constrained to the study
of the stretching and folding of magmas and the
diffusion processes that originate between them (PE-
RUGINI and POLI,2012). These studies have provided a
new perspective for calculating properties and con-
ditions related to magma chamber dynamics, for
example the viscosity ratio between magmas and the
proportions of the magmas involved in the mixing
process.
The physical mixing (mingling) of two magmas
with contrasting physical properties tends to result
in the formation of enclaves (PERUGINI et al., 2007)
and/or the presence of flow banding, which has
been described by some authors as the result of
stretching and folding of magma filaments (PERU-
GINI et al., 2003b,2004). When the two magmas
equilibrate thermally, chemical diffusion also
occurs, thereby generating compositions that are
intermediate between the two initial compositions
(PETRELLI et al., 2006;PERUGINI et al., 2012,2013
MORGAVI et al., 2013). Chemical diffusion is
facilitated by the stretching and folding processes,
because of the increase of contact area between the
two magmas.
During magma mixing two kinds of region,
coherent and active, are generated (PERUGINI et al.,
2003b). Coherent regions remain generally unaf-
fected by diffusion and, therefore, the composition
of the original magmas is preserved. In contrast
with coherent regions, active regions are strongly
affected by stretching and folding, and chemical
diffusion produces a composition that is intermedi-
ate between the two magmas involved in the
mixing process. This means that magma mixing
should not be interpreted as a linear process in
which different hybrid compositions correspond to
different amounts of intruded magma. Typically,
1
Central Geophysical Observatory, Spanish Geographic
Institute (IGN), Madrid, Spain. E-mail: hln.albert@gmail.com
2
Department of Earth Sciences, University of Perugia, Pe-
rugia, Italy.
3
Institute of Earth Sciences Jaume Almera, CSIC, Barce-
lona, Spain.
Pure Appl. Geophys.
Ó2014 Springer Basel
DOI 10.1007/s00024-014-0917-5 Pure and Applied Geophysics

when a mafic magma intrudes into a felsic magma
chamber and mixing starts, magmas of different
hybrid composition will be produced, because of
the generation of coherent and active regions in
which the proportion of the two magmas and the
degrees of chemical diffusion vary (PERUGINI et al.,
2003b).
Magma mixing has been observed in the vol-
canic deposits of Tenerife (Canary Islands) in
pyroclastic rocks (WOLFF,1985;MARTI
´et al., 1990;
EDGAR et al., 2002,2007)andlavaflows(ARAN
˜A,
1985;A
RAN
˜Aet al., 1989,1994). The products of
some of these eruptions are excellent examples of
magma mixing processes resulting from the pre-
sence of enclaves and/or stretching and folding
structures. One of the best known cases of magma
mixing on Tenerife is the 1100 AD (CARRACEDO
et al., 2007)Montan
˜a Reventada eruption (ARAN
˜A
et al., 1994;WIESMAIER et al., 2011). The eruption
center is located in the island’s northwestern rift
zone, on the southwestern flank of the Teide-Pi-
coViejo (TPV) active central volcanic complex
(ABLAY and MARTI
´,2000). The eruption, in which a
batch of mafic magma from deep in the rift zone
probably intruded into the phonolitic chamber of
the TPV, generated basaltic scoria followed by
emplacement of a thick phonolite lava flow char-
acterized by the presence of multiple enclaves.
Previous studies (ARAN
˜Aet al., 1994;WIESMAIER
et al., 2011) focusing on the geochemistry and
mineralogy of the eruption products show that
these enclaves are the result of mixing between
basanitic and phonolitic magmas. Although several
studies have been performed on phonolitic magma
storage conditions in Tenerife (ANDU
´JAR et al.,
2010,2013;A
NDU
´JAR and SCAILLET,2012a,b), to
the best of our knowledge there is no information
about basanitic magma.
The purpose of the study reported in this paper
was to provide a new perspective of the 1100 AD
Montan
˜a Reventada eruption by quantifying the tex-
tural heterogeneities generated by the mixing process.
We show that a textural study performed by use of
fractal geometry methods can be useful for calculat-
ing the water content and the viscosity of the enclaves
and the basanitic magma, providing new and useful
data about this magma.
2. Geological Setting
TPV started to grow approximately 180–190 ka
ago in the interior of the caldera of Las Can
˜adas
(ABLAY and MARTI
´,2000;MARTI
´et al., 2008)
(Fig. 1). This volcanic depression originated as a
result of several vertical collapses of the former
Tenerife central volcanic edifice (Las Can
˜adas edi-
fice) caused by the explosive emptying of high-
level magma chambers. Occasional large-scale, lat-
eral collapses of the volcano flanks also occurred
and modified the resulting caldera depression
(MARTI
´et al., 1994,1997;MARTI
´and GUDMUNDSSON,
2000). Construction of the present central volcanic
complex on Tenerife involved the formation of
these twin stratovolcanoes, which are derived from
the interaction between two different shallow
magma systems that have evolved simultaneously
and have given rise to a complete magma series
from basalt to phonolite (ABLAY et al., 1998;MARTI
´
et al., 2008).
TPV mostly consists of mafic-to-intermediate
products, in which felsic materials are volumetri-
cally subordinate overall (MARTI
´et al., 2008). Felsic
products, however, predominate in the most recent
eruptions that have occurred from the central vents
and a multitude of vents distributed on the edifice’s
flanks (Fig. 1). Both mafic and phonolitic magmas
have erupted from these vents. The Santiago del
Teide and Dorsal rift axes (Fig. 1), the two main
tectonic lineations currently active on Tenerife,
probably join beneath the TPV complex (CARRACE-
DO,1994;ABLAY and MARTI
´,2000). Some flank
vents on the western side of Pico Viejo are located
on eruption fissures that are sub-parallel to fissures
located further down the Santiago del Teide rift and
define the main rift axis. This is the case of the
Montan
˜a Reventada eruption (Fig. 1) studied in this
paper. On the eastern side of Teide some flank vents
define eruption fissures that run parallel to the
Dorsal rift.
The eruptive history of the TPV comprises a
main phase of eruption of mafic-to-intermediate
lavas that form the core of the volcanoes and also
infill most of the Las Can
˜adas depression and the
adjacent La Orotava and Icod valleys. Approxi-
mately 35 ka ago the first phonolites appeared and
H. Albert et al. Pure Appl. Geophys.

since then have become the predominant material
in the TPV eruptions. Basaltic eruptions have also
continued and are mostly associated with the two
main rift zones. Available petrological data suggest
that the interaction between a deep basaltic and a
shallow phonolitic magmatic system beneath central
Tenerife controls the eruption dynamics of TPV
(MARTI
´et al., 2008). Most of the phonolitic erup-
tions from TPV show signs of magma mixing,
suggesting that eruptions are induced by intrusion
of deep basaltic magmas into shallow phonolitic
reservoirs.
The 1100 AD Montan
˜a Reventada eruption is a
clear case of a mafic eruption in the NW rift zones
in which basanitic magma interacted with phono-
litic magma from the TPV system. The result was a
Strombolian eruption that generated a welded sco-
ria deposit of basanitic composition and a
phonolitic lava flow with clear evidence of mixing.
The basanitic scoria deposit has a maximum
thickness of 2 m proximal to the vent. The lava
flow was mainly emplaced a few kilometers from
the vent and has an average thickness of 12 m. The
total volume (DRE) of the deposit estimated from
geological mapping by MARTI
´et al., (2008)is
0.054 km
3
.
3. Methodology
3.1. Fractal Dimension
The enclaves contained in the phonolitic lava flow
can be classified according to their shapes, which
vary from highly irregular to almost round (Fig. 2). A
few have angular profiles. Previous studies have
suggested that angular enclaves correspond to more
mafic compositions (ARAN
˜Aet al., 1994;WIESMAIER
et al., 2011), because of fragmentation of the contact
surface between the intruding mafic magma and the
cooler phonolitic magma (WIESMAIER et al., 2011).
Photographs of 67 samples were taken normal to
the surface of the enclaves to delineate the contact
between the enclaves and the host rock. The images
were processed by use of NIH (National Institute of
Health) software (ImageJ) to generate binary images
in which enclaves and host rock were replaced by
black and white pixels, respectively (Fig. 2). The
contact tracing operation was repeated several times
to estimate the error, which was found to be
approximately 2–3 %.
Enclaves with hybrid compositions can be studied
by using fractal geometry methods to analyze the
morphology of their complex margins. The
Figure 1
Location of the Montan
˜a Reventada lavas (MR) and illustration of rift zones and visible vents. Black dots correspond to felsic vents and white
dots to mafic and intermediate vents. SRZ Santiago rift zone, DRZ Dorsal rift zone, LC Las Can
˜adas, TTeide, PV Pico Viejo (projection UTM
28 N). Modified from MARTI
´et al., 2011
Fractal Analysis of Enclaves as a New Tool

complexity of the morphology of the enclaves was
quantified by the fractal dimension (D
box
). To
compute this value the box-counting method was
used; this consists in placing square mesh of different
sizes (r) over the image then counting the number of
boxes (N) that contain part of the image (Fig. 3).
3.2. Viscosity
PERUGINI and POLI (2005) proposed a method for
establishing the relationship between the complexity
of the morphology of the interface between two fluids
and the their viscosity ratio (V
R
), which is defined as
the ratio of the viscosity of the host fluid to that of the
driving fluid. After several fluid-mechanical experi-
ments they derived the following empirical
relationship:
log VR
ðÞ¼0:013 e3:34Dbox ð1Þ
which shows that the complexity of the interface
increases with the viscosity contrast. This empirical
relationship can be applied to natural cases to
Figure 2
Examples of enclaves and their binary images. From ato cthe morphology becomes less complex. Enclaves aand chave cuspate termination
H. Albert et al. Pure Appl. Geophys.

estimate the viscosity ratio between two magmas
coming into contact during a mixing process. The
relationship is valid only while the two magmas can
be regarded as fluids, therefore before a significant
amount of crystallization has occurred. In this study
the viscosity ratio was calculated by using the fractal
dimension of the morphology of the enclaves.
Because this was a bi-dimensional study D
box
varied
between 1 and 2.
To estimate the viscosity of the magmas as a
function of whole rock composition and temperature
we used the model produced by GIORDANO et al.,
Figure 3
aOriginal image of the enclave. bThresholded contact between the enclave and the host rock. c–eMagnified area indicated by the dashed line
in ashowing the procedure used to measure the fractal dimension (D
box
) by use of the box-counting method. Square mesh of different sizes
(r) is laid over the contact area between the enclaves and the host rock. The number of boxes (N) containing black pixels is counted
Fractal Analysis of Enclaves as a New Tool

(2008). Whole rock analyses were taken from WIESMA-
IER et al., (2011) and ARAN
˜Aet al., (1994). Average
compositions were recalculated to 100 after adding
H
2
O and recalculating all Fe to FeO
tot
(Table 1). This
procedure was used because the calculated viscosity
ratios correspond to magmas located in the magma
chamber. Therefore, it was necessary to calculate the
viscosity of magmas under plausible conditions at that
depth. Previous experimental work has shown that
phonolitic magma erupting from the TPV flank vents
was stored at temperatures of &900 °C, at pressures of
&50 MPa and with &2.5 ±0.5 wt% dissolved H
2
O
(ANDU
´JAR et al., 2010,2013;ANDU
´JAR and SCAILLET,
2012a,b). Consequently, we considered 2, 2.5 and
3 wt% H
2
O for the phonolitic magma. Because there is
no information for the water content of basanite, a range
of 1–2.5 wt% H
2
O was taken into account. An average
composition of enclaves with 65–70 % basanite and
35–30 % phonolite was contemplated, because in the
Harker diagrams shown by WIESMAIER et al., (2011),
which also include the analysis conducted by ARAN
˜A
et al., (1994), data cluster at approximately 65–70 % of
mafic magma. We propose this amount as representa-
tive of the mafic magma present in the system and the
other values as a result of different degrees of mixing,
because of the active and coherent regions. The average
composition was recalculated to 100 after adding 1.5
and 2 wt% H
2
O.
4. Results
When the box-counting method is applied to
fractal patterns the following relationship is satisfied
(MANDELBROT,1982):
N¼rDbox ð2Þ
Equation 1can be also written as:
log NðÞ¼Dbox logðrÞð3Þ
The slope of the linear interpolation of the
log(r) vs. log(N) graph is equal to -D
box
(Fig. 4).
Figure 4a–c illustrate the application of Eqs. 2and 3
to the three enclaves given in Fig. 2a–c. From a to c
the D
box
value decreases with the complexity of the
morphology of the interface. The D
box
of the 67
images of the enclaves ranges between 1.01 and 1.23
(Fig. 5) and has a mode at D
box
=1.09. A histogram
with the regression coefficients of the linear inter-
polation is given in Fig. 6.
The calculation of the logarithm of the viscosity
ratio from D
box
according to Eq. 1is shown in Fig. 7.
Figure 7b is a detail of Fig. 7a that focuses on the
variation in logV
R
. The logV
R
range between 0.39
and 0.81 and the distribution of the values can be seen
in Fig. 8. The class with V
R
=0.49 has the highest
frequency.
Table 1
Major element average from WIESMAIER et al., (2011) and ARAN
˜Aet al., (1994) recalculated to 100 after adding H
2
O
Phonolite Basanite Enclaves
2 wt%
H
2
O
2.5 wt%
H
2
O
3 wt%
H
2
O
0.5 wt%
H
2
O
1 wt%
H
2
O
1.5 wt%
H
2
O
2 wt%
H
2
O
2.5 wt%
H
2
O
1.5 wt%
H
2
O
2 wt%
H
2
O
SiO
2
58.05 57.76 57.46 46.79 46.55 46.32 46.08 45.85 50.24 49.98
TiO
2
1.15 1.14 1.13 3.35 3.34 3.32 3.30 3.29 2.56 2.55
Al
2
O
3
18.39 18.30 18.20 17.26 17.17 17.08 16.99 16.91 17.61 17.52
FeO
tot
4.25 4.23 4.21 10.11 10.06 10.01 9.95 9.91 7.93 7.89
MnO 0.16 0.16 0.16 0.18 0.18 0.18 0.18 0.18 0.17 0.17
MgO 1.16 1.16 1.15 4.54 4.52 4.49 4.47 4.45 3.25 3.24
CaO 2.21 2.19 2.18 9.15 9.10 9.05 9.01 8.96 6.83 6.79
Na
2
O 7.70 7.66 7.62 4.93 4.91 4.88 4.86 4.84 6.23 6.19
K
2
O 4.61 4.59 4.57 1.90 1.90 1.89 1.88 1.87 2.70 2.69
P
2
O
5
0.32 0.32 0.32 1.29 1.29 1.28 1.27 1.27 0.97 0.96
H
2
O 2.00 2.50 3.00 0.50 1.00 1.50 2.00 2.50 1.50 2.00
Sum 100 100 100 100 100 100 100 100 100 100
H. Albert et al. Pure Appl. Geophys.

Figure 4
Calculation of fractal dimension (D
box
). The slope of the linear interpolation of log(r) vs. log(N) is equal to -D
box
Fractal Analysis of Enclaves as a New Tool

Knowing the viscosity of the phonolite (Table 2)
and the viscosity ratio between the phonolitic magma
and the enclaves, the average viscosity of the
enclaves can be calculated as follows:
VR¼lphonolite
lenclave ð4Þ
lenclave ¼lphonolite
VRð5Þ
For the viscosity of the phonolite, computed val-
ues with 2.5 ±0.5 wt% of dissolved H
2
O were
considered. For V
R
the minimum and maximum
values were used (0.39 and 0.81) and also the value
with the highest frequency (0.49). The values
obtained are listed in Table 3.
5. Discussion
PERUGINI and POLI (2005) state that different D
box
values correspond to different V
R
. Accordingly, we
focus here on the relationship between changes in V
R
and changes in magma composition because of dif-
ferent degrees of mixing. More precisely, we propose
the existence of a mixing area in which the two
magmas interacted and produced magma of inter-
mediate composition. Some of the enclaves
considered have cuspate terminations (Fig. 2c),
which have been used as evidence (PERUGINI et al.,
2007) of the detachment of the enclaves from the
mafic magma and their move toward more felsic
magma. As WIESMAIER et al., (2011) showed, some
enclaves still have mingling structures. Enclaves with
cuspate terminations, mingling structures, and vari-
able composition—and hence variable D
box
and V
R
—
must have originated in this mixing zone throughout
the whole process.
In the first stage, when the basanite (&1,200 °C)
reached the phonolite magma chamber (&900 °C), the
more mafic enclaves, characterized by quenching and
angulate shapes, were generated by disruption of the
layer formed as a consequence of the thermic contrast
between the two magmas. According to FOLCH and
MARTI
´(1998) and SNYDER (2000), during this first stage
of mixing the temperature of the basanite started to fall
and the temperature of the phonolite started to increase,
hence the V
R
decreased, thereby facilitating the mixing
process between the basanite and the phonolite. The
cooling and consequent crystallization of the mafic
magma caused accumulation of gas bubbles at the
interface between the two magmas that led, in some
cases, to production of vesiculated blobs of mafic
magma inside the felsic magma (EICHELBERGER,1980;
THOMAS and TAIT,1997). This is consistent with the fact
that the vesiculated enclaves of Montan
˜a Reventada
have higher D
box
(Figs. 2a, b, 4a, b) and are therefore
closer in composition to the mafic end-member. While
the basanite continued to ascend to the surface,
Figure 5
Frequency histogram displaying the distribution of values of the
fractal-dimensions (D
box
) of the enclaves in Montan
˜a Reventada
Figure 6
Frequency histogram displaying the distribution of values of the
regression coefficients for the linear interpolation of log(r) vs.
log(N). Values are always greater than 0.99, indicating the
excellent linear fitting of the data
H. Albert et al. Pure Appl. Geophys.

mingling structures were generated in the contact area.
These structures were captured in the blobs of magma,
which detached from this zone through the felsic
magma and generated enclaves. The presence of both
coherent and active regions yielded enclaves with
different amounts of mafic and felsic magma. Chemi-
cal diffusion inside the enclaves produced different
hybrid composition and hence enclaves with interface
morphology characterized by different D
box
. The
morphology of some enclaves could correspond to
different D
box
values over their contours. This is con-
sistent with the existence of coherent and active
regions within the same enclave. Throughout the pro-
cess the mixing zone becomes more homogenous,
because of mingling and diffusion and because the V
R
continued to decrease and thus to generate enclaves
with lower D
box
.
Figure 7
Variation of D
box
vs. log(V
R
) for the studied enclaves. aThe curve shows the exponential fit of Eq. 3considering 1 \D
box
\2.
bMagnification of the range of variation of D
box
vs. log(V
R
) for the hybrid enclaves. The shaded area indicates the highest frequency range
Figure 8
Frequency histogram displaying the distribution of values of
log(V
R
) calculated by use of Eq. 3. Class 0.49 corresponds to the
shaded area in Fig. 7b
Table 2
Logarithm of the viscosity of the phonolite, the basanite, and the enclaves with 65–70 % mafic magma
Phonolite Basanite Enclaves
wt% H
2
O: 2 2.5 3 0.5 1 1.5 2 2.5 1.5 2
T(°C) logl(Pas)
900 4.11 3.83 3.57 4.28 3.75 3.43 3.19 3.00 3.77 3.49
1,000 3.31 3.06 2.84 3.13 2.72 2.47 2.28 2.13 2.84 2.62
1,100 2.64 2.42 2.23 2.24 1.92 1.71 1.56 1.43 2.11 1.92
1,200 2.07 1.88 1.71 1.54 1.28 1.10 0.97 0.87 1.50 1.34
Fractal Analysis of Enclaves as a New Tool

On the basis of the V
R
between thephonolitic magma
and the enclaves, it is possible to estimate the range of
viscosities of the enclaves. Because the viscosity is
closely related to the water content this enables us to
estimate a plausible range of dissolved water content in
the enclaves. The enclaves were generated at a tem-
perature lower than the basanite and higher than the
phonolite and are the result of the mixing of these two
magmas with different viscosities. Hence the viscosity
range of the enclaves must be between those of the ba-
sanite and the phonolite. This constraint reduces the
water content of the phonolite, the basanite, and the
enclaves to only two possible combinations of the val-
ues. As shown in Fig. 9if the water content of the
phonolite is 2 or 2.5 wt% the water content of the ba-
sanite must be 1.5 or 2 wt% respectively. Because
V
R
=0.49 is a mode value it can be regarded as being
related to the percentage of mafic magma present in the
system and the other values because of different degrees
of mixing. The viscosity of the considered enclaves
(Table 2) overlap with thecurve of V
R
=0.49 (Table 3)
for a water content of 1.5 or 2 wt%.
Another important question concerning the
Montan
˜a Reventada eruption is whether all the ba-
sanite that intruded into the phonolitic magma was
erupted or not. The enclaves represent just &1%of
the outcrop (ARAN
˜Aet al., 1994) and, according to
estimates from the stratigraphic sections in ARAN
˜A
et al., (1994) and WIESMAIER et al., (2011), the
amount of basanite erupted corresponds to up to 15 %
of the total erupted products generated during the
eruption. This suggests that residual basanite magma
was still stored in the magma chamber, which may
have either evolved into more differentiated compo-
sitions or crystallized to form a denser body. Data
from subsequent eruptions on Tenerife are unable to
shed any further light on this question.
6. Conclusions
The results of the fractal study conducted on
Montan
˜a Reventada show that enclaves with different
D
box
—and hence different composition—represent
Figure 9
Variation of logarithm of viscosity with temperature
Table 3
Logarithm of the viscosity of the enclaves calculated accordingly
with the V
R
values and the viscosity of the phonolite
Phonolite: 2 wt% H
2
O 2.5 wt% H
2
O
V
R
: 0.39 0.49 0.81 0.39 0.49 0.81
T(°C) Enclaves logl(Pas)
900 3.72 3.62 3.30 3.44 3.34 3.02
1,000 2.92 2.82 2.50 2.67 2.57 2.25
1,100 2.25 2.15 1.83 2.03 1.93 1.61
1,200 1.68 1.58 1.26 1.49 1.39 1.07
H. Albert et al. Pure Appl. Geophys.

different degrees of mixing in the system, even
though all could have been generated at the same
time and with the same percentage of mafic magma.
Fractal analysis of enclaves of Montan
˜a Revent-
ada offers clues to constraining the dissolved water
content and the viscosities of the enclaves and the
basanitic magma. The initial estimate, based on pre-
vious work, of the water content of the phonolite of
2–3 wt% can be reduced in this case to 2–2.5 wt%.
Acceptable values for the basanite and the enclaves
range between 1.5 and 2 wt%.
Acknowledgments
H. Albert was funded by the Spanish Geographic
Institute (IGN). This research was partially funded by
the IGN and the European Commission (FP7 630
Theme: ENV.2011.1.3.3-1; Grant 282759: VUE-
LCO). We are grateful for the help and support
provided by C. Lo
´pez, H. Lamolda, and A. Felpeto.
We thank the two anonymous reviewers and the
editor for their constructive comments that helped to
improve the manuscript. We also thank the Teide
National Park for their permission to undertake this
research. The English text was corrected by Michael
Lockwood.
REFERENCES
ABLAY, G.J., and MARTI
´, J. (2000), Stratigraphy, structure, and
volcanic evolution of the Pico Teide–Pico Viejo formation,
Tenerife, Canary Islands, Journal of Volcanology and Geother-
mal Research, 103 (1), 175–208.
ABLAY, G.J., CARROLL, M.R., PALMER, M.R., MARTI
´, J., and SPARKS,
R.S.J. (1998), Basanite–phonolite lineages of the Teide–Pico
Viejo volcanic complex, Tenerife, Canary Islands, Journal of
Petrology, 39 (5), 905–936.
ANDU
´JAR, J., and SCAILLET, B. (2012a), Experimental constraints on
parameters controlling the difference in the eruptive dynamic of
phonolitic magmas: the case from Tenerife (Canary Islands),
Journal of Petrology, 53 (9), 1777–1806.
ANDU
´JAR, J., and SCAILLET, B. (2012b), Relationships between pre-
eruptive conditions and eruptive styles of phonolite–trachyte
magmas, Lithos, 152, 122–131.
ANDU
´JAR, J., COSTA, F., and MARTI
´, J. (2010), Magma storage
conditions of the last eruption of Teide volcano (Canary Islands,
Spain), Bulletin of Volcanology, 72, 381–395.
ANDU
´JAR, J., COSTA, F., and SCAILLET, B. (2013), Storage conditions
and eruptive dynamics of central versus flank eruptions in vol-
canic islands: the case of Tenerife (Canary Islands, Spain),
Journal of Volcanology and Geothermal Research, 260, 62–79.
ARAN
˜A, V., APARICIO, A., GARCIA CACHO, L., and GARCIA GARCIA,R.
(1989), Mezcla de magmas en la regio
´n central de Tenerife. Los
volcanes y la caldera del Parque Nacional del Teide (Tenerife,
Islas Canarias), Vol. Ministerio de Agricultura Pesca y Alimen-
tacio
´n, 269–298.
ARAN
˜A, V., Evolucio
´n y mezcla de magmas en Las Can
˜adas del
Teide, In Mecanismos eruptivos y estructuras profundas de
volcanes espan
˜oles e italianos (eds Aran
˜a V. and Coello J.)
(Reun. Cient. CSIC-CNR, Islas Canarias 1985) pp. 38–42.
ARAN
˜A, V., MARTI
´, J., APARICIO, A., GARCI
´A-CACHO, L., and GARCI
´A-
GARCI
´A, R. (1994), Magma mixing in alkaline magmas: an
example from Tenerife, Canary Islands, Lithos, 32 (1), 1–19.
CARRACEDO, J.C. (1994), The Canary Islands: an example of
structural control on the growth of large oceanic-island volca-
noes, Journal of Volcanology and Geothermal Research, 60 (3),
225–241.
CARRACEDO, J.C., RODRI
´GUEZ BADIOLA, E., GUILLOU, H., PATERNE,
M., SCAILLET, S., PE
´REZ TORRADO, F.J., PARIS, R., FRA-PALEO, U.,
and HANSEN, A. (2007), Eruptive and structural history of Teide
Volcano and rift zones of Tenerife, Canary Islands, Geological
Society of America Bulletin, 119 (9), 1027–1051.
EDGAR, C.J., WOLFF, J.A., NICHOLS, H.J., CAS, R.A.F., and MARTıI
¨,J.
(2002), A complex Quaternary ignimbrite-forming phonolitic
eruption: the Poris member of the Diego Herna´ndez Formation
(Tenerife, Canary Islands), Journal of Volcanology and Geo-
thermal Research, 118 (1), 99–130.
EDGAR, C.J., WOLFF, J.A., OLIN, P.H., NICHOLS, H.J., PITTARI, A.,
CAS, R.A.F., and MARTI
´, J. (2007), The late Quaternary Diego
Hernandez Formation, Tenerife: Volcanology of a complex cycle
of voluminous explosive phonolitic eruptions, Journal of Volca-
nology and Geothermal Research, 160 (1), 59–85.
EICHELBERGER, J.C. (1980), Vesiculation of mafic magma during
replenishment of silicic magma reservoirs, Nature, 288, 446–450.
FLINDERS, J., and CLEMENS, J.D. (1996), Non-linear dynamics,
chaos, complexity and enclaves in granitoid magmas, Transac-
tions of the Royal Society of Edinburgh-Earth Sciences, 87 (1),
217–224.
FOLCH, A., and MARTI
´, J. (1998), The generation of overpressure in
felsic magma chambers by replenishment, Earth and Planetary
Science Letters, 163, 301–314.
GIORDANO, D., RUSSELL, J.K., and DINGWELL, D.B. (2008), Viscosity
of magmatic liquids: a model, Earth and Planetary Science Let-
ters, 271 (1), 123–134.
MANDELBROT, B.B., The fractal geometry of nature (San Francisco,
CA, 1982).
MARTI
´, J., AND GUDMUNDSSON, A. (2000), The Las Can˜ adas caldera
(Tenerife, Canary Islands): an overlapping collapse caldera
generated by magma-chamber migration, Journal of Volcanolo-
gy and Geothermal Research, 103 (1), 161–173.
MARTI
´, J., GEYER, A., ANDUJAR, J., TEIXIDO
´, F., and COSTA,F.
(2008), Assessing the potential for future explosive activity from
Teide–Pico Viejo stratovolcanoes (Tenerife, Canary Islands),
Journal of Volcanology and Geothermal Research, 178 (3),
529–542.
MARTI
´, J., HURLIMANN, M., ABLAY, G.J., and GUDMUNDSSON,A.
(1997), Vertical and lateral collapses on Tenerife (Canary
Islands) and other volcanic ocean islands, Geology, 25 (10),
879–882.
MARTI
´, J., MITJAVILA, J., and ARAN
˜A, V. (1994), Stratigraphy,
structure and geochronology of the Las Can˜ adas caldera (Ten-
erife, Canary Islands), Geological Magazine, 131 (6), 715–727.
Fractal Analysis of Enclaves as a New Tool

MARTI
´, J., MITJAVILA, J., and VILLA, I. M. (1990), Stratigraphy and
K-Ar ages of the Diego Herna´ ndez wall and their significance on
the Las Can˜ adas Caldera formation (Tenerife, Canary Islands),
Terra Nova, 2(2), 148–153.
MARTI
´, J., SOBRADELO, R., FELPETO, A., and GRACI
´A, O. (2011),
Eruptive scenarios of phonolitic volcanism at Teide–Pico Viejo
volcanic complex (Tenerife, Canary Islands), Bulletin of Vol-
canology, 74 (3), 767–782.
MORGAVI, D., PERUGINI, D., DECAMPOS, C.P., ERTEL-INGRISCH, W.,
and DINGWELL, D.B. (2013), Morphochemistry of patterns pro-
duced by mixing of rhyolitic and basaltic melts, Journal of
Volcanology and Geothermal Research, 253, 87–96.
PERUGINI, D., and POLI, G. (2000), Chaotic dynamics and fractals in
magmatic interaction processes: a different approach to the
interpretation of mafic microgranular enclaves, Earth and Plan-
etary Science Letters, 175 (1), 93–103.
PERUGINI, D., and POLI, G. (2005), Viscous fingering during
replenishment of felsic magma chambers by continuous inputs of
mafic magmas: field evidence and fluid-mechanics experi-
ments, Geology, 33 (1), 5–8.
PERUGINI, D., and POLI, G. (2012), The mixing of magmas in plu-
tonic and volcanic environments: analogies and
differences, Lithos, 153, 261–277.
PERUGINI, D., BUSA
`, T., POLI, G., and NAZZARENI S. (2003a), The role
of chaotic dynamics and flow fields in the development of dis-
equilibrium textures in volcanic rocks, Journal of Petrology, 44
(4), 733–756.
PERUGINI, D., DECAMPOS, C.P., DINGWELL, D.B., and DORFMAN,A.
(2013), Relaxation of concentration variance: a new tool to
measure chemical element mobility during mixing of mag-
mas, Chemical Geology, 335, 8–23.
PERUGINI, D., DECAMPOS, C.P., ERTEL-INGRISCH, W., and DINGWELL,
D.B. (2012), The space and time complexity of chaotic mixing of
silicate melts: implications for igneous petrology, Lithos, 155,
326–340.
PERUGINI, D., PETRELLI, M., and POLI, G. (2006), Diffusive frac-
tionation of trace elements by chaotic mixing of magmas, Earth
and Planetary Science Letters, 243 (3), 669–680.
PERUGINI, D., POLI, G., and GATTA, G.D. (2002), Analysis and
simulation of magma mixing processes in 3D, Lithos, 65 (3),
313–330.
PERUGINI, D., POLI, G., and MAZZUOLI, R. (2003b), Chaotic advec-
tion, fractals and diffusion during mixing of magmas: evidence
from lava flows, Journal of Volcanology and Geothermal
Research, 124 (3), 255–279.
PERUGINI, D., VALENTINI, L., and POLI, G. (2007), Insights into
magma chamber processes from the analysis of size distribution
of enclaves in lava flows: a case study from Vulcano Island
(Southern Italy), Journal of Volcanology and Geothermal
Research, 166 (3), 193–203.
PERUGINI, D., VENTURA, G., PETRELLI, M., and POLI, G. (2004),
Kinematic significance of morphological structures generated by
mixing of magmas: a case study from Salina Island (Southern
Italy), Earth and Planetary Science Letters, 222 (3), 1051–1066.
PETRELLI, M., PERUGINI, D., and POLI, G. (2006), Time-scales of
hybridisation of magmatic enclaves in regular and chaotic flow
fields: petrologic and volcanologic implications, Bulletin of
Volcanology, 68 (3), 285–293.
POLI, G., and PERUGINI, D. (2002), Strange attractors in magmas:
evidence from lava flows, Lithos, 65 (3), 287–297.
SNYDER D. (2000), Thermal effects of the intrusion of basaltic
magma into a more silicic magma chamber and implications for
eruption triggering, Earth and Planetary Science Letters, 175,
257–273.
THOMAS N., and TAIT S.R. (1997), The dimensions of magmatic
inclusions as a constraint on the physical mechanism of mixing,
Journal of Volcanology and Geothermal Research, 75, 167–178.
WIESMAIER, S., DEEGAN, F.M., TROLL, V.R., CARRACEDO, J.C.,
CHADWICK, J.P., and CHEW, D.M. (2011), Magma mixing in the
1100 AD Montan˜ a Reventada composite lava flow, Tenerife,
Canary Islands: interaction between rift zone and central vol-
cano plumbing systems, Contributions to Mineralogy and
Petrology, 162 (3), 651–669.
WOLFF, J.A. (1985), Zonation, mixing and eruption of silica-
undersaturated alkaline magma: a case study from Tenerife,
Canary Islands, Geological Magazine, 122 (6), 623–640.
(Received July 3, 2014, revised July 22, 2014, accepted July 24, 2014)
H. Albert et al. Pure Appl. Geophys.