NUMERO 3-2007:maquette_geomorpho

Transcription

Géomorphologie : relief, processus, environnement, 2007, n° 3, p. 247-258
Tri-dimensional parameterisation: an automated treatment
to study the evolution of volcanic cones
Apport de la paramétrisation tridimensionnelle à l’étude
de l’évolution des cônes volcaniques
Jean-François Parrot*
Abstract
An automated volcanic parameterisation has been developed in order to measure the evolution of a volcanic cone resulting from erosion, catastrophic events or human activity. In a first step, various parameters have been defined and retained: volume and 3D surface
of the volcanic cone, volcanic base line radius and eventually its elongation, total height of the cone from the base line to the summit,
crater radius when existing, crater depth, mean slope angle outside the crater, mean slope angle inside the crater. All these parameters
are derived from a Digital Elevation Model. They can be used to characterize a volcanic cone and to compare all the cones of diverse
studied regions in order to define different families based on their shape characteristics. On the other hand, the algorithm developed
reconstitutes the original volcanic feature. Then, a comparison between the reconstituted cone and the presently observed shape allows
assess to the erosion rate, to define precisely the eroded zones, and to measure either the degree of evolution or the volume mobilized
during massive erosion processes. The algorithm developed in C++ is based on a calculation that requires only the altitude of the volcanic base line and the coordinates of a point considered as the volcanic center; this requirement is important, especially when the
edifice was subjected to high erosion rates or when it is deeply eroded. Combined with a tomomorphometric approach, this algorithm
represents a new tool to study volcanic landforms. Three applications illustrate and validate the results.
Key words: volcanic cone, parameterisation, denudation volume, DEM simulation, Jocotitlán volcano, Mexico.
Résumé
Une paramétrisation automatisée a été développée en vue de mesurer l’évolution d’un cône volcanique résultant de l’érosion, d’événements catastrophiques ou de l’activité anthropique. Différents paramètres ont été testés et retenus : volume et surface tridimensionnelle du cône volcanique, rayon de la base de l’édifice, hauteur totale, rayon du cratère quand il existe, profondeur de ce dernier, pente
moyenne des flancs et à l’intérieur du cratère. Tous ces paramètres sont obtenus à partir du traitement d’un Modèle Numérique de Terrain et peuvent être utilisés pour définir les caractéristiques morphologique d’un cône volcanique. L’algorithme développé en C++ demande uniquement à l’utilisateur d’indiquer quelle est l’altitude de la ligne de base et les coordonnées d’un point considéré comme
étant le centre du cratère. Cette dernière précision est importante, surtout lorsque l’édifice étudié est fortement disséqué. L’algorithme
engendre une forme susceptible de correspondre à celle que présentait le volcan avant l’érosion, ce qui permet entre autres de mesurer le volume de matériaux érodé. Des applications portant sur le volcan Jocotitlán (Mexique), qui a subi un important glissement de
terrain, ainsi que sur deux volcans de la région de Chichinautzin illustrent et valident les résultats.
Mots clés : paramétrisation, cône volcanique, volume érodé, MNT, volcan Jocotitlán, Mexique.
Version française abrégée
L’étude de l’évolution morphologique des cônes volcaniques formés par des fragments pyroclastiques repose,
entre autres, sur une paramétrisation de ces édifices. Il est
ainsi possible de caractériser à l’aide de paramètres quantitatifs les cônes volcaniques, de mesurer les effets produits
par l’érosion, par des événements catastrophiques ou par
l’activité humaine. Différents auteurs (Porter, 1972 ;
Bloomfield, 1975, Wood, 1980a, 1980b) ont par exemple
défini et quantifié les rapports existant entre la hauteur du
cône et le diamètre de sa ligne de base, entre ce diamètre et
celui du cratère. Le premier rapport est compris entre 0,20
et 0,10 et diminue avec le temps ; le second entre 0,40 et
0,80 augmente au contraire avec le temps, cette évolution
étant essentiellement due à l’érosion. Par ailleurs, la pente
*Instituto de Geografía, UNAM, Apto. Postal 20-850, 01000 México D.F. México. E-mail:[email protected]
Jean-François Parrot
extérieure du cône serait également une caractéristique liée
à la nature du matériel volcanique.
En fait, de telles mesures nécessitent d’étudier des édifices
volcaniques relativement bien conservés, se réfèrent en
général à des observations de terrain et résultent d’une estimation globale dépendant de l’équation employée. Les
modèles numériques de terrain (MNT), en raison des possibilités actuelles de stockage et des progrès technologiques,
se révèlent un moyen efficace d’étudier les cônes volcaniques. L’analyse numérique des MNT (Wilson et Gallant,
2000) permet de définir des attributs primaires, comme la
pente, l’aspect, la courbure, la convexité, etc, produisant
ainsi de nombreux paramètres morphologiques.
L’algorithme mis au point et présenté dans cet article a
trait à la paramétrisation des édifices volcaniques à partir
des MNT. Il est ainsi possible de calculer le volume et la
hauteur du cône (fig. 1), le rayon de la ligne de base, celui
du cratère et sa profondeur, la pente moyenne sur les flancs
du volcan et à l’intérieur du cratère, la surface du cône
(fig. 2). À la différence des estimations antérieures, toutes
ces mesures prennent en compte les valeurs altimétriques de
tous les pixels constituant l’édifice ; c’est par exemple le
cas pour le calcul de la pente moyenne résultant de l’ensemble des valeurs de pente rencontrées en chaque point.
Qui plus est, l’algorithme reconstitue si nécessaire le cône
volcanique en se fondant sur les coordonnées du centre du
cratère et l’altitude de la ligne de base. On peut ainsi, non
seulement étudier des ensembles volcaniques fortement disséqués par l’érosion et dont le cratère se résume parfois à
un unique sommet, mais encore quantifier le volume de
matériel déplacé au cours du temps sous l’effet de l’érosion
ou des événements mentionnés plus haut.
L’application de la méthode au volcan Jocotitlán, précédemment étudié par Siebe et al. (1992), illustre les résultats
obtenus (fig. 4, 5a, 5b, 6a, 6b, 7 ; tab. 1). Les estimations relatives à l’effondrement qui a affecté cet édifice volcanique
valident la méthode qui apporte par ailleurs de nombreuses
informations complémentaires. Par exemple, la valeur
moyenne de la pente confirme la nature dacitique des coulées
volcaniques et indique localement la hauteur du matériel arraché à l’appareil (fig. 7). À titre d’illustration supplémentaire, deux volcans de la région orientale du Chichinautzin ont
été étudiés (fig. 8a et 8b). Le premier est un édifice scoriacé
ne présentant pas de cratère (El Tezoyo), l’autre un cône de
cendres (Volcan del Aire) dont le cratère est parfaitement
conservé, mais dont les flancs sont fortement ravinés. Les résultats obtenus sont reportés dans le tableau 2.
La méthode décrite dans cet article se révèle un nouvel
outil capable de définir les caractéristiques morphologiques
des cônes volcaniques, de quantifier leur âge relatif et de
mesurer le degré de dégradation dû à l’érosion ou à divers
phénomènes érosifs.
Introduction
Volcanic cinder cones formed by cinder and pyroclastic
debris are generally considered as truncated cones with a
248
crater located in the summit (Macdonald, 1972). The first
geomorphological studies have shown that morphologic
changes occur with time and are able to provide information
about the age of the edifice (Colton, 1967; Scott and Trask,
1971). Porter (1972) was the first to define quantitative
ratios between different parameters in order to characterize
the volcanic shape: i.e., the ratio height of the cone versus
the base diameter would be equal to 0.18 and the ratio between the crater diameter and the base diameter would
remain at 0.40. Bloomfield (1975), using radiometric age
determinations, observed that the first ratio decreases from
0.21 until 0.10 with time, meanwhile the second one
increases from 0.40 to 0.83. On the other hand, according to
Settle (1979), the shape characteristics of the volcanic cones
are related to the nature of the material involved in the effusive process, and to the nature and duration of the erosion
activity. Wood (1980a, 1980b) confirms and formalizes the
morphometric parameters proposed by Porter (1972). Until
now, numerous geomorphological studies concerning the
geomorphic definition of the volcanic characteristics or the
effect of the erosion processes, are based on these parameters and ratio (Dohrenwed et al., 1986; McFadden et al.,
1986; Hasenaka, 1994; Noyola-Medrano et al., 1994; Hooper, 1995; Luhr et al., 1995; Hooper and Sheridan, 1998;
Rech et al., 2001; Aranda-Gomez et al., 2003; Nemeth et
al., 2005), even if their use remains problematic when the
studied cone does not present a crater (Hasenaka and Carmichael, 1985a).
The possibility to obtain more detailed geomorphic information has been explored by Garcia-Zuniga and Parrot
(1998) who proposed using a Digital Elevation Model (DEM)
and to define pattern recognition parameters applied to hypsometric slices describing the volcanic cone, from its base
line to its summit. This approach described as tomomorphometric analysis registers the morphologic changes taking into
account parameters such as the convexity index, direction of
the principal axis, etc. This recent approach has been used to
study the lithospheric motion of the Somalian and Arabian
plates (Collet et al., 2000), the Anatolian volcanic massif
(Ozlem et al., 2003) and the Chichinautzin volcanic cinder
cone field, Mexico (Noyola and Parrot, 2005).
Square-grid digital elevation models (DEMs) represent
important and accurate tools to underline the different regional geomorphic features and to simulate various scenarios, as
the possibility of storage and advances in computing technology increased strongly in recent years. The horizontal and
vertical resolutions are sufficient to accurately calculate different parameters extracted from the DEM surface. The
digital terrain analysis (Wilson and Gallant, 2000) allows
defining primary and secondary attributes. The secondary
attributes are devoted to estimate the role played by topography in the distribution of soil water or on the susceptibility of
landscapes to erosion, for instance. Most of the primary attributes such as slope, aspect, plan and profile curvature are
computed directly or by fitting an interpolation function to
the DEM in order to calculate them (Moore et al., 1993b;
Mitasova et al., 1996; Florinsky, 1998). These different attri-
An automated treatment to study the evolution of volcanic cones
butes provide numerous geomorphological indicators (Tribe,
1991). They are used to describe the morphometry, catchment position, stream channels, etc., and to compute
topographic attributes (Jenson and Domingue, 1988; Dikau,
1989; Moore et al., 1993a; Dymond et al., 1995; Giles, 1998;
Borrough et al., 2000). An exhaustive survey of the publications concerning this topic can be found in the Pike’s report
(2002). Various softwares such as TAPES-G (Moore, 1992)
have been developed with such a goal.
This paper aims at defining and computing parameters of
volcanic cones in order to enable the measurement of evolution stages of these cones due to the erosion, catastrophic
events or human activity. The first approach consisted of
defining some characteristic features that can be useful for
this purpose. The algorithm presented in this paper has been
developed in C++. The automated parameterisation of volcanic cones is based on seven parameters: the volume of the
volcanic cone, the volcanic base line radius and eventually
its elongation, the total height of the cone from the base line
until its summit, the crater radius when existing, the depth of
this crater, the mean dipping angle outside the crater and the
mean dipping angle inside the crater.
All these parameters and their relationships are not only
able to characterize a volcanic cone, but can be also used to
reconstitute the original volcanic landform. Moreover, the
comparison between the reconstituted cone and the presently observed shape allows us to assess the erosion and
evolution stages. The developed algorithm is based on a calculation that only requires the altitude of the volcanic base
line and the coordinates of a point considered as the center
of the volcanic cone when it is present or to the summit if
this feature is lacking. The algorithm is described in the following section. In the second section, the procedure that
allows us to reconstitute the cone taking into account the
formerly obtained parameters, is presented. Finally, the
results are discussed in the third section.
Parametrisation procedure
The main lines of the computation consists in defining and
extracting the parameters that characterize the studied volcanic cone and, as a second step, in reconstructing the
original landform of the studied volcanic cone. The difference observed between these two cones also corresponds to
a parametrization of the erosion processes.
The first calculated parameters are the volcanic height H
of the cone, the base line radius BR which present two components: the minimum base line radius BRmin and the
maximum base line radius BRmax allowing calculation of the
elongation ratio ER of the volcanic base line, the depth of
the crater HC as well as the crater radius CR and its two
components: the minimum crater radius CRmin and the maximum crater radius CRmax.
The second group of parameters concerns the mean dipping angle a outside the crater and the mean dipping angle
b inside the crater. One can notice that contrary to the procedure proposed by Wood (op. cit.), these values result from
the slope calculation in each DEM’s point. Complementary
information is provided: the percentage of downward angle
located on the cone flank, as well as the percentage of the
upward angle inside the crater, in order to measure irregularities that can emphasize for instance the presence of eroded
zones (natural or artificial) or to control the degree of the
smoothness of the cone. The third generation of parameters
concerns the calculation of the bi and tri-dimensional surface, as well as the volume of the edifice.
At the beginning of the procedure, the user has to define
the altitude of the base line and the coordinates of the volcanic center CE. As the first step consists of researching on
the DEM all the pixels whose altitude is equal or superior to
the altitude of this base line, a labellization is required in
order to choose among the different pixel components, the
surface corresponding to the first altitude slice of the studied
edifice. This surface is the base on which the different parameters will be calculated.
Radius and elongation of the base line
This measurement needs to research the center of mass
CM of the base surface and the Principal Axis (PA) passing
through this point. PA is calculated as follows:
tg(2α) = 2μxy/(μyy - μxx) if (μyy - μxx) π 0
On the other hand, the center of mass CM (Xc, Yc) and the
moments of second order mxx , myy and mxy are respectively
equal to:
Nbp is the number of pixels of the object and Xi Yi the
coordinates of the pixel i.
The greater distance between CM and the crossing point
between the perimeter of the surface and PA corresponds to
the value of the radius BRmax. The normal of PA passing
through CM is calculated in order to define the value of
BRmin. The elongation is then calculated.
Radius and elongation of the crater
The calculation of the crater radius CR takes into account
the estimated center of the edifice CE (coordinates defined
by the user) and the highest altitude point. The normal of the
line linking these two points allows researching the perpendiular radius, taking into account the highest point located
on the both sides of this normal. The second value is either
greater or lower than the first one. CRmax and CRmin depend
on this comparison and then the elongation of the crater is
computed. One can notice that a difference between the
coordinates of CE and CM previously defined represents
another morphometric parameter, i.e. the existing tectonic
constraints during the volcano formation.
249
Crater depth, height and volume of the
volcanic cone
The crater depth corresponds to the hypsometric difference
between the altitude of the point CE and the highest altitude
of the volcano. The height of the cone is the difference between this latter point and the altitude of the base line.
The procedure used to calculate the volume consists of
computing the volume of each altitude slice (in meters or
decimeters according to the hypsometric resolution of the
DEM). Each slice corresponds to the pixels whose altitude
A’ is equal or greater than the former slice of altitude A that
plays the role of the floor. The difference (A’-A) corresponds
to the hypsometric resolution of the DEM. When the calculation is done on a slice, the roof of this slice plays the role
of the floor for the following upper slice. We have to notice
that the volumetric excess corresponding to the upper half
part of a slice is actually balanced by the loss registered in
the lower half part, blurring the staircase effect inherent in
this procedure.
Surface of the volcanic cone
At this stage, for each resulting triangle issued from the 8
rectangular triangles that form the pixel surface, we know
the values of each triangular side. The Heron’s formula
allows calculating the surface of each triangle. In this case:
where
Then, the 3D surface S3D of the pixel corresponds to the
sum of the 8 resulting triangles:
The total surface S3 corresponds to the sum of all the S3D.
Actually, in the case of the pixel Pp located at the periphery
some of the 8 rectangular triangles are not taken into
account according to the local configuration (fig. 3).
The ratio S3D/S2 is another indication concerning the
smoothing degree of the studied cone. It becomes lower
when the cinder cone is recent and does not present gullies,
as well as when reconstituing the former shape (see table 1).
Slope
Two types of surface can be defined, as well as the difference they present. The first calculated surface is the
topographic surface directly calculated on the surface defined by the base line. In a first approximation (Pratt, 1978),
this surface S2 is equal to:
where Ps and Pp are respectively the pixels describing
the surface and the pixels belonging to the perimeter
(fig. 1). This measure corresponds only to the surface
occupied on the map, but it is also possible to measure the
tri-dimensional surface S3. In order to calculate the 3D surface, a new algorithm has been developed; each pixel is
divided in eight rectangular triangles that converge in the
pixel center. Figure 2 illustrates the computation process
taking into account the altitude value of the studied pixel
and the altitude values of the eight surrounding pixels. The
altitude value of the pixel corners and the altitude of the
center of each pixel side result from a linear interpolation
between the altitude value of the pixel center and the altitude of the neighboring pixels.
A is the difference of altitude between the center of the
pixel and the end of the different segment. It allows the calculation of the length of base and bside following the
formula:
where hps corresponds to half part of the length of pixel side
(in meters) and hd to
a is the difference of altitude between two A. This value
allows measuring the length of aside that is equal to:
250
The mean slope calculation is as follows. Following each
line issued from CE (coordinates defined by the user) and
linking a pixel belonging to the perimeter describing the base
line, the algorithm compares the altitude of the successive
points located on this line in order to know if the calculated
angle corresponds to an ascending (b) or descending (a)
slope. A clockwise linking is done in order to scan the whole
edifice and the local result is plotted if a previous one does
not exist. On the other hand, the presence of local ascending
slopes in the volcanic flank, as well as the presence of local
descending slopes inside the crater are researched in order to
control the regularity of the conic shape.
Volcanic cone reconstitution
In addition, the developed algorithm that can be provided
by the author, reconstitutes the original volcanic cone using
the following considerations. As formerly described a volcanic cinder cone corresponds to a truncated cone with a
crater. The flank of the edifice is quite regular and smooth.
Taking into account the value of the crater radius (CR) and
the altitude of the highest point (HP), a circle is drawn
whose altitude is equal to HP. If the coordinates of the center defined by the user are correct, this circle has to recover
all the remnants of the crater wall.
The calculated crater circle corresponds to the spatial
reference on which the computation is based. Inside the crater, circular curve lines are drawn, the altitude of which are
comprised between the altitude HP and the altitude value of
the crater bottom; similarly on the flank of the volcano, circular curve lines are defined between the crater circle and
the base line. The resulting DEM generation is obtained by
using a curve dilation procedure (Taud et al., 1999).
Jocotitlán
Parameters
Base Line
Crater
Edifice
Flank
Crater
Fig. 1 – Perimeter and surface pixels of an hypsometric slice.
Fig. 1 – Pixels du périmètre et de la surface dans une
tranche altimétrique.
Fig. 2 – Computation of the ‘3D surface’ inside a
pixel.
Fig. 2 – Calcul de la « surface tridimensionelle » à
l’intérieur d’un pixel.
Surface
Volume
Original shape
Reconstructed
cone
Lower radius
3277.50 m
3277.50 m
Greater radius
5964.93 m
5964.93 m
Lower radius *
695.18 m
695.18 m
Greater radius *
695.18 m
695.18 m
Base line
2800 m
2800 m
Maximum altitude
3953 m
3953 m
Height
1153 m
1153 m
Crater depth
220 m
220 m
Computed elements
Mean angle
17.47 °
17.83 °
Descending surfaces
88.76%
95.42%
Mean angle
18.52 °
17.08 °
Ascending surfaces
94.27%
96.38%
2D surface
62.466 734 km2
62.466 734 km2
3D surface
65.370 608 km2
65.664 176 km2
km3
19.314 505 km3
Total
17.338 396
Difference
1.976 109 km3
Table 1 – Parametric values of the Jocotitlán volcano (original form and
reconstituted edifice). * indicates that the involved algorithm encountered only
one summit; for this reason, the two radius of the crater are similar.
Tableau 1 – Valeur des paramètres du volcan Jocotitlán (forme actuelle et
édifice reconstitué). * indique que la séquence algorithmique n’a rencontré qu’un
seul sommet ; pour cette raison, les deux rayons du cratère ont la même valeur.
generation of a reconstituted edifice allows the
quantification of the differences registered by the
volcanic cone due to erosion processes, collapses
or human activity. The parameters, formerly described in the case of the original shape of the
volcanic cone, are calculated in the same way in the
case of the reconstituted cone. Their comparison is
a key to underline the features resulting form erosion processes, collapses or human utilization.
Application and results
When the original altitude in some places is higher than
the interpolated value, the original hypsometric value is preserved in order not to blur these features that can correspond
to adventive effusive centers or local tectonic events. The
This paper was focused on two volcanic regions in
Mexico. The first one comprises the Jocotitlan volcano, and the second is formed by two volcanoes
from the Chichinautzin range.
The Jocotitlán volcano (3950 meters) is a typical
stratovolcano and dome complex, mostly composed by dacite lava flows. It is located in the central
part of the Trans Mexican Volcanic Belt (TMVB),
60 km north of Mexico City. A huge collapse affected the NE sector of this edifice in pre-historic
times. The associated avalanche covered an area of
80 km2 with a maximal runout distance of 12 km and an
estimated volume of 2.8 km3 (Siebe et al., 1992). The presence of a major normal fault interesting the volcano suggests an extensional tectonic stress regime that could be res-
251
Fig. 3 – The 22 first templates, their corresponding bi-dimensional surface values inside the central pixel, and the corresponding
triangular zones inside the central pixel that will be used in order to calculate the surface of an hypsometric slice.
Fig. 3 – Les 22 premiers patrons permettant de définir la portion d’un pixel du périmètre entrant dans le calcul de la surface d’une
tranche d’altitude.
252
Fig. 4 – Contour lines of the
Jocotitlán volcano used to produce the DEM.
Fig. 4 – Courbes de niveau du
volcan Jocotitlán utilisées pour
créer le MNT.
ponsible for triggering such a
slope failure. The objective of
this investigation was not directed towards studying the
relationships between the volcano and the regional tectonic
pattern, but to present and discuss the parameters calculation procedure (table 1), as
well as the information obtained in terms of volume of the
displaced material, and other
measurements associated with
the shape of the edifice. A 11m resolution DEM produced
taking into account a multidirectional interpolation (Parrot
and Ochoa-Tejeda, 2004) method of curve lines was used
as a base (fig. 4). By applying
the proposed calculation procedure, it was possible to precisely characterize the volcanic original shape. They are compatible with the former parameters proposed by Porter (1972) and Wood (1980a, b).
For instance, the ratio Hco/Wco (Height versus Diameter) is
equal to 0.17, and the main dipping angles (17.47 for the
flank and 18.52 for the crater) are comprised within the
range defined by these authors for such a type of volcano.
The calculation of the ratio Wcr/Wco (Crater diameter versus Base line diameter) depends on the position of the base
line. In this case, the lower value obtained for this ratio
(0.21) suggests that the lower limit chosen for the volcanic
complex is located below the original base line in order to
calculate the volume mobilized by the collapse event. The
Fig. 5 – Shadowed DEM of the Jocotitlán volcano. A: original shape; B: reconstituted volcano.
Fig. 5 – MNT avec estompage du volcan Jocotitlán. A : forme actuelle ; B : forme reconstituée.
253
Fig. 6 – 3D diagram of the Jocotitlán volcano. A:
original shape; B: reconstituted volcano.
Fig. 6 – Bloc diagramme du volcan Jocotitlán.
A : forme actuelle ; B : forme reconstituée.
relation 3D surface versus the global volume
is an indicator of the regularity of the edifice.
Considering the original form, this ratio is
equal to 3.77, whereas the value decreased to
3.40 after the volcano reconstitution (fig. 5
and fig. 6). Moreover, such parameters used
to describe the volcanic edifice can be also
utilized to calculate the volume of the displaced material at the time of the collapse. The
volume of the displaced material was calculated as 1.976 km3, that means a smaller volume than the assessment proposed by Siebe
et al. (1992). The later took into account the
volume of the scattered debris-avalanche deposits expressed by a hummocky topography
(see fig. 5). In addition to the analysis of the
changes of the original shape and the reconstituted volcanic edifice, this procedure also
can be used to define different zones affected
by erosion and further calculate the local dissection depth (fig. 7).
On the other hand, two volcanoes of the
Chichinautzin range were also studied. They
are located 40 km south of Mexico City. The
first one, El Tezoyo, a volcanic dome, is
mainly composed by scorias and it lacks of
a crater. The second one, Volcan del Aire, is
a cinder cone with a well preserved circular crater. Same calculation procedure was
applied for the two volcanoes by using a
10-m resolution DEM (table 2). In order to
enhance visual effects, resulting treatments
of both were included within the same
image (fig. 8a and fig. 8b). The analysis
was performed on the upper part of the two
volcanoes, taking into account the lower
closed contour line as the base line. The
treatment was done in order to illustrate
the peculiarity of features. For instance
(table 1), the lower and greater radius of
the crater remain the same. Consequently,
Fig. 7 – Dissection depth provided by the altimetric difference between the original form
and the reconstituted edifice. 1: 1-47 m; 2: 4894 m; 3: 95-141 m; 4: 142-188 m; 5: 189-235 m.
Fig. 7 – Profondeur de dissection calculée en
fonction de la différence hypsométrique
entre la forme actuelle et la forme reconstituée. 1 : 1-47 m ; 2 : 48-94 m ; 3 : 95-141 m ; 4 :
142-188 m ; 5 : 189-235 m.
254
Parameters
Base Line
Crater
Edifice
Computed elements
Lower radius
Greater radius
Lower radius
Greater radius
Original shape
Volcan del Aire
391.15
795.11
197.23
219.32
m
m
m
m
Reconstructed cone
391.15
795.11
197.23
219.32
m
m
m
m
Base line
2 350 m
2 350 m
Maximum altitude
2 435 m
2 435 m
85 m
85 m
Height
Crater depth
14 m
14 m
Flank
Mean angle
14.52 °
16.55 °
Crater
Mean angle
2D surface
3D surface
Total
Difference
7.53 °
0.801 600 km2
0.828699 km2
0.031003 km3
5.69 °
0.801600 km2
0.836409 km2
0.035033 km3
0.004031 km3
Surface
Volume
El Tezoyo
Base Line
Crater
Edifice
Flank
Surface
Volume
Lower radius
Greater radius
Lower radius
Greater radius
482.60 m
3 422.66 m
0m
0m
482.60 m
3 422.66 m
0m
0m
Base line
2495 m
2495 m
Maximum altitude
2606 m
2606 m
Height
111 m
111 m
Crater depth
0m
Mean angle
2D surface
3D surface
Total
Difference
9.76 °
5.564 500 km2
5.623 234 km2
0.164 705 km3
Table 2 – Parametric values of El Tezoyo
and Volcan del Aire volcanoes (original
form and reconstituted edifice).
Tableau 2 – Valeur des paramètres du
volcan El Tezoyo et du volcan del Aire
(forme actuelle et édifice reconstitué).
such result means that the involved
algorithm encountered only one
summit, as it is the case for the
Jocotitlán volcano. On the contrary,
when the crater is almost complete
(Volcan del Aire), these values are
different (see table 2). Moreover,
the value of the flanks mean slope
can be regarded as an indicator of
the volcanic morphology (14° for
the cinder cone, 10° for a dome
structure and 17° for a stratovolcano complex).
Conclusion
The procedure presented in this
paper calculates directly from a
9.72 °
DEM, different parameters in order
5.564 500 km2
to characterize a volcano. This fast
5.623 580 km2
computation procedure (1) can be
0.178 806 km3
applied on a volcanic cone indepen0.014101 km3
dently of the presence or the absence
of a crater, (2) it does not only
concern regular cinder cones, and (3) it can be used
to study a composite volcano. The first selected test
zone, the Jocotitlán volcano, corresponds to a volcanic structure of about 1200 meters in height covering a surface of 62.5 km2. An important collapse of the northern flank occurred in pre-historic
times. The values obtained by applying such procedures are useful to make calculations of parameters
such those proposed by Wood (1980). However, the
method also can be succesfully applied to perform
measurements and analysis such as 3D surface or
edifice volume.
The reconstitution of the former volcanic landforms offers the possibility to accurately compute
the ‘erosion’ and the volume of the displaced material. The whole measurement set can be considered as a new tool, able to discriminate different
volcanic cones located in a volcanic field, to quantify their relative ages and emphasize the degree of
degradation due to erosive processes.
0m
Fig. 8 – 3D diagram of El Tezoyo and Volcan del
Aire volcanoes. A: original shape; B: reconstituted
volcanoes.
Fig. 8 – Bloc diagramme des volcans El Tezoyo et
Volcan del Aire. A : forme actuelle ; B : forme reconstituée.
255
Acknowledgements
I wish to thank the reviewers for their helpful criticism
and suggestions and the Geographical Institute (UNAM,
Mexico) for its support.
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Article soumis le 21 mars 2006, accepté le 15 juin 2007.
257

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