Examensarbete vid Institutionen för geovetenskaper
Degree Project at the Department of Earth Sciences
ISSN 1650-6553 Nr 343
3D Modelling of the Tejeda Cone- Sheet Swarm, Gran Canaria,
Canary Islands, Spain
3D-modellering av Tejedas koniska intrusionssvärm, Gran Canaria, Kanarieöarna, Spanien
Lisa K. Samrock
INSTITUTIONEN FÖR GEOVETENSKAPER
Examensarbete vid Institutionen för geovetenskaper
Degree Project at the Department of Earth Sciences
ISSN 1650-6553 Nr 343
3D Modelling of the Tejeda Cone- Sheet Swarm, Gran Canaria, Canary Islands, Spain
3D-modellering av Tejedas koniska intrusionssvärm, Gran Canaria, Kanarieöarna, Spanien
Lisa K. Samrock
ISSN 1650-6553
Copyright © Lisa K. Samrock and the Department of Earth Sciences, Uppsala University
Published at Department of Earth Sciences, Uppsala University (www.geo.uu.se), Uppsala, 2015
Abstract
3D Modelling of the Tejeda Cone-Sheet Swarm, Gran Canaria, Canary Islands, Spain Lisa K. Samrock
Cone-sheet swarms are magmatic sheet intrusions and part of volcanic plumbing systems and are path- ways for magma to the Earth’s surface, where they feed volcanic eruptions. The analysis of cone-sheets provides information on the geometry of the magmatic plumbing system of a volcano and allows to understand processes and dynamics of magma transport. This is important to interpret information during a volcanic crisis and to help reduce risks to humans and infrastructure.
In order to create a realistic model, the structure and shape of cone-sheet complexes can be recon- structed in three-dimensional space. Most cone-sheet swarms are not sufficiently exposed to allow such a reconstruction. The Tejeda cone-sheet swarm on Gran Canaria (Canary Islands, Spain), however, is an excellent location to study a cone-sheet complex in great detail, as it is exposed over 15 km horizontally and 1000 m vertically. This allows to determine its geometry in 3D space.
The felsic deposits of the Miocene Tejeda caldera were intruded by cone-sheets between 11.7 and 7.3 Ma. Schirnick et al. (1999) assumed straight cone-sheets, based on 2D projections, and suggested that the Tejeda cone-sheet swarm is formed by a stack of uniformly dipping, parallel intrusive sheets that converge towards a common, static, laccolith-like source, forming a concentric structure around a central axis that has the geometry of a truncated cone. This hypothesis was tested in this study, using structural data from Schirnick (1996) as well as additional data collected in the field. Using the software Move™, the extensive data set was visualized and projected in three dimensional space. The underlying magmatic source of the cone-sheets was reconstructed using two different approaches, with the first one based on sets of cross-sections to select intersection points, following an approach prognosed by Burchardt et al. (2013a). To improve the quality of the reconstruction of the magma chamber, a second method was developed using geometric calculations in MATLAB.
The results indicate that individual cone-sheets are straight with parallel to slightly fanning dips, which can be steeper in the central part of the cone-sheet complex. They converge towards a common centre, creating a sub-spherical geometry of the source of the cone-sheet complex. Comparison of the two approaches used for the magma chamber reconstruction indicate that the second approach (geo- metric calculations) produces less uncertainties in data interpretation. The modelling results lead to the proposition of a dynamic model for the emplacement of the Tejeda cone-sheet complex. Cone-sheets would start to intrude from a reservoir situated at about 4500 m below sea level that became successively shallower with time.
Keywords: Cone-sheet swarm, 3D modelling, Tejeda caldera, Gran Canaria, magma chamber recon- struction, sheet intrusions
Degree Project E1 in Earth Science, 1GV025, 30 credits Supervisor: Steffi Burchardt
Departmentof EarthSciences,UppsalaUniversity,Villavägen16, SE-75236 Uppsala (www.geo.uu.se) ISSN 1650-6553, Examensarbete vid Institutionen för geovetenskaper, No. 343, 2015
The whole document is available at www.diva-portal.org
Populärvetenskaplig sammanfattning
3D-modellering av Tejedas koniska intrusionssvärm, Gran Canaria, Kanarieöarna, Spanien Lisa K. Samrock
Inverterade koniska intrusionssvärmar är en del av det underjordiska vulkaniska systemet som möjliggör vägar för magma till jordens yta, där de livnär vulkaniska utbrott. Genom analys av inverterade koniska intrusioner kan information om geometrin hos magmatiska system erhållas vilket gör det möjligt att förstå magmans processer och transportdynamik. Detta är viktigt då det hjälper att tolka information under vulkaniska kriser och kan bidra till att minska risker för människor och infrastruktur.
För att skapa en realistisk modell, kan strukturer och former av komplexa inverterade koniska intrusionssvärmar rekonstrueras i ett tredimensionellt utrymme. De flesta inverterade koniska intrusionssvärmar är inte tillräckligt blottade på jordens yta för att möjliggöra en sådan rekonstruktion.
Tejedasinverterade koniska intrusionssvärm på Gran Canaria (Kanarieöarna, Spanien) är dock utmärkt belägen för att studera ett inverterat koniskt intrusionskomplex i detalj, detta då den är blottad i över 15 kmhorisontell och 1000 m i vertikal utsträckning. Detta gör det möjligt att bestämma dess geometri i tredimensioner.
De felsiska avlagringarna av den Miocena Tejeda kalderan blev intruderade av inverterade koniska intrusioner mellan 11,7 och 7,3 Ma. Schirnick et al. (1999) antog att dessa intrusioner var raka, baserat på 2D-projektioner, och föreslog att Tejedas inverterade koniska intrusionssvärm bildades som en likformigt stupande stapel av parallella intruderande plan som konvergerar mot en gemensam, statisk och lakkolitisk källa, vilken i sin tur bildar en koncentrisk struktur runt en central axel med samma geometri som en inverterad stympad kon. Denna hypotes undersöktes i detta arbete, med hjälp av strukturell data från Schirnick (1996) samt ytterligare data insamlat från fält. Den omfattande datamängden visualiseradesoch projicerades i tre dimensioner med hjälp av mjukvaran Move™. Den underliggande magmatiskakällan till det inverterade koniska intrusionskomplexet rekonstruerades med hjälp av två olika metoder,den första är baserad på tvärsnitt där planens skärningspunkter kan studeras, följt av ett tillvägagångssätt framställt av Burchardt et al. (2013a). För att förbättra kvalitén på rekonstruktionen av magmakammaren utvecklades en andra metod med hjälp av geometriska beräkningar i MATLAB.
Resultaten tyder på att enskilda inverterade koniska intrusioner är raka med parallellt till svagtflackt stupning, vilka kan vara brantare mot den centrala delen av komplexet. De konvergerar mot ett gemensamt centrum, vilket skapar en sub-sfärisk geometri hos källan till det inverterade koniska intrusionskomplexet.
Jämförelse av de två metoderna som används för magmakammarens rekonstruktion tyder på attden andra metoden (geometriska beräkningar) ger färre osäkerheter i tolkningen. Modelleringsresultatet tyder på en dynamisk modell för bildningen av Tejedas inverterade koniska intrusionskomplex. Enligt dessa resultat skulle de inverterade koniska intrusionerna till en början ha utgått från en reservoar ungefär 4500 m under havsytan som med tiden förflyttade sig mot grundare nivåer.
Nyckelord: Inverterade koniska intrusionssvärmar, 3D-modellering, Tejeda caldera, Gran Canaria, rekonstruktion av magmakammare, magmatiska intrusioner
Examensarbete E1 i geovetenskap, 1GV025, 30 hp Handledare: Steffi Burchardt
Institutionen för geovetenskaper, Uppsala universitet, Villavägen 16, 752 36 Uppsala (www.geo.uu.se) ISSN 1650-6553, Examensarbete vid Institutionen för geovetenskaper, Nr 343, 2015
Hela publikationen finns tillgänglig på www.diva-portal.org
List of Figures
1.1 Eroded landscape . . . 2
2.1 Location of the Canary Islands . . . 3
2.2 Geological map of Gran Canaria . . . 4
2.3 Hydrothermal alteration at Los Azulejos . . . 7
2.4 Cone-sheet outcrops . . . 9
2.5 Cone-sheets intruded into syenite . . . 9
2.6 Massive cone-sheet outcrops . . . 10
2.7 TAS-Diagram . . . 10
2.8 Cross-cutting cone-sheets . . . 11
2.9 Cone-sheets cross-cut by radial dyke . . . 12
2.10 Altered cone-seets . . . 12
2.11 Cone-sheet emplacement model of Phillip (1974) . . . 14
2.12 Different geometries of cone-sheet swarms . . . 16
3.1 Location of data points (geological map) . . . 19
3.2 2D cross-sections showing cone-sheet intersections . . . 21
3.3 Frequency of minimal distance . . . 24
3.4 Frequency of intersection angles . . . 25
4.1 Elevation vs. dip . . . 26
4.2 Frequency of dip in elevation groups . . . 27
4.3 Distance to centre vs. dip angle . . . 28
4.4 Dip angle related to location (map) . . . 29
4.5 Stereographic projection and rose diagram . . . 30
4.6 Statistical distribution of cone-sheet thickness . . . 31
4.7 3D model . . . 33
4.8 Magma chamber produced with cross-section approach . . . 34
4.9 Distribution of intersections at depth . . . 34
4.10 Loaction of magma bodies following the geometric approach . . . 35
4.11 Different views of magma bodies (geometric approach) . . . 36
4.12 2D map with magma chamber projection . . . 36
4.13 The complete model (incl. magma chamber) . . . 37
5.1 Topography, surface at 800 m a.s.l. . . 38
5.2 Conceptual Tejeda cone-sheet emplacement model . . . 42
5.3 Phase diagram . . . 43
5.4 Outcrops at Barranco de Agaete . . . 46
Table of Contents
1 Introduction 1
2 Background 3
2.1 Geological Setting . . . 3
2.1.1 The Canary Islands . . . 3
2.1.2 Gran Canaria . . . 5
2.1.3 Tejeda Formation . . . 6
2.2 Lithology . . . 8
2.3 Previous work on cone-sheets . . . 13
3 Methods 17 3.1 Data acquisition . . . 17
3.2 3D modelling . . . 18
3.3 Reconstruction of the Magma chamber . . . 18
3.3.1 Cross-section approach . . . 20
3.3.2 Geometrical approach . . . 22
4 Results 26 4.1 General data analysis . . . 26
4.2 3D Modelling . . . 32
4.3 Magma chamber reconstruction . . . 32
5 Discussion 38 5.1 Morphology of individual cone-sheets and cone-sheet swarm . . . 38
5.2 Reconstruction of the Tejeda cone-sheet swarm . . . 39
5.3 Geometry of the magmatic source . . . 40
5.4 Methodological development . . . 43
5.5 Estimation of volume of the Tejeda cone-sheet complex . . . 44
5.6 Suggestions for future work . . . 45
6 Conclusion 47 7 Acknowledgements 48 References 48 Appendices 54 Appendix A Data table . . . 54
Appendix B Matlab . . . 71
1 Introduction
Cone-sheets swarms are part of many volcanic complexes around the world. Since they have first been described by Harker (1904) as inclined sheet intrusions that dip towards a common centre, many cone- sheet complexes have been discovered all around the world, e.g. in Scotland (Mull central complex, Bailey et al., 1987; Ardnamurchan complex, Richey and Thomas, 1930), Japan (Otoge igneous complex, Geshi, 2005), Iceland (Geitafell Volcano, Burchardt and Gudmundsson, 2009), and Sweden (Alnö com- plex; Kresten, 1980). These cone-sheet swarms are part of the intrusive central complexes of volcanic edifices and are - together with dykes - a major pathway for magma to the Earth’s surface where they feed volcanic eruptions.
Analyses of modern and ancient cone-sheets provide us with vital information on the geometry of a volcanic plumbing system, such as size, depth and shape of the magma chamber (e.g. Burchardt et al., 2013a, Burchardt et al., 2011). This information allows us to interpret processes and dynamics of modern and ancient volcanic edifices and will thus help to provide useful background information during management of volcanic crises and to reduce risks to humans and infrastructure.
The structure and exposed shape of cone-sheet complexes can be reconstructed in three dimensions (3D) in order to make a more realistic model of the unexposed part of the plumbing system. However, most swarms of cone-sheets are not sufficiently exposed vertically and/or laterally to reliably determine their geometry at depth. In particular, convex, straight or concave continuations of cone-sheets down-dip would produce similar traces at the surface (cf. Burchardt et al., 2011 and references therein). The Tejeda cone-sheet complex on Gran Canaria (Canary Islands, Spain; Schirnick, 1996, Schirnick et al., 1999) is probably one of the best exposed cone-sheet swarms due to high erosion levels and relief differences (see e.g. Fig. 1.1) and displays over 1000 m of vertical and more than 15 km of horizontal exposure.
The cone-sheet swarm, emplaced into the volcaniclastic infill of the Miocene Tejeda caldera, is therefore ideal for the analysis of cone-sheet geometry in 3D and provides excellent conditions for studying the volcanic plumbing system of the Tejeda volcano.
Based on 2D projections assuming straight sheet-intrusions, the Tejeda cone-sheet complex has previously been described by Schirnick et al. (1999) as stack of parallel intrusive sheets with a truncated dome geometry that form a concentric structure around a central axis. In my study I test this hypothesis by visualizing the extensive data set to gain insights into the symmetry and the overall geometry of the sheet intrusions below the surface. Additionally, geometric analyses are applied to reconstruct the unexposed plumbing system of the eroded Tejeda volcano.
This study uses structural data published by Schirnick (1996) to model the geometry of the Tejeda cone-sheet complex in 3D. In order to increase the amount of data and to close some gaps in the spatial
Roque Nublo
Roque Bentayga
Tejeda Formation Roque Nublo Formation
Figure 1.1. Gran Canaria has a highly eroded central part with mountains and deep canyons and barran- cos. Note the Roque Bentayga (centre) and Roque Nublo monoliths (background, far left, as seen from Artenara), which are left from the Pliocene Roque Nublo volcano - an extinct volcano unconformably overlying the Tejeda Formation that hosts the cone-sheet complex. The unconformity is marked with a stippled white line.
distribution of structural data, additional structural measurements were taken in the field in March 2015.
This high amount of data (with>2000 data points) makes this study unique. Visualization of the cone- sheet traces and subsurface continuations and a first reconstruction of the magma chamber with the 3D software Move™ follow an approach presented by Burchardt et al. (2013a,b). To improve the quality of the reconstruction of the plumbing system, a second method was developed, using geometrical consid- erations in MATLAB. The model gives insights into the symmetry of the sheets and overall geometry development of the cone-sheet swarm below the surface.
2 Background
2.1 Geological Setting
The Tejeda caldera is situated in the central-western part of Gran Canaria (Canary Islands, Spain). The Canary Islands are situated about 200 km off the West-coast of Africa (see Fig. 2.1). The archipelago comprises seven main islands, of which Gran Canaria is the third largest (after Tenerife and Fuerteven- tura) with an area of about 1560 km2. It has ca. 900.000 inhabitants and is a popular travel destination with more than 3.5 million tourists per year (cf. Patronato de Turismo de Gran Canaria, 2013). The island is almost circular in shape with a diameter of about 45 km. The topography is variable with nu- merous beaches along the coast line and mountains in the central part of the island with elevations up to 1950 m. Erosion has carved out deep radial barrancos and canyons (see e.g. Fig. 1.1). Geologically the island can be divided into a south-western part, which is older and dominated by Miocene volcanics, and a north-eastern part that is dominated by Pliocene-Quarternary volcanism. These parts are divided by a Pliocene rift-zone (Boucart and Jérémine, 1937; see also Fig. 2.2).
Africa Gran Canaria
El Hierro
La Gomera La Palma
Fuerteventura Tenerife
Lanzarote
100 km
N
Figure 2.1. Geographic distribution of the seven main islands of the Canary archipelago, with the east- ernmost islands situated just 100 km off the African coast. Note the dust blown from the Sahara (MODIS satellite image from NASA).
2.1.1 The Canary Islands
The Canary Islands comprise the seven main islands and several smaller islands and seamounts. The main islands show an age progression from East (old) to West (young), with Fuerteventura being the oldest and El Hierro being the youngest (Troll et al., 2015). All islands haven been active throughout Holocene times and even on the older islands historic eruptions were recorded, although the islands are in
Figure 2.2. Simplified geological map of Gran Canaria (modified after Carracedo and Troll (in prepara- tion) and GRAFCAN).
different stages of their evolution from seamounts to evolved oceanic islands. The Canaries are situated on top of some of the oldest and thickest oceanic crust on Earth. While the sedimentary cover is quite thin underneath the eastern islands with 0.5 km to 1 km of sedimentary successions, the western islands are situated on top of thick sedimentary successions of up to 8 km thickness.
Several models have been proposed for the volcanic origin of the Canary Islands, e.g. a) a propagat- ing fracture model connected to the Atlas mountains (Anguita and Hernán, 1975) that proposes the initi- ation and control of volcanism in the Canaries related to a structure cutting the lithosphere, b) a mantle plume (or hotspot) model, which explains volcanism due to a long-lived thermal mantle-anomaly (cf.
Wilson, 1963, Carracedo et al., 1998), and c) a "blob model", which is a refined version of the hotspot model that explains the evolution of the Canary Islands by several ’blobs’ of mantle plume material produced by decompression melting (contrary to a continuous mantle plume; Hoernle and Schmincke, 1993). After years of debate the hotspot and the blob models seem now to be confirmed as they explain for example the age progression of the islands and distribution of sediments below the islands (cf. Zaczek et al., 2015, Troll et al., 2015).
2.1.2 Gran Canaria
The geological history of Gran Canaria has been studied in detail for a long time (cf. Boucart and Jérémine, 1937). Deposits of the submarine seamount stage cannot be found in outcrops on Gran Canaria, but drill cores revealed hyaloclastite tuffs and debris avalanche deposits that are interpreted as products of submarine eruptions (Schmincke and Segschneider, 1998). Interbedding with products from subaerial eruptions implies a gradual change from submarine to subaerial volcanism. During the shield-stage, more than 1000 km3of basaltic lavas were erupted, constructing a 2000 m high shield volcano between 14.5 and 14.0 Ma (van den Bogaard and Schmincke, 1998). Outcrops of these shield basalts can still be found in the SE and E of Gran Canaria (see Fig. 2.2).
At the end of the shield stage, a shallow reservoir with rhyolitic magma got established at a depth of about 4 to 5 km. Magma mixing produced explosive eruptions, creating the ignimbrites of the Mogán group with the widespread ignimbrite P1 at the base (Freundt and Schmincke, 1992). The P1 unit, about 14.1 Ma old, had a volume of ≥60 km3and is compositionally zoned from felsic in the bottom to basaltic at the top. The eruption of this large volume from a shallow magma reservoir caused the collapse of the volcano and created the Caldera de Tejeda (Freundt and Schmincke, 1992). Repeated replenishment with basaltic magma of the shallow magma followed by renewed production of rhyolitic magma and gravitational collapse of the cauldron block lead to repeated explosive eruptions caldera collapses (e.g.
Crisp and Spera, 1987; Freundt and Schmincke, 1995). The opening of ring fractures at the caldera rim lead to the eruption of felsic material towards the interior and exterior of the caldera (Schmincke, 1967).
The first extra-caldera units erupted between 14.0 and 13.3 Ma and comprise several ignimbrite units with a rhyolitic to trachytic composition and an average repose period of ∼40-50 kyrs between eruptions (van den Bogaard and Schmincke, 1998).
The Mogán phase was followed by a second phase of felsic eruptions (13.3 to 8.3 Ma), producing the trachytic to phonolitic ignimbrites of the Fataga group. These ignimbrites are interbedded with lava flows and epiclastic deposits. Both the deposits of the Mogán group and the Fataga group were intruded by the Tejeda Formation (see below) between 11.7 to 7.3 Ma (Schirnick et al., 1999).
After the eruptive activity of the Fataga group declined, a period of volcanic quiescence began (8.8 to 5.3 Ma). During this period, erosion took place, creating a network of radial barrancos. Alluvial fans and mass wasting deposits were also products of intense erosion and can be found mainly in the N, NE and S of the island especially along the coast. The beginning of the rejuvenation stage of volcanic activity coincides with the end of the erosive period that started about 5.5 Ma.
The first phase of this rejuvenation stage comprised the construction of the Roque Nublo volcano, which was situated in the central-southern part of Gran Canaria. This long-lived volcano (about 1.5 Ma) produced basaltic to trachytic and phonolitic effusive products, ignimbrites, breccias, and pillow lavas
along the coast. As the deposits’ composition changed towards trachytic and phonolitic eruptions became more explosive, with a total eruptive volume about 200 km3 (Pérez-Torrado et al., 1995). The Roque Nublo volcano possibly reached an elevation of up to 2500 m above sea level (a.s.l.) and had relatively unstable flanks, which triggered flank collapses and thick debris avalanches (Pérez-Torrado et al., 1995).
At the late stage of the Roque Nublo cycle, evolved magmas intruded into the earlier Roque Nublo deposits, deforming the previously deposited material and forming lava domes. The remains of the Roque Nublo cycle can still be found in many places on Gran Canaria, with the Roque Nublo monolith being the most impressive (see Fig. 1.1). The typically brown to red-coloured rocks often directly overly the Tejeda Formation and are especially abundant in the central-eastern part of the field area.
During the last intrusive activity of Roque Nublo (ca. 3.5 Ma), new eruptive activity began along NW-SE directed fissures in the NE of the island. This concentration of fissure eruptions led to the formation of a rift zone that forced lavas to flow only towards the N and NE of Gran Canaria. This is also the area where Pliocene, Quarternary and more recent volcanism is concentrated, covering the older units, whereas in the SW of the island the older units are still exposed. The younger volcanism is mainly characterized by basaltic and alkaline compositions with low eruption rates. Apart from volcanic activity, traces of several mass-wasting events of Quaternary age can be found on Gran Canaria, as well in volcanic aprons around the island (Schmincke and Sumita, 1998b).
2.1.3 Tejeda Formation
The Tejeda collapse caldera is situated in the central-western part of Gran Canaria. The gravitational and vertical collapse of a magma reservoir at shallow levels led to the initial eruption of large volumes of P1 ignimbrite that emptied the shallow reservoir. Due to repeated replenishment of shallow magma reser- voirs, further eruptions were triggered after the emplacement of P1 along the ring fractures of the initial caldera rim. These led to repeated cycles of inflation and deflation and to further gravitational collapses of the shallow reservoirs (Troll et al., 2002). The repeated eruptions filled the caldera-depression with a series of ingimbrites of the Mogán and Fataga groups. The caldera rim can be easily distinguished in the field due to colourful, mainly bright green to yellow and pink, hydrothermally altered caldera infill deposits that follow the ring fractures of the caldera margin (see Fig. 2.3; Donoghue et al., 2010).
The caldera hosts an intrusive complex, the Tejeda Formation, which has first been described by Schmincke (1967). This complex comprises thousands of trachytic to phonolitic sheet intrusions and syenite plutons that were emplaced into the volcaniclastic infill of the Mogán and Fataga groups between 11.7 and 7.3 Ma (Schirnick et al., 1999) contemporaneously to the emplacement of the Miocene volcanic sequences. According to Schirnick (1996), the intrusive complex can be divided into different zones: a central low density dyke zone (CLDZ) that is occupied by syenites and the intracaldera breccia and hosts
Figure 2.3. The caldera rim at Fuentes de Los Azulejos can be recognized from the distance due to the colourful hydrothermal alterations of the caldera-infill deposits. The shield basalts (left) are unconform- ably overlain by altered intra-caldera tuffs and ignimbrites of the Mogán group (towards the right). The colourful, hydrothermally altered Mogán rocks are intruded by Fataga sills (red-brown rocks surrounded by hydrothermally altered rocks) and overlain by Fataga ignimbrites (top).
only small amounts of cone-sheets (<20%), a high-density dyke zone (HDZ) with 75-90% cone-sheet density, and an annular low density dike zone (ALDZ) with<60% cone-sheet density. In some areas of the cone-sheet complex, more than 90% of the rocks are cone-sheets (see e.g. Fig. 2.4), whereas in other places the host-rock is more abundant. The host rock is dominated by ignimbrites and volcaniclastics of the Mogán and Fataga groups. In the central part of the cone-sheet complex, cone-sheets also intruded breccia and syenites (see Fig. 2.5).
Hernán and Véléz (1980) estimated that the intrusion of about 130 km3of magma belonging to the Tejeda formation created a cone that was about 3-4 km high (from source to highest elevation). They also estimated that the reservoir was very shallow with a depth of about 2 km below present sea level and inferred an ellipsoidal shape for the cone-sheet swarm. The intrusion of cone-sheets and syenites caused an uplift of the host rock roof by approximately 2000 m (Schirnick et al., 1999; Donoghue et al., 2010).
2.2 Lithology
The cone-sheet rocks are usually pale to dark grey and green in colour and have a light brown to orange weathering colour (see e.g. Fig. 2.6). They are usually fine grained with an aphanitic to porphyritic texture. The size of crystals dispersed in the groundmass is variable as they are generally several mil- limetres in size, but can reach sizes of up to a centimetre in some samples. The rocks contain mainly alkali feldspar phenocrysts, and less abundant plagioclase, biotite, pyroxene, fooids and amphibole (such as hornblende) crystals in a fine grained, dark ground mass.
Minor amounts of opaque minerals (e.g. chalcopyrite) can also be observed in thin- and thick- sections. Schirnick (1996) classified the cone-sheets based on petrographic and structural differences into two groups: "D4" cone-sheets that are mainly trachytic and widely abundant, and "D5" cone-sheets that are trachytic to phonolitic and younger than the D4 cone-sheets. This observation could not be followed in the field as one would need chemical data, which is why this distinction has not been made for further processing in this study. The chemical composition of cone-sheet rocks is variable and plots in the trachyte and phonolite fields of a total alkali versus silika (TAS) diagram as shown in Fig. 2.7 (Schirnick, 1996).
Individual cone-sheets show chilled-margins, and cross-cutting of cone-sheets can be observed in many places of the cone-sheet complex, indicating several generations of cone-sheet intrusions (e.g. Fig.
2.8). In various places, especially close to Ayacata, the massive cone-sheets are cross-cut by steeply- dipping radial dykes, which are more weathered than the cone-sheets as they are often not well preserved (see Fig. 2.9). The weathering colour of these dykes is bright white, whereas the cone-sheets often show more brown-orange weathering colours.
While some cone-sheets are relatively well preserved, others are heavily weathered and almost soil- like (Fig.2.10A). Many cone-sheets also show strong Liesegang-textures, i.e. white-orange-brown bands, indicating that the rocks were chemically or hydrothermally altered after emplacement (see Fig. 2.10B).
(A) (B)
Figure 2.4. A Cone-sheet intrusions seen from GC-210 across the valley of the reservoir lake Presa del Parralillo in the central part of the cone-sheet complex. Syenites can be found along the shore of the lake, whereas the rock above the lake consists almost completely of parallel cone-sheet intrusions (photograph courtesy of S. Burchardt). B Cone-sheets cropping out along GC-605 in the southern area of the cone-sheet complex. The red arrows point at individual cone-sheets.
Figure 2.5. Cone-sheets intruded into syenite. A thinner, darker cone-sheet cross-cuts the larger cone- sheet that shows Liesegang texture, and is thinning towards the top (centre) before it dies out.
(A) (B)
Figure 2.6. Massive cone-sheet outcrops in a road cut along GC-605 (A, location: 437588.7, 3091517.9), and along GC-210 (B, location: 431225, 3096308, photo courtesy of M. Jensen). The rock in both places consists dominantly of cone-sheets, while host-rock is almost completely absent.
Figure 2.7. The total alkali versus silica (TAS) diagram reveals that the majority of D4 and D5 cone- sheets are trachytes and that some D5 cone-sheets are also of phonolitic composition. The data plotted in the diagram is from Schirnick (1996), figure courtesy of M. Jensen.
Figure 2.8. Wall with several generations of cone-sheets that cross-cut each other along GC-210 (Loc- ation approximately 428780E, 3095433.1N). The stippled white lines show the borders of some cone- sheets.
Figure 2.9. Massive cone-sheets cross-cut by a radial dyke that displays a white weathering colour in a road cut along GC-605 (location: 443589.8, 3089149.5). The stippled white lines indicate different cone-sheets.
(A) (B)
Figure 2.10. A,B: Cone-sheets of the Tejeda cone-sheet complex can be heavily altered so that they resemble soil. This outcrop shows nice Liesegang textures (enlargement in B; A4-clip board for scale).
2.3 Previous work on cone-sheets
Cone-sheet swarms are thought to feed sill intrusions and flank eruptions (Burchardt, 2008) and are pathways for large volumes of magma on its way from the reservoir to the surface. The emplacement of cone-sheet intrusions thus leads to growth of a volcanic edifice from the inside, and generation of relief (cf. Le Bas, 1971; Klausen, 2004; Siler and Karson, 2009). These intrusions are thought to account for surface deformation prior to eruption (e.g. Galland et al., 2015; Guldstrand, 2015) and to record the local stressfield of the volcanic edifice (cf. Nakamura, 1977; Chadwick and Dieterich, 1995; Mathieu et al., 2015).
The first cone-sheet swarm described in the literature is situated in the Cuillin district of Skye, Scotland (Harker, 1904). Cone-sheet swarms have some common characteristics that are diagnostic:
Individual cone-sheets are usually thin (1 m or less) and dip at angles between 30◦ and 60◦ towards a central magmatic source at a few kilometres depth. The sheet swarms are usually radially symmetrical to the magmatic source and have diameters of several kilometres (but usually not more than 15 km, cf.
Siler and Karson, 2009).
Several models have been proposed to explain cone-sheet emplacement, but a generally accepted model is still missing. Anderson (1937) proposed the first emplacement model for swarms of inclined sheets, which he based on observations from the Ardnamurchan cone-sheet complex. Anderson proposed the formation of cone-sheets from a pressurized magma chamber that lifts the roof and overlying host rock. This point-like excess pressure directed to the top of the magma chamber leads to release of pressure along surfaces that are parallel to the walls (perpendicular to the roof) of the source reservoir.
This would produce cone-sheets that intrude into hydraulic tension fractures that form perpendicular to the minimum principal compressive stress, parallel to the walls (but perpendicular to the roof) of the magma source, whereas ring-dykes would intrude into shear fractures. In Anderson’s model, σ1 (maximum principal compressive stress) is perpendicular to the rock-magma interface and σ3(minimum principle stress) lies in radial planes tangential to the rock-magma interface.
A second model was proposed by Durrance (1967), which is also based on the Ardnamurchan cone-sheet complex and explains the emplacement of cone-sheets due to the formation of spiral fractures based on compression in glass sheets that dome elastically. This model contains a shear-component, but explains growth of cone-sheets in form of spiral fractures by rapid outward extension of the edge of a centre dislocation contrary to additional opening of shear fractures. However, cone-sheets are thought to not grow in this spiral manner (see e.g. Phillips, 1974).
A modification of Anderson’s model was presented by Phillips (1974), in which he also proposed the emplacement of cone-sheets due to upward pressure of magma (see Fig. 2.11). As Phillips (1974) points out, Anderson’s model does not account for the absence of cone-sheets in the centre (where tension
P
Rotational strain σ1
σ3 σ3 σ1
Irrotational strain Central area, no cone-sheets
present
Cone-sheets, shear stress
maintained Sills, hydraulic
tension fractures
Irrotational strain
Irrotational strain
Figure 2.11. Cone-sheet emplacement according to Phillips (1974). Rapid expansion and excess pres- sure in the magma chamber led to an upwards-pushing roof of the chamber and result in rotational strain along the shoulders of the magma chamber. Shear fractures start to form and cone-sheets can intrude.
If the pressure is not sustained, hydraulic fractures are produced and sills form instead of cone-sheets (figure redrawn after Phillips (1974)).
is suggested to be highest), and is also not taking into account a shear displacement during uplift of the host-rock and emplacement of steeply dipping cone-sheets. Additionally to Anderson’s model, however, Phillips explains the absence of cone-sheet intrusions in the centre by shear fractures formed along the hanging walls of the central area during upward expansion and rise of the magma. In his model, he uses dynamical stress and takes body forces (e.g. gravity) into account to explain cone-sheet emplacement.
In Phillip’s model, rotational strain is high at the shoulder area (between roof and walls) of the magma chamber. If the roof is uplifted, simple tension fractures would form first in the rock adjacent to the magma at low deviatoric stress. Rapid expansion (e.g. due to retrograde boiling) would then enable the formation of shear fractures in the areas of high rotational stress, which will then be filled by magma to form cone-sheets. If high deviatoric stresses are maintained, cone-sheets can reach the surface, but if the stresses decrease, fluid pressures might become more important, and the propagation of cone- sheets would then take place in hydraulic tension fractures that dip more gently and will form sills.
This model explains the conical, parallel character of cone-sheet intrusions and the overlap of several individual cone-sheets, but shear displacement cannot be observed in most cone-sheet swarms (Mathieu et al., 2015). The model proposed by Phillips (1974) is therefore not accepted and the most widely used model is still the model proposed by Anderson (1937). Therefore, the relationship between regional and local stress fields and the stress distribution around upward-pushing magma chambers that lead to the emplacement of cone-sheet complexes is still not fully understood (Mathieu et al., 2015).
Different geometries have been proposed for cone-sheet complexes and commonly used to determ- ine size, depth and geometry of the underlying and unexposed source magma reservoir (Fig. 2.12). As
pointed out by e.g. Burchardt et al. (2011), different geometries of cone-sheet complexes can produce similar traces at the surface, but have different implications for the shape and size of the reconstructed magmatic source (see Fig. 2.12). Phillips (1974) proposed a "trumpet"-shaped geometry with concave down-dip continuations of the individual intrusions (see Fig. 2.12E). Bowl-shaped, convex down-dip continuities have been used by e.g. Chadwick and Dieterich (1995) and Gudmundsson (1998) (see Fig.
2.12D). Klausen (2004) modified these two models towards a fanning-geometry. Both models cannot ori- ginate from the same magma reservoir, as the shape of the reservoir has been proposed to be sill-shaped for the trumpet-shaped cone-sheets, whereas the magma reservoir for the bowl-shaped cone-sheets is proposed to be more spherical to ellipsoidal (cf. Chadwick and Dieterich, 1995; Gudmundsson, 1998).
In addition to the two end-members of curved cone-sheet geometries, some models assume straight cone-sheet continuities (e.g. Schirnick et al., 1999; Geshi, 2005; Siler and Karson, 2009, Fig. 2.12A- C). Straight cone-sheet leads to different geometries for the re-constructed intrusive complex, such as stacked sheet intrusions that all have the same dip angle ("Champagne-glass"-geometry, Fig. 2.12A), a variation in dip angles with steep dips at the centre and more gentle dip angles towards the outside (Fig.
2.12C), or a geometry where all cone-sheets have the same dip angle but different diameters, originating from a laccolith-like magma chamber ("Cocktail-glass"-geometry, Fig. 2.12B). This last geometry has been proposed by Schirnick et al. (1999) for the Tejeda cone-sheet complex, as he assumed an average dip angle of ∼41◦for all cone-sheets and observed no correlation between age distribution and distance to the centre of the cone-sheets.
Until recently, most cone-sheet complexes have been projected and modelled in two dimensional space. Richey and Thomas (1930) and Schirnick et al. (1999) for example used 2D projections from maps and vertical cross-sections to determine the geometry of a cone-sheet complex and the size and depth of its magma reservoir. This approach can, however, lead to incorrect results (see Burchardt et al., 2013b) as the complexity of the cone-sheet geometry and the underlying plumbing system, as well as differences in location and topography, cannot be taken into account. The number and choice of location of cross-sections have large effects on the determination of the magmatic source, especially if a static focal point is assumed as origin of the individual intrusions. In the case of the Ardnamurchan cone-sheet complex, for example, the focal points of 2D projections led Richey and Thomas (1930) to propose three different centres of magmatic activity, whereas 3D projections by Burchardt et al. (2013a) show only one ellipsoidal shaped magma body. Recent developments in computational and analytical techniques and software enable simple three-dimensional modelling of cone-sheets, as used e.g. by Siler and Karson (2009); Burchardt et al. (2013a). Modelling of cone-sheet swarms in 3D has the advantage that information on the location of measurements is preserved and that topographical variations can be taken into consideration. Moreover, spatial variations and complexities can be analysed and the geometry
A B
D E
C
Figure 2.12. Different geometries of cone-sheet swarms (modified after Schirnick et al., 1999). A:
Straight cone-sheets that all dip with the same angle towards the same source create a "Champagne- glass" geometry with several stacks of cone-sheets. Additionally, straight cone-sheets that all have the same dip but different diameters can be emplaced from a laccolith-like magma reservoir and form a
"Cocktail-glass" geometry (B). This geometry has been proposed by Schirnick et al. (1999) for the Tejeda cone-sheet complex. A modification of the straight cone-sheet geometry can be seen in C, where the intrusions dip steeply at the center and more gentle towards the outside of the cone-sheet complex. D:
Curved cone-sheets with a convex continuation down-dip produce a "bowl"-shaped geometry with a spherical magma-chamber, whereas a concave downward continuation (E) produces a "trumpet"- shaped geometry originating form a sill-like magma chamber.
can therefore be modelled with better accuracy and high resolution.
The Tejeda cone-sheet complex, which is probably the best exposed cone-sheet swarm known so far, is a superb location to analyse the geometry of a cone-sheet swarm and its underlying volcanic plumbing system in three-dimensional space in great detail. Aim of this study is therefore to model the Tejeda cone-sheet complex in 3D, which has previously only been modelled with a two-dimensional approach (Schirnick, 1996; Schirnick et al., 1999. I will test the hypothesis presented by Schirnick et al.
(1999) that the cone-sheet swarm has a geometry of stacked parallel sheets with dips of about 41◦ and various diameters that show a truncate dome-geometry around a central axis, and that the cone-sheets originate form a shallow laccolith-like magma reservoir.
3 Methods
3.1 Data acquisition
Much of the data (about 75%) used for this study has been published in form of a doctoral thesis by Schirnick (1996). The author divided his data into different groups of dykes, mainly based on petrolo- gical observations. For this study only the cone-sheet "dykes" were chosen (groups D4, D5). According to Schirnick (Schirnick, personal communiation 2015), a linear offset can be found in the location in- formation of the originally published data, which was given in MGRS/NATO notation. In order to correct for an offset of 160 m (Easting) and 110 m (Northing) and to convert the data to UTM coordinates, re- calculations of the coordinates of all data points were done after the following principle: A coordinate of e.g. 28RDR26609619 was converted to
(2660 ∗ 10) − 160 m+ 400000 for the Easting, and to
(9619 ∗ 10)+ 110 m + 300000 (or ...+310000 for 28RDS coordinates, respectively) for the Northing, and would then read: 426440, 306300. The accurracy of these location measurements is about 30 m (Schirnick, personal communication 2015). If several structural measurements were taken for the same cone-sheet (for example from upper and lower margin), the arithmetic mean of these measurement were calculated to correct for undulation as both margins should be more or less parallel. This step is necessary as only one set of plunge and dip can be modelled later for one cone-sheet in the 3D software.
Field work took place from 8-22 March 2015 on Gran Canaria. Aim of the field work was to fill the gaps of spatial distribution of data published by Schirnick (1996) and to collect as many structural measurements as possible to expand the dataset. Structural measurements were taken with a Breithaupt stratum compass in dip direction/dip notation. The dip direction was later corrected by -5◦to account for the magnetic declination towards the West (NCEI Geomagnetic Calculators). If several measurements were taken for the same cone-sheet, the arithmetic mean values for dip direction and dip angles were calculated in order to correct for undulation. Additionally, the thickness of each cone-sheet was recorded.
The measurements were mainly taken along road-cuts due to accessibility and limited amount of time.
For each locality, a GPS measurement was taken with a hand-held Garmin eTrex 30 in order to have an exact location of the measurement on the map. The accuracy of the measurement is 3 m, although measurements were sometimes taken at larger distances than three meters from the coordinate taken.
The error for elevation measurements is larger (>4 m). In this study, all maps and coordinates are shown in UTM WGS1984 notation (zone 28N). The cone-sheet measurements and their spatial distribution is shown in Fig. 3.1.
For the visualization of the cone-sheet swarm in 3D and the reconstruction of the volcanic plumbing
system, all measurements with dips>70◦(n=74) were neglected as they can be classified as radial dykes, as well as measurements with dips<10◦(n=6) as they can be classified as sills. All data collected in the field and used in this study can be found in appendix A (Data table on page 54).
3.2 3D modelling
The modelling of the Tejeda cone-sheet swarm follows an approach first presented by Burchardt et al.
(2013a,b) to model the Ardnamurchan cone-sheet complex. To model the cone-sheet swarm in three dimensions, the data was imported into the software Move™, together with a digital elevation model (DEM, source: GeoMapApp) and a geological map (source: GRAFCAN). Each cone-sheet measurement was projected onto the map with a strike-dip symbol. Each symbol was converted into a line along strike (length: 100 m). From each line on the surface, a 10 000 m long straight surface was created that represents the cone-sheet and its directions in three dimensional space (i.e. plunge/dip direction and dip angles) and its projection into the subsurface. Cone-sheets classified as D4 by Schirnick (1996) were displayed in dark blue, cone-sheets classified as D5 were displayed in light blue and data collected by myself was displayed in green. To be precise, 1148 data points of D4 cone-sheets, 384 data points of D5 cone-sheets and 464 data points of cone-sheets measured by myself were modelled, giving a total of 1996 data points. 80 additional data points that can be classified as radial dykes or sills were modelled but are not shown in the images of the model or taken into account for geometric analysis.
To get a tidy appearance, all cone-sheets that dip towards the outside of the cone-sheet complex and not towards the centre are not displayed in the figures in the results section (n= 201, of which D4:
n=156, D5: n=44, Field: n=11).
3.3 Reconstruction of the Magma chamber
The reconstruction of the magma chamber follows two different approaches. For both methods it is assumed that no tectonic rotations have occurred that could have changed the position of cone-sheets after empalcement, hence no correction as e.g. shown by Klausen (2004) has been applied. The first approach ("Cross-section approach") was first presented by Burchardt et al. (2013a,b) and has been applied to Schirnick’s data only. The second one ("Geometrical approach") was developed by myself in order to improve the quality and accuracy of the reconstruction and has been applied to the complete data set. In the following I will describe both approaches for the magma chamber reconstruction.
Figure 3.1. Geological map showing the distribution of cone-sheet measurements of the Tejeda cone- sheet complex (strike-dip symbols). Data from Schirnick (1996) are displayed in dark red (D4) and orange (D5), additional data is displayed in yellow (geological map from GRAFCAN).
3.3.1 Cross-section approach
The cross-section aproach is based on the traditional method of reconstructing the geometry of cone- sheet complexes using two-dimensional cross-sections. Using this approach, multiple cross-sections were created in Move™ that cover the extent of the whole cone-sheet model. Sixteen sections were created that strike N-S, sixteen that strike NW-SE, sixteen that strike E-W and sixteen that strike SW-NE, resulting in a total of 64 cross-sections. The sections in each set have a spacing of 1000 m. The cone- sheets were projected onto these 2D sections and all intersections of cone-sheets were marked manually with a point-marker in each cross-section. Low-angle intersections that come from the same side of the cone-sheet swarm and intersect with angles<45◦(marked in pink) were distinguished from high-angle intersections that come from different sides of the cone-sheet swarm (see Fig. 3.2). Burchardt et al.
(2013b) proposed that the areas of tensile stress at the upper-lateral end (shoulder) of a magma chamber, where cone-sheet injection is initiated, are marked by clusters of low-angle intersections. High-angle intersections, on the other hand, are thought to be located within or below the magma reservoir.
After the different types of intersections have been marked, they were exported as point-clouds.
In Move™, these point-clouds were then converted into three-dimensional bodies, so called "Alpha- shapes", which are surfaces that contain the points. The accuracy can be changed manually and was chosen to fit the shape and geometry of the modelled cone-sheet complex. Since the body created using
"Alpha-shapes" contained many holes in the surface, three-dimensional ellipsoids were created in order to simplify the surface and shape of the magma body. These can later be converted into a "tetra-volume", which consists of individual three-dimensional tetra-hedra and allows calculation of a volume for the magma chamber.
A different option to create the magma chamber from the point cloud would be to manually create polygones (e.g. freehand polygones) in each cross-section, which roughly encircle the different clusters of intersections. In a second step, ellipses that contain the high-angle intersections and have the low- angle intersections at their upper end can be created that should outline the geometry of the magma chamber. This method has not been used in this study.
Figure 3.2. Example of a 2D cross-section striking NE-SW that shows the manually marked intersec- tions. High-angle intersections are marked in red (A,B), low-angle intersections are marked in pink (A,C). See text for more details.
3.3.2 Geometrical approach
In case of a large data set, the manual selection of intersections in cross-sections is time-consuming and probably inefficient. Apart from that, it is difficult to interpret the angle of intersection (high or low) from looking at a 2D cross-section as it only shows the apparent dip of cone-sheet projection in the cross-section and marks only an extract of the full 3D distribution of cone-sheets. The accuracy of the method depends on the spatial coverage of the model by angle and distance between individual cross- sections (or the total amount of cross-sections), and depends to a certain degree on the interpretation of the data by the author and not on statistical methods. I therefore developed a different approach that enables me to speed up the data analysis and to do the geometrical analysis and reconstruction of the magma chamber for the Tejeda cone-sheet complex using mathematical and geometrical operations in MATLAB. This approach is similar to a method presented by Hernán and Véléz (1980) and Siler and Karson (2009), as the individual cone-sheets are presented as straight vectors in three-dimensional space extending downwards from the point of measurement. However, Hernán and Véléz (1980) and Siler and Karson (2009) define the location of the source of the sheet swarm using horizontal sections at different depths, which are contoured according to cone-sheet density, whereas I am using a three-dimensional grid-density analysis.
To reconstruct the magma chamber geometry and location using a geometrical approach, the table containing the structural data is opened in MATLAB, and each cone-sheet measurement defines a line equation
~g(t) = ~r + t · ~p, (1)
where ~r is a location vector that contains only location information (Loc in the code) and ~pis a directional unit vector that contains only plunge and dip information in cartesian coordinates (Angl in the code).
The angle α, with which the cone-sheet vectors from two data points i and j intersect with each other, can then be calculated in the following way:
αi j= arccos(~pi·~pj). (2)
The cone-sheet lines with the line equation above have to be treated as skew lines. To calculate where the location of the "intersection point" lies (i.e. where the two skew lines come closest) and how far they are separated, one has to determine the line that represents the shortest connection. This connection must be perpendicular to both cone-sheet lines, and its direction is therefore given by the cross product ~ni j:
~ni j = ~pi×~pj
~pi×~pj
. (3)
The distance of the two skew lines can then be calculated as the projection of the difference of the position vectors onto the connecting vector ~ni j :
di j = ~ni j· (~ri−~rj). (4)
So far, only the direction of the connecting lines has been determined. The exact position in 3D space is yet unknown. The condition that the connecting line must be perpendicular to both cone-sheet lines can be used: the scalar product of the arbitrary connecting vector (gi(ti) − gj(tj)) between the skew lines with the directional vector ~phas to be 0:
(~gi(ti) − ~gj(tj)) · ~pi= 0
(~gi(ti) − ~gj(tj)) · ~pj= 0. (5) This system of equations can be solved and unique solutions for ti and tj calculated. With these two values, the mid point of the straight line can be calculated, which gives the intersection point ~Mfor the cone-sheet vectors:
M~ = ~gi(ti)+ ~gj(tj)
2 . (6)
This calculation is done for all measurements, so that all cone-sheets are compared to each other, and the locations of intersection points are calculated. Cone-sheets that do not come closer than a chosen value (in this case 800 m, see Fig. 3.3) are then defined to not intersect, the data volume can therefore be reduced. Using the intersection angles of cone-sheets and the minimum between high-angle and low- angle peaks in a histogram (55◦, see Fig. 3.4)), one can define values for high-angle intersections and low-angle intersections. As explained in the previous section, this distinction is important for the analysis of the magma chamber geometry.
In addition, a coordinate system with grid cells is created (here a 250 m x 250 m x 250 m grid was used). In the next step, the amount of intersection points per grid-cell can be calculated. The grid is then smoothed to reduce statistical fluctuations, which prevents holes in-between areas with a high amount of intersection points, using a Gaussian filter with a convolution-kernel size of 5 and a standard deviation value of 2 (2 grid boxes). The areas with a high amount of high- or low-angle intersections per grid-cell (in this case > 15) can then be visualised with an isosurface (surface with constant density). The vertices of the isosurface can then be imported as points into the cone-sheet model in Move™. The complete MATLAB code can be found in appendix B.
Figure 3.3. Plot showing the frequency of minimal distance of skew lines. Lines that do not come closer than 800 m are defined to not intersect and are therefore disregarded in the following calculations.
Figure 3.4. The histogram of the complete data set shows the intersection angles of skew lines that do not come closer than 800 m. The intersection angles are calculated using the scalar product of the vectors (see 2), which distinguishes between parallel (0◦) and anti-parallel lines (180◦). The majority of vectors intersect at low angles of about 15◦to 20◦, and a second group intersects at high angles between 75◦and 90◦. The minimum between the two groups (55◦) is used to distinguish between high- and low-angle intersections.
4 Results
4.1 General data analysis
The structural data of the Tejeda cone-sheet complex was collected in an area of about 200 km2. The data collected by myself in the field expands the data set from Schirnick (1996) and increases the spatial distri- bution of structural measurements. Observations made in the field have been described in the Lithology section (2.2, p.8). The measurements included in the complete data set were taken at elevations between 74 m a.s.l and 1484 m a.s.l. The measurements hence cover more than 1400 m of vertical exposure of the Tejeda cone-sheet complex. Comparing the distribution of dip angles of cone-sheets with the elevation, one can observe a large gap in the data set between about 500-1000 m a.s.l. (Fig. 4.1). Although values of lower elevations (below 500 m) show a slight trend in the linear fit, a general correlation between dip angle and elevation cannot be observed.
Figure 4.1. Scatter plot showing the relation between elevation and dip angle in the area of the Tejeda cone-sheet complex. The red line is the linear fit of the data between 0-800 m a.s.l. (equation shown top left, R2 = 0.051), the blue line is the linear fit between 800-1500 m a.s.l. (equation at top right, R2 = 6.59e − 04).
The correlation between dip angles and different levels of elevation can also be displayed with histograms showing the frequency of dip angles at different levels of elevation, similar to Fig. 4.3 in Schirnick (1996) (see Fig. 4.2). The histograms have similar distributions of dip angles within the different groups of elevation and show that most data points were taken at elevations above 1000 m a.s.l.
Figure 4.2. Histograms of the frequency of dip angles, divided into groups of different elevations: ≤500 m a.s.l. (top left), 500-1000 m a.s.l. (top right) and ≥1000 m a.s.l. (bottom). The individual plots contain the complete data set used in this study (after Schirnick (1996)).
To analyse the correlation between dip angle and the distance from the swarm centre, a point with the coordinates [433538.19 3095809.26] was chosen as centre point and the distance of the measurements calculated (Fig. 4.3, location of centre point displayed in Fig. 4.4). Most data points were taken at distances between 5000 and 6500 m from the centre and less in the central area. Dip angles range between 30-60◦ in the central area and across the whole scale (10-70◦) further away from the centre. A linear fit shows that the dip angles are up to 10◦ higher close to the centre than in the far distance of 10 000 m. However, the linear fit model does not really describe the distribution of data. A map of all data points that is colour coded by the dip angle displays the spatial distribution of dip angles across the Tejeda cone-sheet complex (see Fig. 4.4).
The arithmetic mean of dip angle is 39◦. The structural measurements of the cone-sheets are also presented in a stereographic projection plot that shows an almost circular distribution with a high density of poles in the SW and a lower density in the NE (see Fig. 4.5A). The rose diagram in Fig. 4.5B displays the direction of azimuths for the two data sets used for this study. The two data sets display a sub-circular distribution and overlap in the SE part, but have different mean vectors (toward the NE and ESE respectively) and peaks between NW and E to SE.
The thickness of the cone-sheets has also been recorded in the field, measured perpendicular to the walls of the cone-sheets. The arithmetic mean of the thickness is 2.6 m. The thickness of the cone-sheets has been compared to statistical distributions as presented by Krumbholz et al. (2014). The best fit for
Figure 4.3. The scatter plot shows the dip angle related to the distance to a chosen centre point (433538.19, 3095809.26). The red line is the linear fit of the data (equation of fit line in bottom left corner of plot; R2= 0.037).
the present data is attained by the Lognormal distribution, as it yields the lowest number for the goodness of fit (GoF) following the Kolomorov Smirnoff (KS) and Leastsquare (LSQ) fits (see Fig. 4.6). Weibull distribution, Exponential and Gamma distributions can also describe the data. The cone-sheet thickness data displays a staircase pattern in all graphs.
Figure 4.4. Map with the location of all data points used for the study of the Tejeda cone-sheet complex, colour coded by the dip angle, with high angles in red and low angles in blue. The black cross marks the location of the chosen centrepoint (see text for details).
(A)
(B)
Figure 4.5. Structural analysis of cone-sheet data. A The stereographic projection of poles to cone-sheet planes displaying data collected in the field (green) and data from Schirnick (1996) (blue) shows that the data is distributed on a small-circle. B Rose diagram with field data in green and Schirnick (1996) in blue, displaying the frequency of direction of azimuths of the two different data sets. The arrows indicate the mean vectors of the two data sets.
Figure 4.6. The cone-sheet thickness has been compared to different statistical distributions, displayed in qq-plots (left column, the cone-sheet data is displayed as blue crosses), best fit probability density functions (middle column, cone-sheet data displayed in red, fit in blue) and corresponding cumulative distribution functions (right column, cone-sheet data in red, fit in blue): Lognormal (A), Weibull (B), Exponential (C) and Gamma (D). The corresponding goodness of fit is displayed below the qq-plots (figures courtesy of M. Krumbholz, statistical analysis based on a script by C.F. Hieronymus).
4.2 3D Modelling
The map in Fig. 3.1 displays the location of individual sheets of the Tejeda cone-sheet swarm. There are clusters of measurements in different locations of the cone-sheet complex. The strike is not uniform at individual locations, but generally follows the outlines of the Tejeda caldera.
The model of the Tejeda cone-sheet swarm, created with the 3D software Move™, has a sub-circular shape with a diameter of about 15 km. Impressions of the model are shown in Fig. 4.7. In the subsurface, the cone-sheets converge towards a common area and intersect at a depth of about 800-5000 m below present day sea-level.
4.3 Magma chamber reconstruction
The reconstruction of the magma chamber following the cross-section approach with marking the differ- ent intersection points and creating a mesh-surface around them results in a magma chamber that is more or less ellipsoidal in shape, with a long-axis that strikes E-W and is about 9 km long, and a short axis that strikes N-S and is about 5 to 6 km long (Fig. 4.8). The magma chamber is situated at a depth between about 800-4000 m and has several protrusions towards the surface. The volume of the main magma body can be roughly estimated to about 90 km3. Note that this approach has only been applied to the data set from Schirnick (1996).
The reconstruction of the magmatic plumbing system below the Tejeda cone-sheet complex with the approach described in section 3.3.2 results in a similar but more differentiated geometry. The calculations indicate that the number of intersections is highest between 2000 and 3000 m below present day sea level (Fig. 4.9). A second peak can be observed at shallow levels of 0 to 500 m below present day sea level.
Below 4000 m, the frequency of intersections decreases drastically.
The calculations result in one major magma body which includes the high-angle intersections, and two smaller ones that are situated closer to the surface and are not connected to the main magma body (Fig. 4.10A). The main magma body is situated between 700 and 4700 m below present day sea level (comparable to the peaks in Fig. 4.9) and is semi-spherical to ellipsoidal in shape (see also Fig. 4.11).
The main body sits right at the centre of the cone-sheet complex and its axes are about 5.5 km long in E- W direction and about 5 km long in N-S directions (see e.g. Fig. 4.12). The volume of this reconstructed magma reservoir is about 73 km3. The low-angle intersections reach from the surface to depths of 5000 m and are mainly found in the eastern part of the swarm (Figs 4.10B, 4.13C).
(A) (B)
(C) (D)
(E) (F)
Figure 4.7. Different perspectives of the Tejeda cone-sheet model in three-dimensional space. Data from Schirnick (1996) is displayed in dark blue (D4) and light blue (D5), additional data in green. In this display, 1785 out of a total of 1996 cone-sheets are shown down to a depth of 6000 m below present day sea level. The scale varies with perspective, see Fig. 3.1 for comparison.
(A)
(B)
Figure 4.8. Magmatic source of the cone-sheets reconstructed using the cross-section approach. The main body is ellipsoidal in shape, with the long axis striking E-W, and three apophyses in the upper part protruding towards the surface. In A the high-angle intersection points are displayed in grey, most of the points are included in the magma body. The complete model including cone-sheets (D4 in dark blue, D5 in light blue) is shown in B down to a depth of 6000 m below present day sea level. The scale varies with perspective, see Fig. 3.1 for comparison.
Figure 4.9. The histogram displays the frequency of intersections of cone-sheets at depth.
(A)
(B)
Figure 4.10. Magmatic source of cone-sheets reconstructed using the geometric approach described in section 3.3.2. The blue points show the locations of structural measurements used for the analysis. A:
The isosurface (red) connects points of the same density and encloses the high-angle intersections (grid cells with more than 15 intersections per cell). It results in a large body at the centre of the cone-sheet complex, and a smaller one closer to the surface. B: Location of isosurface-bodies that enclose low-angle intersections.
(A) (B)
Figure 4.11. The magmatic source reconstructed using the geometric approach displayed in sections in N-S direction (A) and E-W direction (B), which reveal the extends of the magmatic source at depth.
Figure 4.12. Map view of the magmatic source of cone-sheets reconstructed using the geometrical approach. The strike and dip symbols show the location of data points (compare Fig. 3.1), the black crosses trace the outlines of the magma chamber in the subsurface as seen from above.
(A) (B)
(C)
Figure 4.13. A,B: These views of the 3D model of the Tejeda cone-sheet swarm display the reconstructed magmatic source inside the 3D model. The red points outline the magma chamber created with high- angle intersections, the pink points outline the low-angle intersections. Both images show cuts of the 3D model that strike E-W (A) and N-S (B). C displays the 3D point clouds that were created in Move™ from the isosurfaces in Matlab. Pink points are low-angle intersection-bodies, red points surround high-angle intersection bodies.
5 Discussion
5.1 Morphology of individual cone-sheets and cone-sheet swarm
The relation between dip angle and elevation reveals a large gap in the data between 600 m and 900 m, which could be explained by the topography in the centre of the island as there are many cliffs at this altitude (see Fig 5.1), making data acquisition difficult.
The results of the geometric analysis indicate that the dip angles of cone-sheets of the Tejeda cone- sheet swarm change with elevation as a trend can only be observed at low elevations (≤500 m) where the amount of data is low compared to elevations above 1000 m (see Fig. 4.1). If the cone-sheets would show a convex or concave geometry, one would expect that the dip angle varies significantly between high and low elevations. Since a general trend cannot be observed for the whole data set, the assumption of straight cone-sheets as proposed by Schirnick (1996) is likely.
Figure 5.1. Map that displays a blue surface at a level of 800 m a.s.l. Most data points (red/orange/yellow lines) are situated either above or below the surface, whereas only little data is situated around a level of 800 m. Since the blue surface ends at steep cliffs (indicated by red arrows), the gap in data distribution might be explained by the topography of the area.
The spatial distribution of cone-sheet measurements around the chosen centre of the cone-sheet complex shows that most data points were collected in the distal parts of the cone-sheet complex between 4000-7000 m from the centre, whereas data close to the centre is less abundant (Fig. 4.3). This observa-
