How local stress fields prevent volcanic eruptions 1 2

Agust Gudmundsson1, Sonja L. Brenner2 3

1Department of Structural Geology and Geodynamics, Geoscience Centre, University of 4 Göttingen, Goldschmidtstrasse 3, D-37077 Göttingen, Germany 5

(agust.gudmundsson@gwdg.de) 6 2Department of Earth Science, University of Bergen, Allegaten 41, N-5007 Bergen, 7

Norway (sonja.brenner@geo.uib.no) 8 9

ABSTRACT 10 11 Recent studies show that dike injections in stratovolcanoes and rift zones are much 12

more common than dike-fed eruptions. Although this observation is of fundamental 13

importance in volcanic hazard studies, the mechanisms that prevent dikes from 14

reaching the surface are still poorly understood. Here we present new numerical 15

models of active stratovolcanoes and rift zones consisting of alternating layers of 16

contrasting mechanical properties, such as stiff lava flows and soft pyroclastic rocks. 17

The models show that during magma-chamber inflation, local stresses in the stiff 18

layers encourage dike propagation while those in the soft layers tend to arrest 19

propagation and prevent volcanic eruptions. The local stresses in the stiff layers 20

may also trigger seismogenic faulting while the soft layers remain seismically quiet. 21

The results suggest that for an eruption to occur the stress conditions along the 22

potential pathway of a dike must be basically homogeneous. 23

24

Keywords: stratovolcanoes, dikes, stress fields, layered media, volcanic risk 25

26

2

INTRODUCTION 27 28

One principal aim of volcanology is to provide a theoretical understanding of how 29

volcanoes work so as to make it possible to forecast eruptions. There may be several 30

hundred million people living in the vicinity of active volcanoes worldwide (Chester et 31

al., 2002) so that reliable forecasting of eruptions is of a basic concern in hazard studies 32

in many countries. While some eruptions have been predicted, many more have not. And 33

many unrest periods have caused false alarm in the sense that they have, eventually, not 34

lead to eruptions (Newhall and Dzurisin, 1988; Scarth and Tanguy, 2001). 35

Recently, there has been considerable progress in the understanding of the hazards 36

associated with the material produced during volcanic eruptions. In particular, the 37

properties and mechanisms of eruptive columns are now much better understood than a 38

few decades ago (Sparks et al., 1997). By contrast the processes that occur in a volcano 39

before it erupts are less well understood. For example, we are still far from knowing the 40

mechanical conditions that must be satisfied for a magma-driven fracture, a dike, to reach 41

the surface, resulting in an eruption. Also, the reasons why so many volcanic unrest 42

periods with dike injections do not result in eruptions, that is, why most dikes injected in 43

stratovolcanoes never reach the surface (Gudmundsson et al., 1999; Gudmundsson, 2002; 44

Stewart et al., 2003) are still poorly understood. 45

In this paper we focus on how contrasting mechanical properties of the layers that 46

constitute typical stratovolcanoes and rift zones may largely control whether or not 47

eruptions occur during periods of volcanic unrest. We present numerical models that 48

indicate that abrupt changes in mechanical properties between adjacent layers, of the kind 49

that are common in stratovolcanoes, develop temporary local stresses that may prevent 50

3

dikes from reaching the surface. The results suggest that it is only when such unfavorable 51

local stresses have been changed to favorable ones, through a process referred to as 52

stress-field homogenization, that dikes are likely to reach the surface. 53

54

DATA 55

56 Field studies indicate that nearly all volcanic eruptions reach the surface through 57

magma-driven fractures (Gudmundsson et al., 1999; Gudmundsson, 2002; Stewart et al., 58

2003), referred to as dikes if subvertical, and as inclined (cone) sheets if inclined. Here 59

we use the word dike in a generic sense covering also inclined sheets. Until recently it 60

was commonly assumed that most or even all dikes were feeders to eruptions (Walker, 61

1960; Longwell et al., 1969; Macdonald, 1972; Williams and McBirney, 1979). Recent 62

studies, however, show that many more dikes are injected in stratovolcanoes and rift 63

zones than reach their surfaces (Gudmundsson et al., 1999; Gudmundsson, 2002; Stewart 64

et al., 2003). This implies that most dikes become arrested on their way to the surface. 65

For example, in dike profiles in Tenerife (Canary Islands) and in Iceland (Fig. 1) arrested 66

dikes are much more common than feeder dikes (Gudmundsson et al., 1999; 67

Gudmundsson, 2002). Similar results are obtained from ophiolites (Dilek et al., 1998) and 68

dike swarms exposed in the walls of large fracture zones (Karson, 1998; Stewart et al., 69

2003). 70

Observations made during active periods in volcanoes also indicate that the volume of 71

magma intruded greatly exceeds that erupted. For example, the estimated ratio of erupted 72

to intruded volumes of magma in the Etna Volcano in Italy in the period 1980-1995 is 73

4

0.13, whereas the same ratio for the Krafla Volcano in Iceland in the period 1975-1984 is 74

0.30 (Harris et al., 2000). 75

Active stratovolcanoes and rift zones are composed of layers, mostly pyroclastic 76

rocks and lava flows, that commonly have contrasting mechanical properties. In 77

particular, many young pyroclastic layers are soft (with low Young’s moduli) whereas 78

lava flows, especially those of basalt and intermediate rocks, are normally stiff (with high 79

Young’s moduli). We propose that this mechanical layering, and the associated local 80

stress fields, may explain why most dikes become arrested on their way to the surface. 81

82

MODELS 83 84

To test this proposal, we made numerical models using the finite-element program 85

ANSYS (www.ansys.com). We model the stress field around a magma chamber, of 86

circular cross section, subject to internal magmatic excess pressure (pressure in excess of 87

the lithostatic pressure at the margin of the chamber) of 10 mega-pascals (MPa) as the 88

only loading. In the first model (Fig. 2) the chamber has an initial diameter of 0.25 units, 89

whereas the height of the model is one unit and it is fastened in the corners, where the 90

boundary conditions of no displacement are indicated by crosses. 91

The chamber is located in a layered rift-zone crust, where each of the layers A, B and 92

C has a thickness of 0.1 unit, whereas layer D is 0.7 units thick. In a 10-km-thick crust, 93

the chamber would thus be 2.5 km in diameter and each of the mechanical layers A-C 1 94

km thick. The layer thickness in the models, however, is arbitrary. This is in accordance 95

with field observations (A. Gudmundsson, unpublished data) and theoretical studies 96

5

(Hyer, 1998) which indicate that the contrasts in mechanical properties between layers, 97

rather than layer thicknesses, determine the local stress fields. 98

Layer D has a stiffness of 40 GPa, layer C 100 GPa, layer B 1 GPa, and layer A 100 99

GPa. Layers A and C are thus very stiff and may represent piles (acting as mechanical 100

units) of basaltic lava flows; layer B is very soft and may represent soft pyroclastic rocks 101

or sediments, whereas layer D is moderately stiff and corresponds to bodies of various 102

types of rocks (Bell, 2000). 103

In the second model (Fig. 3) the surface layers A and layer C are soft (with a stiffness 104

of 1 GPa) whereas layer B is stiff (with a stiffness of 100 GPa). Otherwise the second 105

model is identical to the first model as presented in Figure 2. 106

The results (Figs 2 & 3) indicate that during a period of unrest in a volcano with 107

magma-chamber inflation and surface doming, the local stresses in some mechanical 108

layers encourage dike injection, while in others they encourage dike arrest and may thus 109

prevent volcanic eruptions. Similarly, some layers become subject to stresses favoring 110

normal faulting and associated seismicity while other layers act as stress barriers to fault 111

propagation. 112

For example, in the second model of a layered stratovolcano during magma-chamber 113

inflation (Fig. 3), the stiff layer B concentrates tensile stresses and encourages normal 114

faulting and associated seismicity, while the high tensile stresses in the layer D next to 115

the magma chamber encourage chamber rupture and dike injection. The soft layer C, 116

however, acts as a barrier to dike propagation and encourages dike arrest. In this model, 117

the soft layers A and C suppress tensile (and shear) stresses and would tend to arrest the 118

upward and downward propagation of the seismogenic normal faults in layer B. 119

6

These model predictions are supported by observations of volcanoes during unrest 120

periods. For example, concentration of tensile stresses in the stiff layer B indicates that 121

there may be layers with seismogenic fault slip (here normal faulting) at certain crustal 122

depths during magma-chamber inflation, whereas the layers above and below would be 123

free of fault slip. Such a confined seismicity has recently been reported from Etna 124

(Brancato and Gresta, 2003). 125

Also, the volcanic unrest in the Campi Flegrei area in Italy in the periods 1969-1972 126

and 1982-1984 can be interpreted in terms of the models presented in Figures 2 & 3. In 127

the period 1969-1972 doming of the Campi Flegrei resulted in a maximum uplift of about 128

1.7 m, while doming in the period 1982-1984 gave rise to a maximum uplift of 1.8 m 129

(Bonafede et al., 1986; DeNatale et al., 1991; Dvorak et al., 1991; Barberi and Carapezza, 130

1996). The total maximum cumulative uplift during these two periods occurred in the 131

town of Pozzuoli and reached about 3.3 m, but did not result in any eruptions. The area 132

was seismically essentially quiet during the earlier uplift period. In the later uplift period, 133

there were earthquakes, but these were mostly confined to a mechanical layer at 3-4 km 134

depth and remained in that layer during the entire period. 135

Similarly, there were 30-40 inflation and deflation events during the 1975-1984 136

Krafla Fires in North Iceland (Bjornsson, 1985). All these events are thought to have 137

been related to dike injections. Also, many of the events were associated with 138

seismogenic normal faulting and changes in geothermal activity of the Krafla Central 139

Volcano. However, in only 9 of these events was the dike able to reach the surface and 140

supply magma to an eruption. 141

7

DISCUSSION 142 143 From these results it follows that dike injections lead to eruptions only if special 144

conditions are satisfied, namely that the stress field along the potential pathway of the 145

feeder dike is favorable up to the surface. Thus, for an eruption to occur, the stress field 146

along the entire pathway of the feeder dike must favor extension-fracture formation or, 147

more specifically, magma-fracture propagation. For this to be possible, the stress field 148

along the potential pathway of the feeder dike must be essentially the same, that is, it 149

must be homogenized. 150

Stress-field homogenization in a volcano occurs through smoothing out the stress 151

differences between the mechanical layers that the potential feeder dike dissects. We 152

propose that the homogenization is reached through two principal mechanisms: host-rock 153

alteration and host-rock deformation. The alteration leads to healing and sealing of 154

contacts and faults, filling of fractures and cavities in the rock with secondary minerals, 155

and gradually increases the thicknesses of layers with essentially the same 156

(homogeneous) mechanical properties. 157

The second process, host-rock deformation, operates primarily through dike injection 158

and faulting. In the upper parts of rift zones and young stratovolcanoes, normal faulting 159

often dominates, but dike injection at deeper crustal levels (Acocella and Neri, 2003; 160

Gudmundsson et al., 1999; Gudmundsson, 2002). Dike injection as well as normal 161

faulting tend to lessen stress differences between layers and make the stress fields 162

basically homogeneous in large rock bodies. 163

Using these results and focusing on the local stresses within a volcanic field, one 164

should in principle be able to infer whether a dike injected from a chamber is likely to 165

8

reach the surface. For example, along a still-molten feeder dike the local stress field is 166

essentially homogeneous, which encourages further eruptions through that conduit. 167

Generally, the local stresses in a stratovolcano or a rift zone are, with current 168

technology, difficult to determine with accuracy. The infrastructure of many 169

stratovolcanoes, active and inactive, however, can be inferred from geological studies of 170

deeply eroded sections. In addition, the seismicity of a volcano is an indication of its state 171

of stress. For example, if during magma-chamber inflation the associated seismicity is 172

widely distributed within the volcano, the stress field is comparatively homogeneous and 173

likely to encourage dikes to reach the surface, resulting in eruptions. By contrast, if the 174

seismicity is largely confined to certain rock bodies or mechanical layers in a 175

stratovolcano or a rift zone, the local stress field must be heterogeneous and likely to 176

prevent volcanic eruptions. 177

178

CONCLUSIONS 179

180

Nearly all volcanic eruptions are supplied with magma through magma-driven 181

fractures, that is, dikes. Thus, normally, if the stress field in a stratovolcano or a rift zone 182

does not allow a dike injected from a magma chamber to reach the surface there will be 183

no eruption. Field observations indicate that most dikes become arrested at certain crustal 184

depths and never reach the surface. 185

The numerical models presented in this paper provide a formal explanation as to why 186

so many dikes become arrested. Most stratovolcanoes and rift zones consist of 187

mechanical layers, such as lava flows and pyroclastic flows, with widely different 188

9

mechanical properties. Consequently, during periods of unrest the mechanical layers 189

develop local stress fields some of which encourage dike propagation whereas others 190

encourage dike arrest. For a dike to reach the surface the stress field along its entire 191

potential pathway must be favorable to dike propagation. Such conditions are met only 192

rarely (and through stress-field homogenization) in stratovolcanoes and rift zones. 193

The models presented here indicate that during most volcanic unrest periods with dike 194

injections the probability of an eruption is low. Only during those comparatively rare 195

periods when the stress field is essentially the same (homogenized) and favorable to dike 196

propagation all the way to the surface can eruptions be expected. 197

198

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ACKNOWLEDGMENTS 201 202 Supported by grants from the Research Council of Norway, Norsk Hydro, Statoil, and the 203

European Commission (through the Prepared project). 204

205

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its possible triggering mechanisms: Bulletin of Volcanology, v. 65, p. 517-529. 208

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Wright, R., Rothery, D.A., 2000, Effusion rate trends at Etna and Krafla and their 241

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263

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Figure Captions 263

264

Figure 1. Tip of a basaltic dike arrested at a contact between a Holocene basaltic lava 265

flow and pyroclastic rock (volcanic tuff). The dike is exposed in sea cliffs where the 266

Reykjanes Ridge comes on land on the Reykjanes Peninsula in Southwest Iceland, and 267

the tip is arrested at only 5 m beneath the present surface of the Holocene rift zone 268

(Gudmundsson, 2002; Gudmundsson et al., 1999). At the bottom of the 8-m-tall 269

exposure the dike is 0.34 m thick, but thins gradually to 0.1 m at the tip. No dike-induced 270

fractures or normal faults occur at the dike tip (cf. Fig. 2B). 271

272

Figure 2. Numerical model of a magma chamber with internal magmatic overpressure of 273

10 MPa as the only loading. The chamber is located in a layered crust of a stratovolcano 274

or a rift zone where layers A and C are very stiff, layer B is very soft, and layer D is 275

moderately stiff. (A) The magnitudes of the minimum principal compressive (maximum 276

tensile) stress ( 3σ ) are given in mega-pascals (MPa). (B) The ticks show the trajectories 277

of the maximum principal compressive stress ( 1σ ) along which ideal dikes should 278

propagate. The change in the direction of 1σ from vertical (favoring dike propagation) to 279

horizontal (favoring dike arrest) at the contact between layers A and B would encourage 280

dike arrest in a very similar way to that observed in Figure 1. 281

282

Figure 3. Numerical model of a magma chamber in a layered crust, identical to the 283

model in Figure 2 except that here the surface layer A and layer C are soft (with a 284

stiffness of 1GPa) whereas layer B is stiff (with a stiffness of 100 GPa). (A) 285

14

Concentration of tensile stresses in the stiff layer B indicates that seismogenic fault slip 286

may be confined to certain mechanical layers during magma-chamber inflation, whereas 287

the layers above and below would be free of fault slip. Such a confined seismicity 288

(presumably in stiff layers) was observed during the 1982-1984 uplift of the Campi 289

Flegrei area in Italy and has recently been reported from Etna. (B) The ticks represent the 290

trajectories of the maximum principal compressive stress ( 1σ ) along which ideal dikes 291

propagate. The change in the direction of 1σ from vertical (favoring dikes) to horizontal 292

at the contact between layers B and C would encourage dike arrest. 293

294