Volcanic eruptions are regulated by the rheology of magmas and their ability to degas. Both detail the evolution of stresses within ascending subvolcanic magma. But as magma is forced through the ductile-brittle transition, new pathways emerge as cracks nucleate, propagate, and coalesce, constructing a permeable network. Current analyses of magma dynamics center on models of the glass transition, neglecting important aspects such as incremental strain accommodation and (the key monitoring tool of) seismicity. Here, in a combined-methods study, we report the first high-resolution (20 μm) neutron-computed tomography and microseismic monitoring of magma failure under controlled experimental conditions. The data reconstruction reveals that a competition between extensional and shear fracturing modes controls the total magnitude of strain-to-failure and importantly, the geometry and efficiency of the permeable fracture network that regulates degassing events. Extrapolation of our findings yields magma ascent via strain localization along conduit margins, thereby providing an explanation for gas-and-ash explosions along arcuate fractures at active lava domes. We conclude that a coupled deformation-seismicity analysis holds a derivation of fracture mechanisms and network, and thus holds potential application in forecasting technologies.
In volcanic systems, the rheology of magmas is of paramount importance. During pre- or syneruptive ascent, magmas undergo decompression resulting in crystallization, temperature change, volatile exsolution, and degassing (Martel and Schmidt, 2003). Any magmatic gas trapped in the porous network will exert stress against the condensed phases of the magma (melt and crystals), whose resultant deformation is distributed in time via melt rheology. These processes typically result in a nonlinearly depth-dependent magma viscosity, which in turn induces nonlinear ascent dynamics and strain rate variation within the magma column. Such rheological changes are ultimately manifested in eruption style, with competition between the characteristic times imposed by the strain rates and the material stress relaxation times posing the volcanic dilemma: “flow or blow” (Dingwell, 1996).
Dome-building eruptions, with their cycles of endogenous and exogenous growth, commonly followed by destruction, epitomize a switch in magma rheology (Hale and Wadge, 2008). Endogenous growth proceeds as long as pervasive viscous and/or plastic deformation mechanisms dominate, but upon strain localization and shear rupture, growth may proceed exogenously (Watts et al., 2002), generating distinct nondestructive, low-frequency, seismic signals (Neuberg et al., 2006) and may, upon further seismic slip, erect spine-like structures (Kendrick et al., 2012). The buildup of internal gas pressure is a threat to the structural stability of lava domes. Failure of lava domes frequently generates Vulcanian eruptions (Lavallée et al., 2012); in extreme cases, dome collapse may lead to severe decompression, triggering catastrophic explosive eruptions (Spieler et al., 2003). The depressurization path of magma during ascent is controlled by the development of permeability via a network of bubbles (Wright and Weinberg, 2009) and microfractures (Mueller et al., 2005), leading to degassing events with contrasting patterns and recurrences (Varley and Taran, 2003). At Santiaguito volcano (Guatemala), for example, the active dome displays spectacular, hourly gas-and-ash explosions along concentric ring fractures (Johnson et al., 2008), posing tempting questions regarding the geometry of the underlying permeable, degassing network and its relationship to strain localization in magma (e.g., Jellinek and Bercovici, 2011). Numerical models of magma ascent have tested the role of conduit geometry changes (as illustrated by petrographical and field studies; Noguchi et al., 2008) and demonstrated their importance in reducing the confining stress acting on ascending magma and in the creation of both shear and extensional faults (Thomas and Neuberg, 2012). Structural studies of domes partially dissected by explosive eruption provide evidence for the development of these fault types in the roots of domes, which expose pervasive and/or localized permeable networks of faults (Watts et al., 2002).
The fragmentation of magma occurs at the ductile-brittle or “glass” transition (Dingwell, 1996). Although fragmentation is common to all explosive eruptions, the path to fragmentation undoubtedly varies considerably with eruption type. The first analysis of magma failure at the glass transition consisted of the application of a Maxwell body analysis to the viscoelasticity of silicate liquids. In this analysis, the conditions of failure are, for a given liquid chemistry, constrained by temperature and strain rate (Dingwell, 1996). Silicate liquids are Newtonian fluids at low to moderate strain rates, but at the extremely high strain rates anticipated in explosive eruptions, the viscosity becomes non-Newtonian and the liquids will, under conditions of sustained stress, fail in a brittle manner, generating as they do seismicity (Tuffen et al., 2008). This situation is further complicated by the fact that the magmas involved in such eruptions contain crystals; the amount may vary remarkably but their presence is ubiquitous. In conditions that yield Newtonian melt viscosity for pure liquids, crystal-bearing magmatic suspensions may adopt a non-Newtonian, shear-thinning rheology (Lavallée et al., 2007). The presence of crystals also impacts the coefficients of brittle response, with failure typically setting in at strain rates two to three orders of magnitude lower than in the crystal-free case (Gottsmann et al., 2009). However, the current lack of any failure criterion (e.g., Mohr-Coulomb) for magma inhibits failure analyses based on the stress tensor. Recent experimental observations demonstrate that deformation leading to failure is accompanied by a supraexponential increase in microseismicity, measured as acoustic emissions (AE) (Lavallée et al., 2008). Bearing in mind that seismic signals constitute a key indicator of volcanic unrest (Papale, 1999; Scarpa, 2001), and that such information thus has broad impact in hazard mitigation scenarios, our investigation of magma failure and its associated permeable network incorporated in situ AE monitoring. This ensemble of (1) experimental deformation, (2) real-time AE monitoring, (3) ultrasonic testing, and importantly (4) recent developments in high-resolution (20 μm) neutron-computed tomography (NCT) imaging places the mechanistic understanding of magma failure and creation of permeable fracture networks in lava domes on a new basis.
MATERIALS AND METHODS
The failure of dome lavas across the ductile-brittle transition (i.e., the nondiscrete transition between deformation behavior considered macroscopically ductile and that considered macroscopically brittle; Rutter, 1986) was investigated by varying the uniaxial stress imposed on dome lava from Volcán de Colima (with 50%–60% crystals and 7% pores) at an eruptive temperature of 940 °C (Lavallée et al., 2012) (see the GSA Data Repository1 for details of the methods and analyses). Following previous observations of the onset of cracking in such lavas (at axial stresses ≥20 MPa), experiments were performed at constant stresses of 20, 28.5, 46, and 76 MPa to assess the total strain-to-failure and monitor the precursory AE activity. The amplitude distribution of recorded AE events was subjected to a statistical analysis analogous to the Gutenberg-Richter seismic b-value (i.e., gradient of frequency of occurrence to magnitude) to assess the relative importance of fracture scaling and localization. The AE data were then subjected to a failure forecast model (Voight, 1988) to test its accuracy across the ductile-brittle transition. For samples in which deformation was arrested immediately prior to complete failure, we probed the degree of fracturing via porosity and ultrasonic measurements, and reconstructed the permeable fracture network via NCT.
DEFORMATION RESULTS AND REGIMES OF MAGMA
At an applied stress of 20 MPa, magma deformation was macroscopically ductile (i.e., the sample did not succumb to failure within the imposed 35% strain limit); yet bulging induced the growth of a pervasive network of fractures near the sample edge. In contrast, deformation at higher stresses of 28.5, 46, and 76 MPa showed an increasingly brittle response manifested by lower total strain-to-failure and lower AE b-values (Table 1), indicating a shift from small-scale distributed cracking (i.e., ductile) to large-scale, more localized cracking (i.e., brittle) (Main et al., 1989). The buildup to failure under compressive stress encompassed the nucleation of tensile fractures, which progressively propagated and coalesced, simultaneously releasing AE at an accelerating rate. Application of the failure forecast method to the recorded AE energy provided equally accurate forecasts, irrespective of the applied stress and thus total strain (or more importantly, time available) to achieve failure. This remained true whether we used the complete AE data set or only the first 50% of recorded AE data. Our initial experimental analyses are therefore generally consistent with field observations, reflecting how transient stress– (and strain rate–) dependent rheologies are driven by the interplay between ductile and brittle components, yielding significant changes in microstructures and, hence, a seismicity-generating mechanism (Main et al., 1989).
Deformation in the brittle regime significantly changes the physical properties of the magma. Optical microscopic analysis revealed an evolution from crystal reorientation and alignment to crystal dislocation and fracturing across the ductile-brittle transition. Specifically, deformation across this transition produced substantial increases in porosity associated with the development of a dilatant fracture network (Table 1). This dilatancy also resulted in significant reductions in ultrasonic P-wave and S-wave velocities of up to 40% and 35%, respectively.
IMAGING THE PERMEABLE FRACTURE NETWORK
The fracture networks developed by the deformation of magma have been imaged via NCT (Fig. 1; tomography Movie DR1A and Movie DR1B are available in the Data Repository). In our analysis, each identified fracture was assigned a location, and the density of fractures was collapsed onto the sample half-space. The geometry of the fracture network was then correlated with the magnitude of the applied stress. Two primary modes of deformation can be recognized over the stress conditions investigated. For deformation at the onset of the ductile-brittle transition (i.e., at an applied stress of 28.5 MPa), we observe a disintegration of the sample through distributed micro- and mesoscopic fractures (Fig. 1A), with axial fractures restricted to within the barreled section. Crosscutting relationships show that axial, extensional microfractures first propagated, and were subsequently crosscut by shear fractures at an angle of ∼45° from the principal compressive stress (Fig. 1A). The axial fractures are wider than the shear fractures, thus dominating the development of the porous network. Conversely, for deformation at the brittle end of the ductile-brittle transition (i.e., 76 MPa), the fault structure is characterized by a more localized distribution of macroscopic shear fractures with minor extensional cracks being restricted to the central region of the sample (Fig. 1B). The shear fractures formed a large hourglass shape at an angle of ∼20° from the applied compressive stress. In this scenario, the macroscopic shear fractures were responsible for the volume increase and the development of a porous network. NCT reveals that nucleation and propagation of fractures is distributed at low applied stresses (and strain rates) whereas failure at high values of applied stresses (and resultant strain rates) develops via strongly localized shear planes.
As noted earlier, the key control on degassing at active lava domes lies in the ability of fracture coalescence to create a permeable network. Using the tomographic reconstruction of the permeable fracture network, we assess the permeability (κ) of the experimentally developed shear zones (e.g., Bai et al., 2011; Pan et al., 2010) via the porosity (φ) following the relationship (Mueller et al., 2005):
This relationship combined with the porous damage induced by shear imaged by NCT provides a first-order map of the permeability development during magma failure (Fig. 2). Although the total porosity increases via fracturing were comparable and led to similar bulk permeability increases, analysis of the directional crack density from the NCT highlighted contrasting anisotropy of the fracture networks in the different experiments. Application of the relationship in Equation 1 to the imaged crack density illustrates the anisotropy of the permeable fracture network (Fig. 2), showing an extreme anisotropy parallel to the direction of applied stress (i.e., axial) in the sample deformed at 76 MPa, compared to the orthogonal (i.e., lateral) anisotropy of the sample deformed at 28.5 MPa. These distinct constructional scenarios carry important consequences to the ability of magma to degas in upper volcanic conduits and ultimately, achieve fragmentation.
AN “ARCHITECTURE” OF MAGMATIC FRAGMENTATION
A reliable forecast of the timing and style of volcanic activity is beyond current methods. Such an approach ultimately requires a thorough understanding of the stress conditions experienced by magma during ascent as well as the mechanics of magma failure, the architecture of the permeable network, and its seismic character. The data presented here illustrate some of these relationships. NCT revealed that the stress exerted on the magma controls the style of fractures, expressed in the microseismic record via the b-value. Even under compression, fracturing nearly always initiates by the generation of tensile cracks, which coalesce to form shear fractures (e.g., Rutter, 1986)—a mechanism especially important to magma ascent and failure in conduits. This fracture style, in turn, controls the development of the fracture network, including the time available to achieve (and thus to forecast) failure. It follows that fragmentation processes proceeding via different ratios of extensional/shear fractures are potentially responsible for the wide range of eruptive styles currently observed at active lava domes. During dome-building eruptions, the flow of non-Newtonian, crystal-bearing magma is not Hagen-Poiseuille, but that of a plug. Rheologically, the shear-thinning nature of magma favors the localization of strain (and stress) along the conduit margins (Thomas and Neuberg, 2012) as demonstrated by the formation of shear bands in magma near conduit margins and fracture-controlled exogenous growth (Hale and Wadge, 2008). It follows from our experimental analysis that such a strain distribution undoubtedly results in an anisotropic permeable fracture network with variable degassing efficiency (Laumonier et al., 2011), which may in turn reduce the potential for large explosive eruptions (Mueller et al., 2005). Our experiments reveal that magma deformation at the ductile end of the ductile-brittle transition produces a monotonically increasing density of tensile microfractures that results in a large volumetric expansion and a pervasive (yet mildly anisotropic) fracture network. At the brittle end of the ductile-brittle transition, deformation proceeds faster and fracturing is more localized, highly anisotropic, and subparallel to the principal shear direction (Fig. 3A). Such contrasting anisotropy of the permeability distribution is likely to strongly influence the pathways for degassing and therefore serves to explain the common occurrence of degassing in the periphery of lava domes (Lavallée et al., 2012; Varley and Taran, 2003) as well as gas-and-ash venting along a ring fracture as seen at Santiaguito volcano (Fig. 3B).
In the implementation of magma rheology to eruptive models, our experimental results suggest that a Maxwell-based approximation of failure cannot explain the strain dependence of crystal-bearing magma rheology. In practice, however, the findings demonstrate that the time window for forecasting magma failure scales with both the progression timescale and imposed stress. This implies that as long as the seismicity originates from magma failure, forecasting may be accurate irrespective of explosive eruption style. Indeed, Vulcanian eruptions at slowly growing and deforming lava domes have been forecast (De la Cruz-Reyna and Reyes-Davila, 2001). More recently, there is growing evidence that rapid fracturing processes during sudden collapse of lava domes may also generate sufficient characteristic seismicity to be used as a forecasting proxy (Hammer and Neuberg, 2009). Regardless of the eruption style, fracturing of magma is required for the occurrence of an explosive eruption, and the development of models to interpret the architecture of magmatic fragmentation via seismicity is therefore an essential component of any accurate hazard mitigation scheme. We conclude that the combination of experimental magma deformation, AE monitoring, and NCT imaging delivers a basis for transferring the conclusions to the field, where deformation and seismic monitoring may ultimately contain the information needed to distinguish not only the timing, but also the style of an impending eruption.
We express our gratitude to J. Neuberg and M. Laumonier for constructive reviews. We acknowledge funding from the DLR, the German Research Foundation (LA2651/1-1, LA2651/3-1, HE4565/2-1), PROCOPE (27061UE), MatWerk, an LMUexcellent Research Professorship, as well as the European Research Council Researcher Grant EVOKES (247076).