Caldera subsidence in extensional tectonics

Bull Volcanol (2014) 76:870 DOI 10.1007/s00445-014-0870-2

RESEARCH ARTICLE

Caldera subsidence in extensional tectonics Stefano Carlino & Anna Tramelli & Renato Somma

Received: 8 October 2013 / Accepted: 10 September 2014 # Springer-Verlag Berlin Heidelberg 2014

Abstract We consider here the effect of extensional tectonics on the dynamics of large calderas. Active calderas are generally characterised by different periods of uplift and subsidence, in some cases spaced out by eruptions. Understanding of mechanisms which produces caldera uplift/subsidence is one of the main topics of volcanological research but is still a matter of debate. Using a simple conceptual model, we show analytically that the tectonic extension and its rate can produce the condition for the subsidence, in early stage, which in turn can also yield the magma migration (uplift) and, eventually, eruption. This work provides a possible hypothesis for caldera dynamic, which initiates due to chamber depressurisation and evolves towards potential conditions for magma re-mobilization as a consequence of tectonic loading. The conceptual model is also applied to the Campi Flegrei caldera (Italy), showing that the observed subsidence may be a result of extensional processes. Keywords Caldera . Subsidence . Extensional tectonics . Campi Flegrei

Introduction The eruption of calderas can be the most intense, but also highly variable, volcanic phenomena in the world. Caldera eruptions span from lava dome emplacement to very large explosive eruptions (VEI>5). Caldera dynamics have been studied by many authors to understand the mechanisms of eruption, resurgence and subsidence using numerical and/or analogue methods (Lipman 1997; Gudmundsson 1998; Editorial responsibility: A. Gudmundsson S. Carlino (*) : A. Tramelli : R. Somma Osservatorio Vesuviano, Sezione di Napoli, Istituto Nazionale di Geofisica e Vulcanologia, Naples, Italy e-mail: [email protected]

Acocella et al. 2000; Acocella 2007 and reference therein). A caldera-forming eruption results mainly from magma withdrawal, producing underpressure within the magma chamber that allows its roof to collapse (Lipman 1997 and references therein; Acocella 2007; Gudmundsson 2007). Other caldera eruptions arise from overpressure within the magma chamber which produces resurgence and tensile stress, leading to magma migration and collapse (Gudmundsson et al. 1997). These mechanisms are generally related to large ignimbrite eruptions. The activity within calderas is characterised by recurrent periods of subsidence and uplift (unrest) which are generally ascribed to a combination of local magmatic, tectonic or hydrologic processes or to external disturbance such as by large regional earthquakes or tectonic strain changes (Newhall and Dzurisin 1988). The caldera dynamic is strongly influenced by regional tectonics, which has effects on the processes of magma emplacement and chamber growth (Bosworth et al. 2003; Gudmundsson 2007). Tectonic extension can increase the magma chamber volume (decreasing overpressure) by stretching the wall rocks up to the failure point. For large magma chambers, extension has a significant effect at the top of the chamber, leading to suppression of dike formation (Jellinek and De Paolo 2003). Furthermore, extension can produce underpressure in the magma chamber, with the caldera floor eventually subsiding (Anderson 1936; Gudmundsson 2008). This subsidence can occur at different rates, from catastrophic collapse to merely slow subsidence. Large catastrophic eruptive collapses are rare events, while more common are episodes of unrest without eruption (i.e. Long Valley caldera, Taal Volcano, Santorini, Campi Flegrei caldera), or accompanied by small to moderate eruptions (Rabaul caldera) (www.volcano.si.edu). In this work, we analyse the possible effect of extensional tectonics on large caldera dynamics. Starting from a simple conceptual model, we show analytically that a slow rate of extensional strain can cause slow subsidence, which in turn

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can also lead to migration of magma and other fluids and eventually to eruption. This is hypothesised to explain the long-term cycles of subsidence and resurgence, in which magma mobilization could occur as a consequence of differential tectonic stress, but is not necessary followed by eruption. This line of reasoning arises from many studies over tens of years by many authors and particularly related to the caldera volcanism of rift zones and extensional tectonic regimes (Gudmundsson 1988, 1990, 2007; Acocella 2007; Acocella et al. 2003; Carlino and Somma 2010). Finally, the conceptual model, which relates subsidence to extension, is applied to a natural caldera. This model suggests that subsidence experienced at Campi Flegrei caldera (Italy) may be a direct result of extensional processes. Although a comprehensive model is beyond the scope of this paper, a promising general framework for future models is emerging from several lines of investigation.

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When underpressured (Fig. 1(a)), which has been less investigated, the rate of chamber widening by extension is not compensated by sufficient magma influx, and large

Methods It is well known that regional stress provides a mechanical control on whether magma feeds into a magma chamber or is transferred out of it, and influences the type of deformation and failure of wall rocks (Gudmundsson 2007; Browning et al. 2013; Dufek et al. 2013). Here, we consider a process in which a reduction in pressure within a large magma chamber (sill-like shaped) is related to extensional tectonic strain rate. Extension has a less effect on small magma chambers but becomes very significant as the involved volume increases. To balance the negative pressure due to extension, an influx of magma must occur (Qin is assumed at constant rate) which must be equal toεV ˙ , where ε˙ is the tectonic extensional strain rate and V is the chamber volume (Jellinek and De Paolo 2003). We assume that chamber and the wall rocks are in thermal equilibrium or that the variation of temperature is small enough to make negligible any effect on the pressure. This assumption is valid for large silicic magma chambers, where the residence times of magma are on the order of hundreds of thousand years (ky) and the cooling rate ranges from 10−2 to 10−4 K ky−1 (e.g. Taupo, New Zealand; Yellowstone, USA; Long Valley, USA; Valles Toledo, USA; La Garita, USA) (Costa 2008). Furthermore, we assume the simplified case in which rocks behave elastically and the medium is isotropic and homogeneous. This approximation, with respect to a more realistic heterogeneous medium, will only significantly affect the result when inversion procedures are considered for retrieving the source parameters (location/ volume or pressure change) (Amoruso et al. 2007). Depending on rate of magma input Qin, the magma chamber behaves differently: pressure-neutral when Qin ¼ εV ˙ , overpressured when Qin > εV ˙ and underpressured when Qin < εV ˙ (Carlino and Somma 2010).

Fig. 1 Proposed mechanism of caldera subsidence and resurgence. Stage 1 a sill-type intrusion develops during tectonic extension at a strain rateε˙ . If the magma influx (Qin) is not sufficient to balance the reduction in pressure in the chamber, subsidence occurs (stage 2). The process continues, and when the lithostatic pressure prevails, the magma in the chamber is squeezed and may move, yielding resurgence (stage 3). At a final stage (4), the loading process can lead to eruption and collapse, with erupted volume primarily a function of ΔP. Illustrated fault dips are merely illustrative (normal faults can be expected in extensional tectonics)

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magma chambers can increase their volume (Fig. 1, stage 1), resulting in a reduction of chamber pressure (−ΔP) and subsidence at the surface. The reduction in pressure, as a function of time, independent of volume, is given by 1 −ΔPðt Þ ¼ εdt ˙ β

ð1Þ

where β is the magma+rock (βm +βr) compressibility (e.g. chamber compressibility) (Rivalta and Segall 2008). Because the pressure decreases the lithostatic loading on the chamber (ρgd, where ρ is the average density of rocks, d is the depth of the chamber, and g is the gravity acceleration), it can produce a shear stress, which is larger at the edge of the chamber (Gudmundsson 1988). If fractures or pre-existing ring faults are present, they are zones of weakness along which slip can occur when the accumulated tectonic strain exceeds the threshold (Walter 2008). When the difference between the lithostatic load and Pi +ΔP (where Pi is the initial pressure of the chamber, assuming lithostatic equilibrium Pi =ρgd) approaches the yield strength of the wall rocks (ys), a progressive slow failure or creep can occur, accompanied by subsidence (Fig. 1, stage 2) P f ¼ ρgd−ðPi −ΔPÞ≥ ys →P f ¼ ΔP ≥ ys

ð2Þ

where Pf is the failure pressure. When failure occurs, the negative pressure in the chamber is re-equilibrated by lithostatic loading, but the process may produce a brief increase in pressure, which squeezes the magma chamber and reduces its volume (−ΔV) (the amount of pressure change depends mainly on the lithostatic loading and on the loading process speed). At this stage, a reversal of ground movement (resurgence) can occur due to magma migration, which eventually leads to eruption (Fig. 1, stages 3 and 4). In the described process, the rate of subsidence (stage 2) and the rocks’ response to pressure variation (failure or creep) will depend on the viscosity of the wall rocks (here, elastic behaviour is considered; whether the response is viscoelastic or elastic will depend on the rate of pressure increase with respect to the retardation time τ=μ/E, where μ and E are the shear and Young moduli, respectively). The magnitude of magma mobilized depends on chamber depth (through vertical loading), chamber volume and magma compressibility. The relative change in pressure produced by the lithostatic loading (ΔPL) is correlated to the volume variation (ΔV) by the following simple equation (Dufek et al. 2013): ΔPL ¼

1 ΔV β V

ð3Þ

where ΔV, based on our hypothesis, provides the values of minimum eruptible magma due to tectonic loading, when the wall rocks are taken as incompressible (Fig. 1, stage 3).

We also consider the relation between the pressure decrease due to extension (Eq. 1) and the subsidence rate. In this case, a large sill-like magma chamber is assumed (Fig. 1, stage 1), which is a common case for caldera volcanoes (Marsh 2000), using the model of a penny-shaped crack in an infinite elastic medium (isotropic and homogeneous). The displacement (w) at the top of a circular sill with radius a and depth d is given by (Ugural 1981; Gudmundsson 1990)    ΔPa4 r4 3 þ υ r2 5 þ υ 4d 2 r2 w¼ þ 1− 2 ð4Þ − þ 64D a4 1 þ υ a2 1 þ υ a2 ð1−υÞ a where ν is Poisson’s ratio, r is the distance from the centre of the sill, and D is the flexural rigidity of the roof and is equal to D¼

Ed 3 12ð1−ν 2 Þ

ð5Þ

where E is Young’s modulus of rocks above the magma intrusion. For r=0, the maximum displacement is obtained. The depth of sills (d) beneath calderas generally ranges between 4 and 10 km; we consider large sills, those having a> 3 km. Applying Eqs. (1), (3) and (4) and using consistent values of elastic parameters and strain rate, we find the variation of pressure with time ΔP(t) depending on extensional strain rate, the depth vs. strain/rate ratio necessary to attain the failure condition, the eruptible volume (ΔV) as function of depth of the sill and the rate of subsidence due to −ΔP(t).

Results The reduction in pressure with time during stages 1 to 2 (Eq. 1) is obtained using two typical tectonic lithospheric strain rates, 10−14 and 10−15 s−1 (Carter and Tsenn 1987) and a typical magma compressibility β=10−11 Pa−1 (Rivalta and Segall 2008; Dufek et al. 2013) (Fig. 2). This corresponds to about 0.03 and 0.003 MPa year−1 for strain rates of 10−14 and 10−15 s−1, respectively. The value of the tensile strength (ys) of rocks generally ranges from less than 1 MPa to few megapascals, depending mainly on the degree of previous fracturing. For large calderas, the value is usually a few megapascals or less (Amadei and Stephenson 1997; Rubin 1995). Based on the above assumptions and using Eqs. (1) and (2), the conditions for rupture due to an increase in vertical stress can be attained in a few hundred or thousand years for strain rates of 10−14 and 10−15 s−1, respectively, giving the range of ys in Fig. 2. This failure can actually occur at very slow deformation rate (creep), depending on the rheology of wall rocks. From Eq. (3), we evaluate the minimum amount of magma eruptible in response to squeezing of the chamber for

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Fig. 2 Reduction in pressure over time as a function of differential strain rate (Eq. 1). The red broken line is the range of yield strength values for which a condition for failure may be met (see text for details)

different chamber depths (Fig. 3). Obviously, the minimum eruptible magma is directly proportional to both lithostatic pressure (the vertical stress) and chamber volume (i.e. about 4 km3 for V=2000 km3 and d=10 km). The decreasing pressure with time, obtained by Eq. (1), is applied to Eq. (4) to obtain the subsidence rate (−w′), neglecting any viscous effects. We show different solutions, in which the depth of the top of the sill is 4, 6 and 10 km, respectively (the typical range for large magma intrusions), for different values of E=10, 30 and 40 GPa and different radii (a) of the sill, while ν=0.27. The obtained value of –w′ varies from