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Evaluating volumes for magma chambers and magma withdrawn for caldera collapse
Earth and Planetary Science Letters 396 (2014) 107–115
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Earth and Planetary Science Letters www.elsevier.com/locate/epsl
Evaluating volumes for magma chambers and magma withdrawn for caldera collapse Nobuo Geshi a,∗ , Joel Ruch b , Valerio Acocella b a b
Geological Survey of Japan, AIST, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8567, Japan Dip. Scienze Geologiche Roma Tre, Largo S. L. Murialdo 1, 00146, Roma, Italy
a r t i c l e
i n f o
Article history: Received 25 June 2013 Received in revised form 25 March 2014 Accepted 28 March 2014 Available online 19 April 2014 Editor: T. Elliott Keywords: collapse caldera magma chamber explosive eruption volcano
a b s t r a c t We develop an analytical model to infer the total volume of a magma chamber associated with caldera collapse and the critical volume of magma that must be withdrawn to induce caldera collapse. The diameter of caldera border fault, depth to the magma chamber, and volumes of magma erupted before the onset of collapse and of entire eruption are compiled for 14 representative calderas. The volume of erupted magma at the onset of collapse aligns between the total erupted volume of the other representative caldera-forming eruptions and the volume of eruptions without collapse during the postcaldera stage, correlating with the structural diameter of the calderas. The total volume of magma chamber is evaluated using a piston-cylinder collapse model, in which the competition between the decompression inside magma chamber and friction along the caldera fault controls the collapse. Estimated volumes of the magma chambers associated with caldera collapse are 3–10 km3 for Vesuvius 79 A.D. to 3000–10 500 km3 for Long Valley, correlating with the cube of caldera diameters. The estimated volumes of magma chamber are always larger than the total volume of erupted magma for caldera formation, suggesting that the magma chambers are never completely emptied by the caldera-forming eruptions. The minimum volumes of erupted magma to trigger collapse are calculated from the correlation between the caldera diameters and the evaluated volume of magma chambers. The minimum eruptive volume for the collapse correlates with the square of the caldera radius r and the square of the depth to the magma chamber h, and inversely correlates with the bulk modulus of magma, which is mainly controlled by the bubble fraction in the magma. A bubble fraction between 5 and 10% at the onset of collapse may explain the distribution of the erupted volumes at the onset of collapse of the calderas in nature. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Collapse calderas are commonly associated with catastrophic explosive eruptions, which can release up to 1000 km3 of pyroclastic material within a few days (Druitt and Sparks, 1984; Self and Blake, 2008). These pyroclastic eruptions associated to caldera collapse are among the most serious natural disasters, releasing widespread ash and gas in the atmosphere, and can affect global climate (e.g., Rampino and Self, 2008). A caldera is formed by the faulting and sinking of the roof of the magma chamber during the rapid withdrawal of magma from the chamber (Lipman, 1997 and references therein). Collapse mechanism has been constrained from theoretical analysis (Scandone, 1990), analogue (Roche et al., 2000) and numerical
*
Corresponding author. E-mail address: [email protected] (N. Geshi).
http://dx.doi.org/10.1016/j.epsl.2014.03.059 0012-821X/© 2014 Elsevier B.V. All rights reserved.
(Hardy, 2008) experiments and field observations in many eroded calderas (Lipman, 1997). These results suggest that the fundamental structure of many collapse calderas is a block surrounded by caldera-border faults, though the structure of the block may exhibits wide variation from coherent (piston) to fragmented (chaotic collapse). Geophysical observations of the recent caldera-forming eruptions also confirm the role of the caldera-border faults. Based on the observation of low-frequency earthquakes and tilt changes during the caldera formation in Miyakejima 2000 A.D., Kumagai et al. (2001) proposed a model in which the competition between the decompression of magma chamber and friction on the ring faults controls the incremental collapse of a cylindrical block. Stix and Kobayashi (2007) discuss the timing of collapse and the vesiculation in the magma chamber of the four caldera-forming eruptions using the model of Kumagai et al. (2001). This model indicates that the decompression of the magma chamber to induce caldera collapse is controlled by the eruption ratio (volume ratio of the magma withdrawn from a chamber against the total volume of
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Fig. 1. Total erupted volume of caldera-forming eruptions (diamond) and erupted volume during the precursory eruption (square) of representative 14 eruptions plotted against the diameter of the calderas. Indexes show the name of caldera-forming eruptions; Ik: Ikeda 6.5 ka, VP: Vesuvius Pompei 79AD, Pi: Pinatubo 1991, Cj: Ceboruco Jala 1 ka, Ma: Mashu 7.5 ka, Ks: Kusdach 240 AD, SM: Santorini Minoa 3.5 ka, CL: Crater Lake 6.8 ka, Sp: Shikotsu 45 ka, CFC: Campi Flegrei 39.3 ka, CFN: Campi Flegrei 15 ka, AT: Ito AT 29 ka, On: Oruanui 26.5 ka, KA: Kikai Akahoya 7.3 ka, LB: Long Valley Bishop tuff 760 ka. The eruptions from Aira caldera and Campi Flegrei are highlighted. Three pre-caldera eruptions (Fukuyama, Iwato and Fukaminato eruptions) and three post-caldera eruptions (Sz-S, 1779 and 1914 A.D. eruptions) without caldera collapse of Aira are identified. Post caldera eruption of Campi Flegrei (AMS: Agnano – Monte Spina eruptions) is also identified. Total volumes of erupted magma of other representative caldera-forming eruptions (small open squares) and post-caldera eruption without caldera collapse (small circles) are also shown.
the chamber), and the bulk modulus of magma that is strongly affected by the bubble fraction in the magma. The volume of magma withdrawn from the chamber prior to the eruption can be deduced from geological evidence (Walker, 1985) or geophysical observations (Stix and Kobayashi, 2007). However, our knowledge on the size of a magma chamber is still limited, though many geophysical observations attempt to figure out the location and size of magma chamber beneath volcanoes (e.g., Sanders et al., 1995; Finlayson et al., 2003). Even though some previous works assumed the total eruptive volume as the total volume of magma chamber, this assumption seems unrealistic. Here, we extend the model of Kumagai et al. (2001) to evaluate: 1) the total volume of a magma chamber associated with caldera collapse and 2) the threshold of the volume of magma that must be withdrawn for a caldera to collapse. First, we compile known structural diameters of caldera border faults, depth to the roof of magma chambers, volumes of erupted magma before the onset of collapse and during the entire period of the calderaforming eruption. Then, we present an analytical model for piston collapse along a vertical ring fault to estimate the volume of the magma chamber and the erupted volume to trigger collapses in nature. We focus on collapse calderas formed by pyroclastic eruptions mainly in silicic systems. In the case of collapse calderas formed by pyroclastic eruptions, most of magma withdrawn from the chamber is released to the Earth’s surface where the erupted volumes can be estimated. In the case of historic eruptions, most magma associated with caldera collapse was erupted within several days, suggesting the rapid decompression of magma chamber and en-mass collapse (Stix and Kobayashi, 2007). Conversely, calderas formed by lateral intrusions, observed mainly in basaltic systems (Michon et al., 2011) are not considered here, because of the difficulty of a quantitative evaluation of the intruded volume of magma, and probably multiple caldera growth with repetition of collapse (Kumagai et al., 2001; Michon et al., 2011).
2. Erupted magma volumes from caldera-forming eruptions 2.1. Size and erupted volumes of calderas To evaluate the relationship between caldera size and erupted volume of magma, we analyzed 36 calderas, with 39 eruptions with caldera collapse and 25 eruptions without caldera collapse (Appendix). They were chosen because of their well-defined caldera structure (structural diameter D s = 2r; Lipman, 1997; Geshi et al., 2012) and erupted volumes (V etotal ). A positive relationship between the size of calderas and erupted volumes is recognized (Fig. 1), as pointed by previous studies (Spera and Crisp, 1981; Scandone, 1990). Calderas of 3 to 5 km in diameter were formed by eruptions of 2–10 km3 of magma, whereas calderas of 10 to 20 km in diameter were formed by eruptions >100 km3 of magma. Calderas wider than 50 km were formed by eruptions producing more than 1000 km3 of magma (e.g., Toba, 74 ka; Rampino and Self, 2008). For a given caldera diameter, the erupted volumes of magma without caldera collapse are smaller than those of the caldera-forming eruptions (Fig. 1). The positive correlation between caldera size and volume of the caldera-forming eruptions is weak for calderas less than 3 km in diameter. For example, some caldera-forming eruptions produced more than 10 km3 of magma with relatively small structural diameter ∼2 km (e.g., Krakatau 1883; Carey et al., 1996; Deplus et al., 1995). 2.2. Precursory eruptions Most of the collapse-episodes are accompanied by pyroclastic eruptions from central vents or ring fractures just before the onset of collapse, without significant time gap (here termed “precursory eruptions”; Scandone, 1990). In the case of historic collapses, the climatic stage of the precursory eruptions lasts within a few days (Vesuvius 79 A.D.; Sigurdsson et al., 1982, and Tambora 1815 A.D.; Self et al., 1984) though in some cases, minor eruptions and/or anomalies starts several month prior to the collapse (e.g., Krakatau 1883 A.D.; Self, 1992).
D s : structural diameter of caldera, a: aspect ratio, h: depth of magma chamber, R: roof aspect ratio, V eprec : erupted volume of magma during precursor eruption, V etotal : erupted volume of magma throughout caldera-forming eruption. Depth of magma chamber (h) are constrained by deformation (d), petrological evidence (p), and seismic tomography (s). Onset of collapse are constrained by seismic signal (s), layer of breccia (b), change of eruption style (e) and tsunami (t). “low”, “medium” and “high” show the probability of the evaluation.
0.20 low (b, e) 50 150 0.2 (d, p) 5–6 1.7 24 LB Bishop tuff 760 ka USA Long Valley
6
(p) (p) (p) (p, s) (d, s) (p) (p)
750
100
Ui (1967), Suto et al. (2007) Stix and Kobayashi (2007) Cioni et al. (2008) Gardnar and Tait (2000) Kishimoto et al. (2009) Braitseva et al. (1996) Cottrell et al. (1999) Bacon (1983), Lipmann (1997) Yamagata (2000) Perrotta and Scarpati (2003) Aramaki (1984), Iguchi (2013) Wilson et al. (2001) Saito et al. (2003), Maeno et al. (2006) Wallace et al. (1999), Anderson et al. (2000) 0.70 0.56 0.93 0.80 0.36 0.75 0.32 0.36 0.16 0.27 0.10 0.17 0.35 0.2 0.8 0.2 0.5 1 1 8 5 10 50 40 50 20 0.2 0.6 0.2 0.2 1.0 1 3 13 2 10 10 30 10 1.4 2.5 1.3 2.8 3.6 6 13 20 22 40 40 90 30 2.3 2.7 2.4 1.7 1.5 1.3 1.1 1.0 0.5 0.3 0.4 0.3 0.2 (∼5) 6 5–6 >5 (∼5) (∼5) ∼4 5–8 ∼5 4 6 ∼4 4 1.2 1.2 1.2 1.4 1.7 1.7 1.3 1.4 1.2 1.4 1.2 1.7 1.3 0.2 0.2 0.2 0.5 1 1 0.5 1 1 2 1 3.8 2.5 2.2 2.2 2.3 3 4 4 4.5 6.5 9.5 12.5 14 14.75 17 Ik Pt VP Cj Ma Kd SM CL Sp CF AT On KA Ikeda 6.5 ka Pinatubo 1991 AD Pompei 79 AD Ceboruco Jala 1 ka Mashu 7.5 ka Kusdach 240 AD Minoa 3.5 ka Crater Lake 6.8 ka Spfa-1 + Spfl 45 ka Campanian ignimbrite 39.3 ka AT 29 ka Oruanui 26.5 ka Akahoya 7.3 ka Japan Philippines Italy Mexico Japan Russia Greece USA Japan Italy Japan New Zealand Japan Ikeda Pinatubo Vesuvius Ceboruco Jala Mashu Kusdach Santorini Crater Lake Shikotsu Campi Flegrei Aira Oruanui Kikai
Table 1 Characteristics of selected caldera-forming eruptions.
Ds (km) ID Eruption Caldera
±
a
(p) (p) (p)
R h (km)
V eprec
±
(b, e) (s) (b, e) (b, e) (b, e) (e) (b, e) (b, e) (b, e) (e) (b, e) (b, e) (b, e, t)
low high medium high medium low medium high high high low medium low
2.0 4.5 1.4 3.5 10 8 41 55 140 150 400 530 85
V eprec / V etotal V etotal
±
References
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Fig. 2. Volume ratio of the erupted magmas between precursory eruption (V eprec ) and the entire period of caldera-forming eruption (V etotal ) plotted against the diameter of calderas. The IDs for each eruption are same in Fig. 1.
The onset of caldera collapse is marked by a significant increase in lithic fragments in the deposit (Walker, 1985; Hildreth, 1991) and/or rapid change of eruption style from Plinian eruption from concentrated vent(s) to multiple vents emitting ignimbrite (Bacon, 1983). The release of large amount of seismic energy during the historical caldera formation (Katmai 1912 and Pinatubo 1991) also suggests the timing of caldera collapse (Stix and Kobayashi, 2007). Tsunami generation from submarine calderas is also an indicator for the timing of collapse (Maeno et al., 2006). From the 39 caldera-forming eruptions mentioned above, we choose 14 eruptions which provide the volume of erupted magma in the precursory eruption (V eprec ) and the depth to the magma chamber (h) (Table 1). The caldera diameter D s (= 2r) ranges from 2.2 ± 0.2 km (Ikeda) to 24 ± 6 km (Long Valley). The depth to the top of magma chamber h ranges from 4 to 8 km. The V eprec ranges from ∼1.4 km3 (Plinian fall-out of Ikeda, Suto et al., 2007) to 150 km3 (Long Valley, Hildreth and Mahood, 1987), showing a positive correlation with the diameter of the caldera (Fig. 1). The accuracy of the evaluated V eprec depends on the precision of the data of tephra distribution. The caldera-forming eruptions in Table 1 are divided into three groups with the relative accuracy of their V eprec . The V eprec of recent calderas located inland have relatively high accuracy (e.g., Ceboruco Jala, and Crater Lake 6.8 ka), while the older calderas in geological age and/or surrounded by water area have lower accuracy (e.g., 760 ka Bishop tuff eruption of Long Valley, 29 ka AT eruption of Aira caldera and 7.3 ka Akahoya eruption of Kikai caldera). 2.3. Total volume and eruption ratio The eruptions may also continue after the onset of caldera collapse, draining larger erupted volumes enhanced by the rupture and subsidence of the roof of the magma chamber. In many calderas, massive ignimbrite deposits overlay the breccia-rich layer, suggesting the onset of caldera collapse (e.g., 29 ka AT eruption of Aira caldera; Aramaki, 1984). In contrast, particularly in smaller calderas, collapses take place after more than half of the total volume of the eruptive materials is already erupted (e.g. Pinatubo 1991 eruption; Stix and Kobayashi, 2007). For the 14 representative calderas, the ratio of V eprec / V etotal ranges from ∼0.1 to ∼0.9, showing a negative correlation with the caldera size (Fig. 2). 2.4. Individual examples For a given volcano, only the largest eruptions can result in caldera collapse. Many smaller eruptions from the same volcano
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Fig. 3. Schematic caldera collapse sequence in section view. 1. Pre-caldera stage: a magma reservoir develops in a rigid host rock. The top of the reservoir is at depth h. The radius of the area of the roof of magma chamber surrounded by the ring fault is r. Note that the r does not necessary to coincide with the radius of the magma chamber itself. 2. Precursory or initiation caldera stage: the internal magmatic pressure decreases as magma erupts through a central vent or ring fracture. The volume of erupted magma during the precursory stage is V eprec ; 3. Caldera stage: the decrease of magmatic pressure inside the reservoir triggers the subsidence of a caldera block, forming the caldera. Further subsidence of the block may enhance the eruption, squeezing magma upward. The volume of erupted magma including the precursory stage is V etotal .
did not result in caldera formation, though flexural deflation (Aira caldera; Omori, 1916) and partial activation of caldera boundaryfaults (Rabaul caldera: Mori and McKee, 1987) are recognized. For example, Aira caldera (Japan), with a structural diameter of ∼15 km, was formed during the 29 ka eruption (AT eruption) with V etotal ∼ 400 ± 40 km3 DRE of magma (Fig. 1; Aramaki, 1984). The 29 ka eruption started with a plinian eruption emitting ∼40 ± 10 km3 DRE of magma (Osumi pumice fall and Tsumaya pyroclastic flow) as a precursory eruption (V eprec ), and the emission of the Ito pyroclastic flow (∼350 km3 , Ueno, 2007) followed onset of caldera formation (Aramaki, 1984). Many smaller eruptions occurred from the Aira caldera before and after the 29 ka eruption did not contribute to caldera collapse. Though some Plinian eruptions (Fukuyama eruption at 95–86 ka with V etotal ∼ 11 km3 DRE, Iwato eruption at 60 ka with V etotal ∼ 6–8 km3 DRE, and Fukaminato eruption at 31 ka with V etotal ∼ 4 km3 DRE) occurred from the Aira caldera prior to the 29 ka eruption (Nagaoka et al., 2001), they did not cause significant caldera collapse. The later smaller eruptions also did not cause any additional collapse, though the largest eruption at 12.8 ka produced V etotal ∼ 4.4 km3 (Sz-S eruption; Kobayashi and Tameike, 2002). The volumes of the erupted magmas in these eruptions without collapse (<11 km3 DRE) are smaller than that of the Osumi pumice fall and Tsumaya pyroclastic flow (∼40 ± 10 km3 DRE), which is the precursory stage for the caldera collapse at 29 ka (Fig. 1). Even though no caldera collapse occurred during these smaller eruptions, the extraction of magma caused decompression within the magma chamber and resulted in flexural subsidence within and around the caldera. For example, the Aira caldera subsided ∼2 m at its central portion during the 1914 eruption from Sakurajima, which produced V etotal ∼ 1.3 km3 of magma (Omori, 1916; Iguchi, 2013). Some calderas experience multiple collapses. The Campi Flegrei caldera (Italy) repeated at least two collapse events; the Campanian Ignimbrite eruption at 39.3 ka, which erupted V etotal ∼ 150 km3 DRE (Civetta et al., 1997) and the Neapolitan Yellow Tuff eruption at 15 ka, which erupted V etotal ∼ 50 km3 DRE (Scarpati et al., 1993; Deino et al., 2004). The V etotal of the largest post-caldera eruption (4.1 ka Agnano – Monte Spina eruption ∼1.2 km3 DRE; de Vita et al., 1999) is smaller than the V eprec in Campanian Ignimbrite eruption (∼40 km3 DRE; Pyle et al., 2006).
3. An analytical model of erupted volumes required for caldera collapse 3.1. Model The distribution of V eprec of the calderas in nature (Table 1 and Fig. 1) indicates that the collapse occurs when the volume of erupted magma reaches a certain threshold (e.g., Druitt and Sparks, 1984; Marti et al., 2000). We develop an analytical model to evaluate the total volume of the magma chamber V r and quantitatively explain the V eprec in nature (Table 1). In this model, a “magma chamber” consists of a space filled of magma with a finite volume V r , and decompressed by the withdrawal of magma during an eruption. The magma chamber may consist of a single space or possibly a cluster of connected spaces. In this model, we evaluate V r and we do not discuss the shape of the magma chamber. The petrological character (chemical composition, crystal and bubble fractions) of the magmas filling the chamber can be heterogeneous. Since most calderas can be approximated by a subsiding block surrounded by a ring fault (e.g. Lipman, 1997; Roche et al., 2000), our model consists of a cylindrical piston (caldera block) above a magma chamber within a rigid host rock (Fig. 3). Collapse is controlled by the competition between the pressure decrease inside the chamber and the friction along the ring fault supporting the caldera block (Kumagai et al., 2001). The eruption withdraws magma from the chamber and progressively decreases the chamber internal pressure. Assuming negligible flexural deformation of the host rock, the pressure decrease in magma chamber Δ P (−) due to magma discharge from a chamber is
Δ P (−) = κ
Ve
(1)
Vr
where V e is the volume of magma discharged from the chamber, V r , the volume of the chamber and κ the bulk modulus of magma. The difference between the upward force on the roof exerted by the magmatic pressure and the weight of the roof is the driving force F d for the subsidence of the roof.
F d = S r Δ P (−) = S r κ
Ve Vr
(2)
where S r is the area of the roof of magma chamber surrounded by the ring fault.
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The maximum static friction F max of the fault correlates with the mean normal force acting on the fault plane. Assuming a Mohr Coulomb behavior, F max can be written as
F max = S f (c + N tan ϕ )
(3)
where S f is the area of the fault, c is the cohesion and N is the mean normal stress acting on the fault plane and ϕ is the internal friction angle. The fault starts to slip when F d exceeds the maximum static friction F max on the ring fault. From Eqs. (2) and (3), we obtain the ratio of the minimum volume of magma extraction from chamber to induce the collapse V emin against the volume of magma chamber V r as
V emin Vr
c + N tan ϕ S f
κ
Sr
(4)
Here, we assume that the normal stress on the fault plane N is the lithostatic pressure. As the lithostatic pressure is zero at the ground surface (only the atmospheric pressure is acting) and linearly increases to ρ gh at the top of the magma chamber, the mean lithostatic pressure can be written as ρ gh/2, where ρ is the density of the host rock and g is the gravity acceleration. The mean lithostatic pressure ranges from 0.6 to 1.2 × 108 Pa for h = 5–10 km, assuming that the density of the host rock is 2.5 × 103 kg. The cohesion of the host rock c ranges 0.1 to 5 × 106 Pa (Roche and Druitt, 2001 and the references therein) and typically less than 105 Pa for volcanic deposit (Watters et al., 2000 and references therein); that is two orders of magnitude smaller than N. Thus, the effect of cohesion can be neglected. Eq. (3 ) can be approximated as F max ∼ S f N tan ϕ . Assuming a cylindrical caldera block with radius r and height h, F d and F max can be written as
Fd = π r2κ
Ve
(2 )
Vr
F max ∼ 2π rhN tan ϕ
(3 )
Substituting Eqs. (2 ) and (3 ) to Eq. (4) and neglecting cohesion, we obtain the eruption ratio V emin / V r to trigger the collapse as follows.
V emin Vr
2
ρ gh tan ∅ rκ
(5)
This model also gives the decompression value Δ P (−) to induce collapse. As the caldera collapses when F d exceeds the maximum static friction F max , the decompression value Δ P (−) to induce collapse is given by Δ P (−) F max / S r based on Eq. (2). Using the relationship F max ∼ 2π rhN tan ϕ , the underpressure Δ P (−) for collapse is written as
Δ P (−) =
ρ gh2 r
tan ∅
Fig. 4. Underpressure (absolute value) of magma chambers h = 2, 4, 8 and 10 km (h is the depth to the magma chamber) to induce the caldera collapse calculated with Eq. (6). Solid diamonds show the points where the underpressure is equal to the lithostatic pressure at the depth. The possible range of the overpressure in the magma chamber (<107 Pa) is also shown.
Table 2 List of variables. Symbol
Unit Volume of magma erupted during precursory eruption Volume of magma erupted entire period of caldera-forming eruption Volume of magma should be withdrawn from chamberto trigger collapse Total volume of magma chamber Area of the fault Area of the roof of magma chamber surrounded by the ring fault Structural radius of caldera Structural diameter of caldera = 2r Depth to the top of magma chamber
m3 m3
g
Bulk modulus of magma Density of the wall rock Internal fraction angle of the wall rock Gravity acceleration
Pa kg/m3 degree m/s2
Fd F max N
Driving force to subside the caldera block Maximum static friction force Normal component of reaction acting on the fault plane
N N N
V eprec V etotal V emin Vr Sf Sr r Ds h
κ ρ φ
m3 m3 m3 m3 m m m
shallower magma chamber; h = 2 km, to 108 Pa for the smaller and deeper magma chamber h = 10 km (Fig. 4). This value is same or one order of magnitude larger than the estimated Δ P (−) (absolute value), and one-two orders of magnitude smaller than Δ P (−) .
(6)
Eq. (6) shows that the underpressure Δ P (−) to induce the caldera collapse correlates with the depth to the magma chamber h and the roof aspect ratio h/r. Assuming the physical properties of host rock ρ = 2500 kg/m3 , ϕ = 30◦ , and g = 9.8 m/s2 respectively, the Δ P (−) to induce collapse is ∼1.5 × 107 Pa for a large caldera with r = 30 km and h = 4 km. For a caldera with r = 10 km and h = 8 km, the Δ P (−) to induce collapse reaches ∼1.8 × 108 Pa (Fig. 4). As the magma chambers generally have overpressure Δ P (+) at the onset of eruption (Tait et al., 1989), a certain volume of magma is also withdrawn before the magma chamber becomes underpressured. The maximum Δ P (+) is mainly controlled by the tensile strength of the host rock and the range of Δ P (+) is estimated as 0.1–1 × 107 Pa (Tait et al., 1989; Takeuchi, 2004). Conversely, Eq. (6) shows that the Δ P (−) ranges from 106 Pa for the
3.2. Collapse parameters
The horizontal radius of the caldera block r, depth of the roof of magma chamber h, density and internal friction angle ϕ of host rock, and the bulk modulus of magma κ are the fundamental physical parameters responsible for caldera collapse (Table 2). We use physical properties of host rock ρ = 2500 kg/m3 . The gravity acceleration is g = 9.8 m/s2 . Internal friction is assumed as ϕ = 30◦ . Hydrothermal alteration and/or development of the shear zone along the fault can reduce the strength of the rock, and consequently, decrease the internal friction angle of the rocks in the fault. In our considered cases, the depth to the magma chamber ranges from 4 km (Santorini, Campi Flegrei, Kikai) to 8 km (Crater Lake) (Table 1).
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3.3. Bubble fraction and bulk modulus The bulk modulus of magma has wide variation reflecting the presence of bubbles in magma. The bulk modulus of the mixture of melt and bubbles can be written as
κ = ΔP
V
ΔV
= ΔP
V
(Δ V g + Δ V m )
=
κ g κm κm x + κ g (1 − x)
(7)
where κ is the bulk modulus of the mixture, x is the bubble fraction, κ g is the bulk modulus of gas, κm is that of the melt, Δ P is the pressure change, Δ V g is the volume change of bubbles and Δ V m is of the melt and crystals. The bulk modulus of melt and crystal is ∼3 × 1010 Pa (Roche and Druitt, 2001 and references therein). The bulk modulus of vapor phase ranges between 1 × 107 and 2 × 107 Pa at 4–8 km depth (at the top of magma chamber) assuming an ideal gas behavior. The bubble fraction x is controlled by the original water contents in magma and the amount of decompression. The rhyolitic magmas containing 3 wt% and 5 wt% of water reach saturation at 2.5 km depth (6 × 107 Pa) and 4.1 km depth (1 × 108 Pa), respectively (Bower and Woods, 1997). This implies that the magmas start vesiculating from the top of the magma chamber during the decompression during the precursory stage. However, the mean bubble fraction is difficult to know, as unknown parameters such as the vertical extension of magma chamber also contribute to the mean bubble fraction of the magma chamber. Here, we examine the bubble fraction in the magma chamber ranging from 5 to 20%. Using these parameters, the bulk modulus of the bubble-bearing magma in the chamber at 5 km depth ranges between 2.3 × 109 Pa, with 5% of bubble fraction, and 6.0 × 108 Pa, with 20% of bubble fraction, respectively. 3.4. Geometry of ring faults Though the model in this study assumes a circular and vertical caldera fault, the calderas in nature can have elliptical plane view and inclined caldera border faults. The horizontal radius of the caldera block may range from 1.1 ± 0.1 km (Ikeda) to 38 ± 13 km (Yellowstone) (Table 1 and Table Appendix). The oval shape of caldera faults gives a larger S f than that of a circular caldera fault with same S r . Eq. (4) indicates that the critical eruption rate for collapse correlates with S f , if the S r and other parameters are same. In the case of vertical ring fault, the S f correlates with the length of the circumference of the ring fault, which is given by the elliptic integral. Fig. 5A shows the circumference length of ovals with aspect ratio up to 3 normalized by the circumference length of a circle with constant area. In the cases of the calderas examined here, the aspect ratio of the plane view of ring fault ranges from 1.2 to 1.7 (Table 1). This indicates that V emin / V r for oval faults is 0.7–5.3% larger than that obtained assuming a circumferential fault. An outward-inclined ring fault forms a caldera block with a frustum shape (Fig. 5B). The ratio of the lateral area of the frustum (S frustum ) against that of the cylinder with the same bottom diameter (S column ) can vary from 0.5 to 1.05, depending on the roof aspect ratio and the dip of the faults, which varies from 70–90 degrees (Fig. 5B). This means that the V emin / V r with inclined ring fault can vary between 50–105%, compared to that obtained assuming a cylindrical caldera block. 4. Results 4.1. Volume of the magma chamber Eq. (5) indicates that the eruption ratio V emin / V r correlates with the ratios between the lithostatic pressure at the top of magma chamber (ρ gh) and the bulk modulus of magma κ and
Fig. 5. Effects of the geometry of ring fault. A: relationship between the aspect ratio of the oval (rmajor /rminor ) and the ratio of the lateral area of an oval column (S oval ) against the lateral area of a circular cylinder with same basal aria. B: ratio of the lateral area of a frustum against the lateral area of a circular cylinder with same basal diameter. Horizontal axis shows the aspect ratio of the roof (h/r). The solid diamonds show the upper limit of the roof aspect ratio to reach the inclined ring faults (dip = 70◦ and 80◦ , respectively) to the surface.
roof aspect ratio h/r. We assume that V eprec corresponds to the minimum volume of withdrawn magma required to induce collapse (V emin ), as caldera collapse occurs when the volume of magma withdrawn from the chamber reaches V emin . By replacing V emin , in Eq. (5) with V eprec observed in the 14 representative calderas (Table 1), the volumes of the magma chamber (V r ) are evaluated as
Vr =
rκ V prec ρ gh2 tan ∅
(5 )
The depth to the magma chamber h are estimated by the geophysical and/or petrological methods (Table 1). The bulk modulus of magma has large uncertainty, depending on the bubble fraction. Even though we also examine the bubble fraction from 5 to 20%, here we assume a bubble fraction of magma of 10%. The bulk modulus of magma with 10% of bubble fraction ranges from 9.5 × 108 Pa, at 4 km deep, to 1.9 × 109 Pa, at 8 km deep.
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Fig. 6. Calculated total volume of magma chamber (red circles) for 14 calderas. Red line shows the correlation between the calculated volume of magma chamber and horizontal diameter of caldera. The broken lines show the threshold of magma withdraw to trigger collapse calculated with Eq. (8) (for bubble fraction x = 0.05, 0.10 and 0.20, respectively). Total erupted volume of caldera-forming eruptions (yellow diamonds) and the erupted volume during their precursory eruption (orange squares) are also shown.
The evaluated volumes of the magma chamber (V r ) for the 14 calderas range from 5 km3 (3–10 km3 , assuming 5–20% of bubble fraction) for Vesuvius 79 A.D. to 5448 km3 (or 2784–10 446 km3 , assuming 5–20% of bubble fraction) for Long Valley (Fig. 6). The relationship between r and V r can be written as V r ∼ 10r 2.9 (Fig. 6). The calculated V r are always greater than the total erupted volumes (V etotal ). The ratio (V etotal / V r ) ranges from 0.1 to 0.5 (Fig. 7), except for the Pinatubo 1991 caldera (V etotal / V r = 0.9). This implies that the magma chambers were never completely emptied during the caldera forming eruption and more than half of the volume of magma can remain in the magma chamber, even at the end of the caldera-forming eruptions, as supported by geological and petrological observations (e.g., Hildreth and Fierstein, 2000). 4.2. Threshold for collapse We can evaluate the threshold of the volume of erupted magma for caldera collapse from Eq. (5), using the relationship between the volume of magma chamber V r (in m3 ) and the radius of caldera r (in m) as V r = 10r 3 obtained from Fig. 6. Eq. (5) can be modified as follows;
V emin =
10ρ gh2
κ
r 2 tan ∅
(8)
Eq. (8) indicates that the V emin for the onset of caldera collapse correlates with the square of the caldera radius r and the square of the depth to the magma chamber h, and inversely correlates with the bulk modulus of magma. Geophysical and petrological observations suggest a depth to the magma chamber between 4 and 8 km (Table 1). Though the bubble fraction in the magma chamber, which controls the bulk modulus of magma, may not be exactly constrained, a bubble fraction between 5 and 10% (corresponding to the bulk modulus of 1.2–2.3 × 109 Pa) may explain the distribution of V eprep for the 14 calderas (Fig. 6). 5. Conclusions The total volume of a magmatic reservoir below a caldera and the critical volume of magma that must be withdrawn to induce a collapse are evaluated by an analytical model.
Fig. 7. Volume ratio of the volume of erupted magma (V etotal ) against the evaluated volume of the magma chamber (V r ) plotted against the diameter of the caldera (A), and the roof aspect ratio (B). The bubble fraction of the magma is assumed as 0.01. The vertical bars show the range of V etotal / V r for the variation of bubble fraction ranging from 0.05 to 0.20. The threshold for collapse calculated with Eq. (6) also shown.
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Many caldera collapses follow a precursory eruption. The erupted volumes of magma during the precursory eruption V prep correlate with the structural diameter of calderas. The critical eruption ratio V emin / V r for onset of caldera collapse is evaluated using a piston-cylinder collapse model. The volumes of magma chamber V r are evaluated for representative calderas, using the assumption that the eruptive volumes prior to the onset of collapse (V eprec ) correspond to the minimum volume for collapse V min . The estimated volumes of the magma chambers below calderas range from 3–10 km3 for Vesuvius 79 A.D. to 2800–10 500 km3 for Long Valley, correlating with the cube of caldera radius. The estimated volumes of magma chambers are always larger than the total volume of erupted magma for caldera formation. The minimum volumes of erupted magma to trigger collapse are calculated using the evaluated volumes of the magma chambers and caldera diameters. The V emin for the onset of caldera collapse correlates with the square of the caldera radius and the square of the depth to the magma chamber, and inversely correlates with the bulk modulus of magma. A bubble fraction between 5 and 10% (corresponding to a bulk modulus of 1.2–2.3 × 109 Pa) may explain the distribution of V eprep for the 14 calderas. Acknowledgements NG thanks to the financial supports by Japan Society for the Promotion of Science (JSPS) Kakenhi 21710182 (Grant-in-Aid for Young Scientists (B)) and 24510251 (Grant-in-Aid for Scientific Research (C)). We thank John Stix and anonymous reviewer for their helpful reviews. Appendix A. Supplementary material Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.epsl.2014.03.059. References Anderson, A.T., Davis, A.M., Lu, F., 2000. Evolution of Bishop Tuff rhyolitic magma based on melt and magnetite inclusions and zoned phenocrysts. J. Petrol. 41, 449–473. Aramaki, S., 1984. Formation of the Aira caldera, southern Kyushu, ca. 22 000 years ago. J. Geophys. Res. 89, 8485–8501. Bacon, C.R., 1983. Eruptive history of mount Mazama and Crater Lake caldera, Cascade Range, U.S.A. J. Volcanol. Geotherm. Res. 18, 57–115. Bower, S.M., Woods, A.W., 1997. Control of magma volatile content and chamber depth on the mass erupted during explosive volcanic eruptions. J. Geophys. Res. 102, 10273–10290. Braitseva, O.A., Melekestsev, I.V., Ponomareva, V.V., Kirianov, V.Yu., 1996. The caldera-forming eruption of Ksudach volcano about cal. A.D. 240: the greatest explosive event of our era in Kamchatka, Russia. J. Volcanol. Geotherm. Res. 70, 49–65. Carey, S., Sigurdsson, H., Mandeville, C., Bronto, S., 1996. Pyroclastic flows and surges over water: an example from the 1883 Krakatau eruption. Bull. Volcanol. 57, 493–511. Cioni, R., Bertagnini, A., Santacroce, R., Andronico, D., 2008. Explosive activity and eruption scenarios at Somma–Vesuvius (Italy): towards a new classification scheme. J. Volcanol. Geotherm. Res. 178, 331–346. Civetta, L., Orsi, G., Pappalardo, L., Fisher, R.V., Heiken, G., Ort, M., 1997. Geochemical zoning, mingling, eruptive dynamics and depositional processes – The Campanian Ignimbrite, Campi Flegrei, Italy. J. Volcanol. Geotherm. Res. 75, 183–219. Cottrell, E., Gardner, J.E., Rutherford, M.J., 1999. Petrologic and experimental evidence for the movement and heating of the pre-eruptive Minoan rhyodacite (Santorini, Greece). Contrib. Mineral. Petrol. 135, 315–331. de Vita, S., Orsi, G., Civetta, L., Carandente, A., D’Antonio, M., Deino, A., di Cesare, T., Di Vito, M.A., Fisher, R.V., Isaia, R., Marotta, E., Necco, A., Ort, M., Pappalardo, L., Piochi, M., Southon, J., 1999. The Agnano-Monte Spina eruption (4100 yrs BP) in the restless Campi Flegrei caldera (Italy). J. Volcanol. Geotherm. Res. 91, 269–301. Deino, A.L., Orsi, G., de Vita, S., Piochi, M., 2004. The age of the Neapolitan Yellow Tuff caldera-forming eruption (Campi Flegrei caldera – Italy) assessed by 40 Ar/39 Ar dating method. J. Volcanol. Geotherm. Res. 133, 157–170.
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Earth and Planetary Science Letters www.elsevier.com/locate/epsl
Evaluating volumes for magma chambers and magma withdrawn for caldera collapse Nobuo Geshi a,∗ , Joel Ruch b , Valerio Acocella b a b
Geological Survey of Japan, AIST, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8567, Japan Dip. Scienze Geologiche Roma Tre, Largo S. L. Murialdo 1, 00146, Roma, Italy
a r t i c l e
i n f o
Article history: Received 25 June 2013 Received in revised form 25 March 2014 Accepted 28 March 2014 Available online 19 April 2014 Editor: T. Elliott Keywords: collapse caldera magma chamber explosive eruption volcano
a b s t r a c t We develop an analytical model to infer the total volume of a magma chamber associated with caldera collapse and the critical volume of magma that must be withdrawn to induce caldera collapse. The diameter of caldera border fault, depth to the magma chamber, and volumes of magma erupted before the onset of collapse and of entire eruption are compiled for 14 representative calderas. The volume of erupted magma at the onset of collapse aligns between the total erupted volume of the other representative caldera-forming eruptions and the volume of eruptions without collapse during the postcaldera stage, correlating with the structural diameter of the calderas. The total volume of magma chamber is evaluated using a piston-cylinder collapse model, in which the competition between the decompression inside magma chamber and friction along the caldera fault controls the collapse. Estimated volumes of the magma chambers associated with caldera collapse are 3–10 km3 for Vesuvius 79 A.D. to 3000–10 500 km3 for Long Valley, correlating with the cube of caldera diameters. The estimated volumes of magma chamber are always larger than the total volume of erupted magma for caldera formation, suggesting that the magma chambers are never completely emptied by the caldera-forming eruptions. The minimum volumes of erupted magma to trigger collapse are calculated from the correlation between the caldera diameters and the evaluated volume of magma chambers. The minimum eruptive volume for the collapse correlates with the square of the caldera radius r and the square of the depth to the magma chamber h, and inversely correlates with the bulk modulus of magma, which is mainly controlled by the bubble fraction in the magma. A bubble fraction between 5 and 10% at the onset of collapse may explain the distribution of the erupted volumes at the onset of collapse of the calderas in nature. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Collapse calderas are commonly associated with catastrophic explosive eruptions, which can release up to 1000 km3 of pyroclastic material within a few days (Druitt and Sparks, 1984; Self and Blake, 2008). These pyroclastic eruptions associated to caldera collapse are among the most serious natural disasters, releasing widespread ash and gas in the atmosphere, and can affect global climate (e.g., Rampino and Self, 2008). A caldera is formed by the faulting and sinking of the roof of the magma chamber during the rapid withdrawal of magma from the chamber (Lipman, 1997 and references therein). Collapse mechanism has been constrained from theoretical analysis (Scandone, 1990), analogue (Roche et al., 2000) and numerical
*
Corresponding author. E-mail address: [email protected] (N. Geshi).
http://dx.doi.org/10.1016/j.epsl.2014.03.059 0012-821X/© 2014 Elsevier B.V. All rights reserved.
(Hardy, 2008) experiments and field observations in many eroded calderas (Lipman, 1997). These results suggest that the fundamental structure of many collapse calderas is a block surrounded by caldera-border faults, though the structure of the block may exhibits wide variation from coherent (piston) to fragmented (chaotic collapse). Geophysical observations of the recent caldera-forming eruptions also confirm the role of the caldera-border faults. Based on the observation of low-frequency earthquakes and tilt changes during the caldera formation in Miyakejima 2000 A.D., Kumagai et al. (2001) proposed a model in which the competition between the decompression of magma chamber and friction on the ring faults controls the incremental collapse of a cylindrical block. Stix and Kobayashi (2007) discuss the timing of collapse and the vesiculation in the magma chamber of the four caldera-forming eruptions using the model of Kumagai et al. (2001). This model indicates that the decompression of the magma chamber to induce caldera collapse is controlled by the eruption ratio (volume ratio of the magma withdrawn from a chamber against the total volume of
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Fig. 1. Total erupted volume of caldera-forming eruptions (diamond) and erupted volume during the precursory eruption (square) of representative 14 eruptions plotted against the diameter of the calderas. Indexes show the name of caldera-forming eruptions; Ik: Ikeda 6.5 ka, VP: Vesuvius Pompei 79AD, Pi: Pinatubo 1991, Cj: Ceboruco Jala 1 ka, Ma: Mashu 7.5 ka, Ks: Kusdach 240 AD, SM: Santorini Minoa 3.5 ka, CL: Crater Lake 6.8 ka, Sp: Shikotsu 45 ka, CFC: Campi Flegrei 39.3 ka, CFN: Campi Flegrei 15 ka, AT: Ito AT 29 ka, On: Oruanui 26.5 ka, KA: Kikai Akahoya 7.3 ka, LB: Long Valley Bishop tuff 760 ka. The eruptions from Aira caldera and Campi Flegrei are highlighted. Three pre-caldera eruptions (Fukuyama, Iwato and Fukaminato eruptions) and three post-caldera eruptions (Sz-S, 1779 and 1914 A.D. eruptions) without caldera collapse of Aira are identified. Post caldera eruption of Campi Flegrei (AMS: Agnano – Monte Spina eruptions) is also identified. Total volumes of erupted magma of other representative caldera-forming eruptions (small open squares) and post-caldera eruption without caldera collapse (small circles) are also shown.
the chamber), and the bulk modulus of magma that is strongly affected by the bubble fraction in the magma. The volume of magma withdrawn from the chamber prior to the eruption can be deduced from geological evidence (Walker, 1985) or geophysical observations (Stix and Kobayashi, 2007). However, our knowledge on the size of a magma chamber is still limited, though many geophysical observations attempt to figure out the location and size of magma chamber beneath volcanoes (e.g., Sanders et al., 1995; Finlayson et al., 2003). Even though some previous works assumed the total eruptive volume as the total volume of magma chamber, this assumption seems unrealistic. Here, we extend the model of Kumagai et al. (2001) to evaluate: 1) the total volume of a magma chamber associated with caldera collapse and 2) the threshold of the volume of magma that must be withdrawn for a caldera to collapse. First, we compile known structural diameters of caldera border faults, depth to the roof of magma chambers, volumes of erupted magma before the onset of collapse and during the entire period of the calderaforming eruption. Then, we present an analytical model for piston collapse along a vertical ring fault to estimate the volume of the magma chamber and the erupted volume to trigger collapses in nature. We focus on collapse calderas formed by pyroclastic eruptions mainly in silicic systems. In the case of collapse calderas formed by pyroclastic eruptions, most of magma withdrawn from the chamber is released to the Earth’s surface where the erupted volumes can be estimated. In the case of historic eruptions, most magma associated with caldera collapse was erupted within several days, suggesting the rapid decompression of magma chamber and en-mass collapse (Stix and Kobayashi, 2007). Conversely, calderas formed by lateral intrusions, observed mainly in basaltic systems (Michon et al., 2011) are not considered here, because of the difficulty of a quantitative evaluation of the intruded volume of magma, and probably multiple caldera growth with repetition of collapse (Kumagai et al., 2001; Michon et al., 2011).
2. Erupted magma volumes from caldera-forming eruptions 2.1. Size and erupted volumes of calderas To evaluate the relationship between caldera size and erupted volume of magma, we analyzed 36 calderas, with 39 eruptions with caldera collapse and 25 eruptions without caldera collapse (Appendix). They were chosen because of their well-defined caldera structure (structural diameter D s = 2r; Lipman, 1997; Geshi et al., 2012) and erupted volumes (V etotal ). A positive relationship between the size of calderas and erupted volumes is recognized (Fig. 1), as pointed by previous studies (Spera and Crisp, 1981; Scandone, 1990). Calderas of 3 to 5 km in diameter were formed by eruptions of 2–10 km3 of magma, whereas calderas of 10 to 20 km in diameter were formed by eruptions >100 km3 of magma. Calderas wider than 50 km were formed by eruptions producing more than 1000 km3 of magma (e.g., Toba, 74 ka; Rampino and Self, 2008). For a given caldera diameter, the erupted volumes of magma without caldera collapse are smaller than those of the caldera-forming eruptions (Fig. 1). The positive correlation between caldera size and volume of the caldera-forming eruptions is weak for calderas less than 3 km in diameter. For example, some caldera-forming eruptions produced more than 10 km3 of magma with relatively small structural diameter ∼2 km (e.g., Krakatau 1883; Carey et al., 1996; Deplus et al., 1995). 2.2. Precursory eruptions Most of the collapse-episodes are accompanied by pyroclastic eruptions from central vents or ring fractures just before the onset of collapse, without significant time gap (here termed “precursory eruptions”; Scandone, 1990). In the case of historic collapses, the climatic stage of the precursory eruptions lasts within a few days (Vesuvius 79 A.D.; Sigurdsson et al., 1982, and Tambora 1815 A.D.; Self et al., 1984) though in some cases, minor eruptions and/or anomalies starts several month prior to the collapse (e.g., Krakatau 1883 A.D.; Self, 1992).
D s : structural diameter of caldera, a: aspect ratio, h: depth of magma chamber, R: roof aspect ratio, V eprec : erupted volume of magma during precursor eruption, V etotal : erupted volume of magma throughout caldera-forming eruption. Depth of magma chamber (h) are constrained by deformation (d), petrological evidence (p), and seismic tomography (s). Onset of collapse are constrained by seismic signal (s), layer of breccia (b), change of eruption style (e) and tsunami (t). “low”, “medium” and “high” show the probability of the evaluation.
0.20 low (b, e) 50 150 0.2 (d, p) 5–6 1.7 24 LB Bishop tuff 760 ka USA Long Valley
6
(p) (p) (p) (p, s) (d, s) (p) (p)
750
100
Ui (1967), Suto et al. (2007) Stix and Kobayashi (2007) Cioni et al. (2008) Gardnar and Tait (2000) Kishimoto et al. (2009) Braitseva et al. (1996) Cottrell et al. (1999) Bacon (1983), Lipmann (1997) Yamagata (2000) Perrotta and Scarpati (2003) Aramaki (1984), Iguchi (2013) Wilson et al. (2001) Saito et al. (2003), Maeno et al. (2006) Wallace et al. (1999), Anderson et al. (2000) 0.70 0.56 0.93 0.80 0.36 0.75 0.32 0.36 0.16 0.27 0.10 0.17 0.35 0.2 0.8 0.2 0.5 1 1 8 5 10 50 40 50 20 0.2 0.6 0.2 0.2 1.0 1 3 13 2 10 10 30 10 1.4 2.5 1.3 2.8 3.6 6 13 20 22 40 40 90 30 2.3 2.7 2.4 1.7 1.5 1.3 1.1 1.0 0.5 0.3 0.4 0.3 0.2 (∼5) 6 5–6 >5 (∼5) (∼5) ∼4 5–8 ∼5 4 6 ∼4 4 1.2 1.2 1.2 1.4 1.7 1.7 1.3 1.4 1.2 1.4 1.2 1.7 1.3 0.2 0.2 0.2 0.5 1 1 0.5 1 1 2 1 3.8 2.5 2.2 2.2 2.3 3 4 4 4.5 6.5 9.5 12.5 14 14.75 17 Ik Pt VP Cj Ma Kd SM CL Sp CF AT On KA Ikeda 6.5 ka Pinatubo 1991 AD Pompei 79 AD Ceboruco Jala 1 ka Mashu 7.5 ka Kusdach 240 AD Minoa 3.5 ka Crater Lake 6.8 ka Spfa-1 + Spfl 45 ka Campanian ignimbrite 39.3 ka AT 29 ka Oruanui 26.5 ka Akahoya 7.3 ka Japan Philippines Italy Mexico Japan Russia Greece USA Japan Italy Japan New Zealand Japan Ikeda Pinatubo Vesuvius Ceboruco Jala Mashu Kusdach Santorini Crater Lake Shikotsu Campi Flegrei Aira Oruanui Kikai
Table 1 Characteristics of selected caldera-forming eruptions.
Ds (km) ID Eruption Caldera
±
a
(p) (p) (p)
R h (km)
V eprec
±
(b, e) (s) (b, e) (b, e) (b, e) (e) (b, e) (b, e) (b, e) (e) (b, e) (b, e) (b, e, t)
low high medium high medium low medium high high high low medium low
2.0 4.5 1.4 3.5 10 8 41 55 140 150 400 530 85
V eprec / V etotal V etotal
±
References
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Fig. 2. Volume ratio of the erupted magmas between precursory eruption (V eprec ) and the entire period of caldera-forming eruption (V etotal ) plotted against the diameter of calderas. The IDs for each eruption are same in Fig. 1.
The onset of caldera collapse is marked by a significant increase in lithic fragments in the deposit (Walker, 1985; Hildreth, 1991) and/or rapid change of eruption style from Plinian eruption from concentrated vent(s) to multiple vents emitting ignimbrite (Bacon, 1983). The release of large amount of seismic energy during the historical caldera formation (Katmai 1912 and Pinatubo 1991) also suggests the timing of caldera collapse (Stix and Kobayashi, 2007). Tsunami generation from submarine calderas is also an indicator for the timing of collapse (Maeno et al., 2006). From the 39 caldera-forming eruptions mentioned above, we choose 14 eruptions which provide the volume of erupted magma in the precursory eruption (V eprec ) and the depth to the magma chamber (h) (Table 1). The caldera diameter D s (= 2r) ranges from 2.2 ± 0.2 km (Ikeda) to 24 ± 6 km (Long Valley). The depth to the top of magma chamber h ranges from 4 to 8 km. The V eprec ranges from ∼1.4 km3 (Plinian fall-out of Ikeda, Suto et al., 2007) to 150 km3 (Long Valley, Hildreth and Mahood, 1987), showing a positive correlation with the diameter of the caldera (Fig. 1). The accuracy of the evaluated V eprec depends on the precision of the data of tephra distribution. The caldera-forming eruptions in Table 1 are divided into three groups with the relative accuracy of their V eprec . The V eprec of recent calderas located inland have relatively high accuracy (e.g., Ceboruco Jala, and Crater Lake 6.8 ka), while the older calderas in geological age and/or surrounded by water area have lower accuracy (e.g., 760 ka Bishop tuff eruption of Long Valley, 29 ka AT eruption of Aira caldera and 7.3 ka Akahoya eruption of Kikai caldera). 2.3. Total volume and eruption ratio The eruptions may also continue after the onset of caldera collapse, draining larger erupted volumes enhanced by the rupture and subsidence of the roof of the magma chamber. In many calderas, massive ignimbrite deposits overlay the breccia-rich layer, suggesting the onset of caldera collapse (e.g., 29 ka AT eruption of Aira caldera; Aramaki, 1984). In contrast, particularly in smaller calderas, collapses take place after more than half of the total volume of the eruptive materials is already erupted (e.g. Pinatubo 1991 eruption; Stix and Kobayashi, 2007). For the 14 representative calderas, the ratio of V eprec / V etotal ranges from ∼0.1 to ∼0.9, showing a negative correlation with the caldera size (Fig. 2). 2.4. Individual examples For a given volcano, only the largest eruptions can result in caldera collapse. Many smaller eruptions from the same volcano
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Fig. 3. Schematic caldera collapse sequence in section view. 1. Pre-caldera stage: a magma reservoir develops in a rigid host rock. The top of the reservoir is at depth h. The radius of the area of the roof of magma chamber surrounded by the ring fault is r. Note that the r does not necessary to coincide with the radius of the magma chamber itself. 2. Precursory or initiation caldera stage: the internal magmatic pressure decreases as magma erupts through a central vent or ring fracture. The volume of erupted magma during the precursory stage is V eprec ; 3. Caldera stage: the decrease of magmatic pressure inside the reservoir triggers the subsidence of a caldera block, forming the caldera. Further subsidence of the block may enhance the eruption, squeezing magma upward. The volume of erupted magma including the precursory stage is V etotal .
did not result in caldera formation, though flexural deflation (Aira caldera; Omori, 1916) and partial activation of caldera boundaryfaults (Rabaul caldera: Mori and McKee, 1987) are recognized. For example, Aira caldera (Japan), with a structural diameter of ∼15 km, was formed during the 29 ka eruption (AT eruption) with V etotal ∼ 400 ± 40 km3 DRE of magma (Fig. 1; Aramaki, 1984). The 29 ka eruption started with a plinian eruption emitting ∼40 ± 10 km3 DRE of magma (Osumi pumice fall and Tsumaya pyroclastic flow) as a precursory eruption (V eprec ), and the emission of the Ito pyroclastic flow (∼350 km3 , Ueno, 2007) followed onset of caldera formation (Aramaki, 1984). Many smaller eruptions occurred from the Aira caldera before and after the 29 ka eruption did not contribute to caldera collapse. Though some Plinian eruptions (Fukuyama eruption at 95–86 ka with V etotal ∼ 11 km3 DRE, Iwato eruption at 60 ka with V etotal ∼ 6–8 km3 DRE, and Fukaminato eruption at 31 ka with V etotal ∼ 4 km3 DRE) occurred from the Aira caldera prior to the 29 ka eruption (Nagaoka et al., 2001), they did not cause significant caldera collapse. The later smaller eruptions also did not cause any additional collapse, though the largest eruption at 12.8 ka produced V etotal ∼ 4.4 km3 (Sz-S eruption; Kobayashi and Tameike, 2002). The volumes of the erupted magmas in these eruptions without collapse (<11 km3 DRE) are smaller than that of the Osumi pumice fall and Tsumaya pyroclastic flow (∼40 ± 10 km3 DRE), which is the precursory stage for the caldera collapse at 29 ka (Fig. 1). Even though no caldera collapse occurred during these smaller eruptions, the extraction of magma caused decompression within the magma chamber and resulted in flexural subsidence within and around the caldera. For example, the Aira caldera subsided ∼2 m at its central portion during the 1914 eruption from Sakurajima, which produced V etotal ∼ 1.3 km3 of magma (Omori, 1916; Iguchi, 2013). Some calderas experience multiple collapses. The Campi Flegrei caldera (Italy) repeated at least two collapse events; the Campanian Ignimbrite eruption at 39.3 ka, which erupted V etotal ∼ 150 km3 DRE (Civetta et al., 1997) and the Neapolitan Yellow Tuff eruption at 15 ka, which erupted V etotal ∼ 50 km3 DRE (Scarpati et al., 1993; Deino et al., 2004). The V etotal of the largest post-caldera eruption (4.1 ka Agnano – Monte Spina eruption ∼1.2 km3 DRE; de Vita et al., 1999) is smaller than the V eprec in Campanian Ignimbrite eruption (∼40 km3 DRE; Pyle et al., 2006).
3. An analytical model of erupted volumes required for caldera collapse 3.1. Model The distribution of V eprec of the calderas in nature (Table 1 and Fig. 1) indicates that the collapse occurs when the volume of erupted magma reaches a certain threshold (e.g., Druitt and Sparks, 1984; Marti et al., 2000). We develop an analytical model to evaluate the total volume of the magma chamber V r and quantitatively explain the V eprec in nature (Table 1). In this model, a “magma chamber” consists of a space filled of magma with a finite volume V r , and decompressed by the withdrawal of magma during an eruption. The magma chamber may consist of a single space or possibly a cluster of connected spaces. In this model, we evaluate V r and we do not discuss the shape of the magma chamber. The petrological character (chemical composition, crystal and bubble fractions) of the magmas filling the chamber can be heterogeneous. Since most calderas can be approximated by a subsiding block surrounded by a ring fault (e.g. Lipman, 1997; Roche et al., 2000), our model consists of a cylindrical piston (caldera block) above a magma chamber within a rigid host rock (Fig. 3). Collapse is controlled by the competition between the pressure decrease inside the chamber and the friction along the ring fault supporting the caldera block (Kumagai et al., 2001). The eruption withdraws magma from the chamber and progressively decreases the chamber internal pressure. Assuming negligible flexural deformation of the host rock, the pressure decrease in magma chamber Δ P (−) due to magma discharge from a chamber is
Δ P (−) = κ
Ve
(1)
Vr
where V e is the volume of magma discharged from the chamber, V r , the volume of the chamber and κ the bulk modulus of magma. The difference between the upward force on the roof exerted by the magmatic pressure and the weight of the roof is the driving force F d for the subsidence of the roof.
F d = S r Δ P (−) = S r κ
Ve Vr
(2)
where S r is the area of the roof of magma chamber surrounded by the ring fault.
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The maximum static friction F max of the fault correlates with the mean normal force acting on the fault plane. Assuming a Mohr Coulomb behavior, F max can be written as
F max = S f (c + N tan ϕ )
(3)
where S f is the area of the fault, c is the cohesion and N is the mean normal stress acting on the fault plane and ϕ is the internal friction angle. The fault starts to slip when F d exceeds the maximum static friction F max on the ring fault. From Eqs. (2) and (3), we obtain the ratio of the minimum volume of magma extraction from chamber to induce the collapse V emin against the volume of magma chamber V r as
V emin Vr
c + N tan ϕ S f
κ
Sr
(4)
Here, we assume that the normal stress on the fault plane N is the lithostatic pressure. As the lithostatic pressure is zero at the ground surface (only the atmospheric pressure is acting) and linearly increases to ρ gh at the top of the magma chamber, the mean lithostatic pressure can be written as ρ gh/2, where ρ is the density of the host rock and g is the gravity acceleration. The mean lithostatic pressure ranges from 0.6 to 1.2 × 108 Pa for h = 5–10 km, assuming that the density of the host rock is 2.5 × 103 kg. The cohesion of the host rock c ranges 0.1 to 5 × 106 Pa (Roche and Druitt, 2001 and the references therein) and typically less than 105 Pa for volcanic deposit (Watters et al., 2000 and references therein); that is two orders of magnitude smaller than N. Thus, the effect of cohesion can be neglected. Eq. (3 ) can be approximated as F max ∼ S f N tan ϕ . Assuming a cylindrical caldera block with radius r and height h, F d and F max can be written as
Fd = π r2κ
Ve
(2 )
Vr
F max ∼ 2π rhN tan ϕ
(3 )
Substituting Eqs. (2 ) and (3 ) to Eq. (4) and neglecting cohesion, we obtain the eruption ratio V emin / V r to trigger the collapse as follows.
V emin Vr
2
ρ gh tan ∅ rκ
(5)
This model also gives the decompression value Δ P (−) to induce collapse. As the caldera collapses when F d exceeds the maximum static friction F max , the decompression value Δ P (−) to induce collapse is given by Δ P (−) F max / S r based on Eq. (2). Using the relationship F max ∼ 2π rhN tan ϕ , the underpressure Δ P (−) for collapse is written as
Δ P (−) =
ρ gh2 r
tan ∅
Fig. 4. Underpressure (absolute value) of magma chambers h = 2, 4, 8 and 10 km (h is the depth to the magma chamber) to induce the caldera collapse calculated with Eq. (6). Solid diamonds show the points where the underpressure is equal to the lithostatic pressure at the depth. The possible range of the overpressure in the magma chamber (<107 Pa) is also shown.
Table 2 List of variables. Symbol
Unit Volume of magma erupted during precursory eruption Volume of magma erupted entire period of caldera-forming eruption Volume of magma should be withdrawn from chamberto trigger collapse Total volume of magma chamber Area of the fault Area of the roof of magma chamber surrounded by the ring fault Structural radius of caldera Structural diameter of caldera = 2r Depth to the top of magma chamber
m3 m3
g
Bulk modulus of magma Density of the wall rock Internal fraction angle of the wall rock Gravity acceleration
Pa kg/m3 degree m/s2
Fd F max N
Driving force to subside the caldera block Maximum static friction force Normal component of reaction acting on the fault plane
N N N
V eprec V etotal V emin Vr Sf Sr r Ds h
κ ρ φ
m3 m3 m3 m3 m m m
shallower magma chamber; h = 2 km, to 108 Pa for the smaller and deeper magma chamber h = 10 km (Fig. 4). This value is same or one order of magnitude larger than the estimated Δ P (−) (absolute value), and one-two orders of magnitude smaller than Δ P (−) .
(6)
Eq. (6) shows that the underpressure Δ P (−) to induce the caldera collapse correlates with the depth to the magma chamber h and the roof aspect ratio h/r. Assuming the physical properties of host rock ρ = 2500 kg/m3 , ϕ = 30◦ , and g = 9.8 m/s2 respectively, the Δ P (−) to induce collapse is ∼1.5 × 107 Pa for a large caldera with r = 30 km and h = 4 km. For a caldera with r = 10 km and h = 8 km, the Δ P (−) to induce collapse reaches ∼1.8 × 108 Pa (Fig. 4). As the magma chambers generally have overpressure Δ P (+) at the onset of eruption (Tait et al., 1989), a certain volume of magma is also withdrawn before the magma chamber becomes underpressured. The maximum Δ P (+) is mainly controlled by the tensile strength of the host rock and the range of Δ P (+) is estimated as 0.1–1 × 107 Pa (Tait et al., 1989; Takeuchi, 2004). Conversely, Eq. (6) shows that the Δ P (−) ranges from 106 Pa for the
3.2. Collapse parameters
The horizontal radius of the caldera block r, depth of the roof of magma chamber h, density and internal friction angle ϕ of host rock, and the bulk modulus of magma κ are the fundamental physical parameters responsible for caldera collapse (Table 2). We use physical properties of host rock ρ = 2500 kg/m3 . The gravity acceleration is g = 9.8 m/s2 . Internal friction is assumed as ϕ = 30◦ . Hydrothermal alteration and/or development of the shear zone along the fault can reduce the strength of the rock, and consequently, decrease the internal friction angle of the rocks in the fault. In our considered cases, the depth to the magma chamber ranges from 4 km (Santorini, Campi Flegrei, Kikai) to 8 km (Crater Lake) (Table 1).
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3.3. Bubble fraction and bulk modulus The bulk modulus of magma has wide variation reflecting the presence of bubbles in magma. The bulk modulus of the mixture of melt and bubbles can be written as
κ = ΔP
V
ΔV
= ΔP
V
(Δ V g + Δ V m )
=
κ g κm κm x + κ g (1 − x)
(7)
where κ is the bulk modulus of the mixture, x is the bubble fraction, κ g is the bulk modulus of gas, κm is that of the melt, Δ P is the pressure change, Δ V g is the volume change of bubbles and Δ V m is of the melt and crystals. The bulk modulus of melt and crystal is ∼3 × 1010 Pa (Roche and Druitt, 2001 and references therein). The bulk modulus of vapor phase ranges between 1 × 107 and 2 × 107 Pa at 4–8 km depth (at the top of magma chamber) assuming an ideal gas behavior. The bubble fraction x is controlled by the original water contents in magma and the amount of decompression. The rhyolitic magmas containing 3 wt% and 5 wt% of water reach saturation at 2.5 km depth (6 × 107 Pa) and 4.1 km depth (1 × 108 Pa), respectively (Bower and Woods, 1997). This implies that the magmas start vesiculating from the top of the magma chamber during the decompression during the precursory stage. However, the mean bubble fraction is difficult to know, as unknown parameters such as the vertical extension of magma chamber also contribute to the mean bubble fraction of the magma chamber. Here, we examine the bubble fraction in the magma chamber ranging from 5 to 20%. Using these parameters, the bulk modulus of the bubble-bearing magma in the chamber at 5 km depth ranges between 2.3 × 109 Pa, with 5% of bubble fraction, and 6.0 × 108 Pa, with 20% of bubble fraction, respectively. 3.4. Geometry of ring faults Though the model in this study assumes a circular and vertical caldera fault, the calderas in nature can have elliptical plane view and inclined caldera border faults. The horizontal radius of the caldera block may range from 1.1 ± 0.1 km (Ikeda) to 38 ± 13 km (Yellowstone) (Table 1 and Table Appendix). The oval shape of caldera faults gives a larger S f than that of a circular caldera fault with same S r . Eq. (4) indicates that the critical eruption rate for collapse correlates with S f , if the S r and other parameters are same. In the case of vertical ring fault, the S f correlates with the length of the circumference of the ring fault, which is given by the elliptic integral. Fig. 5A shows the circumference length of ovals with aspect ratio up to 3 normalized by the circumference length of a circle with constant area. In the cases of the calderas examined here, the aspect ratio of the plane view of ring fault ranges from 1.2 to 1.7 (Table 1). This indicates that V emin / V r for oval faults is 0.7–5.3% larger than that obtained assuming a circumferential fault. An outward-inclined ring fault forms a caldera block with a frustum shape (Fig. 5B). The ratio of the lateral area of the frustum (S frustum ) against that of the cylinder with the same bottom diameter (S column ) can vary from 0.5 to 1.05, depending on the roof aspect ratio and the dip of the faults, which varies from 70–90 degrees (Fig. 5B). This means that the V emin / V r with inclined ring fault can vary between 50–105%, compared to that obtained assuming a cylindrical caldera block. 4. Results 4.1. Volume of the magma chamber Eq. (5) indicates that the eruption ratio V emin / V r correlates with the ratios between the lithostatic pressure at the top of magma chamber (ρ gh) and the bulk modulus of magma κ and
Fig. 5. Effects of the geometry of ring fault. A: relationship between the aspect ratio of the oval (rmajor /rminor ) and the ratio of the lateral area of an oval column (S oval ) against the lateral area of a circular cylinder with same basal aria. B: ratio of the lateral area of a frustum against the lateral area of a circular cylinder with same basal diameter. Horizontal axis shows the aspect ratio of the roof (h/r). The solid diamonds show the upper limit of the roof aspect ratio to reach the inclined ring faults (dip = 70◦ and 80◦ , respectively) to the surface.
roof aspect ratio h/r. We assume that V eprec corresponds to the minimum volume of withdrawn magma required to induce collapse (V emin ), as caldera collapse occurs when the volume of magma withdrawn from the chamber reaches V emin . By replacing V emin , in Eq. (5) with V eprec observed in the 14 representative calderas (Table 1), the volumes of the magma chamber (V r ) are evaluated as
Vr =
rκ V prec ρ gh2 tan ∅
(5 )
The depth to the magma chamber h are estimated by the geophysical and/or petrological methods (Table 1). The bulk modulus of magma has large uncertainty, depending on the bubble fraction. Even though we also examine the bubble fraction from 5 to 20%, here we assume a bubble fraction of magma of 10%. The bulk modulus of magma with 10% of bubble fraction ranges from 9.5 × 108 Pa, at 4 km deep, to 1.9 × 109 Pa, at 8 km deep.
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Fig. 6. Calculated total volume of magma chamber (red circles) for 14 calderas. Red line shows the correlation between the calculated volume of magma chamber and horizontal diameter of caldera. The broken lines show the threshold of magma withdraw to trigger collapse calculated with Eq. (8) (for bubble fraction x = 0.05, 0.10 and 0.20, respectively). Total erupted volume of caldera-forming eruptions (yellow diamonds) and the erupted volume during their precursory eruption (orange squares) are also shown.
The evaluated volumes of the magma chamber (V r ) for the 14 calderas range from 5 km3 (3–10 km3 , assuming 5–20% of bubble fraction) for Vesuvius 79 A.D. to 5448 km3 (or 2784–10 446 km3 , assuming 5–20% of bubble fraction) for Long Valley (Fig. 6). The relationship between r and V r can be written as V r ∼ 10r 2.9 (Fig. 6). The calculated V r are always greater than the total erupted volumes (V etotal ). The ratio (V etotal / V r ) ranges from 0.1 to 0.5 (Fig. 7), except for the Pinatubo 1991 caldera (V etotal / V r = 0.9). This implies that the magma chambers were never completely emptied during the caldera forming eruption and more than half of the volume of magma can remain in the magma chamber, even at the end of the caldera-forming eruptions, as supported by geological and petrological observations (e.g., Hildreth and Fierstein, 2000). 4.2. Threshold for collapse We can evaluate the threshold of the volume of erupted magma for caldera collapse from Eq. (5), using the relationship between the volume of magma chamber V r (in m3 ) and the radius of caldera r (in m) as V r = 10r 3 obtained from Fig. 6. Eq. (5) can be modified as follows;
V emin =
10ρ gh2
κ
r 2 tan ∅
(8)
Eq. (8) indicates that the V emin for the onset of caldera collapse correlates with the square of the caldera radius r and the square of the depth to the magma chamber h, and inversely correlates with the bulk modulus of magma. Geophysical and petrological observations suggest a depth to the magma chamber between 4 and 8 km (Table 1). Though the bubble fraction in the magma chamber, which controls the bulk modulus of magma, may not be exactly constrained, a bubble fraction between 5 and 10% (corresponding to the bulk modulus of 1.2–2.3 × 109 Pa) may explain the distribution of V eprep for the 14 calderas (Fig. 6). 5. Conclusions The total volume of a magmatic reservoir below a caldera and the critical volume of magma that must be withdrawn to induce a collapse are evaluated by an analytical model.
Fig. 7. Volume ratio of the volume of erupted magma (V etotal ) against the evaluated volume of the magma chamber (V r ) plotted against the diameter of the caldera (A), and the roof aspect ratio (B). The bubble fraction of the magma is assumed as 0.01. The vertical bars show the range of V etotal / V r for the variation of bubble fraction ranging from 0.05 to 0.20. The threshold for collapse calculated with Eq. (6) also shown.
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Many caldera collapses follow a precursory eruption. The erupted volumes of magma during the precursory eruption V prep correlate with the structural diameter of calderas. The critical eruption ratio V emin / V r for onset of caldera collapse is evaluated using a piston-cylinder collapse model. The volumes of magma chamber V r are evaluated for representative calderas, using the assumption that the eruptive volumes prior to the onset of collapse (V eprec ) correspond to the minimum volume for collapse V min . The estimated volumes of the magma chambers below calderas range from 3–10 km3 for Vesuvius 79 A.D. to 2800–10 500 km3 for Long Valley, correlating with the cube of caldera radius. The estimated volumes of magma chambers are always larger than the total volume of erupted magma for caldera formation. The minimum volumes of erupted magma to trigger collapse are calculated using the evaluated volumes of the magma chambers and caldera diameters. The V emin for the onset of caldera collapse correlates with the square of the caldera radius and the square of the depth to the magma chamber, and inversely correlates with the bulk modulus of magma. A bubble fraction between 5 and 10% (corresponding to a bulk modulus of 1.2–2.3 × 109 Pa) may explain the distribution of V eprep for the 14 calderas. Acknowledgements NG thanks to the financial supports by Japan Society for the Promotion of Science (JSPS) Kakenhi 21710182 (Grant-in-Aid for Young Scientists (B)) and 24510251 (Grant-in-Aid for Scientific Research (C)). We thank John Stix and anonymous reviewer for their helpful reviews. Appendix A. Supplementary material Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.epsl.2014.03.059. References Anderson, A.T., Davis, A.M., Lu, F., 2000. Evolution of Bishop Tuff rhyolitic magma based on melt and magnetite inclusions and zoned phenocrysts. J. Petrol. 41, 449–473. Aramaki, S., 1984. Formation of the Aira caldera, southern Kyushu, ca. 22 000 years ago. J. Geophys. Res. 89, 8485–8501. Bacon, C.R., 1983. Eruptive history of mount Mazama and Crater Lake caldera, Cascade Range, U.S.A. J. Volcanol. Geotherm. Res. 18, 57–115. Bower, S.M., Woods, A.W., 1997. Control of magma volatile content and chamber depth on the mass erupted during explosive volcanic eruptions. J. Geophys. Res. 102, 10273–10290. Braitseva, O.A., Melekestsev, I.V., Ponomareva, V.V., Kirianov, V.Yu., 1996. The caldera-forming eruption of Ksudach volcano about cal. A.D. 240: the greatest explosive event of our era in Kamchatka, Russia. J. Volcanol. Geotherm. Res. 70, 49–65. Carey, S., Sigurdsson, H., Mandeville, C., Bronto, S., 1996. Pyroclastic flows and surges over water: an example from the 1883 Krakatau eruption. Bull. Volcanol. 57, 493–511. Cioni, R., Bertagnini, A., Santacroce, R., Andronico, D., 2008. Explosive activity and eruption scenarios at Somma–Vesuvius (Italy): towards a new classification scheme. J. Volcanol. Geotherm. Res. 178, 331–346. Civetta, L., Orsi, G., Pappalardo, L., Fisher, R.V., Heiken, G., Ort, M., 1997. Geochemical zoning, mingling, eruptive dynamics and depositional processes – The Campanian Ignimbrite, Campi Flegrei, Italy. J. Volcanol. Geotherm. Res. 75, 183–219. Cottrell, E., Gardner, J.E., Rutherford, M.J., 1999. Petrologic and experimental evidence for the movement and heating of the pre-eruptive Minoan rhyodacite (Santorini, Greece). Contrib. Mineral. Petrol. 135, 315–331. de Vita, S., Orsi, G., Civetta, L., Carandente, A., D’Antonio, M., Deino, A., di Cesare, T., Di Vito, M.A., Fisher, R.V., Isaia, R., Marotta, E., Necco, A., Ort, M., Pappalardo, L., Piochi, M., Southon, J., 1999. The Agnano-Monte Spina eruption (4100 yrs BP) in the restless Campi Flegrei caldera (Italy). J. Volcanol. Geotherm. Res. 91, 269–301. Deino, A.L., Orsi, G., de Vita, S., Piochi, M., 2004. The age of the Neapolitan Yellow Tuff caldera-forming eruption (Campi Flegrei caldera – Italy) assessed by 40 Ar/39 Ar dating method. J. Volcanol. Geotherm. Res. 133, 157–170.
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