Dynamic weakening of ring faults and catastrophic caldera collapses

Catastrophic caldera collapse following a large volcanic eruption or subsurface magmatic outflow is associated with very large displacements on ring faults. The slip resistance or friction on the ring faults is, thus, a key mechanical property that controls the collapse. However, the dynamic friction on the ring faults during caldera collapse remains unknown. Here, we show that dynamic weakening of ring faults caused by frictional melting can play a critical role in the catastrophic collapse of volcanoes. From direct observations of the ring fault of the ancient Jangsan caldera in southeastern Korea, we identified a layer of solidified frictional melt (or pseudotachylyte) measuring ~0.1 m thick. The dynamic friction (expressed as the ratio of shear to normal stress) estimated from the layer, based on high-velocity shear tests and analyses of microstructures and materials, was lower than 0.1. Given the low resistance, it follows that an extraordinarily large fault slip (>100 m) causing a large earthquake was possible during the formation of the ancient caldera. We conclude that the dynamic weakness of ring faults should be incorporated in mechanical models of caldera collapses. INTRODUCTION The formation of a caldera, defined as a collapse structure in a volcano formed by the subsidence of roof rocks over an evacuated magma chamber, is a highly dynamic geological event (Branney and Acocella, 2015). Caldera formation follows, or is concurrent with, large volcanic eruptions or lateral magmatic outflow (e.g., Cole et al., 2005). Because the large displacement of the roof rocks occurs mostly along the ring faults (i.e., caldera-bounding, circular, steeply dipping faults), the friction on the faults should be considered in mechanical models of caldera collapse (Stix and Kobayashi, 2008). Once underpressure or overpressure has built up within a magma chamber (Gudmundsson, 1988; Cashman and Giordano, 2014), collapse of the roof rocks may be initiated by the formation of, and slip on, ring faults. For continued collapse to be possible with large displacements on the ring faults, the shear resistance or friction on the faults should decrease with increasing displacement. Seismological and geodetic observations of active volcanoes (Mori and McKee, 1987; Bathke et al., 2013) and analog and numerical modeling (Acocella, 2007) have significantly improved our understanding of caldera collapse. However, these approaches alone, without field observations of ring faults, are unable to fully constrain the fault zone processes and frictional properties of the faults that may control the collapse. We investigated an outcrop of a ring fault of the Cretaceous Jangsan caldera in southeastern Korea, which formed in a volcanic arc setting (Yun et al., 2010; Chough and Sohn, 2010). This ring fault has been deeply eroded and exhumed, and portions of the fault that were situated at depth (<5 km) during the caldera collapse are now exposed. Along the fault, we found a thick (up to ~10 cm) layer of pseudotachylyte (PST), that is, a fault rock solidified from friction-induced melting. The presence of the PST indicates a large temperature rise due to rapid slip during the caldera collapse. We estimated the shear resistance on the ring fault during caldera collapse by integrating field observations, materials and microstructural analyses of the PST, and frictional melting experiments. PSEUDOTACHYLYTE IN THE RING FAULT The Jangsan caldera (~8–9 km in diameter, including intrusions) was formed during explosive felsic eruptions in the Late Cretaceous. The pyroclastic volcanic succession in the center, which mainly consists of rhyolitic tuff (K-Ar whole-rock age of 67 ± 4 Ma; Yun and Sang, 1994), is surrounded by rhyolitic ring intrusions (Fig. 1A). A ring fault is observed between the dacitic wall rocks (or silicified andesite from precaldera volcanics) and the rhyolitic intrusions (Fig. 1B; too thin to be displayed along the boundary between the dacite and the volcanic succession in Fig. 1A), and it strikes northeast with a near-vertical dip (88°–90°). The PST layer varies in thickness (from <1 cm to ~10 cm) along the fault (Figs. 1C and 1D). The bulk chemical composition of the PST is very similar to that of the dacitic wall rock and is intimately associated with a brownish, thermally altered zone (TA in Fig. 1) of the cataclastic wall rock. Also, the dark-gray to black PST is associated with light-colored tuffisite (TF; or intrusive tuff; see Fig. 1). The PST has a dacitic composition with a matrix composed of subhedral to euhedral feldspars, chlorite, and Fe-oxides. The TF has a rhyolitic chemical composition and consists mainly of lapilli-sized, quartzofeldspathic fragments and light-colored groundmass. The cuspate boundary of the PST (Fig. 1D) and some mingling structures (not shown in this paper) observed along the boundary between the PST and TF indicate that the intrusion of TF into the fault zone started before the solidification of the frictional melt layer. On the other hand, the PST is sharply intruded and detached by the TF in some other places, indicating that TF intrusion continued after significant cooling of the Manuscript received 18 June 2018 Revised manuscript received 16 November 2018 Manuscript accepted 22 November 2018 https://doi.org/10.1130/G45687.1 © 2019 The Authors. Gold Open Access: This paper is published under the terms of the CC-BY license. Published online 4 January 2019 CITATION: Han, R., et al., 2019, Dynamic weakening of ring faults and catastrophic caldera collapses: Geology, v. 47, p. 107–110, https://doi.org/10.1130/G45687.1. Downloaded from https://pubs.geoscienceworld.org/gsa/geology/article-pdf/47/2/107/4617138/107.pdf by guest on 11 July 2019 108 www.gsapubs.org | Volume 47 | Number 2 | GEOLOGY | Geological Society of America frictional melt (Figs. DR2 and DR3 in the GSA Data Repository1; see also Fig. 3C). At the microscopic scale, the clasts in the PST are dominantly rounded or subrounded (Fig. 2A). The aphanitic matrix consists mainly of ultrafine grains of feldspar, chlorite, quartz, and magnetite. Subhedral or euhedral feldspar grains (mostly a few micrometers in size) in the matrix show chemical zoning, indicating their primary crystallization from a frictional melt of heterogeneous composition (Fig. 2B). Some spiral-shaped objects formed by clasts with cataclastic tails indicate that the central volcanic succession of the caldera was downthrown with respect to the wall rocks (Fig. 2C). The chilled margins of pyroclastic dikes may look like PSTs. Our observations, however, indicate that the PST in the study area was generated by frictional melting of the dacitic wall rocks, not by rapid cooling of the TF, as evidenced by: (1) the similar chemistry of the PST to that of the dacite; (2) the TF intruding the PST; (3) no grain size decrease toward the boundary of the TF; and (4) reproduction of the natural PST by the experimental frictional melting of dacite (see Figs. 3B and 3C). DYNAMIC SHEAR RESISTANCE DURING CALDERA COLLAPSE The shear resistance on a ring fault coated by a frictional melt layer may be calculated as τf = ηV/w, where τf is the shear stress (Pa), η is the melt viscosity (Pa·s), V is the slip rate (m/s), and w is the melt thickness (m), assuming that the melt behaves like a Newtonian fluid. To constrain η and V and to estimate τf, we conducted high-velocity rotary shear experiments, slip zone temperature measurements, and chemical 1 GSA Data Repository item 2019045, description of the methods used in the study, supplementary tables, and supplementary figures, is available online at http:// www.geosociety.org/datarepository/2019/, or on request from editing@geosociety.org. and microstructural analyses of both natural and experimentally formed PSTs. Our approach was to estimate V, which is difficult to measure from natural PST, by combining our experimental data with theoretical work on frictional melts (Nielsen et al., 2008) and estimating η using the measured temperatures, chemical composition data, and microstructural data (e.g., clast fraction; see Fig. DR1 for the details). We conducted the rotary shear experiments on solid cylinders (25 mm in diameter) of the dacitic rock sampled near the natural PST. The tests were performed with a high-velocity rotary shear apparatus (Hirose and Shimamoto, 2005) at room temperature and room humidity. Two tests were performed at a normal stress (σn) of 10 MPa and a V of 0.2 and 0.7 m/s to measure both the shear stress (τss) and melt layer thickness (w) under steady state (dashed boxes in Fig. 3A). Temperature was measured with an infrared radiation thermometer in the four experiments, including the two tests mentioned above (see the methods description in the Data Repository; Table DR1), to determine the melting point of the wall rock (or the temperature at the melt layer boundaries, Tm) and the maximum temperature in the slip zone (TM; e.g., Lee et al., 2017). Because the emissivity (ε) of materials varies with the wavelength of radiation, here we took ε = 0.76 and ε = 1.00 (Ramsey et al., 2012) as end members. Depending on ε, a temperature range was estimated for Tm and TM. Then, we averaged the measured melt boundary temperatures, which was 1071 °C for Tm (see the Data Repository). We note that there is a correlation between TM and clast fraction (φ) in the experimentally formed PST, whereby higher values of TM are associated with lower values of φ (see the Data Repository; Table DR1; Fig. 3). The correlation may be described using the following empirical relationship reported in a previous study on natural PST (Otsuki et al., 2003): TM = Alog(1 – φ) + B, where A and B are constants. The value of TM for the natural PST is difficult to estimate, although various previous attempts have been made (Lin, 2008). Here, instead of 2 km Study area (Fig. 1B) East Sea (Sea of Japan) N 35 .2 0


INTRODUCTION
The formation of a caldera, defined as a collapse structure in a volcano formed by the subsidence of roof rocks over an evacuated magma chamber, is a highly dynamic geological event (Branney and Acocella, 2015).Caldera formation follows, or is concurrent with, large volcanic eruptions or lateral magmatic outflow (e.g., Cole et al., 2005).Because the large displacement of the roof rocks occurs mostly along the ring faults (i.e., caldera-bounding, circular, steeply dipping faults), the friction on the faults should be considered in mechanical models of caldera collapse (Stix and Kobayashi, 2008).Once underpressure or overpressure has built up within a magma chamber (Gudmundsson, 1988;Cashman and Giordano, 2014), collapse of the roof rocks may be initiated by the formation of, and slip on, ring faults.For continued collapse to be possible with large displacements on the ring faults, the shear resistance or friction on the faults should decrease with increasing displacement.Seismological and geodetic observations of active volcanoes (Mori and McKee, 1987;Bathke et al., 2013) and analog and numerical modeling (Acocella, 2007) have significantly improved our understanding of caldera collapse.However, these approaches alone, without field observations of ring faults, are unable to fully constrain the fault zone processes and frictional properties of the faults that may control the collapse.We investigated an outcrop of a ring fault of the Cretaceous Jangsan caldera in southeastern Korea, which formed in a volcanic arc setting (Yun et al., 2010;Chough and Sohn, 2010).This ring fault has been deeply eroded and exhumed, and portions of the fault that were situated at depth (<5 km) during the caldera collapse are now exposed.Along the fault, we found a thick (up to ~10 cm) layer of pseudotachylyte (PST), that is, a fault rock solidified from friction-induced melting.The presence of the PST indicates a large temperature rise due to rapid slip during the caldera collapse.We estimated the shear resistance on the ring fault during caldera collapse by integrating field observations, materials and microstructural analyses of the PST, and frictional melting experiments.

PSEUDOTACHYLYTE IN THE RING FAULT
The Jangsan caldera (~8-9 km in diameter, including intrusions) was formed during explosive felsic eruptions in the Late Cretaceous.The pyroclastic volcanic succession in the center, which mainly consists of rhyolitic tuff (K-Ar whole-rock age of 67 ± 4 Ma; Yun and Sang, 1994), is surrounded by rhyolitic ring intrusions (Fig. 1A).A ring fault is observed between the dacitic wall rocks (or silicified andesite from precaldera volcanics) and the rhyolitic intrusions (Fig. 1B; too thin to be displayed along the boundary between the dacite and the volcanic succession in Fig. 1A), and it strikes northeast with a near-vertical dip (88°-90°).The PST layer varies in thickness (from <1 cm to ~10 cm) along the fault (Figs.1C and 1D).The bulk chemical composition of the PST is very similar to that of the dacitic wall rock and is intimately associated with a brownish, thermally altered zone (TA in Fig. 1) of the cataclastic wall rock.Also, the dark-gray to black PST is associated with light-colored tuffisite (TF; or intrusive tuff; see Fig. 1).The PST has a dacitic composition with a matrix composed of subhedral to euhedral feldspars, chlorite, and Fe-oxides.The TF has a rhyolitic chemical composition and consists mainly of lapilli-sized, quartzofeldspathic fragments and light-colored groundmass.The cuspate boundary of the PST (Fig. 1D) and some mingling structures (not shown in this paper) observed along the boundary between the PST and TF indicate that the intrusion of TF into the fault zone started before the solidification of the frictional melt layer.On the other hand, the PST is sharply intruded and detached by the TF in some other places, indicating that TF intrusion continued after significant cooling of the frictional melt (Figs.DR2 and DR3 in the GSA Data Repository 1 ; see also Fig. 3C).
At the microscopic scale, the clasts in the PST are dominantly rounded or subrounded (Fig. 2A).The aphanitic matrix consists mainly of ultrafine grains of feldspar, chlorite, quartz, and magnetite.Subhedral or euhedral feldspar grains (mostly a few micrometers in size) in the matrix show chemical zoning, indicating their primary crystallization from a frictional melt of heterogeneous composition (Fig. 2B).Some spiral-shaped objects formed by clasts with cataclastic tails indicate that the central volcanic succession of the caldera was downthrown with respect to the wall rocks (Fig. 2C).
The chilled margins of pyroclastic dikes may look like PSTs.Our observations, however, indicate that the PST in the study area was generated by frictional melting of the dacitic wall rocks, not by rapid cooling of the TF, as evidenced by: (1) the similar chemistry of the PST to that of the dacite; (2) the TF intruding the PST; (3) no grain size decrease toward the boundary of the TF; and (4) reproduction of the natural PST by the experimental frictional melting of dacite (see Figs. 3B and 3C).

DYNAMIC SHEAR RESISTANCE DURING CALDERA COLLAPSE
The shear resistance on a ring fault coated by a frictional melt layer may be calculated as τ f = ηV/w, where τ f is the shear stress (Pa), η is the melt viscosity (Pa•s), V is the slip rate (m/s), and w is the melt thickness (m), assuming that the melt behaves like a Newtonian fluid.To constrain η and V and to estimate τ f , we conducted high-velocity rotary shear experiments, slip zone temperature measurements, and chemical 1 GSA Data Repository item 2019045, description of the methods used in the study, supplementary tables, and supplementary figures, is available online at http:// www.geosociety.org/datarepository/2019/,or on request from editing@geosociety.org.and microstructural analyses of both natural and experimentally formed PSTs.Our approach was to estimate V, which is difficult to measure from natural PST, by combining our experimental data with theoretical work on frictional melts (Nielsen et al., 2008) and estimating η using the measured temperatures, chemical composition data, and microstructural data (e.g., clast fraction; see Fig. DR1 for the details).
We conducted the rotary shear experiments on solid cylinders (25 mm in diameter) of the dacitic rock sampled near the natural PST.The tests were performed with a high-velocity rotary shear apparatus (Hirose and Shimamoto, 2005) at room temperature and room humidity.Two tests were performed at a normal stress (σ n ) of 10 MPa and a V of 0.2 and 0.7 m/s to measure both the shear stress (τ ss ) and melt layer thickness (w) under steady state (dashed boxes in Fig. 3A).Temperature was measured with an infrared radiation thermometer in the four experiments, including the two tests mentioned above (see the methods description in the Data Repository; Table DR1), to determine the melting point of the wall rock (or the temperature at the melt layer boundaries, T m ) and the maximum temperature in the slip zone (T M ; e.g., Lee et al., 2017).Because the emissivity (ε) of materials varies with the wavelength of radiation, here we took ε = 0.76 and ε = 1.00 (Ramsey et al., 2012) as end members.Depending on ε, a temperature range was estimated for T m and T M .Then, we averaged the measured melt boundary temperatures, which was 1071 °C for T m (see the Data Repository).We note that there is a correlation between T M and clast fraction (ϕ) in the experimentally formed PST, whereby higher values of T M are associated with lower values of ϕ (see the Data Repository; Table DR1; Fig. 3).The correlation may be described using the following empirical relationship reported in a previous study on natural PST (Otsuki et al., 2003): T M = Alog(1 -ϕ) + B, where A and B are constants.The value of T M for the natural PST is difficult to estimate, although various previous attempts have been made (Lin, 2008).Here, instead of    forming a constraint based on the melting points of molten and surviving minerals, we used an empirical relationship for inferring the T M of the natural PST: For ϕ = 0.14 (mean value taken for the natural PST; see Fig. 3C for the natural PST with ϕ = 0.12; Table DR2), T M = 1399 °C (ε = 1.0;A = 2800.2;B = 1582.4)and 1720 °C (ε = 0.76; A = 3518.6;B = 1950.0).We took 1400 °C as T M to use a conservative estimate (Fig. 3D).The surviving clasts in the PST are mostly quartz and feldspars.The value of ϕ in the natural PST is much smaller than the volume fraction (~75%) of quartz and feldspars in the wall rocks, as determined by quantitative X-ray diffraction analysis (Table DR3), which indicated that some of the quartz and feldspar may have melted.Therefore, our choice of 1400 °C for T M seems reasonable because the metastable melting of β-quartz occurs at ~1400 °C (Lee et al., 2017).Temperature-dependent melt viscosity (η) can be estimated based on the chemical composition of the PST using an empirical non-Arrhenian equation of viscosity: log η = A + B/(T -C), where A, B, and C are adjustable parameters, and η is in Pa•s and T is in K (Giordano et al., 2008).Using T M and the chemical composition (Table DR4) based on X-ray fluorescence analysis (file for the calculation is available online at https://www.eoas.ubc.ca/~krussell/VISCOS-ITY/grdViscosity.html),η of the natural melt was estimated to be 40.74Pa•s, which appears to be comparable to the values of some frictional silicate melts (Spray, 1993).The relative viscosity (η rel ) of the clast-bearing melt was calculated following a viscosity model for crystal-rich magma (Costa et al., 2009; file for the calculation is downloadable from http://datasim.ov.ingv.it/wcosta/#Articles):For ϕ = 0.14, which was determined by image analysis, η rel = 1.49.The effective viscosity (η eff ), which is the product of η and η rel , was taken as 60.70 Pa•s.However, η varies across a layer depending on temperature, so we averaged η between T M and T m to obtain η eff (2555 Pa•s) for shear across the natural PST layer.
V may be estimated from the steady-state temperature profile for a given power density (τ ss V; Nielsen et al., 2008): where W is the characteristic velocity defined by: W  (Nielsen et al., 2008;method M4).For K, we used the thermal conductivity (1.6 W m -1 K -1 ) at 1400 °C (T M ) reported for an andesitic melt (Murase and McBirney, 1973) because of the chemical similarity between the natural PST and the andesitic melt.T c calculated using the parameters above was 30.9 °C.The Arrhenian equation is an approximation that is only valid for T ≈ T m (Nielsen et al., 2008, p. 7), and it appears that the viscosity at 1400 °C (>>T m ) estimated with the equation is two orders smaller than that estimated with the non-Arrhenian equation.Using the parameters W and T c , V was calculated to be 34.7 m/s for the natural PST with a T m of 1071 °C and T M of 1400 °C.
For the estimation of τ f for the natural PST, a value of w = 0.1 m was taken.Because τ f = η eff V/w, then τ f = 0.89 MPa.With the assumption that the mean horizontal stress is equal to the vertical stress (Heim's rule; Zang and Stephansson, 2010), the effective normal stress (σ n ) acting on the vertical ring fault would be ~34 MPa (54 MPa of horizontal stress and 20 MPa of fluid pressure) at 2 km depth.This is a representative depth for the vertical Jangsan caldera fault, considering the emplacement depth of the magma chamber (~5 km) from which the ring intrusion originated (Yun et al., 2010).Therefore, the ratio of τ f to σ n could be <0.1, which indicates an extremely low shear resistance on the ring fault after the thick frictional melt layer was generated.The intrusion of fluid-like tuffisite outlasted the frictional melting (Fig. 3C; Fig. DR2) and might have lowered the effective normal stress and shear resistance on the fault, even after the cessation of melt lubrication.

CALDERA SUPERFAULTING
Here, we determine the size of the fault displacement (d) during the caldera collapse.Assuming that all the frictional work is converted into heat, the d value needed to generate a melt layer with a thickness of w can be estimated by the following equation (Sibson, 1975;Di Toro et al., 2005): where ρ is the wall-rock density (2700 kg/m 3 ), ϕ is 0.14, H is the latent heat of fusion (4.2 × 10 5 J/kg; Stacey and Davis, 2008), c p is the specific heat of the rock (910 J/kg/K; Lavallée et al., 2012), T M is 1400 °C, T wr is the ambient wall-rock temperature (120 °C, assumed for a high-heat-flow region at 2 km depth), and τ f is 0.89 MPa.In that case, a d of ~460 m is estimated for w = 0.1 m.The displacement may be an overestimate: τ f may have been larger than 0.89 MPa before the growth of the melt layer to as thick as 0.1 m (Hirose and Shimamoto, 2005), and the larger τ f may be correlated with smaller fault displacement.However, it should also be noted that, due to the injection and detachment of the melt layer, the current thickness of the PST at the outcrop is a minimum thickness (Fig. DR2), so that its use as w may underestimate the displacement.This type of extraordinarily large fault displacement during a single slip event at seismic slip rates is referred to as "superfaulting" (Spray, 1997).Assuming a simple "piston-type" collapse, a rough estimate of seismic moment (M 0 ) can be made for the Jangsan caldera using M 0 = μAd, where μ is the shear modulus (5 GPa for fluid-saturated fractured rock; De Natale et al., 1991), A is the fault slip area (3 × 10 7 m 2 for the fault length of 2 km and the caldera diameter [excluding the ring intrusions] of ~5 km), and d = ~460 m.In this case, M 0 = 7.2 × 10 19 N•m, which is equivalent to an earthquake with a moment magnitude (M w ) of 7.2.In modern calderas, this magnitude of an earthquake was seismologically recorded during the collapse of Katmai caldera (1912), in Alaska, where the diameter (2 km) is smaller than that of the Jangsan caldera (5 km).The total d and the magnitude of the largest earthquake in the Katmai caldera were 1.2 km and M s (surface wave magnitude) = 7.0, respectively (Abe, 1992;Hildreth and Fierstein, 2012).
Given that evidence of frictional melting has been reported at the Glencoe caldera in Scotland and that flinty crush rocks, which are possible PSTs, are found in ring faults elsewhere around the world (Clough et al., 1909;Kokelaar, 2007), we suggest that frictional melting during caldera collapse may not be uncommon.Depending on the lithology of the wall rocks (e.g., carbonates and clay gouges), thermally activated processes other than frictional melting (Han et al., 2007;Di Toro et al., 2011;Lavallée et al., 2014) may also be expected to occur on ring faults.
Fig. 1C Fig. 1D Figure 1.Jangsan caldera (southeastern Korea) and ring fault.A: Simplified geologic map of study area (marked by small rectangle).GB-Gyeongsang Basin.B: Ring fault zone between wall rock (dacite, DA) and rhyolitic intrusion.Layer of pseudotachylyte (PST) occurs along fault.Tuffisite (TF) intrudes PST.Rhyolitic intrusion and tuffisite belong to ring intrusions displayed in A. C: Distribution of PST, TF, and thermally altered zone (TA) around fault.D: Outcrop photograph of ~10-cmthick PST.

Figure
Figure 2. Microstructures of pseudotachylyte (PST).A: Overview of PST (backscattered electron images) showing large feldsparrich clasts in matrix.B: Euhedral or subhedral ultrafine grains of plagioclase (Pl) in matrix of PST.C: Clast with tail indicating that central volcanic succession of caldera was downthrown with respect to wall rock.
= 8T c K / c .T c (°C) and η c (Pa•s) are the characteristic temperature and characteristic viscosity, respectively, and are defined in an Arrhenius-type equation for the temperature dependence of viscosity, η(T) = η c exp[(T m -T)/ T c ]. K (W m -1 K -1 ) is the thermal conductivity of the melt.The values of W (0.169 m/s) and η c (13,920 Pa•s) were estimated experimentally by conducting two shear tests at different V Figure 3. Data set used for estimating shear resistance of pseudotachylyte (PST).A: Shear stresses measured at two different slip rates, V. B: Experimental PST and brownish thermally altered zone (TA).Clast fraction (ϕ) in PST is 0.35.C: Natural PST and TA, with ϕ = 0.12.D: Plot of maximum temperature in PST (T M ) vs. log(1ϕ).Minimum estimate of T M (intersection of lower dashed line with pink bar [ϕ in natural PST], indicated by arrow) is 1400 °C; ε is emissivity of experimental melt.For reference, melting points of metastable quartz and cristobalite are given.