Sinkholes, Pit Craters, and Small Calderas: Analog Models of Depletion- Induced Collapse Analyzed by Computed X-Ray Microtomography

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Sinkholes, pit craters, and small calderas: Analog models of depletion- induced collapse analyzed by computed X-ray microtomography

Sam Poppe1,†, Eoghan P. Holohan2,†, Elin Pauwels3,†, Veerle Cnudde4,†, and Matthieu Kervyn1,† 1Department of Geography, Earth System Science, Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium 2Helmholtz Centre Potsdam, German Research Centre for Geosciences (GFZ), Section 2.1, Telegrafenberg, 14472 Potsdam, Germany 3Centre for X-ray Tomography (UGCT), Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, B-9000 Ghent, Belgium 4Centre for X-ray Tomography (UGCT), Department of Geology and Soil Science, Ghent University, B-9000 Ghent, Belgium

ABSTRACT bulking of magma reservoir overburden rock For developing early-warning systems and/or may at least partially explain why the volume remediation schemes from such information, it Volumetric depletion of a subsurface body of magma erupted commonly exceeds that of is important to understand the structural devel- commonly results in the collapse of over- the surface depression. opment of gravitational overburden collapses. burden and the formation of enclosed topo- An intrinsic problem is that this mostly occurs graphic depressions. Such depressions are INTRODUCTION underground and so cannot be directly observed. termed sinkholes in karst terrains and pit cra- Consequently, many researchers have turned to ters or collapse calderas in volcanic terrains. Closed, near-circular topographic depres- analog and numerical collapse simulations. This paper reports the fi rst use of computed sions with diameters ranging from several tens to Past analytical and numerical modeling stud- X-ray microtomography (μCT) to image thousands of meters are common morphological ies of collapse have mostly simulated the over- analog models of small-scale (~< 2 km diam- features on Earth and other planets. In regions burden to behave as a linearly elastic continuum eter), high-cohesion, overburden collapse underlain by karst rock units, such as limestone (e.g., Tharp, 1999; Folch and Marti, 2004). A induced by depletion of a near-cylindrical or evaporite (rock salt), these depressions are major limitation of this assumption is that the (“stock-like”) body. Time-lapse radiography termed sinkholes or dolines. In regions affected large and commonly highly discontinuous (i.e., enabled quantitative monitoring of the evo- by igneous activity, such features are termed pit fault- or fracture-related) strains typical of col- lution of collapse structure, velocity, and vol- craters (diameter <~1 km) or calderas (diam- lapse are diffi cult or impossible to simulate. ume. Moreover, μCT scanning enabled non- eter >~1 km). As outlined below, differences in More recent studies have surmounted this limi- destructive visualization of the fi nal collapse geological context lead to some variation of the tation by assuming the overburden to behave as a volumes and fault geometries in three dimen- depression formation mechanisms in detail. An visco-elastic continuum or by treating the over- sions. The results illustrate two end-member overriding similarity, however, is that sinkholes, burden as an assemblage of distinct elements scenarios: (1) near-continuous collapse into pit craters, and calderas commonly form as a (e.g., Baryakh et al., 2008; Hatzor et al., 2010; the depleting body; and (2) near-instan- result of the volumetric depletion of a subsur- Holohan et al., 2011; Shalev and Lyakhov sky, taneous collapse into a subsurface cavity face body and the consequent destabilization 2012), but computational expensiveness has formed above the depleting body. Even within and gravitational collapse of the overburden. hitherto limited them to two dimensions. near-continuously collapsing columns, sub- Sinkholes, pit craters, and calderas formed Analog models readily simulate such large sidence rates vary spatially and temporally, in this way can all develop within days and discontinuous strains in a three-dimensionally with incremental accelerations. The highest with little advance warning (e.g., Dahm et al., complete way (e.g., Sanford, 1959). There have subsidence rates occur before and immedi- 2011; Poland et al., 2008; Stix and Kobayashi, hence been many analog model studies of pit ately after a surface depression is formed. 2008, and references therein). Nonetheless, crater or caldera collapse (e.g., Komuro, 1987; In both scenarios, the collapsing overburden modern monitoring methods can yield abun- Martí et al., 1994; Roche et al., 2000; Walter and column undergoes a marked volumetric ex- dant geophysical and geodetic information Troll, 2001; Kennedy et al., 2004; Lavallée et al., pansion, such that the volume of subsurface related to the onset and evolution of such col- 2004; Geyer et al., 2006; Acocella, 2007; Holo- depletion substantially exceeds that of the re- lapses. This capacity is illustrated by studies han et al., 2008, 2013; Burchardt and Walter, sulting topographic depression. In the karst of recent collapses at the basaltic volcanoes 2010; Ruch et al., 2012), but far fewer of sink- context, this effect is termed “bulking,” and of Miyakejima (Japan), Kilauea (Hawaii), and hole formation (Parker and McDowell, 1955; our results indicate that it may occur not only Piton de la Fournaise (La Réunion) (e.g., Geshi Ge and Jackson, 1998; Howard, 2010). Most at the onset of collapse but also during pro- et al., 2002; Longpré et al., 2007; Michon et al., past analog modeling studies have explored the gressive subsidence. In the volcanic context, 2007; Poland et al., 2008), and at the Wink and general structural geometry and kinematics of Daisetta sinkholes, Texas (Paine et al., 2012), collapse. Dynamic aspects, such as changes in †E-mails: sam.poppe@ vub .ac .be; holohan@gfz as well as subsurface collapses in the sink- subsidence velocity or volume through time, -potsdam.de; elin.pauwels@ ugent .be; veerle.cnudde@ hole-prone city of Hamburg, Germany (Dahm are much more diffi cult, even impossible, to ugent .be; [email protected]. et al., 2011). scale adequately, but even semi-quantitative

GSA Bulletin; Month/Month 2014; v. 1xx; no. X/X; p. 1–16; doi: 10.1130/B30989.1; 9 ﬁ gures; 3 tables.

For permission to copy, contact [email protected] 1 © 2014 Geological Society of America Poppe et al. constraints on these could greatly aid the inter- sidence associated with subsurface dissolution and Jackson, 1998; Roche et al., 2000; Holohan pretation of seismic, geodetic, and gravity data of evaporite (rock salt) bodies (Fig. 1). et al., 2011). In general, (1) sagging is promoted acquired during collapses in nature. Pit craters and small calderas (~< 2 km diam- by low rock mass strength and low T/D ratio; In this paper, we report the novel applica- eter) form mainly through destabilization of (2) foundering of one or more large coherent tion of computed X-ray microtomography the overburden by drainage and critical depres- blocks enclosed by a ring fault occurs at inter- (μCT) to image analog models of vertical col- surization of a subsurface magma body (see mediate rock mass strength and intermediate to lapse. In nature, collapse events at sinkholes, Roche et al., 2001; Geshi et al., 2002; Stix and high T/D ratio; and (3) stoping and ephemeral pit craters, and calderas range in dynamic style Kobayashi, 2008; Michon et al., 2011) (Fig. 2). cavities develop at high rock mass strength and from near-instantaneous (“en mass”) to near- The overburden usually comprises partly to high T/D ratio (e.g., Roche et al., 2000, 2001; continuous (“incremental”), typically occurring fully consolidated igneous material, which Holohan et al., 2011). over periods of a few minutes to a few months, may be of highly heterogeneous mechanical Of these three common subsidence mecha- respectively (Gutiérrez et al., 2008; Stix and character. Depending on the level of emplace- nisms, coherent-block foundering and stoping Kobayashi, 2008). As shown below, our models ment of the magma body below the free surface, are associated with sharply defi ned depressions reproduce these two end-member scenarios. Our the overburden may also include non-igneous bounded by steep sides that are cliffed or over- considerations are restricted to a natural length “basement” rocks. Another pit crater–forming hanging (Gutiérrez et al., 2008). Such a steep- scale of ~< 2 km, and our results are thus most process involves collapse of material into an sided morphology gives rise to the term “pit relevant for collapses during which brittle defor- open subsurface fracture formed by the intru- crater” in volcanic terrains. Time-averaged sub- mation is likely to be dominant. We note that the sion and drainage of a dike. Such a mechanism sidence rates of up to several tens or hundreds formation of larger calderas is more likely to be is evidenced from a detailed study of pit crater of meters per day have been observed during infl uenced by thermal effects from the corre- chains on Hawaii (Okubo and Martel, 1998), the formation of pit craters and calderas (Poland spondingly larger magma reservoir, giving rise and may be considered a variation on the main et al., 2008; Geshi et al., 2002; Michon et al., to an increased importance of ductile overbur- mechanism explored here. 2007, 2011). Although many sinkholes show den behavior (see Burov and Guillou-Frottier, There is a remarkably similar range of over- much slower subsidence rates of 0.2–30 cm/yr 1999; Gregg et al., 2012). The µCT approach burden subsidence mechanisms observed at (Soriano and Simón, 2002; Dahm et al., 2011; reveals the models’ subsurface collapse evolu- sinkholes, pit craters, and small calderas (Gutiér- Paine et al., 2012), some also collapse at rates tions as run in a fully three-dimensional (3D) rez et al., 2008, and references therein; Branney, of up to several tens of meters per day (e.g., medium, rather than against a glass pane (e.g., 1995; Lipman 1997; Okubo and Martel , 1998; Walters , 1978; Johnson, 2005). These high rates Burchardt and Walter, 2010; Ruch et al., 2012). Harris, 2009). Based on these observations, are typically seen with sudden, en-mass over- The advantage is that boundary effects at the overburden subsidence in both terrain types may burden collapses into large underground cavities. observed contact between the analog materials involve: (1) sagging of strata; (2) foundering of Such observations point to an overriding and the glass are avoided. After briefl y com- large intact blocks delimited by ring faults; or importance of brittle overburden deformation paring our simulated collapse structures and (3) “caving” or “stoping,” whereby pieces of in those collapses of highest geohazard. Con- geometries with those of the previous models overburden detach and subside in conjunction sequently, we focus here on the more brittle from the literature, we extract quantitative data with the progressive upward migration of sub- mechanisms (2–3) by considering the effects on model subsidence rate and volume through surface cavities. Many natural cases show com- of subsurface volume depletion on overburden time from the μCT imagery. Finally, we discuss binations of more than one such mechanism. A rock masses of relatively high cohesion and of implications of these data for development and fourth subsidence mechanism particular to the intermediate T/D ratios of roughly 0.8–1.3. monitoring of natural collapses at the studied sinkhole literature is termed “suffosion.” This length scale range. refers to the relatively long-term downward METHODOLOGY fl ushing, tumbling, granular fl ow, and/or vis- BACKGROUND TO DEPLETION- cous creep of unconsolidated cover deposits into Experiment Setup and Material INDUCED COLLAPSE IN NATURE pipes or fi ssures in the bedrock. In volcanic terrains, suffosion may also occur in materials such Dry silica sand sieved to 50–180 µm grain Sinkholes form mainly because of undermin- as poorly consolidated tephras, although the ori- size and mixed with 5% or 10% by volume of ing of the overburden by subsurface dissolution gins of the underlying fi ssures or pipes may or dry plaster served as an analog for a brittle over- (“subrosion”) of karst rock (Gutiérrez et al., may not be directly connected to movements of burden rock mass. The sand and plaster mixes 2008, and references therein) (Fig. 1). Alterna- magma (Ferrill et al., 2004). (SP mix) had bulk densities of ~1.6 × 103 kg m–3 tively, uneven dissolution of karst rock directly The development of each of the sub- and ~1.75 × 103 kg m–3, respectively. Following at or just below the Earth’s surface may produce sidence mechanisms (1–3 above) depends the method of Donnadieu (2000), we estimated so-called “solution sinkholes.” Because the on the mechanical and geometric properties cohesions of ~180 Pa and ~300 Pa, respectively, study of this latter mechanism is not the aim of of the overburden and on those of the under- by averaging 20 measurements of maximum our work, we do not consider it any further here. lying body of rock salt or magma. The most vertical cliff height. In contrast to pure dry sand, Subsurface dissolution is typically a conse- important mechanical and geometric factors which is theoretically cohesionless, the cohesive quence of fresh or undersaturated groundwater are, respectively, the strength (i.e., cohesion) SP mix can support near-vertical cliffs, as seen fl owing through the karst rock body or along of the overburden and the ratio of overburden in the natural collapse-related depressions (Figs. its boundaries (Johnson, 2005, and references thickness to depletion zone diameter (T/D) (e.g. 1 and 2; see also Hubbert, 1937; Roche et al., therein). The overburden may include other Whittaker and Reddish, 1989; Ge and Jackson, 2001; Holohan et al., 2008). karst rock units (bedrock), non-karst rock strata 1998; Roche et al., 2000, 2001; Gutiérrez et al., Our depletion zone comprised a cylindrical (cap rocks), and/or unconsolidated sediments 2008; Holohan et al., 2011). The shape of the body of golden syrup (GS), a Newtonian fl uid (cover). Here, we focus on overburden sub- depletion zone exerts a secondary infl uence (Ge with a density of 1.4 × 103 kg m–3 and a viscos-

2 Geological Society of America Bulletin, Month/Month 2014 Sinkholes, pit craters, and small calderas

A Crater Lake sinkhole, Saskatchewan C Cargill sinkhole, Kansas SE NW 500 500

450 450

Meter a.s.l. 400 400

350 350

Inner cylinder Outer cylinder D B SW NE 0 SE NW

Sand 200 200 50 Red shale

100 Gray shale 600 600

Void Void Depth in meter

Depth in meter 150 Roof fall rubble

1000 1000 200 Salt + shale

500 50 Distance in meter Figure 1. Examples of sinkholes and their potential subsurface structure. (A) Crater Lake sinkhole, Saskatchewan, Canada (adapted from Christiansen, 1971). This structure resulted from natural salt dissolution. Gray (near-)horizontal lines de- limit lithological boundaries as interpreted from borehole data. The Sutherland Group marker layer is presented in gray. These indicate that the near-surface sinkhole structure comprises two ring fault sets. a.s.l.—above sea level. (B) Seismic data indicate that the Crater Lake sinkhole overlies a downward-widening overburden column of increased porosity relative to the surrounding undisturbed rock mass (adapted from Gendzwill and Hajnal, 1971). When the surface trace of the outer cylinder is projected down to meet the subsurface structure, as deﬁ ned by seismic reﬂ ectors, an overall hour glass shape can be seen. (C) Cargill sinkhole, Hutchinson, Kansas (from Walters, 1978). This resulted from sudden collapse in 1974 into a subsurface cavity produced over many years previously by salt-solution mining. (D) Subsurface structure of the Cargill sinkhole (adapted from Walters, 1978). Although the near-surface structure as shown in the cross-section is relatively well known from boreholes drilled into the sinkhole after collapse, the deep structure of the collapse column and exact dimensions of the subsurface cavity are unknown.

ity of 50 Pa s at 22 °C laboratory temperature factors (see below), the analog setup was down- The plastic cylinder was fi xed upon a hori- (Mathieu et al., 2008). The use of an uncon- scaled to a feasible size. The analog materials zontal plastic base with a 0.8 cm circular per- strained fl uid allows for “freer” gravity-driven were hence contained within a plastic cylinder foration. A GS body of height 1.5 cm and deformation of the brittle overburden (Roche of 6.5 cm diameter (Fig. 3), which yielded an diameter 2 cm was emplaced within a tempo- et al., 2000), in contrast to the use of an elastic average µCT voxel size of 80–84 µm (“CCT12” rary cylindrical mold upon the plastic base, and balloon (e.g., Martí et al., 1994) or a solid piston models) and 110–111 µm (“CCT14” models). was connected to an external GS silo via the (e.g., Ruch et al., 2012). This is necessary to image the smallest faults, basal perforation and a fl exible tube. The mold As the attainable µCT image resolution which may be only two sand grains thick was surrounded by SP mix and then removed. depends on the object diameter, among other (Kervyn et al., 2010). Following this, SP mix was added until reach-

Geological Society of America Bulletin, Month/Month 2014 3 Poppe et al.

A N Ring fault C N Outer ring fault ing to a desired height above the GS body and surface was levelled. Finally, the model was placed on the scanning rotor. Following past works Wall debris (e.g. Holohan et al., 2011; Roche et al., 2000; Ruch et al., 2012), the main variables explored Funnel-like crater here were the SP mix’s cohesion and the overburden’s thickness to diameter ratio T/D (see 200 m model descriptions in Table A1). 100 m Wall debris Inner ring fault To enable clearer imaging of deformation structures in the µCT scans, several horizontal Dolomieu, Piton de la Fournaise Miyakejima garnet sand layers with a thickness of ≤1 mm were interlayered within the SP mix above the B D GS body. To further improve the imaging of S N structural offsets in radiography images, the widths of the garnet layers in the direction of the beam were reduced in the CCT14 models; Wall debris such layers were thus strip-like in form. The Ring garnet sand’s bulk density of 2.28 × 103 ± 0.06 × Ring fault fault 103 kg m–3 provides a readily detectable density contrast to the SP mix. Sieved at <250 µm, Closed ? the garnet sand’s mean grain size (~200 µm) cavity exceeded that of the silica sand (~150 µm). Magma depletion As only thin layers or strips were emplaced, into dyke however, there were no signifi cant differences Magma detected between models with or without garnet depletion Magma sand layers and no signifi cant changes in fault reservoir dip at SP mix–garnet interfaces. Magma 500 m Edge effects may infl uence the model stress 500 m reservoir fi eld due to the fi nite size of the experimental setup, as vertical stresses could be redistrib- Figure 2. Examples of pit craters or small calderas and their potential subsurface struc- uted laterally through arch effects to the con- ture. (A) Dolomieu pit crater, Piton de la Fournaise volcano, La Réunion Island, collapsed tainer walls (Roche et al., 2000). These can be during the depletion of a subsurface reservoir in 2007 (adapted from Staudacher et al., assumed to be of secondary importance as long 2009). (B) Interpretation of Dolomieu pit crater subsurface structure after the 2007 collapse as the container diameter is large with respect to (adapted from Michon et al., 2007). The lateral intrusion of a dike from the magma reser- the area affected by deformation. The cylinder voir was evidenced geophysically. Marginal benches within the pit crater indicate several diameter of 6.5 cm is more than twice the 2 cm ring fault splays. (C) Miyakejima caldera, during its 2000 collapse (adapted from Geshi diameter of the analog depletion zone, and as et al., 2002). (D) Interpretation of Miyakejima subsurface structure after the 2000 collapse such, we regard edge effects in our models to be (adapted from Geshi et al., 2002). Magma injection into a lateral dike and several subsur- suffi ciently small. face cave collapses were evidenced in geophysical data before ring faults reached the surface Depletion was started by lowering the GS and formed the caldera. The caldera itself fi lled progressively with debris from wall failures. silo to slightly below, or to the same level as,

Figure 3. X-ray tomography setup at the 3 Ghent University Centre for X-ray Tomog- raphy for imaging analog caldera models. 1—X-ray beam source; 2—plastic stand 5 with central perforation and outlet; 3—plas- T 7 tic cylindrical container; 4—sand-and-plaster 1 D 4 8 mix; 5—thin garnet sand intercalations; 6—golden syrup (GS) analog ﬂ uid body; 6 7—external GS container, adaptable in elevation; 8—PerkinElmer ﬂ at panel detector; 2 T—overburden thickness; D—GS reservoir diameter. 2 cm

4 Geological Society of America Bulletin, Month/Month 2014 Sinkholes, pit craters, and small calderas

7 the model’s plastic base. GS hence fl owed later- (Schultz, 1996), and so we assume Cn = 10 Pa. 2003). More recently, Kervyn et al. (2010) fi rst ally from the reservoir into the silo. For evapo- For a length ratio L* = 2.5 × 10–5, i.e., 1 cm = applied µCT to analog volcanological models. rite karst terrains, this is comparable to lateral ~400 m (Table 1), Cm should hence equal 140 Pa Imaging of models presented here was carried removal of salt by groundwater fl ow or by salt for volcanic and (evaporite) karst rock. The SP out at the Ghent University (Belgium) Centre withdrawal into an adjacent diapir (Ge and Jack- mix cohesion of 180 Pa lies fairly close to this for X-ray Tomography (UGCT; http:// www son, 1998). For volcanic terrains, it represents value. The angles of internal friction in nature .ugct .ugent .be; Masschaele et al., 2007; Cnudde magma withdrawal from a subvolcanic reservoir and in the SP mix are approximately the same, and Boone, 2013). For technical specifi cations, without any concurrent eruptive or explosive and thus φ* ≈ 1. see Appendix 2. activity in the collapsing depression itself, a sce- Scaling of the depletion zone behavior is less µCT is based on the attenuation of X-rays as nario documented several times in nature (e.g., straightforward, given the differences in deple- they pass through a volume of material and yields Hildreth and Fierstein, 2000; Geshi et al., 2002; tion zone materials and depletion processes in the local linear attenuation coeffi cient in that Michon et al., 2007). volcanic and karst terrains. In principle, viscos- material. This coeffi cient depends on the material The experimental series is described in Table ity is scaled through the equation: η* = σ*T*, density and mean atomic number (Kervyn et al., A1. No direct control was exercised on the where T* = L* / V* and V is the time-averaged 2010, and references therein). Material thickness depletion volume or rate. Depletion typically subsidence velocity (Ge and Jackson, 1998; in our models is constant. Thus, the attenuation –6 lasted 200–900 min, and stopped automatically Holohan et al., 2008). From Vm = 1.4–2.8 × 10 observed in a radiograph, as well as the linear –1 –4 –1 when the subsiding overburden touched the m s (~1 cm in 2–4 h) and Vn = 2.3 × 10 m s attenuation coeffi cient observed in a voxel of a bottom of the GS body and plugged the out- (~20 m per day; e.g., Geshi et al., 2002), the GS µCT image, are primarily affected by changes in η fl ow pipe. viscosity of m = 50 Pa s scales up to a natu- material density within the SP mix, and by shifts η 8 ral magma viscosity of n ~10 Pa s. This value in chemical composition within model zones Model Scaling approaches that of rhyolitic magmas (~105–108 where, e.g., SP mix comes to replace GS. Den- Pa s; Dingwell, 1998) and lies between those of sity changes arise in space and time in two ways: To ensure similarity, the physical and mechan- basaltic magmas (~101–103 Pa s; Murase and (1) by using materials of different initial density, ical properties of our analog models should be McBirney, 1973) and rock salt (~1017–1019 Pa s; and (2) by increasing or decreasing the material downscaled with respect to those of the natural Ge and Jackson, 1998). The imprecise scaling volume (i.e., volumetric strain). For instance, prototypes (Hubbert, 1937). A dimensionless of viscosity should not result in dramatically fault formation in the models is associated with ratio Π* was defi ned for each key physical different structural outcomes, because brittle dilation of granular packing. Consequently, fault- Π Π parameter, where * is the ratio of model ( m) deformation of the overburden, the focus of this affected material volumes have a lighter gray Π to nature ( n). The key physical ratios are: typi- work, is theoretically time independent (Ge and value on the µCT imagery compared to the sur- cal length, L*; density, ρ*; angle of internal fric- Jackson, 1998). In addition, although salt disso- rounding material volumes unaffected by fault tion, φ*; cohesion, C*; gravity acceleration, g*; lution drives the formation of natural sinkholes, formation (Panien et al., 2006). viscosity, μ*; and vertical stress, σ* (Table 1). rather than salt withdrawal, a geometric and The setup has two limitations. Firstly, a full In terms of scaling the brittle overburden kinematic analysis by Ge and Jackson (1998) scan for each model takes slightly less than behavior, both the SP mix and natural rock indicates that structural differences between one hour, during which time no deformation masses behave to a large degree as Mohr- withdrawal- or dissolution-driven collapses should take place in order not to induce any Coulomb materials (Byerlee, 1968; Schellart, should be slight. These premises are ultimately image noise. Secondly, rotation of the sample 2000). They hence have a linear failure enve- supported by the above-outlined morpho-struc- is required during scanning. Even at the lowest τ σ φ τ lope defi ned as = C + n × tan , where is tural similarities of collapse-related sinkholes, rotation speed possible, acceleration upon start- the shear stress in Pa, C is the cohesion in Pa, pit craters, and small calderas in nature. ing the rotor can trigger collapse of metastable σ φ n is the normal stress in Pa, and is the angle portions of the models (see below). of internal friction in degrees. As they pos- X-Ray Microtomography Methodology sess the same units, C* = σ* = ρ* × g* × L* = Deformation Quantifi cation on 1.4 × 10–5 (Table 1). A high laboratory-scale µCT has been used as a non-destructive µCT Imagery rock cohesion of 108 Pa is typically lowered by approach for imaging the internal kinematic one or two orders of magnitude at larger rock development of regional-tectonic analog mod- Unlike a full µCT scan, a radiograph image mass scales, due to large jointing and fracturing els since the early 1990s (see Schreurs et al., requires only a short exposure time of 2000 ms

TABLE 1. COMPARISON OF PHYSICAL PARAMETERS IN MODELS AND NATURE Typical Angle of internal ρ σ φ Bulk density, Gravity acceleration, g length, L Stress, friction, Cohesion, C0 Viscosity, µ Parameter (kg m–3) (m s–2) (m) (Pa) (degrees) (Pa) (Pa s) Π –2 model 1560–1750 ~9.8 3 × 10 1.6 × 10²–5.5 × 10² 22–25 180–300 50 Π † 3 7 7 volcano 2400 ~9.8 1.2 × 10 2.8 × 10 25–30 10 10–10³ Π –5 –5 –5 –5 –5 *volcano 0.65–0.73 1.0 2.5 × 10 1.4 × 10 –2.0 × 10 0.7–1.0 1.8 x 10 –3.0 × 10 0.05–5 Π § 5 7 sinkhole 2400 ~9.8 0.2 × 10³ 4.7 × 10 25–30 10 1017–1019 Π –4 –4 –5 –5 –5 –18 –16 *sinkhole 0.65–0.73 1.0 1.5 × 10 9.8 × 10 –1.2 × 10 0.7–1.0 1.8 × 10 –3.0 × 10 5 × 10 –5 × 10 Π Π Π * = model / nature Note: The calculation of stress and cohesion is explained in the section METHODOLOGY—Model Scaling. †Natural properties of basaltic volcanic rock and basaltic magmas from Lockwood and Hazlett (2010). §Natural properties of carbonate-evaporitic rock from Selby (1993).

Geological Society of America Bulletin, Month/Month 2014 5 Poppe et al. and no rotation of the sample. The 3D spatial information of the model is projected on a 2D Surface Surface plane, and so a sequence of time-lapse radio- Depression graphs taken every 0.5 min provided a “2.5D” documentation of the model deformation evolution. In addition, a radiograph taken at the start Brittle Brittle of depletion enabled any deviations from the material Total material affected Subsided ideally cylindrical geometry of the GS body, overburden induced by the emplacement and retraction of overburden the temporary mold, to be constrained. To quantify the velocity evolution of the model, the central point at the base of each garnet sand layer was tracked through each image in the sequence. In addition, syn-deformation Reservoir / Diapir volume changes of certain entities could be Reservoir / Diapir estimated through revolution of their outlines in the radiographs, under the assumption that these Figure 4. Sketch of volumetric entities within a depletion-induced col- entities were more or less axisymmetric volumes lapsing system as defi ned in the radiograph analysis (see Fig. 9). The (see Appendix 3). These entities, which include lateral outline of the “total affected overburden” column is defi ned on the total affected overburden, the depression, the the last radiograph of a radiograph sequence, while its lower limit is subsided overburden column, and the reservoir, defi ned as the reservoir ceiling on the fi rst radiograph. are shown in Figure 4. For complete µCT scans, all data sets were processed in the Octopus software package (Vlassenbroeck et al., 2007) and rendered into 3D by using VGStudioMax software (http:// Consequently, we only briefl y describe such zone was typically enclosed within an outward- www .volumegraphics .com). A digital elevation aspects here to contextualize novel observations dipping ring fault. Garnet sand layers within the model was then extracted from the fi nal 3D ren- revealed by µCT analysis, such as: (1) the effects deformation zone were slightly down-sagged dered model surface by using a LabView user- of downward-varying depletion zone geometry and their dips increased toward the fault sur- defi ned interface (http:// www .ni .com). This on collapse kinematics; (2) structural similari- face. The upper section of the overburden sub- enabled the calculation of the surface depres- ties and dissimilarities between the end-member sequently collapsed in discrete upward-propa- sion’s fi nal volume in ArcMap software (http:// dynamic collapse styles; and (3) the quantifi ed gating steps, as newer and progressively steeper www .esri .com/). volumetric evolution of the collapse. ring fault surfaces splayed from the older ring For each collapse scenario, we begin by fault bounding the lower roof section (see also RESULTS describing the collapse evolution as seen in the Burchardt and Walter, 2010). After formation of radiography sequences. We then present the a surface depression, the initially overhanging Here we present results from models rep- fi nal collapse structures as observed in full-3D ring fault scarp degraded by means of numerous resenting the two end-member collapse sce- µCT scans, and compare the structural out- failures of various sizes (see also Geshi et al., narios mentioned above: (1) near-continuous comes of each collapse scenario. Finally, we 2012). Consequently, the surface depression’s collapse into a gradually depleting fl uid body; examine the evolution of subsidence rates and diameter increased, and the retreating ring fault and (2) near-instantaneous collapse into a sub- collapse volumes during several representa- scarp steepened and became near-vertical to surface metastable cavity. For model param- tive near-continuous collapses, as derived from inward-inclined (e.g., Fig. 5). Along the trace of eter descriptions, refer to Table A1. In some quantitative radiograph analysis, and quantify the ring fault itself, progressive drag of garnet experiments, radiograph sequences showed how the fi nal deformation-related volume changes sand layers formed a tight footwall syncline. several small cavities formed in an upward- for both scenarios. The radiograph sequences in Figure 5 also migrating succession, similar to that observed show some previously unreported structural by Ruch et al. (2012). Consequently, these mod- Near-Continuous Collapse into a Gradually effects stemming from the initial depletion zone els showed a collapse scenario between the end Depleted Subsurface Body geometry. In the late stages of both models members. Radiographs taken at drainage onset CCT12-12 and CCT14-6, one or more centrally showed that metastable cavity formation at the This scenario is illustrated and described by located ring faults (F4 in Fig. 5A, F4 and F5 in lower T/D ratios occurred when GS bodies had the representative models CCT12-12 (T/D ~0.80), Fig. 5B) formed within the previously coher- a notably convex-upward top surface. This is in CCT14-5 (T/D ~1.2), and CCT14-6 (T/D ~1.2) ently subsiding column. These new faults all line with results of previous studies (e.g., Holo- (Table A1), as each shows aspects of interest par- dipped outward, but whereas the one in model han et al., 2011), as is the observation that cavity ticularly well. CCT12-12 had a normal slip sense, those in formation occurred in all cases with a combina- model CCT14-6 had reverse slip senses. The tion of highest cohesion and highest T/D ratio Results of Radiograph Sequences late-stage formation of these faults and their dif- (Table A1). As described in many previous works, early fering slip senses can be related to whether the Previous modeling studies (cited in the Intro- evolution of collapse involves the formation of a overburden column subsided into a downward- duction) have extensively documented the main conical deformation zone within the lower two- widening or downward-narrowing depletion geometric and kinematic features of collapse. thirds of the overburden (Fig. 5). This conical zone. The normal fault in CCT12-12 accommo-

6 Geological Society of America Bulletin, Month/Month 2014 Sinkholes, pit craters, and small calderas

A top

F3 F3 F2 F1 F2 Figure 5. Time-lapse radio- F1 graphs of models undergoing collapsing F4 gradual depletion-induced col- overburden

lapse. Dark and light gray values Model CCT12-12 represent respectively dense and reservoir / diapir less dense materials (see Kervyn min. 20 min. 60 min. 120 et al., 2010). The model surface and ring faults are shown by black dashed lines. (A) Model depression CCT12-12, with ratio of overburden thickness to syrup reservoir diameter (T/D) ~0.8. F4 Images were acquired respec- F4 F4 tively 20, 60, 100, 140, 180, and 220 min after initiation of depletion. Note the concave-upward min. 140 min. 180 min. 220 geometry of the reservoir roof, 1 cm allowing for the development of B top a secondary, outward-inclined, normal ring fault F4. (B) Model F3 F3 CCT14-6, with T/D ~1.2. Images were acquired respectively 2, F4 100, 300, 600, and 900 min after F1 F1 F2 initiation of depletion. Note the collapsing time for complete depletion here Model CCT14-6 overburden F2 was longer relative to CCT12-12 due to a higher ﬂ uid reservoir. (C) Temporal sequence of out- F5 lines of the collapsing overbur- reservoir / den column of model CCT14-6, diapir wetting displaying the three main pro- aureole cesses involved in expanding min. 2 min. 100 min. 300 the column: 1—lateral enlarge- ment; 2—downward subsidence C depression with density decrease, i.e., 2 “bulking”; 3—addition of material from failure of the surface 3 depression scarp. Note how the lateral inclusion of unaffected 1 brittle material, i.e., process 1, plays a major role in the ﬁ rst 100–200 min, but is very limited 50 min0

afterwards. 100 min0 F5 F5 2 300 min0 min. 600 min. 900 1 cm dated a horizontal extension of the column as it Results of 3D scans that collapses of the unstable overhanging subsided into a markedly downward-widening Figures 6 and 7 show the rendered 3D ring fault scarp, probably during the scanning GS body. Conversely, the new reverse faults in scans of models CCT12-12 and CCT14-5, process, further changed the shape and diam- CCT14-6 accommodated a horizontal contrac- the latter’s initial parameters and ﬁ nal struc- eter of the surface depression. In CCT12-12, a tion of the column as it progressed into a mark- ture being very similar to those of CCT14-6. secondary near-cylindrical intra-column col- edly downward-narrowing GS body. Vertical slices through these models indicate lapse structure (Fig. 6) formed immediately

Geological Society of America Bulletin, Month/Month 2014 7 Poppe et al.

Collapsed column Topographic (sagged layers) Wetting aureole margin Intra-column collapse Horizontal Slices Inﬁll

Ring Fault (buried) Ring Fault H1 H2 Ring Fault H3Collapsed column H4

H1 H2

Debris H3 fans

2.5 cm H4 Topographic margin

V4 V3 V2 3 cm V4 V1 Intra-column collapse structure

Collapsed column (sagged) Reservoir / diapir V3 remnants Ring Fault

es lic l S ca V2 rti Ve Ring Wetting Fault aureole Model CCT12-12 V1

Figure 6. Three-dimensionally scanned and rendered volume of model CCT12-12 with ratio of overburden thickness to golden syrup reservoir diameter (T/D) ~0.8, with horizontal and vertical cross-sections. Note that here, and in Figures 7 and 8, the dark and light gray values represent less dense and dense materials, respectively, i.e., the inverse of the radiograph gray scale. Note the intra-column collapse above the drainage opening in slice V4, due to post-collapse subsidence of the sand-and-plaster mix within the drainage tube.

above the drainage pipe at the very end of of previous analog studies: debris fans from e.g., Roche et al., 2000; Geshi et al., 2012; Ruch the simulation, as the GS withdrew slightly depression wall erosion covering the initial et al., 2012). below the plastic cylinder’s base. Also visible topographic surface; an overall hourglass shape Importantly, the slices through the 3D scans in each model are remnants of the initial GS from the combination of a funnel-shaped shal- also illustrate how the collapse geometry seen in reservoir and a ring-shaped wetting aureole low-level morphology and cone-shaped deeper- any plane of section can vary markedly depend- where some of the GS permeated locally into level structure; down-sagging of layers close to ing on the horizontal or vertical position of the SP mix. the collapse-bounding ring faults; and repeated that section. In particular, the further a vertical In general, the 3D collapse structures and stratigraphy stacks or the break-up of the over- section lies from the true center of the collapsed morphology in our models agree with those burden column into several distinct blocks (see, region, the more strongly exaggerated the col-

8 Geological Society of America Bulletin, Month/Month 2014 Sinkholes, pit craters, and small calderas

Topographic margin Collapsed column Wetting aureole Collapsed column (sagged) (sagged layers) Horizontal Slices Collapsed column

Ring fault Ring fault (buried) H1 H2Ring Fault H3 H4

Debris fans

Topographic margin H2 H3 Collapsed column 5 cm H4 (sagged) Topographic margin Ring V3 fault V3 Preserved garnet V2 sand strips V1

3 cm V2 Ring fault Reservoir / diapir es remnants lic l S Wetting ca aureole Wetting rti aureole Ve Model CCT14-5 V1

Figure 7. Three-dimensionally (3D) scanned and rendered volume of model CCT14-5, with ratio of overburden thickness to golden syrup reservoir diameter (T/D) ~1.2, with horizontal and vertical cross-sections. The collapse evolution and ﬁ nal structure is very similar to the one of model CCT14-6, of which no 3D scan is available (Table A1). Note the overall preserva- tion of sand-and-plaster mix–garnet sand stratiﬁ cation.

lapse’s hourglass geometry becomes and the of the column that occurs progressively through cavity formed above the block and grew down- more the collapse’s true width may be under- the course of subsidence. ward as the block subsided. The cavity remained estimated. stable until the end of GS depletion. In addition, the 3D scans show that the gray Near-Instantaneous Collapse into value of the subsided overburden column dif- a Metastable Cavity Results of 3D Scan fers markedly from that of the surrounding, Acceleration at the onset of rotation for 3D undeformed SP mix. This indicates a density This scenario is described by the representa- µCT scanning was insufﬁ cient to trigger col- contrast that, in the absence of mass transfer, tive model CCT14-2 (T/D ~1.25) (Table A1). lapse in this case, but shaking the model cylin- can be interpreted as arising from volumetric der only very slightly after scanning was suf- expansion (dilation) of grain packing within Results of Radiography Sequence ﬁ cient. Consequently, 3D scans of the model the overburden column (see also Kervyn et al., As in the cases of near-continuous collapse, could be made before (Fig. 8B) and after (Fig. 2010). The radiographs demonstrate that this collapse began with development of a coni- 8C) a “dynamically triggered” collapse of the difference in gray value, and hence volumetric cal deformation zone in the lower part of the cavity roof. expansion, develops from the onset of collapse overburden (Fig. 8A). However, the conical The pre-collapse 3D scan shows that the lower (e.g., Fig. 5A). Moreover, sequential tracings deformation zone developed into an overbur- part of this cavity coincided with the former of the column growth in model CCT14-6 (Fig. den block that detached from the overlying location of the GS body (Fig. 8B). The upper 5C) illustrate that the volumetric expansion brittle material and subsided coherently into the part of the cavity lies within the overburden, there is primarily a result of vertical extension depleting GS body. Consequently, a subsurface where upward propagation of collapse halted

Geological Society of America Bulletin, Month/Month 2014 9 Poppe et al.

The post-collapse 3D scan (Fig. 8C) exhibits A During depletion B Pre-collapse an overall collapse geometry that has a similar hourglass shape to that seen in the near-contin- Initial L4 uous collapses. Consequently, and although not shown here for brevity, the points made above Outline L3 on how the collapse geometry and dimensions of later L2 collapse in section view depend strongly on the plane of Initial depletion zone outline L1 section’s position with respect to the collapse center also pertain to the cases of near-instan- Cavity Peak of taneous collapse into a large cavity. In addition, Reservoir / roof the gray value of the collapsed column is again diapir block markedly different from that of the surrounding unaffected SP mix, and so indicates a collapse- Coherent roof block related volumetric expansion. Importantly, and although a remnant pre-collapse stratigraphy is Intermediate Reservoir / preserved within it, the upper part of the over- Wetting aureole (collapsed) diapir remnant burden column that collapsed en mass into the Peak of roof cavity is much more structurally disturbed on a block Cavity small scale (Fig. 8C) than in the near-continuous outline 5 cm collapses (compare with Fig. 7 in particular). V Coherent Quantitative Analysis of 4 cm roof block Near-Continuous Collapse C Post-collapse Vertical subsidence rates of garnet sand

Depression levels and the reservoir–SP mix interface were Final recorded for model CCT14-6 (Fig. 9A). The volumes of the GS body, collapsed SP mix column, and depression were also tracked through L4 time (Fig. 9B). The evolution of collapse veloc- Outline of Highly ity and volume in this and in several other ana- Peak of roof pre-collapse disrupted Cavity block cavity L3 roof lyzed models (e.g., CCT12-8, CCT12-12, and material L2 CCT14-4), whose results are not shown for brevity, are quite similar, and may be divided L1 into a minimum of three phases.

Wetting aureole Coherent roof block Phase 1

Model CCT14-2 (collapsed) Phase 1 (pre–surface collapse) is character- ized by an upward-propagating zone of elevated Figure 8. Evolution of collapse into a major subsurface metastable cavity in model subsidence velocity and rapid increase in col- CCT14-2. (A) Time-lapse radiographs at the beginning, halfway during, and after golden lapsed column volume. This refl ects the upward syrup depletion. A roof block detached above the reservoir ceiling along a bell-shaped propagation of the column-bounding ring rupture plane, and subsided coherently during depletion. Note in the fi nal radio graph fault(s) (Figs. 5A, 5B). Because deformation is how the wetting aureole also collapsed; thus, the roof above the cavity is self-supporting confi ned to the subsurface during this phase, the and not reliant on the wetting aureole for stability. (B) Central vertical slice of the three- model top surfaces remained at a constant level, dimensionally (3D) scanned and rendered volume of the metastable cavity prior to trig- and there were hence no surface depressions. gered collapse. The apex of the cavity lies about halfway between the initial reservoir ceiling and the model surface. (C) Central vertical slice of the 3D scanned and rendered Phase 2 volume of the overburden collapsed into the cavity space. The coherent roof block is still Phase 2 (post–surface collapse) is marked observed in the bottom part of the column, and the layering of the collapsed roof is highly by initially high subsidence rates down the disrupted if compared to results from more gradual collapse models (Figs. 6 and 7). whole column, with periodic accelerations affecting mainly its upper part. The collapsed overburden column continues to grow, and about halfway between the reservoir ceiling and un affected SP mix. The cavity’s stability is there- depression volume begins to increase. These the surface. Radiographs illustrate that model fore a consequence of neither an arched reservoir changes refl ect the rapid collapse of the upper- CCT14-2 had an initially fl at-topped GS body. geometry nor any increase in cohesion caused most part of the overburden and the formation Furthermore, both the radiographs and the 3D by the local wetting. Instead, the cavity likely of a depression at the surface. With time, sub- scan show clearly that a ~1–2-mm-thick GS– formed spontaneously, and its roof remained sidence velocities decrease along the whole SP mix wetting aureole formed initially around self-supporting under the appropriate combina- column length, although sporadic accelerations the GS body itself, and later detached from the tion of high T/D ratio and high cohesion. are still seen at different levels. Depression and

10 Geological Society of America Bulletin, Month/Month 2014 Sinkholes, pit craters, and small calderas

The fi nal depression volumes are substantially smaller than their related depletion vol- A Phase 1 Phase 2 Phase 3 umes (Fig. 9B). For CCT12-12, the fi nal “pla- Vertical 0.20 teau” value of the estimated depression volume subsidence is within error of the fi nal 3D-defi ned depression Topographical surfacerate 0.10 volume of 1180 ± 20 mm3, and thus our volume –10 (mm/min) estimates on radiographs may be considered as 0.00 reliable within error. Table 2 reports the quantifi ed volumes for six representative models. In all models, differences –20 between depleted GS volumes and fi nal surface depression volumes are on average 39%, with a minimum of 28% ± 9% and a maximum of –30 51% ± 7%. On the other hand, fi nal overburden Reservoir ceiling column volumes are substantially greater than Vertical displacement (mm) displacement Vertical the respective initial volumes. Final column volume values, determined at the last radio- –40 graph, are on average 23% larger than the ini- B tial volumes of the affected overburden before subsidence, with a minimum of 10% ± 10% and 3 14.10 a maximum of 40% ± 13%. These effects are illustrated by model CCT14-6, where the fi nal depression volume is 30% ± 9% smaller than Voverburden,initial 3 the depleted volume and the fi nal affected over- 10.10 V ovb burden column increased 17% ± 11% in volume Vres compared to the initial volume of the affected Vdep overburden before subsidence (Fig. 9B). The 3 surface depression volume being substantially

Volume (mm³) Volume 6.10 less than the depletion volume is thus accounted for by volumetric expansion of the column.

3 2.10 DISCUSSION

0 100 300 500 700 900 The Use of µCT for Imaging Analog Stoping Time (min) Subsidence end Depletion-Induced Collapses Figure 9. Quantifi ed subsidence rates and volume evolution of model CCT14-6 (ratio of overburden thickness to golden syrup reservoir A key advantage of µCT is that it is non- diameter (T/D) ~1.2), representing near-continuous collapse into a destructive (Schreurs et al., 2003; Cnudde and gradually depleting body. The three designated collapse stages are Boone, 2013, and references therein), and so discussed in the text. (A) Vertical subsidence rate interpolated from 3D model scans can be sliced in any direction measurements of the vertical positions of fi ve garnet sand layers and revisited at any time. The 3D geometry of and the reservoir ceiling on 2.5-min-spaced radiographs. (B) vol- fault surfaces can hence be assessed in a spa- ume changes for the depression (“dep,” blue), overburden (“ovb,” tially complete manner, in contrast to extrapo- green) and reservoir (“res,” orange), as calculated from 5-min- lation between multiple but spatially restricted spaced radiographs. Errors are designated by shaded areas. No planes of cross-section when sectioning wetted fi nal topographic depression volume could be measured as a three- models. The µCT shows clearly how the outcrop dimensional computed X-ray microtomography scan failed techni- pattern of a collapse structure, in map view or in cally. Note the ~17% difference between initial and fi nal affected cross-section, can vary dramatically depending overburden volume, refl ecting brittle material volumetric expan- on the depth and lateral position of the plane of sion (i.e., dilation or bulking) during collapse. section (Figs. 6 and 7). This is because collapse is accommodated by a system of annular faults whose geometry is highly variable in three column volumetric growth trends seem more tual tapering off and fi nal cessation of growth of dimensions. Consequently, structural or topo- closely linked to depletion rate during this sec- the depression and column, while the GS deple- graphic dimensions given for ancient eroded ond phase (Fig. 9B). tion also tapers off (Fig. 9B). In this last phase, sinkholes, pit craters, or small calderas must be the central part of the subsiding overburden col- treated with caution. Phase 3 umn has met the base of the GS body, ending A second advantage is that radiographs Phase 3 (post–surface settling) is marked by through-going subsidence of the column’s top enable a check on the pre-collapse geometry very low to no central subsidence and by even- surface and growth of the depression. of a fl uid depletion zone, which can often devi-

Geological Society of America Bulletin, Month/Month 2014 11 Poppe et al.

ate from that planned (see also Ge and Jackson, Failure of the hanging wall, either by normal 1998). Here, radiographs reveal that differing faulting (e.g., Martí et al., 1994; Roche et al.,

8 late-stage structures formed within the column 2000) or by mass wasting (e.g., Roche et al., ± (%) 50 ± 18 51 ± 7 30 ± 9 33 41 ± 8 28 ± 9 can be related to whether the depletion zone 2001; Geshi et al., 2012; this study), ultimately depletion Volumetric Volumetric mismatch of (i.e., magma reservoir or salt diapir) is markedly produces an inward-inclined annular scarp at

depression versus downward widening or downward narrowing the surface (Figs. 1 and 2). Our study further (Fig. 5), rather than ideally cylindrical. Such shows that these morphological and structural structural effects are undocumented in other features develop in both end-member scenarios modeling studies, but could manifest themselves of: (1) near-continuous collapse into a slowly

(mm³) in nature under similar geometrical conditions. depleting body; and (2) near-instantaneous col- depletion Volumetric Volumetric

mismatch of Thirdly, radiograph sequences provide a lapse into a large, metastable cavity.

depression versus high-temporal-resolution “2.5D” insight into Subsurface cavities are known or inferred to subsurface model development as generated in have developed prior to the formation of many a true 3D space. It is thereby unnecessary either sinkholes, pit craters, and small calderas. Exam- to stop and cross-section multiple models run to ples in karst terrains include natural caves and

(mm³) different deformation stages (e.g., Roche et al., caverns and related sinkholes in the Kunguras- reservoir Final volume depleted from 2000) or to construct a model against a glass kaya cave complex, Russia (Andrejchuk and pane with attendant edge effects (e.g., Geyer Klimchouk, 2002), in the Delaware Basin gyp- et al., 2006; Burchardt and Walter, 2010; Ruch sum deposits of Texas and New Mexico (John- et al., 2012). A limitation of radiograph images son, 2005, and references therein), and in and is that the central collapsed zone is overprinted around the city of Hamburg, Germany (Dahm (mm³) by the projection of unaffected material located et al., 2011). There are also numerous examples depression 1180 ± 201180 2348 ± 400 ± 420 1168 3333 ± 167 6793 ± 340 3460 ± 507 4793 ± 240 6823 ± 341 ± 581 2030 4910 ± 246 7287 ± 364 2377 ± 610 6185 ± 310 8574 ± 429 2389 ± 739 4460 ± 223 7570 ± 379 ± 602 3110

Final volume of between the source and the detector. This study of collapses into cavities formed by manmade hence shows how such µCT imagery, even if salt dissolution, such as the 1974 Cargill col- limited scanning time and costs require careful lapse in Kansas (Fig. 1C, 1D) and the 1980 beforehand planning, can be used for quantita- Wink Sink collapse in Texas (Johnson, 1989). tive analyses of analog model evolution, a main Examples in volcanic terrains include cavities (%) 29 ± 11 17 ± 11 29 ± 11 40 ± 13 10 ± 10 ± area of technical development in recent years with arched ceilings exposed in pit crater chains of affected of affected overburden (e.g., Burchardt and Walter, 2010; Ruch et al., on Hawaii (Okubo and Martel, 1998) and in the Volumetric growth Volumetric 2012; Holohan et al., 2013). These analyses are scarp of the 2002 pit crater collapse at Piton de discussed further below. la Fournaise (Carter et al., 2007, their ﬁ gure 9). At Miyakejima volcano (Figs. 2C, 2D), seismic, gravity, and magnetic data indicated upward Near-Continuous versus

(mm³) migration of a steam-ﬁ lled cavity toward the Near-Instantaneous Collapse: of affected of affected overburden volcano summit over the course of ~12 days Morphological and Structural Features Volumetric growth Volumetric before a caldera developed at surface (Geshi et al., 2002, and references therein). The analog models shown here reproduce Previous analog or numerical collapse stud- many of the main structural and morphological ies that produced cavities (e.g., Roche et al., features observed in or inferred for the collapse 2001; Holohan et al., 2011; Ruch et al., 2012) (mm³) TABLE 2. QUANTIFIED AFFECTED OVERBURDEN COLUMN VOLUMES 2. QUANTIFIED TABLE of affected of affected overburden of sinkholes, pit craters, and small calderas have simulated an intermediate behavior to Final volume in nature. Structures include steeply dipping the abovementioned end members, whereby normal or reverse ring faults, ephemeral cavi- several, relatively small “metastable” cavities ties, and sagged strata. Morphological features open and close at the top of the upward-grow- include overhanging to cliffed depression ing collapse column. The collapsed overburden boundaries, intra-depression debris fans, and an column in these cases typically comprises an (mm³)

of affected of affected overall hourglass geometry from a combination assemblage of structurally disrupted blocks overburden Initial volume of cone-like and funnel-like shapes of the lower (e.g., Roche et al., 2001). This intermediate and upper sections of the collapsed overburden behavior was also observed in some of our mod- column (e.g., Figs. 1A, 2A, and 2B). els with relatively lower cohesions, and is prob- As shown by previous studies, the conical ably reﬂ ective of natural collapses such as that lower section geometry develops during the pro- at Miyakejima. gressive upward failure of the overburden along Complementary to this, our highest-cohesion multiple conical ring fault splays, with the even- models also include the end member of near- tual establishment of a single ring fault that cuts instantaneous collapse of most of the roof into a through to the surface (see also Roche et al., single, relatively large, subsurface cavity. Here, 2000; Ruch et al., 2012; Geshi et al., 2012). coherent detachment of the lowermost part of The funnel-like upper section geometry the overburden gave rise to a stable compressive develops as the hanging wall of the conical ring arch-like geometry in the remainder of the over- CCT14-6 Near-continuous 12,368 ± 618 ± 725 14,493 ± 1343 2125 CCT14-2 Near-instantaneous 13,784 ± 689 17,715 ± 886 3931 ± 1575 Model name Collapse mode CCT14-4 Near-continuous 14,915 ± 748 19,190 ± 960 4275 ± 1708 CCT12-8CCT12-12 Near-continuous Near-continuous 15,059 ± 753 3138 ± 200 16,618 ± 831 4405 ± 200 1559 ± 1584 1267 ± 400 CCT14-5 Near-continuousfault 16,252 ± 813 system 17,904 ± 895 becomes 1652 ± 1708 gravitationally unstable. burden, such that further upward growth of the

12 Geological Society of America Bulletin, Month/Month 2014 Sinkholes, pit craters, and small calderas column was prevented. The cavity formed above from analysis of related very-long-period (VLP) In addition, Geshi et al. (2012, and references the detached block instead grew to a large size seismic signals by Kumagai et al. (2001). therein) reported values for several other (explo- relative to the remaining overburden. Collapse The volumetric growth of the collapse- sive) caldera-forming eruptions that exhibited a into the cavity was ultimately “dynamically trig- affected overburden over the three phases takes similar apparent volume mismatch. As shown gered”; a similar mechanism is suspected at sev- place via three processes. Firstly, material is by our models, the process of bulking could, eral sinkholes in nature (Walters, 1978; Dahm added to the column as deformation propagates perhaps in combination with magma compress- et al., 2011; Jousset and Rohmer, 2012). upward and laterally within the overburden. As ibility, help explain this longstanding “volume The structure of this end-member collapse seen in the temporal evolution of the outline of mismatch” problem in volcanic terrains, par- differs slightly from the intermediate scenarios the overburden column in Figure 5C, lateral col- ticularly for small-scale collapses (depression seen in the previous studies cited above. On a umn growth diminishes rapidly and comes to a diameter <~2 km). large scale, the collapsed material formerly halt relatively early in phase 2. Secondly, mate- overlying the cavity is seemingly coherent, in rial within the overburden column undergoes a CONCLUSIONS that stratigraphic order is preserved. On a small volumetric expansion, as evidenced by lighter scale, however, the material is highly disrupted. gray values in it than in the surrounding SP mix. This study illustrates a fi rst use of combined These observations are characteristic of other Thirdly, material is added as debris derived from “2.5D” and 3D computed X-ray microtomog- gravity-driven collapse processes that involve the failure of ring fault scarps once the collapse raphy (µCT) techniques to quantitatively study the fragmentation of the collapsing mate- reaches the surface. The synchronous occur- analog models of small scale (<2 km diameter), rial upon its rapid initial acceleration into an rence of the fi rst and second processes explains gravity-driven collapses, induced by deple- unconfi ned region, such as rockslide avalanches the rapid increase in column volume at the onset tion of a subsurface body. Two end-member (Glicken, 1996; Shea and van Wyk de Vries, of collapse in the subsurface (Figs. 5 and 9). scenarios were actively investigated: (1) near- 2008; Thompson et al., 2010). The more gradual increase of column volume continuous collapse into a gradually depleting thereafter is mainly derived from a combination subsurface body, and (2) near-instantaneous col- Evolution of Velocity and Volume of the second and third processes, of which the lapse into a subsurface cavity. The main fi ndings During Collapse second (volumetric expansion) is more domi- of this work are as follows: nant (Fig. 5C). 1. Time-lapse radiographs show that late-stage Vertical subsidence rates calculated at dis- The volumetric expansion of collapsed over- structures formed during near-continuous col- crete levels inside the collapsing model overbur- burden is well known in studies of mining lapse of an overburden column into a slowly den column indicate that even within an appar- collapse (e.g., Whittaker and Reddish, 1989) depleting subsurface body depend on downward ently coherent column, there may be spatially and sinkhole formation (e.g., Andrejchuk and changes in the body’s geometry. Within the sub- and temporally distinct slip events during model Klimchouk, 2002). This is termed “bulking,” siding overburden column, late-stage outward- subsidence (Fig. 9A). This observation in a fully and is particularly prevalent in overburden rock inclined normal faults may form if the body 3D medium validates the assumption that simi- masses of high cohesion. The effect of bulking widens downward; late-stage outward-inclined lar patterns obtained previously in 2D experi- is seen geophysically as reduced seismic veloci- reverse faults may form if the body narrows ments against a glass pane (Ruch et al., 2012) ties (e.g., Gendzwill and Hajnal, 1971) and downward. are only minimally affected by related edge potentially also as a negative gravity anomaly 2. 3D X-ray µCT scans of models represent- effects. In agreement with Ruch et al. (2012), (e.g., Paine et al., 2012). Our model results ing both end-member scenarios reveal that the our models suggest that such discrete velocity indicate that bulking occurs not only during the fi nal collapse morphology and geometry of changes could be a cause of collapse-related initial upward propagation of the overburden both end members are quite similar. The main earthquakes in nature (cf. Dahm et al., 2011; deformation (e.g., Andrejchuk and Klimchouk, difference is a greater small-scale disruption Shuler et al., 2013). Future analysis and model- 2002) but may also continue, albeit to a lesser of the overburden during near-instantaneous ing of collapse-related earthquakes could hence extent, as an overburden column progressively collapse into a large cavity, probably resulting include non-uniform displacements along a subsides. from large acceleration and free fall upon col- down-going overburden column. Bulking of the collapse column compen- lapse. The susceptibility of both volcanic and Estimations of volume evolution during sates for a substantial portion of the subsurface evaporite terrains to such cavity formation and model collapses reveal that the depletion zone, body’s volumetric depletion. This volumetric near-instantaneous collapse is to be considered affected overburden column, and surface compensation, which reached 10%–40% in our for hazard-risk assessment purposes. depression show partly different, but also partly models, leads to a depression volume at sur- 3. Subsidence velocity analysis of the time- mirroring, trends of volumetric change in the face that is 28%–51% smaller than the depleted lapse radiographs reveals subtle differential post–surface collapse phases (Fig. 9B). The volume at depth. A similar observation is often movements of discrete sections of even appar- depletion zone undergoes near-linear or power- made for natural pit crater and small caldera ently coherently collapsing overburden col- function trends of volume decrease, while the collapses, albeit with uncertainties concerning umns formed in 3D space. This supports similar overburden column and surface depression con- intrusive magma volumes at depth. At Piton de results from a recent study made in quasi-2D versely undergo near-linear or power-function la Fournaise in 2007, for example, 1.0–1.4 × 108 space (Ruch et al., 2012). Future modeling of trends of volume increase. m3 in dense rock equivalent (DRE) of magma collapse-related earthquake sequences should A similar near-linear growth of depression was erupted but the fi nal Dolomieu pit crater hence consider non-uniform displacements volume was observed during the 2000 collapse volume was only 9.6 × 106 m3 (Michon et al., along a down-going column. of Miyakejima (see Geshi et al., 2002, their fi g- 2007). At Katmai, a slightly larger caldera of 4. The density reduction in the collapsing ure 4d). Our models indicate that this relates to ~2.5 km by 4 km, 13.5 km3 of DRE volume overburden occurs from its volumetric expan- a near-linear volumetric depletion of the under- of magma was erupted, but the caldera volume sion, which accounted for 10%–40% of lying reservoir, behavior deduced independently was only 8 km3 (Hildreth and Fierstein, 2000). expanded brittle material volume in our models.

Geological Society of America Bulletin, Month/Month 2014 13 Poppe et al.

This phenomenon, termed “bulking” in studies APPENDIX 2. TECHNICAL SPECIFICATIONS of the object of interest in a radiography image. It is of mining and sinkhole collapses, occurs not OF THE X-RAY MICROTOMOGRAPHY acknowledged that the assumption in this procedure SCANNING SETUP that all structural entities are axisymmetric volumes only at the onset of collapse but also during pro- may lead to signifi cant error in some cases. The edge gressive subsidence of the overburden column. µCT imaging of the models was carried out at of the area of each entity was tracked through each Final surface depression volumes in our mod- the Ghent University Centre for X-ray Tomography radiograph in a sequence by defi ning a polygon, the (UGCT; http:// www .ugct .ugent .be; Masschaele et al., node coordinates of which were recorded. After defi n- els were consequently 28%–51% lower than 2007) with the following technical specifi cations. the volumes depleted from the subsurface fl uid ing the central gravity axis of each polygon for each The beam source was a high-power directional tube object of interest (e.g., depression or overburden col- reservoir. For small-scale (<2 km diameter) head, used at a voltage of 150 kV and a tube current umn) in one model, polygons were split into left and caldera and pit crater collapses, this volumet- of 400 µA target current. This resulted in an effective right half polygons. The area A of the half polygon (in ric increase of the overburden column may— target power of 60 W. To avoid beam hardening ef- pixels) was then calculated from the so-called “Shoe- fects, 3 mm Al fi ltered the X-ray beam. A PerkinElmer lace” or “Gauss’s area” formula: at least partially—play a role in producing the XRD 1620 CN3 CS a-Si fl at panel detector with CsI long-standing “volume mismatch” observed at screen was placed vertically behind the models, al- = 1 n−1 + − n−1 − A ∑ xi yi+1 xn y1 ∑ xi+1 x1 yn . (1) several volcanoes, whereby the volume depleted lowing an image width of 2048 pixels of 200 × 2 i=1 i=1 2 from the subsurface body exceeds the volume 200 µm . While the model rotated, 1200 projection The x-coordinate of the centroid of the half polygon images were acquired, where each projection was one C is then defi ned by: of the depression formed at surface, or Vdepletion frame with 2000 ms exposure time. A magnifi cation x n−1 > Vdepression. of 4.74 was obtained through a source-to-object dis- = ∑ (x + x + )(x y + + x + y ) Cx i=1 i i 1 i i 1 i 1 i , (2) tance of 282 mm and a source-to-detector distance of 6A ACKNOWLEDGMENTS 1338 mm. The detector was used in binning 2 mode, where x and y represent the respective x- and y- which means that four pixels are averaged out in one i i This work is based upon an Master of Science coordinates of each half-polygon node. The volume V pixel, dividing the amount of pixels in the height and thesis conducted by SP at Ghent University. EPH described by revolving the half polygon about the axis in the width by two. Such a binning method comes acknowledges support from GFZ-Potsdam and from is defi ned by the Guldinus theorem as V = A × 2Π × at the expense of the spatial resolution, but attenuates a Marie Curie International Mobility Fellowship co- d, where d is the horizontal distance between centroid noise. The corresponding voxel size is 80–84 µm, funded by Marie Curie Action and the Irish Research and revolving axis: d = Cx – Xaxis, where the latter is which yields a much better resolution than in medical Council. EP acknowledges the Special Research the revolving axis’s x-coordinate. Finally, the two re- CT scanners. For the CCT14 models, a Varian Paxscan Fund of Ghent University (BOF) for fi nancial support sulting half-polygon volumes (in voxels) for each time a-Si fl at panel detector with CsI screen was placed (GOA01GO1008). MK acknowledges the support step were averaged and converted to volumetric units horizontally behind the models, allowing image di- of the Flemish Fund for Scientifi c Research (FWO- by using the voxel size specifi c to each model. mensions of 2000 × 1600 pixels of 127 × 127 µm2. A Flanders) for developing the volcano analog lab at magnifi cation of 2.30, through a source-to-object dis- VUB. Pieter Vanderniepen and Matthieu Boone and REFERENCES CITED tance of 375.77 mm and source-to-detector distance of the entire UGCT team are greatly acknowledged 862.8 mm, combined with binning 2 mode, yielded a for technical support, scanning, and initial data set Acocella, V., 2007, Understanding caldera structure and de- corresponding voxel size of 110–111 µm. reconstruction. We thank P. Jacobs and A. Delcamp velopment: An overview of analogue models compared to natural calderas. Earth-Science Reviews, v. 85, for commenting on the original work and the devel- APPENDIX 3. METHOD FOR VOLUME opment of our analog models, and for enthusiastic p. 125–160, doi: 10 .1016 /j .earscirev .2007 .08 .004 . ESTIMATION FROM RADIOGRAPHS Andrejchuk, V., and Klimchouk, A., 2002, Mechanisms moral support. Reviews of the original manuscript by of karst breakdown formation in the gypsum karst of Shan de Silva, Olivier Roche, Nobuo Geshi, and two Syn-deformation volume changes of specifi c enti- the fore-Ural region, Russia (from observations in the anonymous reviewers helped to considerably improve ties could be estimated through an axisymmetric Kungurskaja Cave). International Journal of Speleol- the fi nal version of this paper. revolution of a half polygon defi ned by the outline ogy, v. 31, p. 89–114, doi: 10 .5038 /1827 -806X .31 .1 .5 .

APPENDIX 1.

TABLE A1. DESCRIPTION OF THE EXPERIMENTAL SERIES Brittle overburden Brittle GS reservoir GS reservoir Roof τ thickness, T cohesion, 0 height diameter, D aspect Model name (cm) (Pa) (cm) (cm) ratio, ~T/D Roof shape Collapse mode† Comments§ CCT12-1 2.5 ~180 2.0 3.0 0.8 Curved Near-instantaneous No radiograph series, no 3D scan CCT12-2 1.5 ~180 2.0 3.0 0.5 Curved Near-instantaneous No time-lapse radiographs CCT12-3 2.0 ~180 2.0 3.0 0.65 Horizontal Near-continuous No time-lapse radiographs CCT12-4 2.5 ~180 1.9 2.0 1.25 Curved Near-instantaneous No time-lapse radiographs CCT12-5 1.5 ~180 1.5 2.6 0.6 Horizontal Near-continuous No time-lapse radiographs CCT12-6 1.5 ~180 2.0 2.0 0.75 Horizontal Near-continuous No time-lapse radiographs CCT12-7 2.5 ~180 1.5 3.0 0.8 Horizontal Near-continuous No time-lapse radiographs CCT12-8 2.8 ~180 2.2 2.4 1.2 Gently curved Near-continuous – CCT12-11 1.5 ~180 0.9 2.2 0.7 Horizontal Near-continuous No time-lapse radiographs, no 3D scan CCT12-12 1.6 ~180 0.9 2.0 0.8 Curved Near-continuous – CCT14-1 3.4 ~300 2.0 2.7 1.25 Horizontal Near-instantaneous Radiographs only fi rst 45 min CCT14-2 3.1 ~300 2.0 2.5 1.25 Horizontal Near-instantaneous Radiographs only fi rst 75 min CCT14-3 2.7 ~300 2.0 2.5 1.1 Gently curved Near-instantaneous No 3D scan CCT14-4 3.0 ~180 2.0 2.5 1.2 Horizontal Near-continuous – CCT14-5 3.0 ~180 1.8 2.5 1.2 Horizontal Near-continuous – CCT14-6 2.6 ~180 1.9 2.15 1.2 Horizontal Near-continuous No 3D scan Note: Tests or failed models are not included; radiographs were acquired systematically from CCT12-8 onward, but the X-ray source sometimes stopped in mid-experiment due to unidentified technical reasons. GS—golden syrup; 3D—three-dimensional. †Near-instantaneous collapse into a metastable subsurface cavity versus near-continuous collapse through to the surface. §An initial and fi nal radiograph were acquired in most cases, even for models for which no time-lapse series was available.

14 Geological Society of America Bulletin, Month/Month 2014 Sinkholes, pit craters, and small calderas

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16 Geological Society of America Bulletin, Month/Month 2014