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The role of pre-existing tectonic structures and magma chamber shapeon the geometry of resurgent blocks: Analogue models

Enrica Marotta, Sandro de Vita ⁎Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Napoli Osservatorio Vesuviano, via Diocleziano, 328-80124 Napoli, Italy

a b s t r a c ta r t i c l e i n f o

Article history:Received 6 September 2013Accepted 24 December 2013Available online 3 January 2014

Keywords:Analogue modelCollapse calderaResurgenceMagma chamberExtensional tectonics

A set of analogue models has been carried out to understand the role of an asymmetric magma chamber on theresurgence-related deformation of a previously deformed crustal sector. The results are then compared withthose of similar experiments, previously performed using a symmetric magma chamber. Two lines of experi-ments were performed to simulate resurgence in an area with a simple graben-like structure and resurgencein a caldera that collapsed within the previously generated graben-like structure. On the basis of commonlyaccepted scaling laws, we used dry-quartz sand to simulate the brittle behaviour of the crust and Newtoniansilicone to simulate the ductile behaviour of the intruding magma. An asymmetric shape of themagma chamberwas simulated bymoulding the upper surface of the silicone. The resulting empty spacewas thenfilledwith sand.The results of the asymmetric-resurgence experiments are similar to those obtained with symmetrically shapedsilicone. In the sample with a simple graben-like structure, resurgence occurs through the formation of a discretenumber of differentially displaced blocks. The most uplifted portion of the deformed depression floor is affectedby newly formed, high-angle, inward-dipping reverse ring-faults. The least uplifted portion of the caldera is af-fected by normal faults with similar orientation, either newly formed or resulting from reactivation of the pre-existing graben faults. This asymmetric block resurgence is also observed in experiments performed with a pre-vious caldera collapse. In this case, the caldera-collapse-related reverse ring-fault is completely erased along theshortened side, and enhances the effect of the extensional faults on the opposite side, so facilitating the intrusionof the silicone. The most uplifted sector, due to an asymmetrically shaped intrusion, is always in correspondenceof the thickest overburden. These results suggest that the stress field induced by resurgence is likely dictated bythe geometry of the intruding magma body, and the related deformation is partially controlled by pre-existingtectonic and/or volcano-tectonic structures.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Caldera collapse and resurgence are quite common phenomena, rec-ognized worldwide and usually interpreted as generated by regionaltumescence, major eruption, caldera collapse and intracaldera resurgentdoming, which is commonly related to inflation–deflation processesin magma reservoirs (Smith and Bailey, 1968; Henry and Price, 1984;Lipman, 1984, 1997; Newhall and Dzurisin, 1988; Orsi et al., 1996,1999a; Di Vito et al., 1999).

In the past few decades, analoguemodelling has been carried out bymany authors, using variable methods, to investigate caldera collapseand resurgence mechanisms and structures (Withjack and Scheiner,1982; Komuro et al., 1984; Komuro, 1987; Marti et al., 1994; Merleand Vendeville, 1995; Roman-Berdiel et al., 1995; Benn et al., 1998;Kennedy et al., 1999; Acocella et al., 2000a, 2001; Roche et al., 2000;Walter and Troll, 2001; Troll et al., 2002). However, after the pioneeringwork of Withjack and Scheiner (1982), almost all these authors only

modelled the effects of the near-field stress induced by the intrusion,and did not consider the possible role of a far-field (i.e. regional) stress,in terms of pre-existing regional structures (inherited strain), whichmay influence the propagation of the stresses or also be reactivated dur-ing collapse and resurgence, or in terms of direct control (simultaneousstress) on the geometry of collapse calderas and resurgence. Althoughmost calderas are located in extensional tectonic settings, more recentexperiments tried to simulate collapse and resurgence in a crustal sectorwith both an inherited extensional or compressional strain, responsiblefor the pre-existence of regional structures (Acocella et al., 2004;Holohan et al., 2005). A very few analoguemodels have been performedin order to investigate the role of magma chamber geometry on thestructure of collapse calderas (Acocella et al., 2004; Holohan et al.,2008).

The most relevant results of these studies suggest that high-anglereverse faults border calderas and resurgent areas, whereas normalfaults form subsequently as a result of gravitational readjustment(Acocella et al., 2000a, and references therein). Resurgence is theuplifting of a portion of a caldera floor, due to the injection of newmagma into the system. It may form asymmetric resurgent blocks

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⁎ Corresponding author. Fax: +39 0816108359.E-mail address: sandro.devita@ov.ingv.it (S. de Vita).

0377-0273/$ – see front matter © 2014 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jvolgeores.2013.12.005

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(Orsi et al., 1991; Acocella and Funiciello, 1999) or domes (Smith andBailey, 1968; Bailey et al., 1976; Lipman, 1984; Self et al., 1986) depend-ing on the thickness/width (T/W) ratio of the crust overlying themagma chamber: resurgent blocks form for T/W ~ 1, whereas domesform for T/W ~ 0.4 (Acocella et al., 2001). The elliptical shape of calderasand resurgent blocks may develop even with circular magma chamber,and is the result of the interplay between newly formed structures andpartial or total reactivation of pre-existing faults. Moreover, the pres-ence of previously formed extensional structures, strongly influencesthe geometry of the resurgent block and the kinematics of resurgence,which occurs through the formation of a discrete number of differen-tially displaced blocks, the most uplifted of which is bordered, alongone side, by inward dipping reverse faults. Normal faults with similarorientations form on the opposite side together with the reactivationof one or more pre-existing faults (Acocella et al., 2004).

Here we report the results of a new set of analogue models thatideally represent the continuation of the experiments performed byAcocella et al. (2004). This modelling has been carried out in order tosimulate resurgence in an extensional setting, with different configura-tions of themagma chamber top surface, aimed at better understandingthe effects of different magma chamber geometries on the structure ofthe resurgent block. This is the first attempt to reproduce the local stressfield induced by the asymmetric intrusion ofmagma at shallowdepth ina strongly fractured crustal sector (both affected or not by previouscaldera collapse), which ultimately can account for the differentialdisplacement of blocks in the resurgent portion of a caldera and the dis-tribution of volcanic vents at surface (e.g. Ischia, Pantelleria and CampiFlegrei calderas in Italy; Orsi et al., 1991, 1996, 1999a; Di Vito et al.,1999; de Vita et al., 2010).

According to scaling laws (Appendix A), dry-quartz sand andNewtonian silicone putty have been used as analogue materials to sim-ulate the brittle behaviour of the Earth's crust and the ductile behaviourof magma, respectively (Acocella et al., 2000a, 2001, 2004). We com-pared our results with those obtained (using the same materials andsimilar methods) by previous experiments performed to simulate cal-dera resurgence in a non-deformed crustal sector with both symmetric(Acocella et al., 2000a) and asymmetric (Acocella et al., 2001) intrudingmagma body, and in a previously deformed crustal sector with asymmetric intruding magma body (Acocella et al., 2004). Moreover,we compared our experimental results with available data on naturalresurgent calderas.

2. Experimental equipment and procedure

Following Acocella et al. (2004), the experimental equipmentincludes two superimposed machines used to simulate extension andcollapse or resurgence in a stratified sand-pack. Extension is controlledby a mobile plate that slides at a constant velocity along the table sur-face. Collapse or resurgence are generated by the downward or upwardmovement of a piston accommodated inside a silicone-filled cylinder(Fig. 1).

The upper surface of the silicone in the cylinder was hand mouldedto simulate an asymmetric intrusion starting from one side of themagma chamber (Fig. 2a). The resulting empty space above the siliconewas filled with sand up to the table surface (Fig. 2b). Two different setsof experiments were performed, starting from two different geometri-cal configurations of the magma chamber, which generated an asym-metric strain field in the overlying sand-pack. In the first configuration

Fig. 1. Sketch of the experimental equipment. The first component (Acocella et al., 2000b and references therein), includes a fewmm-thick plate that slides at a constant speed upon thesurface of a table, in which a hole connects to the second part. The sliding plate is fixed to a vertical wall, which is in turn connected to an engine through an endless screw. This plate hasbeen suitably placed upon the second component of the equipment, used for simulating collapse and/or resurgence (Acocella et al., 2000a, 2001), which consists of a piston, accommo-dated inside a silicone-filled cylinder, whose nozzle lies underneath the hole in the Table. A constant diameter D = 5 cm of the nozzle has been imposed in our experiments. The pistonis connected to a second engine, which can be pulled down to simulate collapse, or pushed up to simulate resurgence. A sand model simulating the brittle crust, was built partly on thesliding plate and partly on the table. The thickness of the sand-pack (T) was fixed at 5 cm for all the experiments on the basis of the results of previous experiments (Acocella et al., 2000a,2001, 2004). These experiments showed that the deformation pattern induced by collapse and/or resurgence in a previously deformed sand-pack, with a T value between 3 and 7 cm, isunrelated to the overburden thickness but depends on both the amount of extension and position of the extensional faults, relative to the caldera and/or resurgence faults. D = nozzlediameter; T = sand-pack thickness; VD = velocity discontinuity.

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(Fig. 3a), the upper surface of the silicone is more elevated along theside of the nozzle toward which the sliding plate shifts; as a simplifica-tion this geometry will be called left-asymmetric (l-a). In the secondconfiguration, the upper surface of the silicone is more elevated alongthe opposite side of the nozzle (Fig. 3b), and the resulting geometrywill be called right-asymmetric (r-a). For one experiment, the siliconehad a completely flat surface in order to simulate a radial symmetry(r-s) of the magma chamber surface (Fig. 3c), as in the case of earlieranalogue modelling (Acocella et al., 2004).

A total of eight experiments were carried out, imposing variable ini-tial and ongoing conditions and aimed at investigating variable aspectsof resurgence-induced deformation (Table 1). Six of these (RIS 1, 2, 3, 4,5 and 7)were designed to simulate resurgence induced by an asymmet-rical intruding body in a previously deformedmedium, subject to a var-iable amount of extension. One experiment (RIS 8) was carried out inorder to integrate similar previous experiments (Acocella et al., 2004),in which extension was followed by resurgence, induced by a symmet-rical intruding body. In the last experiment (RIS 9), resurgence inducedby an asymmetrical intruding body followed a first step of extension,and a second step in which a caldera collapse was simulated.

According to the length of the preliminary extension (Eext) to be sim-ulated, at the beginning of each experiment the sliding plate was placedin a different position (Fig. 4) before starting the collapse/resurgencestage (Table 1), in order to completely expose the nozzle at the end ofthe extension.

A sandmodel (with stained horizontal layers) simulating the brittlecrust, was then built partly on the sliding plate and partly on the table

(Fig. 1). In all the experiments, the first step was the simulation of a re-gional extension, induced in the sand-pack by pulling the sliding plateoutward at a constant rate of 50 mm/h (Fig. 1). This movement gener-ates a velocity discontinuity (VD) at the edge of the sliding plate that in-duces the development of extensional structures in the sand-pack,during its outward migration (Fig. 1). These structures border agraben-like depression in which a couple of inward-dipping normalfaults initially nucleate from VD, lying one on the sliding plate and oneon the table, respectively (Fig. 1). With the continuation of the exten-sion, one fault remains attached to VD on the sliding plate (masterfault), whereas a series of antithetic faults form on the opposite side,at a constant interval of about 1 cm (Fig. 1), increasing in number asthe amount of extension increases (Table 1; Fig. 4). Additional horizon-tal layers of suitably stained sand were placed within the depressionduring its formation, for each 0.5 cm of extension, in order to simulatesyn-rift deposits (Fig. 1) and to provide a horizontal topography beforecollapse or resurgence, for studying the deformation process withouttopographic controls.

After extending the sand-pack, the extension engine was switchedoff and collapse or resurgence were simulated with the downward orupward movement of the piston within the cylinder. This induced thesilicone to be pulled down or pushed up, respectively, and further de-formed the overlying sand-pack. The piston moved at a constant rateof about 3.80 cm/h. Every deformational phase (resurgence or collapse)lasted about 3 h (Table 1). Resurgence directly followed the extensionalphase in all the experiments but one, in which a caldera collapse wassimulated before resurgence (Table 1). In this case, additional stained

Fig. 2. Preparation of the silicone within the cylinder. The upper surface of the silicone has been hand moulded, in order to simulate an asymmetrical surface of the magma chamber(2a) The resulting empty space above the silicone has been filled with sand, up to the table surface (2b).

Fig. 3.Detail of the experimental equipment showing the geometry of the silicone surface. In the first configuration (a) The top of the silicone is higher toward the side where the slidingplate extends; as a simplification it has been called left-asymmetric (l-a). The opposite case (b) has been called right-asymmetric (r-a). The flat surface of the silicone (c) Simulates a sym-metric configuration of the magma surface, which has been called radial-symmetric (r-s). T = thickness of the sand–pack.

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sand was laid down in the depression (post-collapse deposits) in orderto provide a horizontal topography. At the end of each experiment, themodels were buried with additional sand, saturated with water and cutinto a cross section, parallel to the direction of extension, in order to vi-sualize and measure the produced deformational features.

Inspection of map views of models enabled us to follow the geomet-ric evolution of the resurgent area through time. As the resurgent areawas sub-circular to elliptical in shape, its eccentricity Ec = Lmin/Lmax

(with Lmin and Lmax being the length of the minor and major axis ofthe ellipse, respectively) was measured step by step, although onlythe final Ec value is reported in Table 1.

In cross-section view, the comparison betweenmodels only affectedby extension and models in which resurgence followed extension,allowed the measurement of the dip separation (d) along the planesof both newly formed and pre-existing faults, reactivated during resur-gence. Moreover, the real vertical rise values (r) of blocks, measured bycomparing the position of the topographic surface before and after the

resurgence phase, were plotted together with d-values in histogramsfor each performed experiment.

In Table 1, both imposed parameters and obtained results for eachexperiment, are summarised.

3. Experimental results

In the following, the performed experiments will be describedand discussed in order of increasing extension, starting with thosethat simulated resurgence in a simple graben-like structure, withan asymmetrical configuration of the upper surface of the magmachamber.

As the experiment RIS 1 was performed with the main objective oftesting the equipment, and it qualitatively shows the same results asRIS 2, only the latter will be described here as it allowed a better quan-titative definition of the measured deformational parameters.

Table 1Summary of the initial conditions imposed in carrying out RIS 2–9 experiments, and resulting caldera and resurgent-block geometry.

T = Thickness of the sand pack; D = Diameter of the nozzle; Eccentricity = Lmin/Lmax (being Lmin and Lmax the length of the minor and the major axes, respectively, of the elliptically-shapecaldera depression and resurgent); l-a = left-asymmetric; r-s = radial-asymmetric.

Fig. 4. Detail of the experimental equipment showing the different initial and final positions of the sliding plate, for an extension of 1.3, 6.0 and 7.0 cm, respectively.

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Fig. 5. Evolution of resurgence over extension: Experiment RIS 4. a) Section view after extension; b) Section view after resurgence; c)Map view at the end of the experiment: dashed lineshighlight the visible fault tracks. The numbers refer to the order of development of the faults, the arrows to their kinematics. Faults with the same number formed during the samedeformational phase, letters refer to the order of the development unless otherwise stated in the text (see the text for explanation). Dashed, yellow fault-lines represent resurgence-related ring faults and/or shear zones.

Fig. 6. Evolution of resurgence over extension: Experiment RIS 5. a) Section view after extension; b) Section view after resurgence; c)Map view at the end of the experiment: dashed lineshighlight the visible fault tracks. The numbers refer to the order of development of the faults, the arrows to their kinematics. Faults with the same number formed during the samedeformational phase, letters refer to the order of development unless otherwise stated in the text (see the text for explanation). Dashed, yellow fault-lines represent resurgence-related ring faults and/or shear zones.

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3.1. Extension and resurgence

3.1.1. Experiment RIS 4In running experiment RIS 4 the following conditionswere imposed:

T/D = 1, text = 16′, Eext = 1.3 cm, and tres = 180′; furthermore, thetop of the silicone in the cylinder was moulded to simulate a left-asymmetric (l-a) upper surface of the magma chamber (Table 1;Fig. 3a).

During the first phase of the experiment, the sandmodel underwentextension that generated a graben-like structure delimited by twoopposite-verging normal faults (1a and 1b in Fig. 5). After filling thegraben with sand, the model was affected by resurgence.

A cross section of themodel, cut parallel to the extension direction atthe end of the experiment (Fig. 5b), shows at least three differentiallydisplaced blocks (B1, B2, B3), the two regional faults 1a and 1b, anewly formed resurgence reverse ring-fault (whose trace in crosssection is given by faults 2a and 2b), and a newly formed resurgencenormal fault (2c). The most uplifted sector includes blocks B1 and B2,which correspond to the thickest overburden above the silicone. BlockB1 is bordered by the newly formed, high-angle, inward-dipping reversefault 2a and by the regional fault 1b (Fig. 5b). B2 is included between theregional fault 1b and the newly-formed, outward-dipping normal fault2c. B3 is the less uplifted block and is bordered by fault 2c and thenewly-formed, inward-dipping reverse fault 2b. The sector includedbetween faults 2b and 1a is not involved in the resurgence kinematics,as it has been not uplifted (Fig. 5b).

In plain view (Fig. 5c), the whole resurgent area shows an ellipticalshape with an eccentricity Ec = 0.97 (Table 1), and the major axis(Lmax) perpendicular to the extension direction and parallel to theregional faults. The trace of fault 1b appears early, about 20′ after thebeginning of resurgence. At 40′, the shape of the resurgent area is welldefined by faults 2a and 2b, which appear as parts of a single ring-structure, together with the trace of fault 2c. Fault 2c continues togrow until the end of the experiment, increasing its extension.

From this sequence, it is evident that, in the early stages of resur-gence, an initial reactivation of 1b as a normal fault, causes the tiltingof block B1. Following this, the activation of the reverse ring fault(2a–2b, Fig. 5b) defines the resurgent area that, due to the geometryof the ring fault, undergoes a horizontal extension, which is accommo-dated by the nucleation of the normal fault 2c. Fault 2c nucleates atthe intersection between 1b and the edge of the nozzle only after theactivation of the ring fault. As no equivalent of 2c exists in resurgenceexperiments with a symmetrically shaped silicone (Acocella et al.,2000a, 2001, 2004), it seems likely that its nucleation is due to the stressinduced by the intruding silicone. Fault 2c also plays an important rolein allowing blocks B1 and B2 to be uplifted as one, as testified by themaximum values of dip-separation recorded in cross-section alongfaults 2a and 2c (11.5 and 15.5 mm respectively), compared to thevery small dip-separation measured along 1b (−0.7 mm; Fig. 5b).Despite this small amount of dip separation, the maximum value ofreal vertical rise (11 mm, Fig. 5b) has been measured between blocksB1 and B2, which have been uplifted mainly due to the movementalong faults 2a and 2b.

The occurrence of gravitational sand sliding at the surface was ob-served during resurgence, accompanying the movement along faults2a, 2b and 2c.

3.1.2. Experiment RIS 5Experiment RIS 5was performed imposing the same conditions as in

experiment RIS 4 (T/D = 1, text = 16′, Eext = 1.3 cm, and tres = 180′)but with a right-asymmetric (r-a) upper surface of the silicone (Table 1;Fig. 3b). Extension produced the same regional faults as in RIS 4 (1a and1b, Fig. 6a). A cross section of themodel, cut parallel to the extension di-rection at the end of the experiment, shows a newly-formed resurgencereverse ring-fault (whose trace in cross section is given by faults 2a and2b; Fig. 6b), a newly-formed resurgence normal-to-vertical fault (2c;Fig. 6b), and the two opposite-verging regional faults (Fig. 6b). Resur-gence generated three differentially displaced blocks (B1, B2 and B3;

Fig. 7. Evolution of resurgence over extension: Experiment RIS 2. a) Section view after extension; b) Section view after resurgence; c)Map view at the end of the experiment: dashed lineshighlight the visible fault tracks. The numbers refer to the order of the development of the faults, the arrows to their kinematics. Faults with the same number formed during the samedeformational phase, letters refer to the order of development unless otherwise stated in the text (see the text for explanation). Dashed, yellow fault-lines represent resurgence-related ring faults and/or shear zones.

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Fig. 6b). B1 is the most uplifted block. It corresponds to the thickestoverburden above the silicone and is included between the newly-formed, resurgence high-angle reverse ring-fault 2b and the regionalfault 1b. B2 is bordered by fault 1b and the newly-formed, resurgencenormal-to-vertical fault 2c. B3 is the less uplifted block and is includedbetween fault 2c and the newly-formed, resurgence high-angle reversering-fault 2a. The sector included between the regional fault 1a and fault2b is likely not involved in the resurgence kinematics, as it has been notsignificantly uplifted.

In plain view (Fig. 6c), the whole resurgent area is elliptical in shape,with an eccentricity Ec = 0.94 (Table 1), and themajor axis perpendic-ular to the extension direction and parallel to the extensional faults. Atthe beginning of the resurgence phase of the experiment, a very smallamount of uplift occurs due to the reactivation as reverse faults of theregional faults 1a and 1b, along which dip separations of 0.5 and0.8 mm have been measured, respectively. Almost contemporaneousis the formation of the resurgence, reverse ring-fault (2a–2b in cross-section) that defines the resurgent area (Fig. 6c). Despite the smallamount of dip separation measured along 1b, the maximum value ofreal vertical rise of 8.5 mm was measured between blocks B1 and B2(Fig. 6b). This likely means that, after an early displacement of B1 rela-tive to B2, after the activation of the ring fault, the three blocks wereuplifted as one until fault 2cwas generated. At this stage, themovementalong a portion of the ring fault stopped (2a in cross section, whichreached a maximum dip separation value of 4.8 mm; Fig. 6b), andblocks B1 and B2 continued their uplift until the end of the experiment,mainly through displacement along faults 2b and 2c (d = 10.6 and9.1 mm, respectively; Fig. 6b). The uplifting of blocks B1 and B2 is alsocharacterized by an oblique component, which causes the tilting ofthe most uplifted portion of the resurgent area (Fig. 6b). Due to thegeometry of the faults driving resurgence, the most uplifted part ofthe resurgent area is affected by a horizontal elongation at surface,which is accommodated in a ductile way, as demonstrated by the thin-ning of the uppermost sand layer of the model. Fault 2c represents the

kinematic equivalent of fault 2c of experiment RIS 4, being nucleatedat the intersection between the highest part of the uprising siliconeand the resurgence ring-fault.

Also as in experiment RIS 4, the occurrence of gravitational sandsliding at surface was observed during resurgence, accompanying themovement along faults 2a, 2b and likely 2c (Fig. 6b).

3.1.3. Experiment RIS 2Experiment RIS 2 was performed in the following conditions:

T/D = 1, text = 72′, Eext = 6 cm, tres = 180′ and right-asymmetric(r-a) upper surface of the silicone (Table 1; Fig. 3b). During the firstphase of the experiment, extension induced the formation of a masternormal fault (1a in Fig. 7a) and five antithetic normal faults (1b, 2, 3,4, 5 in Fig. 7a). Due to the amount of extension, the nozzle of the equip-ment underneath the sand pack was completely included within thedownthrown area. The resurgence phase of the experiment startedafter filling the so-formed graben-like structure with sand. A cross sec-tion of themodel, cut parallel to the extension direction at the endof theexperiment (Fig. 7b) shows four differentially displaced blocks (B1, B2,B3, B4), themaster extensional fault (1a), the five antithetic extensionalfaults (1b, 2, 3, 4, 5), a newly formed, resurgence, reverse fault (6a), andtwo brittle–ductile shear zones (6b and 6c; Ramsay and Huber, 2002).The resurgent area is included between faults 2 and 6a; therefore faults1a and 1b in this case are not involved in the resurgence kinematics. Allthe other pre-existing structures were reactivated during this phase ofthe experiment. However fault 1a is characterized in its deepest portionby a dip separation of 3 mm, which does not correspond to an uplift atsurface, and the sector included between faults 1a and 6a is tilted. Thislikely means that the initial upthrust of the silicone, in addition to thetilting of this sector, results in a tamping of the basal sand layers. Themovement of this sector stops with the activation of fault 6a, alongwhich the maximum dip separation is recorded, allowing B1 to be themost uplifted block, also thanks to the reactivation of fault 5 as normalfault. Fault 6a is the kinematic equivalent of the resurgent ring-faults

Fig. 8. Evolution of resurgence over extension: Experiment RIS 3. a) Section view after extension; b) Section view after resurgence; c)Map view at the end of the experiment: dashed lineshighlight the visible fault tracks. The numbers refer to the order of the development of the faults, the arrows to their kinematics. Faults with the same number formed during the samedeformational phase, letters refer to the order of development unless otherwise stated in the text (see the text for explanation). Dashed, yellow fault-lines represent resurgence-related ring faults and/or shear zones.

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of experiments RIS 4 and RIS 5. It is a ring-fault too, whose developmentis free in the sector in which there are no pre-existing structures, andstrongly interferes in the opposite side with faults 2, 3 and 4, alongwhich the resurgence movement is partially transferred. This interfer-ence is evidenced in cross section by the presence of the two shearzones that partially displace the planes of faults 2 and 3 and deformthe plane of fault 4.

In plain view, the resurgent area is well defined at tres = 20′ by theactivation of the reverse ring-fault 6a and by the reactivation as reversefaults of the pre-existing structures 3 and 4 that interfere with the ringfault along the shear zones 6b and 6c. The resurgent area shows a rough-ly irregular elliptical shapewith an eccentricity Ec = 0.95 (Table 1) andthemajor axis (Lmax) perpendicular to the extension direction and coin-ciding with the regional faults 3 and 4 (Fig. 7c). These faults are veryevident within the elongated resurgent block, bordering a crest depres-sion parallel to VD. At tres = 80′, the uplifted area acquired a more reg-ular elliptical shape, and fault 5 started to be reactivated. At this stage,the most uplifted area corresponds to the thickest overburden abovethe silicone, and the amount of uplift progressively decreases towardsB4, which is the least uplifted block. In this area, the deformationinduced by the wedge intrusion of the silicone is mainly transferred tofaults 3 and 4 through the shear zones 6b and 6c (Fig. 7b).

The horizontal elongation of the resurgent area is completely accom-modated by the horizontal component of the faults throw, and noductile deformation of the sand layers is observed in this case.

The occurrence of gravitational sand sliding at surface was observedduring resurgence, only accompanying the movement along faults 6aand 4 (Fig. 7b).

3.1.4. Experiment RIS 3Experiment RIS 3 was performed in the same condition as RIS 2

(T/D = 1, text = 72′, total Ex of 6 cm and tres = 180′) but with aleft-asymmetric (l-a) surface of the silicone (Fig. 3a; Table 1). As in ex-periment Ris 2, extension induced the formation of a master normal

fault (1a) and five antithetic normal faults (1b, 2, 3, 4, 5; Fig. 8a),with the nozzle of the equipment completely included within thedownthrown area. The resurgence phase of the experiment startedafter filling the graben-like structure with sand. The cross section ofthe model, cut parallel to the extension direction at the end of theexperiment (Fig. 8b) shows five differentially displaced blocks (B1, B2,B3, B4, B5), the master extensional fault (1a), the five antithetic exten-sional faults (1b, 2, 3, 4, 5), a newly formed, resurgence, reverse fault(6a), and a single brittle–ductile shear zone (6b; Ramsay and Huber,2002). The resurgent area is included between faults 1b and 6a,although only a small amount of dip separation (1.5 mm) was mea-sured along fault 1b, without any recordable uplift at surface. The sectorincluded between faults 1a and 6a is not involved in the resurgencekinematics as no dip separation was measured along fault 1a. Howeverall the sector included between faults 1a and 5 was tilted by the initialupthrust of the silicone, which also caused the reactivation of fault 5as normal fault, and faults 1a, 2, 3 and4 as reverse faults, allowingblocksB1, B2, B4 and B5 to be uplifted. The activation of a resurgence, reverse,ring-fault (whose evidence in cross-section is given by fault 6a and theshear zone 6b), defines the geometry of the resurgent area. This ring-fault was free to propagate between faults 1a and 5, where no pre-existing structures were present, whereas it was strongly influencedby faults 2 and 3 in the opposite side. Fault 2 was cut in its deepest por-tion by the shear plane of 6b and therefore the resurgent movementwas completely transferred along fault 3, freezing blocks B4 and B5 inposition, and allowing blocks B1 and B2 to continue their uplift untilthe end of the experiment. As the maximum dip separation valueswere measured along faults 6a (10.5 mm) and 3 (12 mm), it is verylikely that, after the activation of the ring-fault, blocks B1, B2 and B3were uplifted as a whole (Fig. 8b). The most uplifted block B1 corre-sponds, also in this case, to the thickest overburden above the silicone,and the amount of uplift progressively decreases towards B3 and B5,which is the least uplifted block (Fig. 8b). The shortening of the modelbetween faults 5 and 1b, mainly due to the reverse movement along

Fig. 9. Evolution of resurgence over extension: Experiment RIS 7. a) Section view after extension; b) Section view after resurgence; c)Map view at the end of the experiment: dashed lineshighlight the visible fault tracks. The numbers refer to the order of the development of the faults, the arrows to their kinematics. Faults with the same number formed during the samedeformational phase, letters refer to the order of development unless otherwise stated in the text (see the text for explanation). Dashed, yellow fault-lines represent resurgence-related ring faults and/or shear zones.

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fault 3, in this case is accommodated by the elongation of the sectorbetween faults 6a and 5, which occurs in a ductile way, as testified bythe stretching and thinning of the uppermost sand layer.

In plain view, at tres = 20′, before the resurgent area is clearly de-fined, the reactivation of fault 5 is well evident. After 40′, the activationof the reverse ring-fault 6a and the reactivation as reverse faults of thepre-existing structures 3 and 4 defines the geometry of the resurgentarea. Fault 3, in particular, interferes with the ring fault along theshear zone 6b delimiting the area in which uplift is more evident. Thisarea is characterized by an irregular elliptical shape, with the majoraxis perpendicular to the extension direction and an eccentricityEc = 0.98 (Table 1).

The occurrence of gravitational sand sliding at the surface wasobserved during resurgence, accompanying the movement along faults6a and 3 (Fig. 8b).

3.1.5. Experiment RIS 7Experiment RIS 7 was performed in the following conditions:

T/D = 1, text = 84′, for a total Eext of 7 cm, tres = 180′, and with aleft asymmetric (l-a) surface of the silicone. The extensional phase ofthe experiment generated a master normal fault (1a in Fig. 9a) andseven antithetic normal faults (1b, 2, 3, 4, 5, 6, 7 in Fig. 9a), with thenozzle of the equipment completely included between faults 1b and 6.Resurgence started after the graben-like structure was filled withsand. The cross section of the model, cut parallel to the extension direc-tion at the end of the experiment (Fig. 9b) shows six differentiallydisplaced blocks (B1, B2, B3, B4, B5 and B6), the master extensionalfault (1a), the seven antithetic extensional faults (1b, 2, 3, 4, 5, 6 and7), and a newly formed, resurgence, reverse ring-fault (whose trace incross section is given by faults 8a and 8b; Fig. 9b). The resurgent areais included between faults 1b and 8a, although the dip separation mea-sured along fault 1b (3.2 mm; Fig. 9b) was only related to its basal part,without any recordable uplift at surface, likely due to a complete brittle-to-ductile transition of the deformation along the fault plane. The sectorincluded between faults 1a and 8a is not involved in the resurgencekinematics as no dip separationwasmeasured along fault 1a. The initial

upthrust of the silicone caused the reactivation of fault 5 as a reversefault, and faults 6 and 7 as normal faults, determining the early upliftof blocks B4 and B5. After that, the activation of the resurgence, reverse,ring-fault defined the geometry of the resurgent area. This ring-faultstarted to nucleate along the nozzle, at the intersection between the up-rising silicone and the sand-pack. It cut in cross-section fault 7, whichthen became inactive, and deformed the basal part of fault 2, along theplane of which it propagated toward the surface. After the activationof this ring-fault, the most uplifted part of the model (B1, B2, B3)corresponded to the thickest overburden above the silicone. The upliftof this sector also occurred by the reactivation of faults 2, 3, 4, and 5as reverse faults, which, due to their geometry, determined the shorten-ing of themodel between faults 3 and 2. This shorteningwas accommo-dated by reactivation of fault 6 as a normal fault, which caused theelongation of the model in this sector between faults 8a and 6.

In plain view, at tres = 20′, before the resurgent area was clearly de-fined, upliftingwas evidenced by the reactivation of faults 5 and 6. Fromtres = 40′ and tres = 80′, the geometry of the resurgent areawas clearlydefined by the activation of the resurgent, reverse, ring-fault. It had analmost circular shape, with an eccentricity Ec = 0.99 (Fig. 9c) and themajor axis perpendicular to the extension direction. At tres = 100′,the reactivation of fault 4 defined the position of the most upliftedblock, B1, which was differentially displaced relatively to blocks B2, B3and B6 due to the reactivation of fault 3 and to the transfer of themove-ment of the ring-fault along the plane of fault 2. Gravitational slidingoccurred during resurgence, accompanying the movement along faults3 and 8a.

3.1.6. Experiment RIS 8Experiment RIS 8 was performed imposing the same conditions as

RIS 7 but with a radial symmetric (r-s) surface of the silicone, in orderto fill the gap existing in Acocella et al. (2004), in which there is notan equivalent counterpart of RIS 7. The early extensional phase of theexperiment generated a master- normal fault (1a in Fig. 10a) andseven antithetic normal faults (1b, 2, 3, 4, 5, 6 and 7; Fig. 10a). The noz-zle of the equipment was completely included between faults 1b and 6.

Fig. 10. Evolution of resurgence over extension: Experiment RIS 8. a) Section view after extension; b) Section view after resurgence; c)Map viewat the end of the experiment: dashed lineshighlight the visible fault tracks. The numbers refer to the order of the development of the faults, the arrows to their kinematics. Faults with the same number formed during the samedeformational phase, letters refer to the order of development unless otherwise stated in the text (see the text for explanation). Dashed, yellow fault-lines represent resurgence-related ring faults and/or shear zones.

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As usual, resurgence started after filling the graben-like structure withsand. The cross section of the model, cut parallel to the extension direc-tion at the end of the experiment (Fig. 10b) shows five differentiallydisplaced blocks (B1, B2, B3, B4 and B5), the master extensional fault(1a), the seven antithetic extensional faults (1b, 2, 3, 4, 5, 6 and 7),and a newly formed, resurgence, reverse ring-fault (whose trace incross section is given by faults 8a and 8b; Fig. 10b). The resurgent areawas included between faults 2 and 8a (Fig. 10b and c). The sectorincluded between faults 1a and 8a was not involved in the resurgencekinematics, as no dip separation was measured along fault 1a. Fault 7,whose plane is displaced by the reverse ring-fault, was not reactivatedduring resurgence. At the beginning of resurgence, fault 6 wasreactivated as a normal fault, determining the initial uplift of block B3.Immediately after, the nucleation of the reverse ring-fault 8a–b beganto define the geometry of the resurgent area, in which blocks B1, B2and B4 were differentially displaced due to the reactivation of faults 5,4, 3 and 2 as reverse faults. This fault geometry and kinematics deter-mined the shortening of themodel between faults 5 and 2. This shorten-ing was accommodated by reactivation of fault 6 as a normal fault,which caused the elongation of the model in this sector between faults8a and 6.

Block B5 is characterized by a very small amount of uplift, whichlikely occurred in the initial stage of the resurgence before the move-ment had been transferred along faults 5 to 2. The ring-fault started tonucleate along the nozzle at the intersection between the uprisingsilicone and the sand-pack. As in RIS 7, it cut fault 7 in cross-sectionand deformed the basal part of fault 2, along the plane of which it prop-agated toward the surface. At the end of the resurgence, the originallyradially symmetric surface of the silicone, developed an articulatedtexture and preferentially intruded into the fault bordering the volumeof the model under extension at the intersection with the resurgencering-fault (Fig. 10b). The axis of the most uplifted portion of the

resurgent area (blocks B1, B2 and B3) was not located right abovethe centre of the nozzle, being slightly shifted toward the volume ofthe model under compression that corresponds to the part in whichintrusion was inhibited.

Fault 1bwas reactivated as a normal fault due to the geometry of thereverse ring-fault, which propagated along the plane of fault 2 in the lat-est stages of resurgence, creating a stress drop that was accommodatedby the downsagging of the sector included between faults 2 and 1b(Fig. 10b). Intrusion of the silicone is also recorded at the intersectionbetween fault 1b and the base of the resurgence ring-fault, in the areain which the local stress-drop occurred (Fig. 10b).

In plain view, at tres = 30′, before the resurgent area was clearlydefined, uplifting was evidenced by the reactivation of fault 6. Attres = 40′, the geometry of the resurgent area was clearly defined bythe activation of the resurgent, reverse, ring-fault. It had an almostcircular shape, with an eccentricity Ec = 0.99 (Fig. 10c) and the majoraxis perpendicular to the extension direction. The nucleation of thering fault was accompanied by the reactivation of faults 5 and 2 as re-verse faults, and fault 1b as a normal fault. At tres = 60′, the reactivationof fault 4 as a reverse fault is well evident, which allows the identifica-tion and the uplift of block B1, whereas at tres = 180′, block B2 wasdifferentially displaced as an independent block due to the reactivationof fault 3. Gravitational sliding occurre during resurgence, accompany-ing the movement along faults 6 and 2.

3.2. Extension, collapse and resurgence

3.2.1. Experiment RIS 9Experiments RIS 9was performed in order to simulate resurgence in

a collapsed area within a graben-like structure. In running this experi-ment, the following conditions were imposed: T/D = 1, text = 16′, fora total extension of 1.3 cm. The surface of the silicone in the cylinder

Fig. 11. Evolution of resurgence over extension and collapse: Experiment RIS 9. a) Section viewafter extension; b) Section viewafter resurgence; c)Map viewat the end of the experiment:dashed lines highlight the visible fault tracks. The numbers refer to the order of development of the faults, the arrows to their kinematics. Faults with the same number formed during thesame deformational phase, letters refer to the order of development unless otherwise stated in the text (see the text for explanation). Dashed, yellow fault-lines represent structuresformed during caldera collapse (yellow arrows) and reactivated during resurgence (red arrows).

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was moulded in order to simulate a left-asymmetric top of the magmachamber, as in Ris 4. In experiment RIS 9 a caldera collapse, followedby resurgence, was simulated after the extensional phase, withtcol = tres = 180′.

During the first phase of the experiment, the sandmodel underwentextension,which generated a graben-like structure bordered by two op-posite verging normal faults (1a and 1b in Fig. 11a). After the grabenwas filled with sand, the model was affected by collapse. As the modelwas cut only after the resurgence phase of the experiment, a quantita-tive estimate of dip separation and vertical displacement before andafter each deformational event is not possible. However, by comparingthis experiment with the experiment carried out by Acocella et al.(2000a), it is possible to state that, during the early stages of the collapsephase, the outward-dipping reverse ring fault activated, and the trace isgiven by faults 2a and 2b (Fig. 11b). During the late stages of this phase,faults 3a and 3b represent the trace of an inward-dipping normal ringfault developed as a consequence of gravitational instability of the pe-riphery of the collapsed area (see also Fig. 10 in Acocella et al., 2000a).

The resurgence phase started after filling the depressed structureformed during extension and collapse. The cross section of the model,cut parallel to the extension direction at the end of the experiment(Fig. 11b), shows three differentially displaced blocks (B1, B2 and B3),and all the described structures formed during the early extension andcollapse stages of the experiment. The sector included between faults1a and 3a, is not involved in the resurgence kinematics, as no dip sepa-ration has been measured along fault 1a. The resurgent area is includedbetween faults 3a and 3b, which were reactivated as reverse faultsduring the early stages of resurgence (Fig. 11b). These structures arekinematically equivalent to faults 2a and 2c of experiment RIS 4, eventhough in this case they are not newly formed structures. The uplift ofthe resurgent block was permitted by the displacement along a surfacethat resulted from the merging of the basal part of faults 2(a–b) andfaults 3(a–b) (Fig. 11b). Afterward, the reactivation of faults 2a and 1bwith a normal and a reversemovement, respectively, allowed the asym-metrical uplift of block B1, whichwas also themost uplifted block at theend of the experiment (Fig. 11b). Fault 2b could not be reactivated in re-surgence, due to both its geometry and resurgence kinematics. It wascut by fault 1b and deformed during the movement of block B2, whichoccurred through the displacement along fault 3b. The measurementof vertical displacement shows that, as in RIS 4, uplift was asymmetrical,and themost uplifted portion corresponded to the sector inwhich therewas the thickest overburden above the left-asymmetric shaped surfaceof the silicone. This fault geometry and kinematics determined theshortening of the model between faults 1b and 3b. This shorteningwas accommodated by reactivation of fault 2a as a normal fault, whichcaused the elongation of the model in this sector, between faults 2aand 3a.

In plain view, the collapse phase of the experiment can be followed.At tcol = 20′, the first approximately circular caldera structure wasformed, reaching the maximum diameter of 4.5 cm at tcol = 60′. Attcol = 80′, an outer caldera begun to form, and at the end of the collapsephase (tcol = 180′) it reached the maximum diameter of 7.0 cm andhad an elliptical shape, with an eccentricity Ec = 0.91 and the majoraxis perpendicular to the extension direction. The following resurgencephase started to produce visible effects at tres = 45′, when the geome-try of the resurgent area was clearly defined by the reactivation as areverse fault of the ring-structure whose trace is given by faults 3aand 3b. At tres = 105′, the reactivation of fault 2a as a reverse faultwas well evident, and, together with fault 1b, marked the uplift ofblock B1. Starting from this moment, the only active structures were2a, 1b and 3b, which allowed the differentially displaced resurgentblock to achieve its final asymmetrical configuration (Fig. 11c), charac-terized by an eccentricity Ec = 0.98 and themajor axis perpendicular tothe extension direction.

Gravitational sliding occurred during resurgence, accompanying themovement along faults 2a and 1b.

4. Discussion and conclusions

4.1. Interpretation and comparisons with previous experiments

This paper represents the last step of a series of analogue modellingexperiments, started with Acocella et al. (2000a), aimed at betterunderstanding the process of resurgence in progressively complexboundary conditions. Acocella et al. (2001) and Acocella et al. (2004)approached the problem of caldera collapse and later dome or block(both symmetric and asymmetric) resurgence as a function of the over-burden thickness and/or in the presence of pre-existing tectonic orvolcano-tectonic structures. We refer to these papers for detailed me-chanical interpretations of nucleation and evolution of the structuresformed in the conditions imposed at that time. Here we focus onthe main elements of novelty that emerged in the RIS 2–9 set ofexperiments, and the most significant similarities and differences withprevious experiments.

All the experimentswere performed imposing a T/D = 1 in order toproduce a block resurgence, as suggested by Acocella et al. (2001).

The experiments that reproduced resurgence due to an asymmetricsilicone body over pre-existing extensional structures, can be comparedto previous experiments, carried out with a radial symmetric siliconebody and similar amounts of extension (CALTEC 9, 11 and 13 byAcocella et al., 2004). These two sets of experiments are characterizedby an asymmetric resurgence that occurred through the differential dis-placement of blocks, bordered by both newly formed or pre-existingfaults. The resurgent volume has a more or less irregular ellipticalshape in a plain view, with the major axis orthogonal to the extensiondirection and parallel to the regional faults.

Eccentricity in the RIS experiments is very low, likely due to thegeometry of the resurgent ring-fault that, unlike in the CALTEC experi-ments, is always reverse and inward dipping or at most subvertical.Therefore, the low degree of ellipticity and the irregular shape mainlydepend on the geometry of the pre-existing extensional faults.

For amounts of previous extension ≥5 cm, and as a consequencemore than two regional faults, the regional fault 1b (Figs. 7, 8, 9and 10) is: a) reactivated as normal if the surface of the silicone is sym-metric, as already observed in CALTEC 9 (Acocella et al., 2004); b) notreactivated in the case of right-asymmetric silicone; and c) reactivatedas reverse in case of left-asymmetric silicone. For a lesser amount of pre-vious extension, fault 1b is entirely included in the sand volume lyingabove the silicone, and is reactivated as normal in the case of symmetricsilicone, and as reverse in the case of asymmetric silicone. This behav-iour can be interpreted as dependent on both the position of the faultafter the extensional phase and the local stress field induced by thedifferent geometry of the silicone body.

The comparison between experiments carried out with symmetricand asymmetric silicone bodies (RIS 2–8, this paper, and CALTEC 9and 13, Acocella et al., 2004) with variable amounts of previous exten-sion showed some significant differences, mainly in the nucleationand kinematics of resurgence-related structures. For a small amount ofextension (RIS 4 and RIS 5; Eext = 1.3 cm) an asymmetric resurgencering-fault nucleates at the margin of the nozzle, as occurred in CALTEC13 but, unlike in this earlier experiment, it is mainly inward-dippingand curviplanar and is characterized along one side (2b in cross-section of Figs. 5 and 6) by a normal-to-reverse movement from itsnucleation point upward. The newly formed resurgence normal fault2c nucleates in both RIS 4 and RIS 5 at the intersection between theapex of the uprising silicone and the nucleation point of the reversering-fault. As no equivalents of this feature have been observed in theexperiments with symmetric silicone, it can be hypothesized that itsnucleation is directly linked to the geometry of the silicone body andto the asymmetric upthrust related to its uprising.

For larger amounts of extension (i.e. RIS 2 and RIS 3; Eext = 6 cm),the nucleation of the resurgence reverse ring-fault is strongly influ-enced by pre-existing regional faults, which are partly displaced and

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reactivated by the propagation of a poorly defined shear-zone, alongone side of the ring-fault (6b and 6c in Figs. 7 and 8). Unlike in theCALTEC experiments (Acocella et al., 2004) one regional fault isreactivated as normal, and three or four are reactivated as reverse faultsin the case of right-asymmetric or left-asymmetric silicone, respectively,suggesting that the asymmetric upthrust due to the geometry of the up-rising silicone is the main factor responsible for this kind of kinematics.Further amounts of extension (RIS 7 and RIS 8; Eext = 7 cm) do notsignificantly change the overall geometry of the model. The regionalfault 1b (Figs. 9 and 10) can be reactivated as normal or reverse fault,depending on the presence of a symmetric or a left asymmetric siliconebody, respectively.

The experiment reproducing resurgence due to an asymmetric sili-cone body over pre-existing extensional structures and caldera collapse(RIS 9; Fig. 11), shows significant differences in terms of fault reactiva-tion, when compared to previous experiments in which resurgencewas induced by a symmetric silicone body (CALTEC 11; Acocella et al.,2004). In particular, the outer caldera is bordered by an inward-dipping, normal ring-structure that converges downward into a shear-zone, including also the reverse, outward-dipping ring-fault, formedduring the collapse of the inner caldera. In CALTEC 11, one of the

extensional faults was reactivated as normal during the collapse of theouter caldera, but in RIS 9, fault 1b was not reactivated during collapse,as it is entirely included within the inner caldera due to the reducedamount of extension. The outer caldera normal faults and the regionalfault 1b were reactivated as reverse during resurgence, whereas theinner caldera reverse faults were reactivated as normal. Regional fault1a was not involved in either collapse or resurgence.

Themain outcome, resulting from our experiments presented in thispaper, is that the most uplifted block corresponds to the sector of thethickest overburden above the asymmetrically-shaped surface of thesilicone. Previous experiments with an asymmetric silicone dome atthe base of a homogeneously and laterally isotropic stratified sand-pack, without pre-existing structures, showed the development ofasymmetric uplift, in which the point of maximum rise of the siliconeand the point of maximum uplift of the resurgent body coincide withthe top of the silicone dome (Fig. 12a; RIS 13 in Acocella et al., 2001).In this case the resurgent body is bordered by inward-dipping high-angle reverse faults and is characterized by an internal structure inwhich an upward-convex dome evolves laterally into a monocline.Such a configuration has been compared to a hinged or trapdoor upliftby Acocella et al. (2001). On the other hand, a radial-symmetric siliconebody in experiments with pre-existing extensional structures (CALTEC9 and 13 in Acocella et al., 2004; RIS 8; this paper), produced only aslightly asymmetric block resurgence (Fig. 12b), suggesting that pre-existing structures do not significantly affect the overall architectureof the resurgent dome, not considering smaller perturbation due tothe activity of the faults.

The main difference between previous experiments and ours is thepresence in ours of a sand-wedge, interposed between the uppersurface of the silicone and the sand-pack in order to fill the emptyspace generated by the moulding of the silicone (Fig. 12c).

Fig. 12. The geometry of resurgent areas in different boundary conditions. The sketches at the bottom of the picture represent the models before the resurgence phase. The upper profilesrefer to the topography of the resurgent areas at the end of the deformation. a. Asymmetric upthrust in a lateral isotropic medium induces an asymmetric resurgence, with the mostuplifted part coincidingwith the uppermost part of the uprising silicone (Acocella et al., 2001); b. Symmetric upthrust in an anisotropic medium induces a slightly asymmetric resurgencedue to the geometry o the pre-existing faults (Acocella et al., 2004); c. Asymmetric upthrust in an anisotropic medium induces asymmetric resurgence with the most uplifted partcorresponding to the thickest overburden (this paper).

Fig. 13. Transferring of the vertical stress σ to the overlying sand-wedge, through thesilicone surface S, which is inclined at an angle θ to the horizontal. The vertical stress isresolved into a normal (σn) and a shear (σs) component, connected to θ by the followingrelations: σn = σ cos2θ; σs = σ/2 sin2θ. Fig. 14. Variation of σn and σs with θ (modified after Hobbs et al., 1976).

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Therefore themost important controlling factors in determining theresurgence kinematics described in this paper, have to be the geometryof the surface of the silicone body, the sand-wedge and the way inwhich pre-existing structures accommodate the resulting deformation.The silicone geometry likely acts in different ways depending on therelative attitude of the pre-existing structures. Irrespective of theamount of previous extension, if the extensional structures plunge op-posite to the silicone surface, they enhance the effect of the asymmetricupthrust, determining the maximum dip separation along the faultplanes and real vertical rise of the uplifted block. In this case all thepre-existing structures are reactivated during resurgence. Conversely,if the fault dip is consistentwith the plunge of the silicone surface for in-termediate to large amount of previous extension, one or more regionalfaults may not be involved in the resurgence kinematics (Fig. 7).

Due to the presence of the sand-wedge and the discontinuity sur-faces given by the pre-existing faults, the sand-pack under deformationcannot be considered a homogeneous and isotropic medium. Therefore,we suggest that the asymmetric geometry of the silicone body inducesan equally asymmetric state of stress in the overlying sand-pack. Theoriginally vertical upthrust (σ) is transferred to the sand-wedgethrough the silicone surface and is resolved into normal (σn) andshear (σs) components, relative to this surface. The normal componentof the stress applied to the surface S (Fig. 13) is:

σn ¼ σ cos2θ

where θ is the angle of dip of surface S; and the shear stress is:

σs ¼ σ=2 sin2θ:

The variation of σn and σs with θ is shown in Fig. 14, fromwhich it isevident that for:

a) 0° b θ ≤ 45° = N σn ≥ σs;b) θ N 45° = N σs N σn;c) θ = 90° = N σn = σs = 0.

As the surface of the silicone in our experiments is characterized byan angle of dip lower than 45°, the normal component of the stressprevails, and its orientation could explain the larger amount of upliftingrecorded by the blocks corresponding to the thickest overburden,provided that the overlying sand-pack has been previously affected bybrittle deformation.

4.2. Comparison with nature

Natural examples of asymmetric block resurgence in calderasmainlycome from Italian, medium-size calderas, such as Campi Flegrei, Ischiaand Pantelleria (Orsi et al., 1991, 1996, 1999a; Acocella and Funiciello,1999; Di Vito et al., 1999; Acocella et al., 2000a, 2001, 2004; de Vitaet al., 2005, 2006, 2010; Marotta et al., 2005; Di Napoli et al., 2011;Della Seta et al., 2012). These volcanoes show more than one elementof analogy with the experiments described in this paper.

Ischia and Campi Flegrei calderas are part of the Phlegraean VolcanicDistrict, which developed in a regional stress field due to the anticlock-wise rotation of the Italian peninsula. This rotation is related to theopening of the Tyrrhenian basin, which occurred in Plio-Quaternarytime through the activation of extensional structures that affected theTyrrhenian margin of the Apennine chain. NW–SE-trending normalfaults, downthrown to the southwest, mark this margin, and NE–SWtrending normal to strike slip faults acted as transverse structures(Liotta, 1991; Faccenna et al., 1994), allowing magmas to reach the

Fig. 15. Schematic cross section through an idealized resurgent caldera, representative of the real case of Italian medium-size calderas of Campi Flegrei, Ischia and Pantelleria. The sketchhas been drawn putting together all the available information on these volcanic areas. The scale is indicative (modified after Orsi et al., 1999b and integratedwith data fromDi Renzo et al.,2011).

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surface. Themain caldera-forming eruptions occurredwithin transversedepressions at the intersection between NW–SE and NE–SW trendingfault systems (Acocella and Funiciello, 2002).

The island of Pantelleria is located in the NW–SE-trending SicilyChannel Rift Zone, which results from transtensional tectonics alongthe northern margin of the African plate. Rifting began in the lateMiocene epoch and was intense in Pliocene to Pleistocene time, likelyconcentrated in two main tectonic phases. The early rifting phase (lateMiocene–Early Pliocene) caused the development of several tectonicdepressions, bounded by NW–SE-trending normal faults; the laterrifting phase (Quaternary)was characterized by twomain fault systemstrendingNNE–SSW andNW–SE. The first system shows normal dip-slipmovements whereas the second system, which partially reactivatesprevious extensional structures, presents a right-lateral component ofmotion (Civile et al., 2008).

For all these volcanoes a close relation between regional and volcanotectonic systems has been postulated in order to better explain the ob-served structural and volcanological features. Volcanismwas character-ized by dominant explosive and subordinate effusive activity, severalcaldera collapses followed by resurgence, and renewed intra-calderavolcanism from ventswhose locationwas strongly influenced by the re-surgencemechanism (Orsi et al., 1991, 1996, 1999a; de Vita et al., 2006,2010; Paoletti et al., 2013). This occurred through the asymmetric upliftof differentially displaced blocks, determining the conditions formagma ascent only along one edge of the resurgent area, opposite tothe most uplifted block, or along regional structures reactivated duringresurgence (Orsi et al., 1991, 1999a; de Vita et al., 2010; Di Renzo et al.,2011).

The magmatic feeding systems of the three volcanoes have beenconsidered broadly similar to each other and composed of a deep reser-voir, inwhichmantle-derived parentalmagmas underwent an early dif-ferentiation process, and shallow reservoirs in which the evolvedmagmas further differentiated and mingled/mixed before eruptions(Civetta et al., 1998; Di Renzo et al., 2011). Very shallow reservoirs likelyformed as dyke intrusions of small-volume magma batches thatfed many of the most recent eruptions of Campi Flegrei, Ischia andPantelleria as well (de Vita et al., 1999; Orsi et al., 1999b).

The upper part of this kind of magmatic system architecture, as wellas the resurgence mechanism can be effectively represented by our ex-periments, in which the asymmetry of the silicone surface simulates anintrusion starting from one side of the shallower magma chamber andinducing a local stress field that determines the asymmetric uplift ofthe resurgent block (Fig. 15). Experiment RIS 8 is particularly suitableto simulate magma intrusions that feed eruptions along regional faultsbordering the resurgent block also along the margin under compres-sion. In this experiment, intrusion of the silicone is recorded at the inter-section between the regional fault 1b and the base of the resurgencering-fault, in the area in which a local stress-drop occurs (Fig. 10).

Acknowledgements

All the staff of the Analogue Modelling Laboratory of Roma TreUniversity (directed by Claudio Faccenna) is warmly thanked formaking the equipment available to perform the experiments, for theirsupport during the progress of the laboratory work, and for the stimu-lating discussions. Valerio Acocella is particularly thanked for giving usthe boost to perform the experiments presented in this work and forhis criticism in reading a draft version of the paper. Francesca Cifellideserves our thanks for her logistical, technical and scientific supportduring the performance of the experiments. We are grateful to OlivierMerle and another anonymous referee who greatly improved thequality of this paper with their suggestions. We also wish to thank ourcolleague and dear friend Mike Ort for his helpful comments and forrevising an early version of the manuscript.

Appendix A. Scaling and analogue materials

The analogue models, constructed in order to reproduce resurgencein a pre-existing extensional stress regime, were geometrically, kine-matically and dynamically scaled following the principles discussed byHubbert (1937) and Ramberg (1981). On the basis of scaling laws, wechose analogue materials that simulate the brittle behaviour of theearth's crust (dry sand) and the ductile behaviour of the magma cham-ber (Newtonian silicone putty). They provide for an adimensional ratiodefinition (X* = Xm/Xn) between the main physical parameters of themodels (Xm) and those in nature (Xn), necessary to make the experi-ments analogous to the simulated natural phenomena.

In our experiments we imposed a length ratio of L* = 10−5 (1 cm inthe model corresponds to 1 km in nature). The gravity ratio was g* = 1since the models were run under normal gravity. The densities of thenatural rocks (ρn = 2.0 ÷ 2.7 g/cm3) and used sand (ρm ≈ 1.5 g/cm3)imposed a density ratio of ρ* ≈ 0.5. These values produce a stress ratioσ* = ρ*g*L* ≈ 5 × 10−6. The adopted scaling ratios are shown inTable A1.

For the brittle crust we assumed a Mohr-Coulomb failure criterionτ = σtgϕ + c (in which τ is the shear stress, σ the normal stress ap-plied on the material, c the cohesion and ϕ the internal friction;Coulomb, 1773), with ϕn ≈ 30° and cn ≈ 107 Pa (which represent theaverage values belonging to many rocks in nature; Handin, 1966;Hoek et al., 1995). As cohesion has the dimension of a stress, its ratioc* must be scaled at approximately the value of σ* (5 × 10−6).Therefore, since c* = cm/cn, the cohesion of the material to be used tosimulate the brittle crust, must be cm ≈ 50 Pa. The material used as ananalogue is in accordance with these scaling laws. It is a dry, well-sorted sand, composed predominantly of rounded quartz grains, withϕm = 38° and almost cohesionless (cm ≅ 0). To simulate the ductile be-haviour of magma, whose rheology depends on the time over which

Table A1Scaling procedure adopted in the experiments. Based on scaling laws, dry cohesionless sand was chosen to simulate the brittle behaviour of the earth's crust and in the upper part of thetable is represented the adopted scaling ratios betweenmodels and nature. ANewtonian silicone puttywas chosen to simulate the ductile behaviour of themagma chamber. For theductilebehaviour of magma the values of the various scaling ratios are shown (in the lower part of table) assuming different natural viscosities (Merle and Vendeville, 1995), a silicone puttyviscosity of μm ≈ 104 Pa s and a model velocity of Vm = 5 mm/h = 5 × 10−3 m/h.

Brittle behaviour

Length ratio Gravity ratio Density ratio Stress ratio

L* = Lm/Ln = 10−5 g* = 1 ρ* = 0.5 σ * = ρ*g*L* = 5 × 10−6

Ductile behaviour

Natural viscosity (μn)(Pa s)

Viscosity ratio (μ*)(μm = 104 Pa s)

Strain rate ratioe* = σ*/μ*

Time ratiot* = 1/e*

Velocity ratio v* = vm/vn = e*L*(vm = 5 mm/h = 5 × 10−3)

Natural velocity (vn)(m/h)

104 1 5 × 10−6 2 × 105 5 × 10−11 1 × 108

107 10−3 5 × 10−3 2 × 102 5 × 10−8 1 × 105

101 10−7 5 × 101 2 × 10−2 5 × 10−4 1 × 101

1015 10−11 5 × 105 2 × 10−6 5 1 × 10−3

1018 10−14 5 × 108 2 × 10−9 5 × 103 1 × 10−6

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stress is applied, we had to take into account that parameters such asviscosity (μ), length (L), stress (σ), and time (t) are not independent,but are linked by dimensional equations. This directly affects the calcu-lated scaling ratios for time and strain rate between the model and itsprototype (Table A1; Merle and Vendeville, 1995). As the magma ana-logue, we used aNewtonian silicone puttywhose rheological propertieshave been discussed by several authors such as Weijermars et al.(1993), Merle and Vendeville (1995), Donnadieu and Merle (1998),Hailermariam and Mulugeta (1998) and Merle (1998). Since magmaviscosities are very sensitive to temperature variation (Talbot, 1999),the variable scaling ratios have been calculated assuming different naturalviscosities (Merle and Vendeville, 1995), a silicone putty viscosity ofμm ≈ 104 Pa s, and a model velocity of Vm = 5 mm/h = 5 × 10−3 m/h(Table A1) at which silicone was pushed down or up to simulate col-lapse or resurgence in the sand-pack, respectively.

The extent to which the experimental results are applicable islimited by current knowledge of such natural parameters as viscosities,timescales and strain rates (Merle and Vendeville, 1995). In addition, alaboratory experiment can have many different equivalent prototypesin nature, each with different values of these parameters. However,the goal of these experiments was not to reproduce a specific naturalcase, but rather to investigate the deformation mechanisms acting dur-ing resurgence, which might be valid for a wide range of natural cases,independent of magma viscosities, timescales and strain rates.

Afterward

During the preparation of this paper, our acknowledged master,Renato Funiciello, passed away. We just want to celebrate his many-sided geological genius and great kindness, still surviving inside us,like a spark in the dark.

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