Reconstructing palaeo-volcanic geometries using a Geodynamic Regression Model (GRM): Application to Deception Island volcano (South Shetland Islands, Antarctica)

UNCORRECTED PROOF 1Highlights 2Geomorphology xxx (2012) xxx–xxx 4 5Reconstructing palaeo-volcanic geometries using a Geodynamic Regression 6Model (GRM): Application to Deception Island volcano (South Shetland 7Islands, Antarctica) 8 9C. Torrecillas a, ⁎, M. Berrocoso b , A. Felpeto c , M.D. Torrecillas a , A. Garcia d 10 11 a Escuela Tecnica Superior de Ingenieros, University of Seville,Av. De los Descubrimientos s/n, 41092 Seville, Spain 12 b Facultad de Ciencias, University of Cadiz,Campus Puerto Real, 11510,Puerto Real, Cadiz, Spain 13 c Central Geophysical Observatory, Spanish Geographic Institute,Alfonso XII, 3, 28014 Madrid, Spain 14 d Departamento de Volcanologia,Museo Nacional de Ciencias Naturales,C/Jose Gutierrez Abascal, 2,28006 Madrid, Spain 15 16►Reconstruction of an island previous to the formation of its caldera is proposed. ►Input data: topography, bathymetry, pre-caldera deposits and deforma- 17tion rates. ►Taken into account: mass balance due to ice, erosion and sea level. ►The palaeo-summit height calculated for the palaeo-stratovolcano is 640 m. 18►The method reveals the pre-existence of parasite volcanoes. 19 20 Geomorphology xxx (2012) xxx GEOMOR-04155; No of Pages 1 0169-555X/$ –see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.geomorph.2012.10.032 Contents lists available at SciVerse ScienceDirect Geomorphology journal homepage: www.elsevier.com/locate/geomorph Please cite this article as: Torrecillas, C., et al., Reconstructing palaeo-volcanic geometries using a Geodynamic Regression Model (GRM): Application to Deception Island volcano (Sout..., Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.10.032 UNCORRECTED PROOF 1Reconstructing palaeo-volcanic geometries using a Geodynamic Regression Model 2(GRM): Application to Deception Island volcano (South Shetland Islands, Antarctica) 3C.Q1 Torrecillas a, ⁎,M. Berrocoso b ,A. Felpeto c ,M.D. Torrecillas a ,A. Garcia d 4 a Escuela Tecnica Superior de Ingenieros, University of Seville,Av. De los Descubrimientos s/n, 41092 Seville, Spain 5 b Facultad de Ciencias, University of Cadiz,Campus Puerto Real, 11510,Puerto Real, Cadiz, Spain 6 c Central Geophysical Observatory, Spanish Geographic Institute,Alfonso XII, 3, 28014 Madrid, Spain 7 d Departamento de Volcanologia,Museo Nacional de Ciencias Naturales,C/Jose Gutierrez Abascal, 2,28006 Madrid, Spain 8 9 abstractarticle info 10 Article history: 11 Received 6 May 2011 12 Received in revised form 25 October 2012 13 Accepted 27 October 2012 14 Available online xxxx 1516 17 18 Keywords: 19 Palaeo-volcano 20 Palaeo-surface 21 Terrain reconstruction 22 Volcanic deformation 23 Digital elevation model 24This article describes a reconstruction made of the palaeo-volcanic edifice on Deception Island (South 25Shetland Islands, Antarctica) prior to the formation of its present caldera. Deception Island is an active Qua- 26ternary volcano located in the Bransfield Strait, between the South Shetland Islands and the Antarctic 27Peninsula. The morphology of the island has been influenced mainly by the volcanic activity but geodynamics 28and volcanic deformation have also contributed. A volcanic reconstruction method, the Geodynamic Regres- 29sion Model (GRM), which includes a terrain deformation factor, is proposed. In the case of Deception Island, 30the directions of this deformation are NW–SE and NE–SW, and match both the observed deformation of the 31Bransfield Strait and the volcanic deformation monitored over the last 20 years in the island, using Global 32Navigation Satellite System (GNSS) techniques. Based on these data, possible volcanic deformation values 33of 5–15 mm/yr in these directions have been derived. A possible coastline derived from a current bathymetry 34is transformed, according to values for the chosen date, to obtain the palaeo-coastline of Deception Island of 35100 k years ago. Topographic, geomorphologic, volcanological and geological data in a GIS system have been 36considered, for computation of the outside caldera slope, palaeo-coastline, palaeo-summit height and palaeo 37digital elevation model (DEM). The result is a 3D palaeo-geomorphological surface model of a volcano, 38reaching 640 m in height, with an increase of 4 km 3 in volume compared to the current edifice, covering 394km 2 more surface area and the method reveals the previous existence of parasite volcanoes. Two 40photorealistic images of the island are obtained by superposition of textures extracted from a current 41Quick Bird satellite image also. This technique for reconstructing the terrain of an existing volcano could be 42useful for analysing the past and future geomorphology of this island and similar locations. 43© 2012 Elsevier B.V. All rights reserved. 4445 46 47 48 1. Introduction 49 Many volcanic processes, including caldera formation and sector 50 collapses, may drastically change the early morphology of volcanic 51 edifices. Although the reconstruction of these early morphologies is 52 complex, 3D software and GIS technology allow reconstruction of 53 the palaeo-topography of volcanoes. Different parameters need to 54 be deduced for the size and shape of old edifices. Szekely and 55 Karatson (2004), using parameters derived from a digital elevation 56 model (DEM), infer the original shape of highly-degraded volcanic 57 structures in the Börzsöny Mountains (Hungary). Rodriguez et al. 58 (2004) proposed a reconstruction of a volcanic edifice in Paipa 59(Colombia) using pyroclastic deposits and 3D software to model 60flows. Rodriguez-Gonzalez et al. (2010) described a methodology 61for reconstructing the volcanic landform prior to a monogenetic ba- 62saltic eruption in El Lentiscal (Canary Islands, Spain), modelling 63both the scoria cone and the lava flow using morphometric modelling 64from the present-day DEM. Other methodologies for reconstructing 65original surfaces use inward extrapolation of the mean slope to define 66the main conic centre and height, and kriging with linear variograms 67as method of interpolation (Hildenbrand et al., 2008). Vogel and 68Marker (2010) reconstructed areas from the thicknesses of identified 69layers and then interpolated them with spline functions, as in 70Coleman et al. (2009) and Isaia et al. (2004), in their computation 71of the total volume of eruptions of the Astroni volcano (Italy). 72The multiplicity of the above methodologies indicates that a stan- 73dard procedure for the reconstruction of palaeo-volcanic surfaces is 74still lacking; significantly, none of the proposed methodologies takes 75into consideration a deformation parameter. 76Deception Island is an active Quaternary volcano located in the 77Bransfield Strait, between the South Shetland Islands and the Antarctic Geomorphology xxx (2012) xxx–xxx ⁎Corresponding author at: Departamento de Ingenieria Grafica, Escuela Tecnica Superior de Ingenieros, Av. de los Descubrimientos s/n, 41092 Seville, Spain. Tel.: +34 95448659; fax: +34 954486158. E-mail addresses: [email protected] (C. Torrecillas), [email protected] (M. Berrocoso), [email protected] (A. Felpeto), [email protected] (M.D. Torrecillas), [email protected] (A. Garcia). GEOMOR-04155; No of Pages 10 0169-555X/$ –see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.geomorph.2012.10.032 Contents lists available at SciVerse ScienceDirect Geomorphology journal homepage: www.elsevier.com/locate/geomorph Please cite this article as: Torrecillas, C., et al., Reconstructing palaeo-volcanic geometries using a Geodynamic Regression Model (GRM): Application to Deception Island volcano (Sout..., Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.10.032 UNCORRECTED PROOF 78 Peninsula (Fig. 1). The area is characterised by complex tectonics related 79 to the interaction of two main plates (the South American and Antarctic 80 plates), and three micro-plates (the Scotia, Phoenix (also known as 81 Drake) and South Shetland plates (Baraldo, 1999)). The bathymetric 82 study of the island and the surrounding area indicates that the defor- 83 mation is due to regional extension across the basin, with local, 84 superimposed effects related to caldera collapse and magma inflation. 85 Due to this geodynamic complexity, the reconstruction of Deception Is- 86 land palaeo-geometry requires the application of a new methodology, 87 as presented in this study. 88 The technique of terrain reconstruction described herein can be use- 89 ful for analysing the past and future geomorphology of the island. The 90 reconstruction of past conditions on this Island may help to clarify its 91 evolution, by establishing whether or not certain geomorphological sce- 92 narios are possible, and may give some clues to support or rule out one 93 of the proposed theories on its evolution. Furthermore, the construction 94 of likely scenarios for the near future could contribute to a better evalu- 95 ation of the volcanic hazard by the identification of the geomorphic fea- 96 tures symptomatic of possible instability related to future volcanic 97 eruptions or earthquakes. 98 2. Methodology 99 A new method for the reconstruction of palaeo-geometries here 100 applied here to the pre-caldera volcano of Deception Island. This ap- 101 proach can be divided into two distinct and successive stages: 102 a) In the first stage, the existing remains of the palaeo-surface are 103 extracted, and the relevant geometries of the palaeo-volcano are 104 determined. Data from the geological, topographic, bathymetric 105 and geomorphological maps are fundamental to this stage. 106 Existing hypotheses of the island's geological evolution must be 107analysed carefully to define peculiar aspects of the shape and sur- 108faces to be reconstructed; these include the palaeo-coastline, the 109number of the main parasitic volcanoes and their height, and 110palaeo- or pre-caldera deposits. These data are used to define 111the most likely palaeo-surface, 112b) In the second stage, a Geodynamic Regression Model (GRM) is ap- 113plied to this palaeo-surface to transform it to a specific time in the 114past. The regional and local deformation of the volcano surface is 115studied and quantified to calculate a geometric transformation to 116the selected time using deformation vectors. The date in the past 117for this GRM is also established in this stage. Before calculating 118the final surface, important parameters are estimated, such as 119the mass balance due to ice, glaciation periods and sea level 120values, which are potential factors of influence, for re-analysing 121or re-calculating the volcano's height in the reconstruction. Final- 122ly, a DEM is interpolated with the palaeo-data, and the definitive 123morphology is recreated. To improve the visual aesthetics of the 124reconstruction, real or postulated surface textures are applied. 1252.1. Palaeo-reconstruction of the pre-caldera volcano on Deception 126Island 1272.1.1. Geomorphology and geological evolution of Deception Island 128Deception Island (South Shetland Islands, Antarctica) is an emerged 129volcano less than 780 kyr old (Baraldo et al., 2003) whose geological 130evolution is marked by the formation of a large, though hitherto 131undated, central caldera that clearly separates the island'sstratigraphy 132into pre-caldera and post-caldera deposits. 133The island has a submerged basal diameter of 30 km, an altitude of 1341500 m from the sea bottom (Barclay et al., 2009), and 540 m m.a.s.l. 135The emerged portion is horseshoe-shaped with a diameter of about Fig. 1. Regional tectonics and location of Deception Island (South Shetland Islands, Antarctica). 2C. Torrecillas et al. / Geomorphology xxx (2012) xxx–xxx Please cite this article as: Torrecillas, C., et al., Reconstructing palaeo-volcanic geometries using a Geodynamic Regression Model (GRM): Application to Deception Island volcano (Sout..., Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.10.032 UNCORRECTED PROOF 136 15 km. The central sector of the island is a sea-flooded caldera depres- 137 sion (Port Foster), with a diameter of 8–10 km connected to the open 138 sea through Neptune'sBellows(Fig. 2). 139 The morphology of the island exhibits a large variety of landforms 140 and deposits derived from the volcanic activity. Approximately 57% of 141 the surface is covered by glaciers (Smellie et al., 2002). Therefore, the 142 main processes that control the geomorphology of Deception Island 143 are volcanic activity and glacial action. Streams and lakes formed by 144 melting of ice and snow, periglacial activity producing gelifraction, 145 slope processes and the presence of permafrost have also contributed 146 to the evolution of the island's relief (Smellie et al., 2002). The slopes 147 of the outer side of the caldera rim preserve landforms of a 148 pre-caldera edifice, but the original morphology of the caldera is not 149 completely preserved because of marine erosion, collapse of inner 150 flanks, and post-caldera volcanic and hydrothermal activity. The 151 outer perimeter consists mainly of sub-vertical cliffs about 20–40 m 152 high; these are remarkably uniform in height along the northern 153 and western coast (Kendall Terrace) and in the southern area (Cathe- 154 dral Crags) (Fig. 2). The cliffs show signs of landward retreat caused 155 by sea erosion, with numerous islets, stacking and rocks. The mor- 156 phology of the surrounding marine shelf indicates an early larger vol- 157 cano eroded to form an extensive 3–5 km wide submarine platform 158 at depths b100 m on the north and west sides. With respect to glacial 159 geomorphology, the stability of the ice front and ice cover has been 160 influenced by both climate fluctuations and volcanic eruptions 161 (Smellie et al., 2002). 162 Nearly 60 well-preserved craters, fumaroles, areas of heated 163 ground and deposits from fumarole activity concentrate in the inner 164 sector of the caldera and are associated with the post-caldera volcanic 165 activity (Fig. 2). The most extensive and voluminous flows are located 166 in the north, in Kendall Terrace. 167 Several hypotheses exist on the shape of Deception Island's before 168 the caldera formation. Hoteldahl (1929) and Olsacher (1956) propose 169 that, before the collapse, there was a single stratovolcano, whilst 170 Hawkes (1961) considers the island a collapsed structure deriving 171 from the subsidence of four pre-existing volcanoes along a ring frac- 172 ture affecting the underlying basement. Casertano (1963) and Baker 173 et al. (1975) explain the present shape of the island as the result of 174 the collapse of a single volcano, as also Hawkes (1961), but with 175 some parasitic cones in the Neptune Bellows area (see Fig. 3); 176 Birkenmajer (1992) supports the hypothesis of a single volcano 177 with smaller, satellite vents located on its slopes. In contrast Marti 178 and Baraldo (1990),Smellie (2001) and Baraldo et al. (2003) propose 179a large central stratovolcano with a basement diameter of between 20 180and 30 km; their hypothesis is based on the radial distribution of the 181pre-caldera deposits, as well as multiple small eruptive centres, al- 182though they do not fully agree with the polygenetic volcano 183suggested by Hawkes (1961). 184Regarding the formation of the caldera, no geochronological data 185are available and several hypotheses have been proposed in this re- 186spect. The collapse has been attributed to the existence of a large 187ring fault caused by tangential dislocation and associated radial faults 188(Olsacher, 1956), or to the presence of various ring-shaped and radial 189faults (Hoteldahl, 1929; Hawkes, 1961; Birkenmajer, 1992). Smellie 190(2001) suggests that the edifice collapsed in a major eruption, 191which reactivated pre-existing structures related to the tectonics of 192the Bransfield Strait. Vila et al. (1992),Ortiz et al. (1992),Rey et al. 193(1995) and Garcia et al. (1997) also linked the present-day structure 194of the island with regional seismic activity generated by a fracture 195zone in the Bransfield Strait. Baraldo (1999) suggested that the col- 196lapse of the central part of the island had its roots in an area of 197transtension, and compared the collapse to the formation of a 198‘pull-apart’basin. Marti et al. (1996) rejected the existence of circular 199and radial faults, and explained the collapse as a reactivation of nor- 200mal faults orthogonal to the Bransfield Strait extension, following a 201relatively large eruption in terms of volume ejected. 202Great differences, of almost 2000 m, exist regarding the estimated 203height of the stratovolcano. An altitude of 700–900 m.a.s.l. can be cal- 204culated using the data provided by Baker et al. (1975).Birkenmajer 205(1992) proposed a height of 2500 m.a.s.l., whilst Ben-Zvi et al. 206(2009) assumed a height of 500 m.a.s.l. in recreating a cone with 207the material emitted in the great eruption before the collapse. 208Post-caldera volcanism on Deception Island mainly developed 209within the central depression, with small-volume eruptions (about 2100.1 km 3 of volcanites between 1956 and 2003, according to 211Torrecillas et al., 2012) that generated phreatomagmatic and 212strombolian deposits (Marti et al., 1996; Smellie, 2001). All the ex- 213posed post-caldera rocks appear to be late Pleistocene and recent, 214probably b100 kyr, in age (Shultz, 1970; Smellie, 2001). Recent erup- 215tions (see Fig. 2) since 1842 occurred in the 1829–1912, 1829–1956, 2161912–1917 and 1967–1970 periods. All were moderate in magnitude, 217with small volumes of magma emitted, and of short duration, from a 218few hours to 2–3 days (Roobol, 1973). Previously, Orheim (1971, 2191972) reported between 8 and 33 eruptions during the last 220200 years, whilst Björck et al. (1991) refers to 14 eruptions during 221the last 5 kyr. Fig. 2. Morphotectonic elements (Paredes et al., 2007), historical eruptions, names of geographical features and research stations on Deception Island, and pre-caldera deposits according to Smellie et al. (2002). 3C. Torrecillas et al. / Geomorphology xxx (2012) xxx–xxx Please cite this article as: Torrecillas, C., et al., Reconstructing palaeo-volcanic geometries using a Geodynamic Regression Model (GRM): Application to Deception Island volcano (Sout..., Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.10.032 UNCORRECTED PROOF 222 2.1.2. Current palaeo-surface: pre-caldera deposits and palaeo-coastline 223 The first stage of the methodology proposed here the currently- 224 available data of the palaeo-surface before collapse. The latest pub- 225 lished hypothesis on the caldera formation process (Marti et al., 226 1996; Smellie, 2001) states that it formed by the collapse that 227 followed an eruption of large volume, so the available points of the 228 palaeo-surface are represented by the highest levels of the 229 pre-caldera deposits. The digital geological map, at a 1:25,000 scale 230 (Marti and Baraldo, 1990; Smellie et al., 2002), shows the location 231 of the outcrops of the pre-caldera. First, the pre-caldera deposits 232 were extracted (Fig. 2) and second, a digital topographic map 233 1:25,000 (SGE, 2006) and its corresponding DEM, with spatial reso- 234 lution of 2 m, were used to determine the highest elevation of each 235 deposit inside and outside the caldera. The highest points of these 236 deposits on the adjacent islands, Låvebrua and New Rock (Fig. 2) 237 were also included. The elevation of the deposits extracted from 238 this reconstruction represents a minimum estimate because may 239 have been greater in areas where the deposits are not exposed. 240 Another important item of data on the current surface is the outer 241 shoreline and bathymetry of Deception Island; this is necessary for 242 the determination of the palaeo-coastline. The present coast exhibits 243a complex evolution, with high lava cliffs rising to a height of over 244100 m, and scattered with pre-caldera deposits on the northern and 245western shorelines; there is a linear coastline due to the action of sub- 246marine faulting to the east of the island (Fernandez-Ibañez et al., 2472005). There are some adjacent islands which, to judge from their 248stratigraphic correlation (New Rock Island) or their possible associa- 249tion with a parasitic vent (Låvebrua Island) (Birkenmajer, 1992), 250must have once been part of Deception Island itself. 251The first geometric approximation of the palaeo-coastline is the 252graphic proposed from Baraldo's hypothesis for the formation of the 253island with a stratovolcano and several parasitic volcanoes (Baraldo, 2541999), see Fig. 4. With the aim of improving this geometry, the ex- 255trapolation of the dips of the pre-caldera deposits from the digital 256geomorphological map (Smellie et al., 2002) to bring the surface clos- 257er to sea level was considered. Only six dip values are near the coast- 258line. Then an exterior bathymetry of the island (scale 1:500,000) in 259raster format (Barclay et al., 2009), in an attempt to find the shape 260near the location of the volcanoes that predated the collapse (scale 2611:200,000), as proposed by Baraldo (1999) (Fig. 4), including the ad- 262jacent islands was considered. The initial selection was the −100 m 263bathymetry, although this has to be interpolated in zones where no Fig. 3. Geological evolution models. a) Polygenetic volcano model and geological cross-section of Deception Island proposed by Hawkes (1961). b) Theory of Deception Island's evolution according to Baker et al. (1975). 4C. Torrecillas et al. / Geomorphology xxx (2012) xxx–xxx Please cite this article as: Torrecillas, C., et al., Reconstructing palaeo-volcanic geometries using a Geodynamic Regression Model (GRM): Application to Deception Island volcano (Sout..., Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.10.032 UNCORRECTED PROOF 264 information is available; and in the south and east of the island, the 265 curve is extended slightly to include some of the boundaries of the 266 parasitic volcanoes. 267 2.1.3. Current palaeo-surface: location and height of the stratovolcano 268 An attempt was made to define the pre-caldera edifice by studying 269 the actual topography of the island. With that aim, four possible pla- 270 nimetric locations of the summit were selected based on geometric 271 criteria. The four centres considered are the geometric centres 1 of 272the present dividing line (cD); 2 of the outer coast (cOC); 3 of the 273inner coastline (cIC), and 4 of the deepest (−170 m) bathymetry of 274the inner bay (cB). As can be observed in Fig. 5a, cD, cOC and cIC 275are very close each other, so it was decided to take their arithmetic 276mean value (cM) and then study only two points (cB and cM). 277The radial slopes extrapolated from these possible summit loca- 278tions were then studied. Starting from these two points (cB and 279cM), eight radial profiles were selected to compute the mean slope, 280which was then extrapolated, in both cases, to find the point of inter- 281section, over Port Foster, that is taken as one possible location of the 282central peak. This methodology has been widely used previously, for 283example by Hildebrand et al. (2008, Fig. 5). As the Deception Volcano 284is an island with high cliffs along its coastline, the mean slope com- 285puted with the present topography is not very representative, so it 286was decided to consider the mean slope closer to the highest point 287of each profile. Fig. 5b shows the planimetry of the profiles considered 288with a line joining the summit of each profile for the two centres and 289two cases of slopes studied, mean slope and the mean slope closer to 290the highest point. The possible planimetric locations of the summit 291tend to be in the south, with only six points out of the total of thirty 292two in the north. This may indicate the location in the southern 293zone of the parasitic volcanoes that several authors hypothesised 294(Casertano, 1963; Baker et al., 1975; Marti and Baraldo, 1990; 295Birkenmajer, 1992; Smellie, 2001; Baraldo et al., 2003), in view of 296the fact that the mean slope value is higher in the south, correspond- 297ing with a rough relief. It was decided to eliminate profiles running 298N–S and NNE–SSE to reduce this possible influence of the parasitic 299volcanoes. The mean location of summit is x=619,309 m, y= 3003,015,645 m and z=1267 m.a.s.l, in UTM projection, zone 20S and 301geodetic system WGS84, with standard deviations of σ x =± 3021431 m, σ y =±1348 m and σ z =±413 m. This is at a distance of 3031200 m from the planimetric location proposed by Baraldo (1999), 304and falls within the margin of error in location. 305With respect to the height, the values proposed by previous au- 306thors should be recalled: 700–900 m.a.s.l by Baker et al. (1975), 3072500 m.a.s.l. by Birkenmajer (1992) and 500 m.a.s.l. by Ben-Zvi et Fig. 4. Baraldo's hypothesis for the formation of the island (Baraldo, 1999), with the defined palaeo-coastline partly coinciding with the −100 m bathymetric curve (Barclay et al., 2009), extended in the southern zone to cover the limits of the parasitic volcanoes. Fig. 5. a) Geometric centres on the island initially studied as possible palaeo-summits; b): The figure obtained by joining 1)the summit elevations given by the profiles from the midway point between the coast and the caldera (cM) and 2)the centre of the bathymetric curve (cB). 5C. Torrecillas et al. / Geomorphology xxx (2012) xxx–xxx Please cite this article as: Torrecillas, C., et al., Reconstructing palaeo-volcanic geometries using a Geodynamic Regression Model (GRM): Application to Deception Island volcano (Sout..., Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.10.032 UNCORRECTED PROOF 308 al. (2009). The only value that agrees with the height obtained in the 309 present study, and its standard deviation, is that of Baker et al. (1975). 310 2.1.4. GRM: geometric transformation 311 In this second stage,the digital tectonic model of the area, the 312 local deformation of the Island obtained by Berrocoso et al. (2008), 313 and the digital morphotectonic alignments (scale 1:25,000, Paredes 314 et al., 2006, 2007; Perez-Lopez et al., 2007), see Fig. 2, were used. 315 The other main parameter is the past date; the period of regression 316 selected was 100 kyr (Smellie, 2001), corresponding with the dating 317 of the oldest rock before the formation of the caldera (carried out 318 by Shultz, 1970): hence the most recent date estimated for that event. 319 Deception Island is located at the north-western end of the expan- 320 sion axis of the Central Bransfield Basin; its superficial deformation is 321 due to expansion of the Bransfield Rift (Gracia et al., 1996; Barker et 322 al., 2003; Berrocoso et al., 2008), with superimposed local effects 323 due to caldera collapse and magmatic activity (Vila et al., 1992; 324 Berrocoso et al., 2008). 325 Gonzalez-Ferran (1991) suggested a mean value for the Bransfield 326 Rift expansion of 2.5–7.5 mm/yr in the NW–SE direction for the last 327 2 Myr. More recently, Dietrich et al. (2004) indicated a general value 328 for this displacement of ~10 mm/yr in the NE–SW direction for South 329 Shetland Islands; and the research group led by Prof. Berrocoso esti- 330 mates a global horizontal mean displacement 20.5 mm/yr from 1999 331 to 2009 in Deception Island, in the same direction as Dietrich et al. 332 (2004), both using Global Positioning system (GPS) data. Although 333 Graciaetal.(1996,Fig.5)show strike directions of fault scarps in the 334 Central Bransfield Basin, where Deception Island is located, in both di- 335 rections, NE–SW and NW–SE, the number of faults in the latter direction 336 is one order of magnitude lower than in the former. It is therefore pos- 337 sible that, over the years since the formation of the caldera, the general 338 direction of displacement has been the present-day NE–SW direction, 339 but always of less magnitude than the NW–SE displacement. 340 Regarding local deformation, Perez-Lopez et al. (2007) proposes 341 the existence of the same two main directions of deformation to ex- 342 plain the elliptical form of the caldera's lip. Geodetic studies carried 343 out between 1987 and 2011 by Berrocoso's team also computed de- 344 formation models for Deception Island, without any regional dis- 345 placement of South Shetland Island; horizontal deformation rates 346 up to 40 mm/yr were obtained in 1989–96 at the GPS stations of 347 BARG and FUMA (Ramirez et al., 2008); these models confirm the 348 two main directions of extension of the Bransfield Rift (NW–SE and 349 NE–SW) as the directions of local deformation (see Fig. 6, for 350 2002–2003). In the last 20 years, the local deformation can be quan- 351 tified, with values of 15 mm/yr for NE–SW, and 5 mm/yr for NW–SE. 352 Although 20 years of deformation study are not significant on a time 353 scale of 100 kyr, these values and directions are in accordance with 354 the morpho-structural evolution of the Central Bransfield Basin 355 presented by Gracia et al. (1996, Fig. 10), where the NE–SW deforma- 356 tion direction is predominant over the NW–SE one. Therefore, these 357 conservative values as input parameter for our GRM were taken. 358 Taking into account the combined regional and local geodynamic 359 deformation, a geodynamic regression model (GRM) with a planimetric 360 transformation for a period of 100 kyr using values of 1.5 km (NE–SW) 361 and 0.5 km (NW–SE) was applied. 362 This transformation converts an approximate circle to an ap- 363 proximate ellipse due to differences in the values for the two direc- 364 tions, and has been applied to the current palaeo-coastline, to the 365 pre-caldera deposits points, to the circular limits of Baraldo's para- 366 sitic volcanoes, and to the centre of the main volcano (Fig. 7). 367 After transformation, the circular boundaries of Baraldo's parasitic 368 volcanoes became ellipses, but after applying the value of the 369 semi-major axis, they recovered their circular shape. Although this 370 final shape obtained for the palaeo-coastline is not approximately 371 circular, by the date of reconstruction selected (100,000 years 372 ago) this volcano was already some 600,000 years old, according 373to the estimates of its date of initial formation, and so some of its 374original circularity could have been lost. The presence of parasitic 375volcanoes could also modify the final shape. 3762.1.5. GRM: recalculated heights of the main volcano and parasite cones 377The summit height calculated in the first stage has an elevation 378error of σ z =±413 m; taking this into account, the maximum height 379estimated for the Deception Island volcano is 540 m. It was decided to 380re-calculate the summit height with the palaeo-boundary data and 381the spot heights obtained from the GRM in an initial interpolation 382of the island's topography, but only up to the lip of the caldera. This 383was done using the Topogrid method, an iterative finite difference 384method based on a thin-plate spline technique, using ESRI's ArcGIS™ 385software (version 10). Eight profiles were studied: two oriented 386along the main deformation axes and six others. Extrapolating the 387maximum final slope of each profile, a mean value of 580 m±62 m 388(Fig. 8) was obtained; accepting this uncertainty, this value is taken 389as the height of the original stratovolcano. 390Taking into account the mass balance due to ice, Orheim (1972, 391p.7) defines a current equilibrium line at between 200 and 250 m, 392with accumulation zones of more than 40 m. The last glaciation 393began approximately 100 kyr ago (Newnham et al., 1999), so the 394mass of snow and ice had to be considered, and the value of the defin- 395itive height needs to be increased. By raising the altitudes by values of 396between 200 and 250 m, the mean slope changes, and the summit 397height increases. From the profiles, a mean increase of 70±30 m is 398determined for the summit height, and this is then rounded off to 399650 m. 400Before the final interpolation, it was necessary to determine the 401height of the proposed parasitic volcanoes. To do this, data on the el- 402evation of the pre-caldera deposits located within the limit of each 403initial volcano were used as minimum height. To calculate the sum- 404mit heights of the parasitic cones, a slope of 10° is considered, 405which corresponds to the mean slope of Deception Island's 406palaeo-volcano and to the current mean slope. 4072.1.6. GRM: interpolation, sea level and virtual model 408Final values for the pre-caldera topography have been calculated 409using a two-stage process of interpolation. First, the principal strato- 410volcano was reconstructed, and then the adjacent parasite volcanoes 411were added. The Topogrid method was used for both the interpola- 412tions. The first interpolation shows irregular small mounds in the 413southern zone; these forms were interpreted as parasitic vents 414existing in the areas presently known as Neptune's Bellows and Mac- 415aroni Point. In the second interpolation these mounds were replaced 416by parasitic volcanoes. 417Before stating the definitive volume and perimeter values 418obtained, it is worth looking at one more factor of potential influence 419on our reconstruction: Antarctic sea level trends for the Holocene– 420Late Pleistocene. For King George Island, which also belongs to the 421South Shetland archipelago, around 40 kyr ago, Nakada et al. (2000) 422estimated a value of 10 m above the present sea level. In the Vestfold 423Hills, East Antarctica, Zwartz et al. (1998) proposed values ranging 424from 7.5 m (8000 years ago) to a 9 m above the present sea level 425(6.2 kyr ago). Rohling et al. (2009) estimated the sea level for the 426Middle Pliocene epoch (3.0–3.5 Myr) at 25±5 m above the present 427level in Antarctica, presenting a study of this period which included 428periodic cycles when the sea level rose above present-day levels. 429The graphic material presented by Rohling et al. (2009) correspond- 430ing to 100±5 kyr ago, shows relative sea levels between 0 and 40 m. 431As a conservative value, it was decided to take the value given by 432Nakada et al. (2000) for the geographic zone closest to Deception Is- 433land, and the upper sea level height used in the proposed model was 434reduced by 10 m to obtain the final result. 435The change in sea level reduced the estimated emerged stratovol- 436cano volume by 1 km 3 , leaving the final palaeo-volume at 19.6 km 3 , 6C. Torrecillas et al. / Geomorphology xxx (2012) xxx–xxx Please cite this article as: Torrecillas, C., et al., Reconstructing palaeo-volcanic geometries using a Geodynamic Regression Model (GRM): Application to Deception Island volcano (Sout..., Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.10.032 UNCORRECTED PROOF 437 as opposed to the present-day volume of 15.7 km 3 . In the reconstruc- 438 tion, the palaeo-surface area is 104.8 km 2 compared with the 439 present-day area of 96 km 2 ; the perimeter is 42 km compared to 440 the present outer perimeter of 57 km (excluding the internal coast- 441 line). This value of the perimeter has been obtained from a map at a 442 scale of 1:100,000, and these values are partly the result of including 443Port Foster. The height of the volcano is also affected, so the final 444palaeo-volcanic summit height takes a definitive value of 640 m. 445Fig. 9a shows the palaeo-DEM with the current coastline, and, in 446Fig. 9b and c, two 3D views. In Fig. 10a and b there are two 447photorealistic images of the island obtained by superposition over 448the palaeo-surface of textures extracted from the 2003 Panchromatic Fig. 6. Horizontal displacement rates of surface deformation values for the period 2002–2003 at several points of the deformation control network on Deception Island. Fig. 7. Result of applying the Geodynamic Regression Model to pre-caldera deposits, Baraldo's parasite volcanoes and palaeo-coastline, the latter with new sizes after reshaping them as circles using the semi-major axis value as radius value. 7C. Torrecillas et al. / Geomorphology xxx (2012) xxx–xxx Please cite this article as: Torrecillas, C., et al., Reconstructing palaeo-volcanic geometries using a Geodynamic Regression Model (GRM): Application to Deception Island volcano (Sout..., Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.10.032 UNCORRECTED PROOF 449 Quick Bird satellite image of the island and photographs. For the sake 450 of greater realism, the summit peak has been replaced by a ring. 451 3. Summary and conclusions 452 The morphology of a volcano is obviously influenced by the erup- 453 tive activity but geodynamics and volcanic deformation may also con- 454 tribute. The diversity of methodologies proposed by various authors 455 for the reconstruction of palaeo-volcanic surfaces indicates that a 456 standard procedure is still lacking. Significantly, the methodologies 457 previously proposed do not take into consideration geodynamics 458 and superficial deformation parameters, as well as differences in sea 459 level or mass balance due to ice. A volcanic reconstruction method 460 is proposed which differs from the other ones because it includes 461 the Geodynamic Regression Model (GRM) and takes into account 462 the tectonic and volcanic deformation. There are two stages in the 463 GRM approach proposed here. The objective in the first stage is to ob- 464 tain the palaeo-surface from the existing remains and from existing 465 hypotheses of the particular volcano's evolution. In the second 466stage, deformations are included and deformation vectors are de- 467fined. The palaeo-surface is obtained with a geometric transforma- 468tion. If the volcano's height is not considerably above the sea level 469or it is affected by permanent ice and snow, the influence of these fac- 470tors on the height must be evaluated. 471In the reconstruction present here, the influence of the GRM on 472the final shape of Deception Island volcano is verified. Although this 473final shape is not approximately circular, which is the normal shape 474in most volcanoes, by the selected time of reconstruction (100 kyr 475ago) this volcano was already some 700,000 years old, according to 476the age estimates, and some of its original circularity could have 477been lost. The final surface reveals the existence of early parasitic vol- 478canoes with altitudes of much less than 650 m in the locations pres- 479ently known as Neptune's Bellows and Macaroni Point. 480A pre-collapse 100 kyr time period age was selected for the recon- 481struction of the Deception Island palaeo-edifice. The results show an 482old stratovolcano with a perimeter slightly less than 42 km and a vol- 483ume of 19.6 km 3 . With respect to the palaeo-summit height, our ini- 484tial value of 580 m (with σ z =±62 m) was modified to 640 m by 485taking into account the estimated changes in the sea level and the 486mass of ice and snow cover. A new value for σ z has been estimated 487at about ±100 m because of the influence of the snow has an error 488of ±30 m and the palaeo-sea level error is unknown. 489The accuracy of this reconstruction depends on the degree of deg- 490radation of the volcanic flanks and on the knowledge of the volcano's 491evolution. The geological evolution of Deception Island is not clear, 492and the relicts of the palaeo-volcano are scarce due to more recent 493volcanic activity. 494The main outcome of our study is that GRM method can be applied 495to other scenarios provided that reliable local deformation data are 496available. 4974. Un Q2cited reference 498Orheim, 1975 499Acknowledgements 500This geodetic research has been carried out with the support of the 501Spanish Ministry of Education and Science as part of the National Ant- 502arctic Program. To date, the following research projects have been Fig. 8. DEM resulting from the interpolation of data, with the subsequent elimination of the caldera, to calculate a possible summit height, and location of main profiles used to determine a palaeo-summit. Fig. 9. a) Deception Island DEM before caldera formation with superposition of present-day limit and Holocene limit without considering differences in sea level, b) 3D view from the E with 3×exaggeration in Z and c) 3D view from the NW with 3×exaggeration in Z. 8C. Torrecillas et al. / Geomorphology xxx (2012) xxx–xxx Please cite this article as: Torrecillas, C., et al., Reconstructing palaeo-volcanic geometries using a Geodynamic Regression Model (GRM): Application to Deception Island volcano (Sout..., Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.10.032