1 Combining shock barometry with numerical modeling: insights into 2 formation – The example of the 3 () 4 5 S. Holm-Alwmark1*, A. S. P. Rae2, L. Ferrière3, C. Alwmark1, and G. S. Collins2 6 7 1Department of Geology, Lund University, Sölvegatan 12, 223 62 Lund, Sweden. 8 2Department of Earth Science and Engineering, Imperial College London, SW7 2BP, UK. 9 3Natural History Museum, Burgring 7, A-1010 Vienna, Austria. 10 11 * Corresponding author. E-mail: [email protected] 12 13 14 Abstract 15 Siljan, central Sweden, is the largest known impact structure in Europe. It was formed at 16 about 380 Ma, in the late period. The structure has been heavily eroded to a level 17 originally located underneath the crater floor, and to date, important questions about the 18 original size and morphology of Siljan remain unanswered. Here we present the results of a 19 shock barometry study of quartz-bearing surface and drill core samples combined with 20 numerical modeling using iSALE. The investigated 13 bedrock granitoid samples show that 21 the recorded shock pressure decreases with increasing depth from 15-20 GPa near the 22 (present) surface, to 10-15 GPa at 600 meters depth. A best-fit model that is consistent with 23 observational constraints relating to the present size of the structure, the location of the down- 24 faulted , and the observed surface and vertical shock barometry profiles, is 25 presented. 26 The best-fit model results in a final crater (rim-to-rim) diameter of ~65 km. According to 27 our simulations, the original Siljan impact structure would have been a peak-ring crater. 28 Siljan was formed in a mixed target of sedimentary rocks overlaying crystalline 29 basement. Our modeling suggests that, at the time of impact, the sedimentary sequence was 30 approximately 3 km thick. Since then, there has been around 4 km of erosion of the structure. 31 32 Introduction 33 Impact cratering was once considered a minor geologic process without significance for the 34 evolution of Earth. Now, after more than 50 years of space exploration, we know that almost 35 all solid bodies in the Solar System display evidence of impact. The process is now known to 36 play a key role in the evolution of the Solar System, dominant in the formation of 37 planetesimals, and later planets, and it also most likely played an important role in shaping the 38 early crust of both Earth and other planets. Later in Earth’s history, impact cratering has 39 caused major environmental crises, even leading to at least one major mass extinction event, 40 at the Cretaceous-Paleogene boundary (Alvarez et al. 1980; Schulte et al. 2010). 41 In order to understand the major processes involved in impact cratering, a combination of 42 observations of impact structures, laboratory experiments, and numerical modeling has 43 proved to be successful, answering questions on the development of the transient cavity into 44 the final crater, the displacement of target rocks and formation of , the ejecta 45 process and the induced environmental effects (e.g., Melosh 1989; Pierazzo et al. 1998; 46 Melosh and Ivanov 1999; Collins et al. 2004; see also Osinski and Pierazzo 2013, and 47 references therein). However, some major questions regarding the crater-forming process 48 remain unanswered, e.g., how the energy of the impact is distributed in the target rocks, and 49 the details on how geologic materials behave under the extreme conditions prevailing during 50 crater forming processes. Also, more specific questions relating to the formation of complex 51 impact structures, with the genesis of central uplifts, remain to be answered. 52 Understanding the formation of impact structures, especially large ones, is complicated 53 due to the fact that the process has never been directly observed. Laboratory experiments 54 cannot replicate the exact conditions prevailing due to physical limitations, and in addition, 55 impact structures on Earth are rapidly obscured by tectonic processes, erosion, and 56 sedimentation, complicating their study. For these reasons, numerical modeling of the 57 formation of impact craters has become an increasingly important and successful tool to 58 understand the mechanisms behind crater formation, and in describing individual impact 59 structures (e.g., Collins et al. 2002; Collins & Wünnemann 2005; Wünnemann & Ivanov 60 2003; Goldin et al. 2006; Ferrière et al. 2008; Morgan et al. 2016; Rae et al. 2017). However, 61 the success of the numerical simulations relies on being able to ground-truth them against 62 actual observations made from impact structures and/or samples subjected to shock 63 metamorphism. One way to do this is to compare the distribution of modeled shock pressures 64 in an with determined shock pressures in physical samples from the modeled 65 impact structure (e.g., Rae et al. 2017). Determining peak shock pressures that rocks have 66 experienced can be achieved by characterizing the abundances and properties of shock 67 metamorphic features in rock-forming minerals of the target rocks. Previous detailed shock 68 barometry studies include the Charlevoix, Manicouagan, , Puchezh-Katunki, 69 Bosumtwi, Siljan, and West Clearwater Lake impact structures (see e.g., Robertson 1975; 70 Grieve and Robertson 1976; Dressler 1990; Fel’dman et al. 1996; Ferrière et al. 2008; Holm 71 et al. 2011; Rae et al. 2017). 72 In this paper, we present the results of a detailed study of samples from two drill cores 73 combined with numerical modeling to gain information on the characteristics of the large and 74 deeply eroded Siljan impact structure (Sweden). Our goals were to better constrain the 75 original size and morphology of the , to estimate the pre-impact sedimentary 76 sequence overlying the crystalline bedrock in the area, and to evaluate the amount of post- 77 impact erosion. We constrain our numerical simulations by comparison with the presently 78 observed structure, as well as the results of shock barometric analysis across the present 79 erosional level of Siljan that was presented by Holm et al. (2011), and also drill cores from the 80 structure (this study). This comparison provides robust insights into complex crater formation. 81 82 83 Geological Setting 84 The Siljan impact structure, located in the region of central Sweden, consists of a 85 central area with a diameter of 28-30 km surrounded by a partly lake-filled annular depression 86 (Fig.1). The structure lacks original crater morphology due to extensive erosion exposing 87 rocks that were originally located below the crater floor (Grieve 1988). The apparent annular 88 depression is thus also an effect of preferential erosion, and not an original crater feature 89 (Holm et al. 2011). The central area, and the area to the west of the structure, is dominated by 90 Dala granites of Järna and Siljan types, intruded as part of the Trans-Scandinavian Igneous 91 Belt (intrusion ages 1.85-1.65 Ga; Högdahl et al. 2004 and references therein), with rare 92 occurrences of mafic intrusive, extrusive, and sedimentary rocks. To the east of the structure, 93 granitic Svecofennian rocks of older ages dominate (2.1-1.87 Ga; Högdahl et al. 2004 and 94 references therein). The impact structure was formed in the end of the Devonian period, at 95 380.9 ± 4.6 Ma (Reimold et al. 2005; Jourdan et al. 2012). 96 Inside the 10 km wide annular depression, Paleozoic sedimentary rocks constituting a 97 megabreccia of m- to km-sized blocks (Collini 1988) have been preserved. The apparent 98 stratigraphic thickness of the sedimentary sequence varies around the structure, with 99 maximum values of ~600 m in the western part of the Siljan ring (Juhlin et al. 2012; Lehnert 100 et al. 2013). At the time of impact, the thickness of the overlying sedimentary rocks/sediments 101 is not known, a fact relating to the absence of exposed Paleozoic sedimentary rocks outside of 102 the Siljan ring, due to erosion. This sequence has been quoted as being 400-500 (or even 650) 103 m thick at the time of impact (Rondot 1975; Collini 1988; Vlierboom et al. 1986; Lindström 104 et al. 1991). However, a substantially thicker sedimentary sequence associated with a thick 105 Caledonian foreland basin, up to 4 km, has been suggested based on studies of thermal 106 indicators, such as δ18O/δ13C, conodont alteration indices, and fission track data (Tullborg et 107 al. 1995; Larson et al. 1999; Cederbom et al. 2000; Cederbom 2001). The interpretation of 108 Larson et al. (1999) and Cederbom et al. (2000) based on fission track data, of a several km 109 thick Caledonian foreland basin was challenged by Hendriks & Redfield (2005), who 110 suggested that there is no evidence, either from fission track, or from the geological data of 111 the region, for a substantial Caledonian foreland basin covering Fennoscandia, prompting a 112 so-far unresolved discussion (Larson et al. 2006; Hendriks & Redfield 2006). The large 113 discrepancy in the estimated thickness of the sedimentary unit in the Siljan area, at the time of 114 impact, is a result of uncertainty regarding the location of Siljan in relation to the foreland 115 basin and bulge of the Caledonides, along with the exact quantity of erosional products 116 transported to the Caledonide foreland basin being unknown. At the time of impact, this 117 sedimentary sequence was most likely composed of unconsolidated sediments overlying 118 consolidated sedimentary rocks. However, the relative thicknesses of each is not known and, 119 as we discuss later in the paper, we use both terms to describe this unit of /rock. 120 After the impact, the area has remained tectonically stable, and apart from extensive 121 erosion, the structure is well preserved, presently partly buried under Quaternary deposits, 122 dense forest, lakes, and swamps. Estimates of the amount of erosion were presented by Grieve 123 (1988) to a minimum of 1.5 km of the rim area and 1 km for the central area, and Kenkmann 124 and von Dalwigk (2000) suggested a minimum of 2 km of erosion for the structure. This was 125 essentially based on the thickness of the overlying sedimentary rocks, which defines the 126 minimum erosion level. 127 The size of the Siljan impact structure has been the subject of analysis on a number of 128 occasions in the past. The most commonly quoted diameter, 52 km (Grieve 1982, 1988), 129 essentially corresponds to the outer limit of Paleozoic sedimentary rocks. Kenkmann and von 130 Dalwigk (2000, p.1194) made a conservative estimate that the “final crater diameter” of Siljan 131 was 65 km (with a transient cavity diameter of 42 km), based on the geographical limit of the 132 zone of intense fracturing of the crater basement. Furthermore, Kenkmann and von Dalwigk 133 (2000, p.1197) suggested a final crater diameter of 75-80 km based on the scaling relationship 134 between central uplift diameter and final crater diameter (Therriault et al. 1997), and taking 135 the estimated level of erosion into account. Henkel and Aaro (2005, p.254, 281) suggested the 136 “erosional crater diameter” of Siljan to be 75 km based on topographic features around the 137 structure, and argued that the “final diameter” of the structure could have been as large as 85 138 km. Holm et al. (2011) furthered the size discussion by applying a number of scaling 139 relationships based on the lateral distribution of planar deformation features (PDFs) in quartz 140 grains from target rocks, and provided numbers on the apparent crater diameter of Siljan with 141 a maximum in the 90 km region (see Table 4 in Holm et al. 2011). Most recently, the apparent 142 distribution of shatter cones at Siljan has been used to estimate a minimum apparent crater 143 diameter of 75 km (Osinski and Ferrière 2016). 144 145 146 Material and Methods 147 Shock barometry 148 The studied material consists of granitic bedrock (Dala granites) samples from two drill cores 149 obtained from the Siljan impact structure. The drill cores were obtained prior to the drilling of 150 the Gravberg-1 deep borehole in Siljan in 1986, as part of a pre-investigation campaign 151 resulting in nine shallow boreholes, drilled between 1983 and 1986 (e.g., Collini and Al 152 Dahan 1991; Juhlin et al. 1991). One drill core was recovered at Hättberg (approximate 153 coordinates N61°04.200’, E14°50.610’; Fig. 1) and has a total length of 602.83 m (below the 154 present day surface). From this core, ten samples were selected for investigation, at the 155 following depths: 5, 45, 99, 200, 300, 351, 400, 451, 500, and 601 m. The petrography of the 156 rocks recovered during the Hättberg drilling was recently described in detail by Reimold et al. 157 (2015). The other drill core was recovered at Vålarna (approximate coordinates N61°04.258’, 158 E14°57.545’; Fig. 1) and has a total length of 112.78 m. From this core, three samples were 159 taken at the following depths: 1, 50, and 99 m. From each sample from the two drill cores, 160 two to six thin sections were prepared after completion of macroscopic description and photo 161 documentation. The samples (Fig. 2) are all comparable in terms of lithology, representing 162 porphyritic grey-reddish granitic rocks with a medium to coarse grain size. 163 In Figure 3, all samples, with their relative positions in the drill cores, are displayed. From 164 here on, the samples are referred to as a one letter, and one-three numbers name (e.g., H99), 165 where the letter represents the drill core (H = Hättberg and V = Vålarna), and the numbers 166 correspond to the depth below the present surface in meters, at which the samples were 167 recovered. 168 169 Petrographic analysis and universal-stage measurements 170 The thin sections were first characterized based on mineral assemblages and shock 171 metamorphic features using a petrographic microscope. A more detailed study of the thin 172 sections was then performed using a Leitz 5-axis universal-stage (U-stage; Emmons 1943) 173 following the techniques described in von Engelhardt and Bertsch (1969), Stöffler and 174 Langenhorst (1994), and Ferrière et al. (2009). For PDF analysis, the orientations of optic axis 175 (c-axis) and poles perpendicular to PDF planes in individual quartz grains were determined 176 and then indexed using a stereographic projection template (presented by Ferrière et al. 2009). 177 Note that all PDFs with orientations that fall in the overlapping zone between the {101̅3} and 178 {101̅4} orientations were treated as {101̅3} orientations, as recommended by Ferrière et al. 179 (2009). 180 In this study, we aimed at measuring PDFs in 40 quartz grains per sample, in order to reach 181 an acceptable level of precision of the resulting dataset (see Ferrière et al. 2009). For most 182 samples, the number of grains in which PDFs were measured is 40, or just above, but for two 183 samples it was not possible to reach this number (see below). 184 The indexing of PDFs was done by hand, but polar angles between PDFs and the c-axis of 185 grains were also checked with the help of a computer program (Stereo32, developed by K. 186 Röller and C. Trepmann at Ruhr-Universität Bochum, Germany) to guarantee precise angular 187 relations. 188 All percentage calculations represent absolute frequencies, as defined by von Engelhardt 189 and Bertsch (1969), meaning that presented percentages are calculated as the number of 190 symmetrically equivalent planes measured in n quartz grains, divided by the total number of 191 measured PDF sets in n quartz grains. 192 193 Shock barometry 194 Peak shock pressures are most commonly estimated in naturally shocked rocks by identifying 195 and characterizing shock metamorphic features in quartz grains. This is because of the range 196 of shock metamorphic features that this mineral develops, in combination with the abundance, 197 robustness, and simple optical features of quartz. PDFs in quartz are of specific use as a shock 198 barometer because they form along specific crystallographic planes depending on the pressure 199 that the host crystal was subjected to (see e.g., Hörz 1968; Müller and Défourneaux 1968; von 200 Engelhardt and Bertsch 1969; Stöffler 1972; Stöffler & Langenhorst 1994; Grieve et al. 1996; 201 French 1998). For example, the onset of {101̅3}-equivalent planes requires shock pressures of 202 8-10 GPa, or pressures of 15 GPa, depending on experiment (Hörz 1968; Stöffler & 203 Langenhorst 1994; Huffman & Reimold 1996; French 1998, and references therein), whereas 204 above ~20 GPa (22-28 GPa), {101̅2}-equivalent planes should be as frequent as, or more 205 common than, ones oriented along {101̅3} (Hörz 1968; von Engelhardt & Bertsch 1969; 206 Grieve et al. 1996). Less common sets parallel to e.g., the {112̅1}, {213̅1}, {224̅1}, and 207 {314̅1} orientations, and their relationship with shock pressures are rarely discussed in detail 208 in the literature, but some of these planes are expected to require pressures of at least 13-15 209 GPa to form (Hörz 1968). They are generally seen as indicative of pressures exceeding the 210 pressures required for formation of {101̅3}-equivalent planes (e.g., Robertson 1975; Grieve 211 and Robertson 1976; Holm et al. 2011). In this study, we have used the same method (and 212 thus the same groups) for assigning shock pressures that was used in Holm et al. (2011), 213 which was based on the experimental studies cited above. This means that samples are first 214 grouped based on common characteristics, and then each group is assigned a specific range of 215 shock pressures that represents that group (see details below). The shock pressure range is 216 based primarily on the specific orientations of the population of PDFs in the samples. The 217 average number of PDF sets/grain is also considered when grouping the samples, because this 218 can be used to display the shock attenuation (e.g., Ferrière et al. 2008; Holm et al. 2011; Rae 219 et al. 2017). 220 221 Numerical modeling 222 The Siljan impact event, and in particular the formation of the crater, was simulated using the 223 impact-Simplified Arbitrary Lagrangian Eulerian (iSALE) shock physics code. iSALE is a 224 multi-rheology, multi-material code based on the SALE hydrocode (Amsden et al. 1980). The 225 original code was improved throughout the 1990s by several authors, incorporating an elasto- 226 plastic constitutive model, fragmentation models (Melosh et al. 1992), and various equations 227 of state (Ivanov et al. 1997). By the early 2000’s, subsequent developments resulted in the 228 SALEB (e.g., Ivanov 2005) and SALES-2 (e.g., Collins et al. 2002) codes, from which the 229 iSALE shock physics code is based. Development of the iSALE shock physics code has 230 included: a porous compaction model (Wünnemann et al. 2006), a dilatancy model (Collins 231 2014), and updated equations of state (Collins and Melosh 2014). 232 The iSALE code has been used to model several terrestrial impact structures, such as 233 Chesapeake Bay (Collins and Wünnemann 2005; Kenkmann et al. 2009), Ries (Wünnemann 234 et al. 2005; Collins et al. 2008a), Sierra Madera (Goldin et al. 2006), Chicxulub (Collins et al. 235 2008b), (Vasconcelos et al. 2012), West Clearwater Lake (Rae et al. 2017), 236 and Haughton and El’gygytgyn (Collins et al. 2008a). 237 Transient cavity size is a function of the impactor parameters: velocity, diameter, density, 238 and obliquity, and the target parameters: density, strength, and the acceleration due to gravity 239 (Melosh, 1989). In all simulations, a number of parameters were fixed; firstly, due to the 240 axisymmetric nature of 2D simulations, the angle of incidence of the impactor was 241 perpendicular to the target surface, significantly steeper than the most probable angle of 45˚. 242 Final crater size has been shown to scale with the vertical component of impact velocity, 243 rather than the velocity magnitude (e.g., Chapman and McKinnon 1986; Elbeshausen et al. 244 2009). Therefore, based on an average asteroidal impact velocity on Earth of 20.5 km/s (Le 245 Feuvre and Wieczorek 2011), an impact velocity of 15 km/s was used, approximately equal to 246 the vertical component of an impactor travelling at 45˚. Furthermore, adopting a slightly 247 lower impact velocity increases computational efficiency as it reduces the volume of 248 vaporized rock. 249 The impactor density was fixed between all simulations. Here, a granitic impactor was 250 used. Whilst the actual impactor is unlikely to be granitic in composition, importantly, it does 251 possess a similar density to stony asteroidal material. Furthermore, it is more computationally 252 efficient to use fewer materials in iSALE, hence the material of the impactor was matched to 253 the equation of state (EoS) of the basement rocks. The thermodynamic behavior of all 254 materials simulated here used the Analytic EoS program (ANEOS; Thompson and Lauson 255 1974). Consequently, until the nature of the impactor that struck Earth to form Siljan is 256 known, there will be some uncertainty in the impactor parameters selected in this study. 257 Nevertheless, the transient cavity sizes in our simulations possess considerably less 258 uncertainty. 259 After initial sensitivity testing, the material of the sedimentary sequence was fixed. The 260 initial sensitivity testing included quartzite (porous and non-porous), weak quartzite, and 261 calcite; analogous to sandstone, mudstone, and limestone, respectively. It was found that there 262 was no discernable difference between craters generated by simulations with both 2 and 4 km 263 of sedimentary rocks where the material parameters were varied. Consequently, porous 264 quartzite was used for all simulations. The basement material in the simulations was chosen to 265 be granitic. Here, we use the granite EoS of Pierazzo et al. (1997). 266 To ensure comparability between models, the same resolution (relative to the impactor 267 size) was used. Here, a high resolution of 50 cells per impactor radius was used. This results 268 in cell widths between 40 and 70 m for the range in impactor sizes investigated in this study. 269 A high resolution was required in order to ensure that the cell width was smaller than the 270 length of the cores investigated in the study. The constitutive model of materials in the 271 simulations account for variations in shear strength due to changes in pressure, temperature, 272 and damage (Ivanov et al. 1997). The strength properties of granite in all simulations were 273 constant, based on the properties used in previous studies (e.g., Wünnemann et al. 2005). The 274 strength properties of the sedimentary target were varied based on the parameters of 275 Güldemeister et al. (2015), although it was found that the final crater structure had little 276 sensitivity to the strength properties of the sedimentary rocks, as such the strength parameters 277 were fixed for all simulations. The constitutive model is supplemented by the block model of 278 acoustic fluidization, a transient weakening model, such that gravitational collapse of the 279 transient cavity is facilitated (Melosh 1989; Melosh and Ivanov 1999; Wünnemann and 280 Ivanov 2003). 281 In principle, acoustic fluidization supposes that acoustic vibrations in the target material 282 temporarily release overburden pressure. In turn, the release of overburden pressure allows 283 shear stresses in the material to overcome frictional forces. This facilitates the movement of 284 faults if vibrations are of sufficient magnitude. Observed over a large length-scale (at least an 285 order of magnitude larger than the size of individual rock blocks), the block model of acoustic 286 fluidization produces a Bingham-fluid rheology, i.e., a material with a yield strength and 287 viscosity (Melosh and Ivanov 1999). There are two principle input parameters of the block 288 model of acoustic fluidization: viscosity and decay time. These parameters were initially fixed 289 based on parameters from Rae et al. (2017), while the roles of impactor size and sediment 290 thickness were investigated. Subsequently, the effect of varying acoustic fluidization 291 parameters was also investigated. The fixed global and material parameters used in our 292 simulations are summarized in Tables 1 and 2. 293 294 295 Results 296 All the investigated granitic samples from the two drill cores are briefly described in 297 Appendix 1. They all display features related to . PDFs in quartz grains 298 were measured in all samples except H451 (Table 3). The reason is that this sample is 299 strongly fractured and affected by local cataclasis, and is poor in quartz grain content. In 300 sample H601, PDFs were measured in 27 quartz grains, and not in ~40 grains as in the others 301 cases, due to scarcity of quartz grains. Aside from PDFs in quartz, other shock metamorphic 302 features occur in the investigated samples, including planar fractures (PFs) in quartz, feather 303 features (FFs) in quartz, and PDFs in potassium feldspar. Some samples also contain 304 pseudotachylitic veinlets (e.g., Mohr-Westheide and Reimold 2011; Reimold et al. 305 2015) and cataclastic shear zones, namely samples H5, H45, H351, H451, H500, H600, and 306 V99. In this study, we refer to PDFs parallel to (0001), i.e., the basal plane of the crystal, as 307 basal PDFs, although these PDFs are multiple mechanical Brazil twin lamellae (e.g., Goltrant 308 et al. 1992). 309 310 Petrographic description of shock metamorphic features 311 Planar microstructures were observed in quartz grains in the form of PDFs, from one to nine 312 distinct PDF sets per grain (the average number of sets/grain ranging from 1.4 to 4.5 in the 313 samples, as seen using the U-stage), shock induced Brazil twins (one set per grain), PFs (in 314 general also one set per grain), and FFs (one set, associated with PFs) (Table 3; Fig. 4). In 315 general, for a given sample, 100% of the quartz grains contain shock-induced planar 316 microstructures, with the exception of samples H351, H601, V1, and V50, in which 2.5, 3.7, 317 25, and 2.4%, respectively, of the quartz grains display no apparent signs of shock 318 metamorphism. The PDFs are generally decorated, i.e., the original glass planes (now 319 recrystallized to quartz) are marked by planar arrays of small fluid inclusions (Fig. 4; e.g., 320 Goltrant et al. 1992; Trepmann and Spray 2006), although, at the optical microscope scale, 321 some "fresh-looking" lamellae were also seen. Basal PDFs appear more strongly decorated 322 than those oriented parallel to other crystallographic planes, which was already noted by 323 Holm et al. (2011). PDFs oriented parallel to especially the {101̅3} and {101̅4} orientations 324 generally cross entire grains, whereas higher polar angle PDFs, oriented parallel to e.g., the 325 {101̅1}, {224̅1}, and {213̅1} planes, look somewhat more faint, and are almost always seen 326 only in restricted areas of the grains. In some cases, they are so faint that they can be easily 327 overlooked, something that was already discussed by Losiak et al. (2016). 328 The majority of the PDF sets (Table 3, Fig. 5) are oriented parallel to the {101̅ 3} 329 orientation (representing from 48.6 to 65.2%, and in average 55.3%; excluding sample V1 in 330 which basal PDFs dominate). A large proportion of these PDFs cannot be uniquely indexed as 331 parallel to the {101̅3} orientation due to the overlap with the {101̅4} orientation, and are thus 332 reported in Figure 5 (in grey) on top of the uniquely indexed sets parallel to the {101̅3} 333 orientation (see above and Ferrière et al. 2009). 334 The second most abundant orientation is (0001), i.e., basal PDFs, constituting on average 335 about 24.2% (from 16.7 to 26.1%; excluding sample V1 in which basal PDFs represent 336 72.2%) of the total population of measured PDFs. In addition to these two dominant 337 orientations, planes parallel to the {101̅4}, {101̅2}, {101̅1}, {101̅0}, {112̅2}, {112̅1}, {213̅1}, 338 {516̅1}, {224̅1}, {314̅1}, and {404̅1} orientations occur in minor amounts (each between, on 339 average, less than 0.1% and up to 7.9% of the total measured PDFs). Of these, planes parallel 340 to the {101̅4} orientation are the most common, representing on average 7.9% (up to 13.1% in 341 sample H300). On average, only 3.2% of the planes could not be indexed (with a maximum of 342 unindexed sets of 7.6% for sample H400). These unindexed planes are either not parallel to 343 any rational crystallographic orientations presently represented in the stereographic projection 344 template from Ferrière et al. (2009) or reflect errors in the initial measurements 345 (indexing/plotting errors can be excluded since when sets were unindexed, the data were 346 plotted again a second time to confirm the results). 347 PFs occur sporadically in quartz grains in samples H5, H45, H99, H351, H400, H500, 348 V50, and V99 (Fig. 4), as one set of open fractures (some of which are filled with secondary 349 minerals). They are in most cases oriented parallel to (0001) and always occur together with a 350 set of basal PDFs. FFs occur in samples H5, H400, and V99 (Fig. 4), always associated with 351 PFs, as one set per grain. One of the investigated samples, V99, contains a much larger 352 number of PFs and FFs in quartz than the other samples. This is likely due to the fact that this 353 specific sample was subject to more shearing than the other investigated samples (Poelchau 354 and Kenkmann 2011). In the other samples, apart from the presence of basal PDFs, evidence 355 of shearing is limited. Sample V99 is also more heavily fractured than the other samples and 356 contain veins of material with a reduced grain size. In addition, this sample has the highest 357 number of PDF sets/grain and the highest percentage of high-index PDF sets. 358 359 Vertical shock attenuation at the Siljan impact structure 360 Quartz grains in samples from the Hättberg core record shock pressures corresponding to 361 levels C and D from Holm et al. (2011), i.e., 10-15 and 15-20 GPa, respectively (Table 4). For 362 level C, all samples display PDFs parallel to the {101̅3} and (0001) orientations, and with rare 363 sets parallel to less common orientations, such as {101̅1} and {224̅1}. Level D samples 364 recorded low percentages (typically less than 20% of the total amount of measured sets) of 365 basal PDFs, high frequencies of less abundant sets, such as those parallel to the {101̅1} and 366 {224̅1} orientations, and the highest number of sets/grain (more than 3.5 PDF sets per grain). 367 Regarding the samples from this study, V1, V50, H99, H200, H300, H351, H400, H500, and 368 H601 are assigned a shock pressure of 10-15 GPa. Among these samples, V1 stands out as the 369 sample that records evidence of the lowest level of shock. This statement is due to the fact 370 that the number of sets/grain is only 1.4, and 72.2% of all measured PDFs are basal (the rest 371 are parallel to the {101̅3} orientation). Otherwise, in these samples, on average, between 2.5 372 and 4.0 PDF sets were measured in each quartz grain. They have more than 20% basal PDFs, 373 and less than 10% high-index sets, defined as sets with polar PDF angles to the c-axis of more 374 than 37.4°, such as for example {101̅1}, {112̅2}, and {224̅1}. 375 Samples V99, H5, and H45 are assigned a shock pressure of 15-20 GPa. The average 376 number of PDF sets/grain in these samples is between 3.8 and 4.5. Two samples contain less 377 than 20% basal PDFs (V99 and H45), and H5 contains 23.3% basal PDFs. The frequency of 378 high-index PDFs is high at 16.7, 18.5, and 25.8%, respectively. The uppermost pressure, of 20 379 GPa, is set due to the lack of {101̅2}-oriented PDFs, which according to experiments should 380 become more frequent at pressures exceeding ~22 GPa (e.g., Hörz 1968; von Engelhardt & 381 Bertsch 1969; Grieve et al. 1996). 382 For the Hättberg core, the shock pressure recorded by the investigated samples decreases 383 with increasing depth (see Fig. 3). On Figure 3, the number of PDF sets/grain and the 384 percentage of high-index PDF sets is also represented, showing a clear decrease of the number 385 of PDF sets/grain with increasing depth. H5 and H45, the two samples from the uppermost 386 part of the core, are the most strongly shocked samples investigated for this core. 387 For the Vålarna core, the results of the PDF measurements with assigned shock pressures 388 give a pattern that is more difficult to interpret (Fig. 3). The pressure does not decrease with 389 increasing depth (as would have been expected) but, on the contrary, it increases. V99 is the 390 most strongly shocked sample, with the highest amount of high angle planes and an average 391 number of PDF sets/grain of 4.4. Sample V50 has 2.5 sets/grain and 2.7% high-index PDF 392 sets, whereas sample V1 only has 1.4 sets/grain and no high-index sets. 393 394 Numerical modeling of the Siljan impact structure 395 The observational constraints used for producing a model for the formation of the Siljan 396 structure was the presence of sedimentary rocks at ~15 km radial distance, the correlation 397 with the shock barometry (as presented here and in Holm et al. 2011), and a final crater size 398 of at least ~50 km (i.e., the current geological expression of the downfaulted sedimentary 399 rocks within the structure, which corresponds to the commonly quoted diameter, as estimated 400 by Grieve (1982, 1988)). 401 Using the constraint of the position of downfaulted sedimentary rocks within 15 km of the 402 crater center, the effect of sediment thickness and impactor size was tested. It was found that 403 increasing sediment thickness and decreasing impactor size resulted in the occurrence of 404 sedimentary rocks closer to the center of the structure (Fig. 6, Appendix 2). Large impactor 405 sizes result in larger transient crater diameters and therefore, in the final crater, greater 406 distances to the collapsed crater rim where downfaulted sediments can be found. For a given 407 transient crater size, thinner sedimentary layers constitute a smaller proportion of the 408 collapsing transient crater rim, as such, because of their position stratigraphically above the 409 basement rocks, they are not transported as far towards the center of the structure during 410 collapse. 411 The effect of varying acoustic fluidization parameters on final crater structure was tested. It 412 was found that neither viscosity nor decay time affect the position of down-faulted sediments 413 (Appendix 3). Whilst lower viscosity and increased decay time causes increased rim collapse, 414 the innermost extent of sediments in the final crater is fixed because of the effect of enhanced 415 central uplift formation. Low viscosities and increased decay times result in larger final crater 416 rim diameters, larger structural uplifts, but similarly positioned innermost sediments. Remnant 417 structural information can therefore not be used to differentiate between models with different 418 acoustic fluidization parameters, however, the shock distribution pattern between simulations 419 with varying acoustic fluidization parameters do vary (Appendix 3), therefore direct 420 comparison between shock barometry and the numerical models can be used to differentiate 421 models. Furthermore, the width of the remnant sediments changes with varying the model 422 parameters; width increases as the degree of fluidization in the target rocks increases. 423 The final frame of our best-fit model (see the Discussion for details on this model) is 424 shown in Figure 7, the produced core shock pressures compared with the estimated pressures 425 (based on our shock barometry work) in Figure 8, and the slices where modeled shock 426 pressures are compared with observed surface shock barometry (from Holm et al. 2011) in 427 Figure 9. An animated video of the best-fit model is also presented as supplementary online 428 material. Please refer to the Discussion for details regarding the erosion level of the present 429 Siljan impact structure. 430 431 432 Discussion 433 434 Shock barometry 435 Pressures in the Hättberg core decrease from 15-20 GPa in the uppermost two samples to 10- 436 15 GPa in the rest of the investigated samples. The sample from 5 meters does however 437 record a somewhat higher pressure than sample 52 from Holm et al. (2011), which was given 438 an estimated pressure range of 10-15 GPa, and which was sampled only a few hundred meters 439 away from the drill site at Hättberg. However, the two samples are of different lithology, the 440 sample from Holm et al. (2011) represents a sandstone, whereas sample H5 is a porphyritic 441 granite. 442 For the Vålarna core, unexpectedly, an increase in the recorded shock pressures with depth 443 was observed. However, based on previous similar studies at other impact structures (e.g., 444 Masaitis and Pevzner 1999; Ferrière et al. 2008; Rae et al. 2017) and considering the size of 445 Siljan, we attribute the observed pattern to faulting and block-wise movements during central 446 uplift formation, rather than localized shock-pressure increase. Also, as previously noted, 447 sample V99 is very different from all other samples investigated in this study, in that it 448 records shearing in the form of FFs and frequent PFs and other types of fractures. The 449 shallowest sample from the Vålarna core does agree well with the shock pressure that was 450 previously estimated at locality 31 of Holm et al. (2011), which was sampled essentially at the 451 place where the drilling took place. 452 By comparing the shock barometry determined by the samples and the one derived from 453 the numerical modeling we have been able to discern a best-fit model (see below), which is in 454 relatively good agreement with the observed shock barometry from both horizontal (at present 455 day surface) from Holm et al. (2011) and the vertical shock barometry presented here. The 456 numerical impact simulations do not produce an increase in shock pressure in the simulated 457 Vålarna core. This is likely to be due to the lack of resolution of sub-grid scale strain 458 localization within the model. Numerical simulations treat the material as a continuum, and 459 therefore do not produce individual coherent rock blocks. 460 However, it should be noted that for the two cores, the observed shock pressures, which are 461 on the order of 15-20 GPa in the shallow Hättberg samples, and 10-15 GPa in the deeper 462 samples, systematically differ by 5-10 GPa from the shock pressures derived from the 463 numerical models (i.e., the models relatively overestimate the recorded shock pressures 464 regardless of erosional level; Figs. 8 and 9). A similar observation has been made by Rae et 465 al. (2017) based on comparisons between numerical simulations and shock barometry at the 466 West Clearwater Lake impact structure (Canada). We see two possibilities for this divergence; 467 (1) the models overestimate the shock pressures, or (2) the peak shock pressures, estimated on 468 the basis of PDF orientations, based on experimental studies, are somewhat underestimated. 469 There are many possible reasons for a discrepancy between features observed in shock 470 recovery experiments and in naturally shocked rocks, such as the shock pulse duration, the 471 strain rate range, polymineralic natural samples vs. experimentally shocked single crystals, 472 and the post-shock history of the affected material, as previously discussed in Chao (1968), 473 Stöffler (1972), Boslough (1991), Stöffler and Langenhorst (1994), and Huffman and 474 Reimold (1996). The early shock experiments that have served as calibrators for shock 475 pressure estimations based on PDFs in quartz, at least those involving higher pressures (>~15 476 GPa; see e.g., Stöffler 1972), were based on multiple shock waves caused by reverberations 477 rather than a single shock wave. However, the reverberation technique might actually mimic 478 the situation in natural, polymineralic, rocks subjected to shock waves, where reverberations 479 between minerals are expected (Stöffler and Langenhorst 1994). Also, the shock pulse 480 duration is only of a few microseconds in experiments, but much longer in the case of large 481 natural impacts (Stöffler 1972; Boslough 1991; Huffman et al. 1993; Huffman and Reimold 482 1996). The geometry of the shock wave also varies between experiments and nature, from a 483 plane wave geometry to a spherical geometry of wave propagation (e.g., Stöffler 1972). In 484 natural cases, shocked material records evidence of shock metamorphism formed through 485 interactions between the shock wave and various coexisting phases in the same sample, 486 whereas experimentally shocked samples, at least for early shock experiments, on which the 487 shock pressure calibration using PDFs orientations is based on, were made on single crystals 488 (see e.g., Hörz 1968; Stöffler 1974). It is also known that the direction of shock propagation 489 with respect to the crystallographic orientation of the rock-forming minerals is relevant (e.g., 490 Hörz 1968; Müller and Hornemann 1969; Huffman and Reimold 1996), which can explain in 491 part why a single sample of a polymineralic rock records such a variety of shock metamorphic 492 features (i.e., some grains are highly shocked when other grains within the same sample are 493 not shocked or are minimally shocked). Furthermore, the pre-shock temperature of the rock- 494 forming mineral is also important for the development of PDFs (Huffman et al. 1993; 495 Langenhorst and Deutsch 1994; Huffman and Reimold 1996), and especially of importance in 496 the case of large impact structures (i.e., in which the pre-shocked rocks may have originally 497 been deep within the crust and then uplifted many kilometers during crater modification). The 498 differences in the PDF orientation pattern for crystals at different temperatures 499 likely represents the structural differences between α- and β-quartz, and are thus relevant in 500 rocks that were heated to above 630 °C (Langenhorst and Deutsch 1994). As far as we know, 501 the relevance of this fact has not been considered when comparing experimentally shock 502 metamorphosed samples with naturally shocked rocks. 503 504 Numerical modeling 505 It is apparent that in reproducing the observed structure of the "Siljan ring", there is a trade- 506 off between the impactor size and the thickness of the sediments at the time of the impact, i.e., 507 large impactor sizes (e.g., 6 km) need correspondingly thick sequences (of 508 ~4 km) in order to reproduce the Siljan structure, whilst small impactor sizes (e.g., 4 km) need 509 only a moderately thinner sedimentary rock sequence, on the order of ~2 km (Fig. 6). Due to 510 the lack of preservation of sedimentary rocks outside the Siljan structure, the thickness of 511 sediments in each model gives us a minimum value for the amount of erosion. 512 By adding the constraint that the crater can be no smaller than the maximum extent of the 513 Siljan ring, ~50 km, our numerical simulations indicate that the minimum impactor energy 514 and momentum are 9.9 x 1021 J and 1.3 x 1018 kg m/s, respectively, corresponding to an 515 impactor diameter of 4 km, given an impactor velocity of 15 km/s. Using this impactor size, it 516 was found that a minimum sediment thickness of 2 km was needed to allow sedimentary 517 rocks in the crater rim to collapse in to within 15 km of the crater center, independent of the 518 level of erosion. If a sediment thickness of 2 km is used, the lateral width of the down-faulted 519 sedimentary rocks is sufficient, even if the sedimentary rocks outside of the crater is eroded. 520 However, with this level of erosion, the shock pressure levels recorded in target rocks are too 521 high in magnitude, and with 4 km erosion, which is required for the surface barometry to fit 522 the model, the sedimentary rocks in the down-faulted ring are completely removed (Fig. 6, 523 Appendix 3). 524 In our simulations, a maximum sediment thickness of 4 km was used; based on the fission 525 track data from previous workers (see section 2 for references). In turn, due to the trade-off 526 between sedimentary rock thickness and impactor size in achieving down-faulted sedimentary 527 rocks within 15 km of the crater center, it was found that, given a velocity of 15 km/s, the 528 maximum impactor size consistent with the position of the sedimentary rock collar was 6 km. 529 This model produces a crater of ~70 km in diameter, which is reasonable. However, in order 530 for the surface barometry to match the observations, a minimum of >6 km of erosion is 531 required. Also for the drill cores to match the modeled shock pressure distribution, >6 km of 532 erosion is required. While the decrease in shock pressures across the surface is too gradual, 533 we cannot exclude such a scenario, although it is improbable that such an extremely high 534 amount of erosion has taken place since the impact event (e.g., Lidmar-Bergström 1997). 535 Proceeding with models with a sedimentary rock cover of 3 km and an impactor of 5 km in 536 diameter, the resulting simulation fulfills the constraints provided by the present 537 morphological features of the impact structure (see more details below). Also the shock 538 barometry profiles, both radial and vertical, are broadly consistent with this model. At present, 539 the shock barometry and the crater morphology, as given by the numerical model, indicate 540 that about 4 km of the central part of the impact structure has been eroded, and ~4.5 km of the 541 rim area. The model suggests that the original morphology of the Siljan structure was a peak- 542 ring crater, in accordance with earlier classification by Grieve et al. (1988), of Siljan being 543 either a central peak, or a remnant peak-ring impact structure. 544 545 Implications on the original Siljan crater 546 In our study, we were able to produce a best-fit model for the formation of the Siljan impact 547 structure, with a transient cavity of 22-33 km in diameter (the diameter of the cavity at the 548 point of maximum depth up to the diameter at the point of maximum cavity volume), and a 549 final crater with a rim-to-rim diameter of ~65 km, reproducing the observed shock attenuation 550 pattern across both the surface of the structure, and within drill cores, and also consistent with 551 structural observations. The observed shock attenuation pattern is consistent with a level of 552 erosion corresponding to 4 km or greater relative to the level of pre-impact topography. All 553 material in the simulation subjected to shock pressures exceeding 25 GPa have been removed 554 by erosion at the level that is presently exposed, which is consistent with field and laboratory 555 observations, with quartz grains in all investigated samples almost completely lacking PDFs 556 oriented parallel to the {101̅2} orientation. The impactor size in this model is 5 km in 557 diameter, and the thickness of the pre-impact sedimentary sequence is 3 km. The model 558 predicts the present-day sedimentary rock sequence to preserve up to 1.5 km where it is the 559 thickest, and to be ~10 km wide. This model also predicts the uppermost sedimentary 560 sequence at the time of impact (i.e., the youngest sediments) to have been removed by erosion 561 at present time (Fig. 7). The energy release of the impact with parameters corresponding to 562 those in our best-fit model is 1.94 × 1022 J. 563 Our new estimation of the original size of Siljan, with a rim-to-rim diameter of 65 km, is 564 not easily comparable to those made in previous studies, such as in Kenkmann and von 565 Dalwigk (2000), Holm et al. (2011), and Osinski and Ferrière (2016). The reason for this is 566 that, compared to the structural deformation in the target rocks and the spatial distribution of 567 these deformations, it is not exactly known how the rim-to-rim diameter of an impact crater 568 can be compared with the apparent crater diameter (see definitions in Turtle et al. 2005). Our 569 estimated rim-to-rim diameter of ~65 km is smaller than the apparent crater diameter 570 suggested to be ~75 km (Kenkmann and von Dalwigk 2000; Henkel and Aaro 2005; Osinski 571 and Ferrière 2016). Some similar studies presented for other structures (e.g., Vasconcelos et 572 al. 2012) have resulted in final craters of more similar dimensions to the present-day observed 573 expressions, but this is of course much dependent on the erosion level of the structure in 574 question (and what type of diameter is meant). For the three impact structures investigated by 575 Collins et al. (2008a; El’gygytgyn, Haughton, and Ries), the apparent crater diameters vary 576 with different amounts from the modeled rim-to-rim diameters, but all apparent crater 577 diameters are larger than the rim-to-rim diameters. For comparison, in the case of Ries, the 578 rim-to-rim diameter is ~60% of that of the apparent crater diameter (Collins et al. 2008a), and 579 in this study, our estimated rim-to-rim diameter is ~86% of that of the apparent crater 580 diameter, based on an apparent crater diameter of 75 km (see above). 581 The observation of intense fracturing up to 32.5 km from the center of the Siljan structure 582 (Kenkmann and von Dalwigk 2000) is entirely consistent with our best-fit model of the 583 formation of the Siljan impact structure. With a final crater diameter of ~65 km, and 4 km of 584 erosion, it is expected that rocks will have experienced ~10% total plastic strain at a radial 585 distance of 35 km (see Fig. 7). Furthermore, the amount of strain due to the passage of the 586 shock wave accommodated in the basement rocks outside of the Siljan ring is likely to be 587 locally enhanced due to the impedance contrast between sedimentary and crystalline rocks. 588 Importantly, estimations of the final crater size based on scaling the width of the central 589 uplift to the final crater size (Therriault et al. 1997; Kenkmann and von Dalwigk 2000) 590 require considerable care, since the diameter of the centrally uplifted rocks in an impact crater 591 varies with the amount of erosion through the crater (see Fig. 7). In the case of the Siljan 592 impact structure, it has always been assumed that the limit of the central uplift is marked by 593 the contact between the Palaeozoic sediments and the basement rocks (e.g., Grieve 1988), 594 instead, our simulations show that the basement rocks found just within the Siljan ring are 595 beneath their original position, having been transported downwards and inwards from the 596 collapsing transient cavity rim during crater modification. This results in an overestimate of 597 the final crater diameter using this scaling method. We would interpret that the faulting 598 observed at the contact between the Palaeozoic sedimentary rocks and the basement rocks by 599 Kenkmann and von Dalwigk (2000) is caused by flexural slip as the collapsing transient 600 cavity rim interacts with the upwardly and outwardly flowing collapsing central uplift. 601 602 603 Conclusions 604 A total of 13 bedrock samples (all granitoids of similar grain size) from two drill cores 605 recovered from the Siljan impact structure were investigated in detail and the results show 606 that the recorded shock pressure decrease with increasing depth from 15-20 GPa near the 607 (present) surface, to 10-15 GPa at 600 meters depth. 608 These results, together with previous studies, and combined with numerical modeling 609 allow us to estimate the (original) rim-to-rim diameter of the Siljan structure to ~65 km, with 610 a transient cavity diameter of 22-33 km. We are also able to estimate that since the formation 611 of the impact structure ~4 km of erosion has taken place, removing the original crater 612 morphology. Our numerical models suggest that the original morphology of the Siljan 613 structure was a peak-ring crater. 614 Furthermore, our best-fit model indicates that the pre-impact sedimentary cover was on the 615 order of 3 km thick. 616 Finally, our study also shows that a weakening mechanism that substantially reduces the 617 viscosity of the target rocks, such as acoustic fluidization, is important in the formation of 618 complex impact craters. 619 620 621 Acknowledgments 622 Jerry Hedström (from the Swedish Geological Survey) is thanked for sampling drill cores and 623 for sending them to Lund. The authors thank Prof. Erik Sturkell (Gothenburg University) for 624 providing important reference material for this study. 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Meteoritics 950 & Planetary Science 32:71–77. DOI: 10.1111/j.1945-5100.1997.tb01242.x. 951 952 Thompson S. L. and Lauson H. S. 1974. Improvements in the CHART D radiation 953 hydrodynamic code III: revised analytic equations of state (No. SC-RR-710714). 954 Sandia National Laboratory, Alberquerque, New Mexico. 955 956 Trepmann C. A. and Spray J. G. 2006. Shock-induced crystal-plastic deformation and post- 957 shock annealing of quartz: microstructural evidence from crystalline target rocks of the 958 Charlevoix impact structure, Canada. European Journal of Mineralogy 18:161–173. DOI: 959 10.1127/0935-1221/2006/0018-0161. 960 961 Tullborg E-L., Larson S. Å., Björklund L., Samuelsson L., and Stigh J. 1995. Thermal 962 evidence of Caledonide foreland, molasse sedimentation in Fennoscandia. SKB Technical 963 Report 95-18. Stockholm: Svensk Kärnbränslehantering AB. 38 p. 964 965 Turtle E. P., Pierazzo E., Collins G. S., Osinski G. R., Melosh H. J., Morgan J. V., and 966 Reimold W. U. 2005. Impact structures: What does crater diameter mean? Geological Society 967 of America Special Paper 384:1–24. DOI: 10.1130/0-8137-2384-1.1. 968 969 Vasconcelos M. A. R., Wünnemann K., Crósta A. P., Molina E. C., Reimold W. U., and 970 Yokoyama E. 2012. Insights into the morphology of the Serra da Cangalha impact 971 structure from geophysical modeling. Meteoritics and & Planetary Science 47:1659–1670. 972 DOI: 10.1111/maps.12001. 973 974 Vlierboom F. W., Collini B., and Zumberge J. E. 1986. The occurrence of petroleum in 975 sedimentary rocks of the meteor impact crater at Lake Siljan, Sweden. Advances in Organic 976 Geochemistry 10:153–161. DOI: 10.1016/0146-6380(86)90019-7. 977 978 Wünnemann K. and Ivanov B. A. 2003. Numerical modelling of the impact crater depth– 979 diameter dependence in an acoustically fluidized target. Planetary and Space Science 51:831– 980 845. DOI: 10.1016/j.pss.2003.08.001. 981 982 Wünnemann K., Morgan J. V., and Jödicke H., 2005. Is Ries crater typical for its size? An 983 analysis based upon old and new geophysical data and numerical modeling. Geological 984 Society of America Special Paper 384:67–83. DOI: 10.1130/0-8137-2384-1.67. 985 986 Wünnemann K., Collins G. S., and Melosh H. J., 2006. A strain-based porosity model for use 987 in hydrocode simulations of impacts and implications for transient crater growth in porous 988 targets. Icarus 180:514–527. DOI: 10.1016/j.icarus.2005.10.013. 989 990 991 Figure captions 992 993 Fig. 1. Geologic map of the Siljan impact structure (after Kresten and Aaro 1987; Kresten et 994 al. 1991) with locations of the two drill cores studied. Dashed circle represents an estimated 995 transient cavity with a diameter of 22 km, i.e., the minimum value in the range 22-33 km 996 representing the transient cavity development according to the best-fit model (see text). 997 998 Fig. 2. Macrophotographs of granitic samples from the Hättberg drill core. a) 5 meters, with 999 pseudotachylitic breccia-vein (see text). b) 45 meters. c) 500 meters. 1000 1001 Fig. 3. Stratigraphic profile of the Hättberg and Vålarna drill cores. The Hättberg profile is 1002 redrawn from Hagconsult AB Hättberg drill core drawing. Displayed are also the average 1003 number of planar deformation feature sets/grain, the percentages of high-index sets, and the 1004 pressure estimates for the samples from the cores. Question marks on the Vålarna profile 1005 indicate that we do not know the lithology other than where we have samples. 1006 *This reference to the rock type is taken from the original drawing, but as Reimold et al. 2015 1007 describes frequent pseudotachylitic breccia veins throughout the core, it is very likely that 1008 these ”mylonites” are in fact pseudotachylitic breccia veins. 1009 1010 Fig. 4. Thin section photomicrographs of Siljan samples, all under cross polarized light. a) 1011 Quartz grain with two sets of decorated planar deformation features (PDFs) with {112̅2}- and 1012 {213̅1}-equivalent orientations, and one set of basal PDFs (Sample H5). b) Quartz grain with 1013 three sets of decorated PDFs (Sample H5). c) Quartz grain with two sets of decorated, faint, 1014 PDFs parallel to the {112̅2}-orientation, and one planar fracture (PF) parallel to the basal 1015 plane, and one set of feather features (FFs) emanating from the PF (Sample V99). d) Quartz 1016 grain with two sets of PDFs with {101̅3}-equivalent orientations and one set of basal PDFs 1017 (Sample H5). 1018 1019 Fig. 5. Histograms of the absolute frequency percent of indexed planar deformation features 1020 (PDFs) in quartz from 9 drill core samples from Hättberg, plus 3 drill core samples from 1021 Vålarna. PDFs that plot in the overlapping zone between the {10 1̅ 4} and {10 1̅ 3} 1022 crystallographic orientations are plotted in gray on top of the uniquely indexed {101̅3} planes 1023 (see text). 1024 1025 Fig. 6. The effect of varying the sedimentary thickness and impactor size on the morphology 1026 of the final crater. All other parameters, including acoustic fluidization parameters ( = 2.5  -2 2 1027 10 and  = 1.5  10 ; see Wünnemann and Ivanov 2003) remain constant between the 1028 different simulations. Sedimentary rocks are highlighted in gray. 1029 1030 Fig. 7. Frames from the best-fit numerical simulation showing the progressive changes from 1031 the initial condition, transient cavity formation which reaches its maximum depth at 16 s, and 1032 maximum volume at 46 s, through the formation and collapse of the central uplift, to the 1033 morphology of the final crater. The final frame illustrates the condition of the final crater after 1034 4 km of erosion. The pink highlighted regions in the final two frames indicate the material 1035 that has been uplifted by at least 200 m (therefore excluding material in the uplifted crater 1036 rim) relative to its original depth in the crater. Contours indicate the percentage of total plastic 1037 strain accumulated during the impact simulation (see also the Supplementary Video of the 1038 best-fit numerical simulation). 1039 1040 Fig. 8. Simulated shock pressures in the best-fit model plotted together with observed shock 1041 pressures (filled circles with error bars) from the Hättberg drill core (magenta), and the 1042 Vålarna drill core (cyan). In this figure, the samples (filled circles with error bars) are plotted 1043 at a starting erosional surface of 4 km. The lower half of the figure shows the original location 1044 of the core material in the model (left), and the position of the drill cores in the final structure 1045 (right). 1046 1047 Fig. 9. Simulated horizontal slices showing the shock pressures across the Siljan impact 1048 structure as solid lines in shades of gray, dependent on the amount of erosion (4, 5, and 6 km). 1049 Black dots (with error bars) are the shock pressures from the surface samples from Siljan, as 1050 estimated by Holm et al. (2011). Table 1. Global model parameters. Symbol Definition Value

푣푖 Impact velocity (km/s) 15.0 3 휌푖 Impactor density (kg/m ) 2630 -4 휀푓푏 Minimum failure strain for low pressure states 1  10 퐵 Constant of proportionality between failure strain and pressure 1  1011

8 푃푐 Pressure above which failure is compressional (Pa) 3  10

Cvib Vibrational particle velocity as a fraction of particle velocity 0.1

Vibmax Maximum vibrational particle velocity (m/s) 200

toff Time after which no new acoustic vibrations are generated (s) 16

Table 2. Material model parameters. Symbol Definition Sediments Crust/Impactor Material Quartzite Granite 3 휌푖 Reference density (kg/m ) 2650 2630 휈 Poisson’s ratio 0.25 0.3

푌0 Cohesion (MPa) 24 10

푌푀 Von Mises plastic limit (MPa) 300 2500

휇푖 Coefficient of internal friction 1 2

푌푑0 Cohesion of damaged material (MPa) 0.03 0.01

휇푑푖 Coefficient of internal friction of damaged material 0.826 0.6

푇푚 Melting temperature (°K) 1200 1400 휉 Thermal softening parameter 1.2 1.2  Initial porosity (%) 10 0

Table 3. Universal-stage data for planar deformation feature (PDF) set abundances and crystallographic orientations of these sets. Sample no. H5 H45 H99 H200 H300 H351 H400 H500 H601 V1 V50 V99 No. of investigated grains 45 41 40 41 42 40 47 46 27 40 42 41 No. of measured sets 172 186 146 164 130 148 145 134 83 54 107 179 No. of measured sets1 166 181 139 164 122 146 134 127 82 54 106 174 No. of PDF sets/grain (N) 3.8 4.5 3.7 4.0 3.1 3.7 3.1 2.9 3.1 1.4 2.5 4.4 No. of PDF sets/grain (N')1 3.7 4.4 3.5 4.0 2.9 3.7 2.9 2.8 3.0 1.4 2.5 4.2 Relative abundance of PDF sets/grain (%) 1 set 13.3 7.3 7.5 2.4 14.3 15 .0 12.8 21.7 18.5 77.5 19 .0 7.3 2 sets 11.1 4.9 15.0 14.6 26.2 17.5 21.3 23.9 18.5 15.0 31.0 9.8 3 sets 13.3 17.1 30.0 22.0 21.4 12.5 27.7 21.7 25.9 2.5 28.6 9.8 4 sets 24.4 24.4 17.5 19.5 16.7 20.0 25.5 17.4 22.2 5.0 19.0 24.4 5 sets 22.2 17.1 15.0 26.8 16.7 17.5 6.4 6.5 7.4 n.d. 2.4 19.5 6 sets 11.1 14.6 12.5 12.2 4.8 7.5 6.4 6.5 3.7 n.d. n.d. 14.6 7 sets 4.4 7.3 2.5 2.4 n.d. 10 n.d. 2.2 3.7 n.d. n.d. 14.6 8 sets n.d. 2.4 n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. 9 sets n.d. 4.9 n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. Total 100 100 100 100 100 100 100 100 100 100 100 100 Indexed PDF crystallographic orientations (absolute frequency percent2) c (0001) 23.3 16.7 24 24.4 22.3 23 24.1 26.1 20.5 72.2 29.9 17.3 {101̅4}3 4.1 9.7 7.5 7.9 13.1 6.8 6.2 10.4 12.0 n.d. 11.2 5.6 ω {101̅3} 50.6 54.3 62.3 65.2 56.2 60.1 57.2 50.0 63.9 27.8 55.1 48.6 Π {101̅2} 2.3 1.1 n.d. 0.6 1.5 0.7 n.d. 3.7 n.d. n.d. 0.9 1.1 r, z {101̅1} 5.2 3.8 1.4 0.6 n.d. 2.7 4.8 2.2 1.2 n.d. n.d. 11.1 m {101̅0} n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. 0.6 ξ {112̅2} 2.9 1.6 n.d. 0.6 n.d. 1.4 n.d. 0.7 n.d. n.d. n.d. 2.8 s {112̅1} n.d. 1.1 n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. 0.6 ρ {213̅1} 1.7 1.1 n.d. 0.6 n.d. 0.7 n.d. n.d. n.d. n.d. n.d. 0.6 x {516̅1} n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. 0.9 n.d. a {112̅0} n.d. 0.5 n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. {224̅1} 5.2 5.9 n.d. n.d. 0.8 2.0 n.d. 0.7 1.2 n.d. 0.9 7.8 {314̅1} 1.2 1.1 n.d. n.d. n.d. 0.7 n.d. n.d. n.d. n.d. n.d. 0.6 t {404̅1} n.d. 0.5 n.d. n.d. n.d. 0.7 n.d. 0.7 n.d. n.d. n.d. 0.6 k {516̅0} n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. Unindexed 3.5 2.7 4.8 n.d. 6.2 1.4 7.6 5.2 1.2 n.d. 0.9 2.8 Total 100 100 100 100 100 100 100 100 100 100 100 100 1Excluding unindexed sets. 2See text and Engelhardt and Bertsch (1969) for description of method . 3PDFs with measured orientations that plot in the overlapping zone between {101̅4} and {101̅3} were treated as {101̅3}. See text and Ferrière (2009) for details. n.d. = none detected Note that no measurments are recorded for sample H451 due to lack of quartz grains in thin sections

Table 4. Grouping of, and shock pressure estimates for shocked samples from the Siljan structure based on planar deformation feature (PDF) sets in quartz.

Average No. Estimated Percentage high- Group1 Sample(s) Discriminative features (maximum) pressure index2 PDF sets of PDF sets range (GPa) per grain C2 V1 PDFs: >50% (0001), {1013} n.d. 1.35 (4) 10-15 GPa

H99, H200, H300, PDFs: >50% {1013}, >20% C3 0.8-4.8 2.5-4.0 (7) 10-15 GPa H351, H400, H500, (0001) + other H601, V50 PDFs: {1013}, ~<20% (0001) + D H5, H45, V99 15.6-24.7 3.8-4.5 (9) 15-20 GPa >15% other

1See text and Holm et al. (2011) 2Defined as sets with polar PDF angles to the c-axis exceeding 37.4 degrees (see text) n.d. = none detected

ORSA

Vålarna

Hättberg

MORA

RÄTTVIK

Lake Siljan

0 km 10

Paleozoic sedimentary rocks Town TIB-volcanites and sedimentary rocks Core drilling Siljan HELSINKI Svecofennian units Geographical center OSLO STOCKHOLM Transient cavity diameter 22 km Järna granite Siljan granite COPENHAGEN Gabbro/diorite a b c

2.5 cm 2.5 cm 2.5 cm surface Bedrock Percentage 0 Avg. number1 PDF sets/grain 2 Percentage of high-index3 PDF sets Avg. estimated4 shock pressure (GPa)5 3 4 5 100.0 15 520.0 2510.0 5 15.100 1520.0 20 Depth (m) 0 350 100 100

200 400 200 s 300 r e 300 t e 150 450 Hättberg m

n i

h t p

400 e 400 D 200 500

500 500 Legend Granite

”Mylonite”* 250 550 Sample 600 600

1 2 3 4 5 5 10 15 20 25 5 10 15 20

? 300 600 700

Vålarna ? 100

Legend

60 60 70 {1122} {1011} (0001) (0001) {1014} {2131} {2241} {3141} {1013} {1014} {1013} {1012} {1011} {1012} {1122} {1121} (0001) {1014} {1013} {1011} {4041} {3141} {1120} {2131} {2241} 60 50 50 50 40 40 Sample H5 Sample H45 40 Sample H99 30 30 172 sets in 45 grains 186 sets in 41 grains 30 146 sets in 40 grains 20 3.5 % unindexed planes 20 2.7 % unindexed planes 4.8 % unindexed planes 20

10 10 10

0 0 0 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 {2241} {1122} {1014} {2241} {2131} {3141} {4041} {1013} {1012} {1011} {1011} {2131} {1013} {1013} (0001) {1014} {1012} {1122} (0001) {1014} {1012} 60 60 70 (0001)

50 50 60 50 40 40 Sample H200 Sample H300 40 Sample H351 30 30 164 sets in 41 grains 130 sets in 42 grains 30 148 sets in 40 grains 20 no unindexed planes 20 6.2% unindexed planes 1.4 % unindexed planes 20

10 10 10

0 0 0 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 {1122} {1014} {4041} {2241} {1013} {1012} {1011} (0001) {1014} {1013} {1011} (0001) {1014} {1013} {2241} {1011} 70 60 70 (0001)

60 50 60 50 50 40 40 Sample H400 Sample H500 40 Sample H601 30 30 145 sets in 47 grains 134 sets in 46 grains 30 83 sets in 27 grains 7.6 % unindexed planes 20 5.2 % unindexed planes 1.2 % unindexed planes 20 20

10 10 10

0 0 0 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 (0001) {1014} {1013} {1012} {1122} {1121} {1011} {1010} {4041} {3141} {2131} {2241} (0001) {1013} {5161} {1014} {2241} {1013} {1012} 80 60 (0001) 60 70 50 50 60 40 40 50 Sample V1 Sample V50 Sample V99 40 30 30 54 sets in 40 grains 107 sets in 42 grains 179 sets in 41 grains 30 no unindexed planes 20 0.9 % unindexed planes 20 2.8 % unindexed planes 20 10 10 10 0 0 0 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90

APPENDIX 1

Petrographic description of granitic drill core samples that were investigated. Sample1 Grain size Mineral content2 Notes Kfs altered, red/brown in color. Shock metamorphic H5 coarse Kfs, Pl, Qz, Hbl, Bt, Opq, Ttn features in Kfs. Feldspars altered, Pl more than Kfs. Hbl and Bt Kfs, Pl, Qz, Hbl (Chl), Bt H45 coarse chloritized to variying degree. Shock metamorphic (Chl), Opq, Ttn features in Kfs. Feldspars showing little alteration. Hbl and Bt Kfs, Pl, Qz, Hbl (Chl), Bt H99 coarse chloritized to varying degree. Shock metamorphic (Chl), Opq features in Kfs. Kfs, Pl, Qz, Bt (Chl), Hbl Feldspars altered, Pl more than Kfs. Bt chloritized to H200 coarse (Chl), Opq variying degree. Shock metamorphic features in Kfs. Feldspars showing little alteration. Hbl and Bt Kfs, Pl, Qz, Bt (Chl), Hbl H300 coarse chloritized to varying degree. Shock metamorphic (Chl), Opq, Ttn features in Kfs. Kfs, Pl, Qz, Bt (Chl), Hbl Feldspars altered, Pl strongly. Hbl and Bt chloritized H351 coarse (Chl), Opq, Ttn to variying degree. Shock metamorphic features in Kfs. Breccia vein with signs of localized melting. Kfs, Pl, Qz, Bt (Chl), Hbl Feldspars altered, Pl more than Kfs. Hbl and Bt H400 coarse (Chl), Opq, Ttn chloritized to variying degree. Shock metamorphic features in Kfs. Feldspars strongly altered, Pl more than Kfs. Signs Kfs, Pl, Qz, Hbl (Chl), Bt of crushing and/or melting/brecciation. Hbl partly H451 coarse (Chl), Opq, Ttn chloritized, Bt completely chloritized. Shock metamorphic features in Kfs Feldspars strongly altered, Pl more than Kfs. Signs Kfs, Pl, Qz, Bt (Chl), Hbl of crushing and/or melting/brecciation. Bt H500 coarse (Chl), Opq, Ttn chloritized, Hbl partly chloritized. Shock metamorphic features in Kfs Feldspars strongly altered, Pl more than Kfs. Hbl Kfs, Pl, Qz, Hbl (Chl), Bt H601 coarse and Bt showing strong chloritization. Few examples (Chl), Opq, Ttn of shock metamorphic features in Kfs. Kfs, Pl, Qz, Hbl (Chl), Bt Feldspars strongly altered, Pl more than Kfs. Hbl V1 coarse (Chl), Opq, Ttn and Bt showing strong chloritization. Kfs, Pl, Qz, Hbl (Chl), Bt Feldspars strongly altered, Pl more than Kfs. Hbl V50 coarse (Chl), Opq, Ttn and Bt showing strong chloritization. Feldspars strongly altered, Pl more than Kfs. Signs Kfs, Pl, Qz, Hbl (Chl), Bt of crushing and/or brecciation. Hbl chloritized, Bt V99 coarse (Chl), Opq, Ttn completely chloritized. Shock metamorphic features in Kfs 1 Sample names correspond to drill core name (i.e., H=Hättberg, V=Vålarna) and depth in meters. 2 Minerals are listed in order of decreasing abundance in the thin section. Potassium feldspar (Kfs), plagioclase (Pl), quartz (Qz), biotite (Bt), hornblende (Hbl), chlorite (Chl), titanite (Ttn), opaque minerals (Opq).

APPENDIX 2

The figure below is an extension of Figure 6, illustrating the final timesteps of 25 different iSALE simulations with varying impactor diameters (L) (4000 – 6000 m) and sediment thicknesses (S) (1000 – 4000 m). Acoustic fluidization parameters are fixed throughout all -2 these simulations, where  = 2.5  10 and  = 150. Through this figure, it is clear that in order for sediments in the collapsed transient cavity rim to be 15 km of the center of the structure; thin sedimentary layers must have small impactors, whilst thick sedimentary layers must have larger impactors. Following these simulations three combinations of sedimentary layer thickness and impactor size were investigated to see the effect of changing acoustic fluidization parameters: (1) L = 4500 m and S = 2000 m, (2) L = 5000 m and S = 3000 m, and (3) L = 5500 m and S = 4000 m. See Appendix 3 for more details

APPENDIX 3

Following simulations investigating the effects of varying sedimentary layer thickness and impactor size, three combinations of those two parameters were investigated to determine the effect of varying the extent of transient weakening: (1) L = 4500 m and S = 2000 m, (2) L = 5000 m and S = 3000 m, and (3) L = 5500 m and S = 4000 m.

Here, we vary the two acoustic fluidization parameters,  and , to investigate the effect of these parameters on a) the distribution of sediments in the final crater, b) final crater size, and c) the shock distribution pattern and the amount of erosion required to match the observed shock pattern to the numerical simulations.

Our best fit model corresponds to sedimentary layer and impactor size combination (2) L = -2 5000 m and S = 3000 m, where  = 1.25  10 and  = 300.

Presented below are three figures from each sedimentary layer and impactor size combination, (1), (2), or (3), showing a) the final crater morphology and structure, b) the shock distribution pattern in simulated drill cores compared to the observed pattern (See Fig. 8), and c) the shock distribution pattern in simulated radial transects at varying erosional levels compared to the observed pattern (See Fig. 9).

(1) L = 4500 m and S = 2000 m

(a)

(b)

(c)

(2) L = 5000 m and S = 3000 m

(a)

(b)

(c)

(3) L = 5500 m and S = 4000 m

(a)

(b)

(c)