New discovery of two seismite horizons challenges the Ries–Steinheim double-impact theory

The Nördlinger Ries and the Steinheim Basin are widely perceived as a Middle Miocene impact crater doublet. We discovered two independent earthquake-produced seismite horizons in North Alpine Foreland Basin deposits potentially related to both impacts. The older seismite horizon, demonstrated to be associated with the Ries impact, is overlain by distal impact ejecta in situ, forming a unique continental seismite-ejecta couplet within a distance of up to 180 km from the crater. The younger seismite unit, also produced by a major palaeo-earthquake, comprises clastic dikes that cut through the Ries seismite-ejecta couplet. The clastic dikes may have formed in response to the Steinheim impact, some kyr after the Ries impact, in line with paleontologic results that indicate a time gap of about 0.5 Myr between the Ries and Steinheim events. This interpretation suggests the Ries and Steinheim impacts represent two temporally separate events in Southern Germany that, thus, witnessed a double disaster in the Middle Miocene. The magnitude–distance relationship of seismite formation during large earthquakes suggests the seismic and destructive potential of impact-induced earthquakes may be underestimated.

. Geographic and geologic situation in the study area in southern Germany and northern Switzerland and Austria. Outcrops with Ries seismites overlain by the distal Ries ejecta layer (DREL), in turn cross-cut by clastic dikes presumably linked to the Steinheim impact 15 , are situated within a distance of 80 to 180 km from the centres of the two impact structures. Supposed different impact directions (orange arrows) of Ries and Steinheim asteroids are taken from the literature 1,8 and are discussed in detail within these studies. www.nature.com/scientificreports/ palaeo-earthquakes in the surroundings of the two impact structures in the form of seismites. Recently, a clastic dike was discovered in sandy deposits of the North Alpine Foreland Basin and interpreted as an impact-related seismite 15 . That dike cuts through the DREL and might, thus, represent a long-distance effect of the Steinheim impact event that appears to postdate the Ries impact by several kyr 15 . We here present additional evidence for two separate seismite horizons exposed at several localities within the North Alpine Foreland Basin in southern Germany and northern Switzerland. Both seismite occurrences are consistent with at least two strong, independent palaeo-earthquakes.

Results and discussion
Ries-related seismite. We discovered sedimentary successions with distinct soft-sediment deformation structures in a temporary construction site near Ochsenhausen 15 , in three ravines (locally called 'Tobel' in southern Germany) at the 'Tobel Oelhalde-Nord' and 'Wannenwaldtobel' close to Biberach an der Riß (Figs. 1, 2, Supplementary Fig. 1), and at the 'Kleintobel' near Ravensburg (Fig. 3, Supplementary Fig. 2). The discovery of one large clastic dike from the 'Tobel Oelhalde-Nord' was described by our group in an earlier study 15 . The softsediment deformation structures include metre-sized slumps (Figs. 2,3,4), all with NW-SE-striking slump axes (Figs. 1, 2), convolute bedding, ball-and-pillow and flame structures, and clastic dikes. The dip of the slumps and the strike of the slump axes ( Fig. 1) are consistent with a seismic source in the Ries-Steinheim region and are, therefore, unrelated to a source region in the Alps and nearby intracontinental volcanic fields that were active during the Miocene. Such soft-sediment deformation features in continental deposits are typical of seismites caused by large earthquakes 15,32,37 . As an analog example, soft sediment deformation (slumps) with preferred orientations of slump-fold axes perpendicular to the probable epicentre (the Manicouagan impact event in eastern Canada) were reported in latest Triassic (Rhaetian) deposits in central Britain 34 . The DREL that caps the seismite unit (Figs. 2,4,5) provides compelling evidence that the Ries impact was the source for this seismic event, causing soft-sediment deformation within a radial distance of ~ 100 to 180 km from the impact site. The restricted occurrence of the seismite horizon within the study area may reflect variable properties of the near-surface Molasse sediments within the North Alpine Foreland Basin (as opposed to an area-wide distribution in the sur-   17 . During field work, we found additional outcrops of distal Ries ejecta in three ravines south of Biberach an der Riß and west of Ravensburg, recpectively. In addition to the larger cobbles and bolders at the base of the cm-to dm-thick primary ejecta horizon, the ejecta layer also consists of sand and small pebbles mainly made up of grains of limestone, quartz, and feldspar 15 . These finer-grained deposits locally show a distinct fining-upward trend. Quartz grains in the ejecta horizon are often very angular and show a weak to moderate shock overprint (e.g., indistinct planar deformation features in one or two directions) in agreement with pressures at the lower end of the shock metamorphic regime (mostly < 5 GPa). Only a small proportion of quartz grains in the distal Ries ejecta horizon of the study area show a higher degree of shock-metamorphic overprint in the form of planar deformation features in up to six optically visible directions (Fig. 4f, Supplemetary Fig. 5). These highly shocked quartz grains were probably derived from the crystalline basement and, hence, from deeper parts of the Ries target (at least ~ 600 m below the former land surface). At all outcrop sites analyzed in this study, distal Ries ejecta overlie a seismite unit, thereby forming a distinct seismiteejecta couplet. The ejecta horizon occurs either as a primary, in situ ( Fig. 2), or secondary (fluvially reworked; Fig. 3) layer of ejecta 16 . At the Tobel Oelhalde-Nord (Biberach; Fig. 2 Fig. 3) of Upper Jurassic limestone locally produced small dents (Fig. 4b) caused by the impact of Ries-ejected pebbles, cobbles, and boulders ( Fig. 4c) into the soft sediment after ballistic air-travel over > 100 km 10,15,16,18 . Some of the clasts (mainly of Upper Jurassic limestones) contain shatter-cones (Fig. 4e). These observations suggest the seismite in the underlying pre-Ries deposits is genetically related to the Ries impact. The exposures of the seismite-ejecta couplet are situated within a distance of ~ 100 km (Ochsenhausen), ~ 110 km (Biberach), and ~ 140 km (Ravensburg) from the centre of the Ries crater, respectively (Fig. 1). The most distant known occurrence of coarse-grained Ries ejecta occurs ~ 180 km SSW of the Ries crater, in an outcrop near Berhardzell in NE Switzerland ( Fig. 1) from which shocked quartz grains were reported (pers.comm. Carl Alwmark). In this study, we present new evidence for shocked quartz grains with up to four sets of planar deformation features in loose sands constituting Ries ejecta exposed in the Tobel Oelhalde-Nord (Biberach; Fig. 4f, Supplementary Fig. 3), and with up to six sets of planar deformation features in Ries ejecta from the Kleintobel (Ravensburg, Supplementary Fig. 5). The Upper Freshwater Molasse deposits that overlie (i.e., postdate) the DREL are typically cross-bedded or horizontally layered and generally appear undisturbed and unaffected by dewatering processes.  www.nature.com/scientificreports/ related seismite, ejecta (the DREL), and undisturbed post-Ries deposits and, hence, clearly postdate the Ries impact event and earthquake. A horizon of distal Ries ejecta associated with smaller clastic dikes is also known from Bernhardzell, Switzerland 17 . Those dikes also seem to postdate the Ries impact and, overall, the local facies and structural situation resemble those at Biberach and Ravensburg 15 . The genetic relationship between the seismite-hosting deposits and the Ries impact is evidenced by the primary (Supplementary Fig. 4) DREL in situ sitting right on top of these deposits. The large clastic dike that cross-cuts both the Ries seismite and ejecta near Biberach was recently tentatively linked to the somewhat younger Steinheim impact 15 . Notably, this scenario-suggesting two spatially and temporally separate impacts-challenges the widely accepted binary asteroid hypothesis for the Ries-Steinheim event [1][2][3]8 .
The Ries and Steinheim craters: not the binary asteroid impact it seems? The distinct SW-NE alignment of the Steinheim Basin, the Nördlinger Ries impact structure, and the Central European tektite strewn field seemingly supports the general notion that both impact structures represent an impact crater doublet formed by an incoming pair of asteroids entering the Earth's gravitational field from the SW 1,8 . While a precise and accurate 40 Ar/ 39 Ar age has been established for the Ries impact (14.808 ± 0.038 Ma 12,13 ), isotopic dating has, thus far, failed to yield a geologically meaningful age for the Steinheim impact. Several studies pointed out that the simultaneous formation theory for the two impact structures is, in fact, not evidenced by palaeontologic and structural geologic constraints 5 Both the Nördlinger Ries and the (possibly) slightly younger Steinheim impacts would have imparted significant energy into the sedimentary target, causing at least regional-scale disturbances. Although seismites linked to Alpine seismotectonic activity have been reported in the literature 15 (references and discussion therein), no such seismites are known north of the line Lake Constance -Oberstaufen -Immenstadt 15 (see Fig. 1, green line). However, as described in this study, a laterally extensive seismite occurs in sandy deposits of the Upper Freshwater Molasse of pre-Ries age several tens of kilometres north of that line (near Biberach, Ochsenhausen, and Ravensburg) and is capped by a primary horizon of distal Ries ejecta in situ and undisturbed younger deposits. This suggests the seismite is the product of a Ries impact-induced giant earthquake. At Biberach 15 , Ravensburg, www.nature.com/scientificreports/ and Bernhardzell 17 , clastic dikes cut through the Ries-related seismite-ejecta couplet and portions of the overlaying Upper Freshwater Molasse. This provides tangible evidence for a second, high-magnitude earthquake in the region that had previously been affected by the 'Ries earthquake' . The Biberach clastic dike exposed at the Tobel Oelhalde-Nord reached the former land surface forming an extrusive fossil sand volcano 15,42 . Based on the age constraints for the dike-hosting sediments 15,16,39 the dike is the product of a seismic event that occurred between ~ 14.81 Ma (Ries impact 12,13 ) and approximately 14.3 Ma (terminal sedimentation of the 'Fluviatile Untere Serie unit 15,39 ). In contrast to the precise isotopic age for the Ries 12,13 , the latter age is not very well constrained and may be associated with an error of a few kyr 15 . A seismo-tectonic (alpine tectonism) or volcanoseismic event (within the Paleogene to Quaternary European Volcanic Province) was recently discussed 15 as a potential source for the younger earthquake some ~ 0.5 Myr after the Ries impact. However, considering their distant geographical position and rather low seismic potential 15 , none of these earthquake centres can convincingly explain the formation of the post-Ries clastic dikes 15 . The dimensions of sandstone dikes significantly decrease towards the South, from the giant Biberach clastic dike in the North and the dikes near Ravensburg to the dm-long clastic dikes of Bernhardzell in Switzerland. These localities are situated at 80 km, 110 km, and 150 km south of the Steinheim crater, respectively. Dike dimensions are a function of host rock properties and seismic energy 15,32,33 . Taking the comparable rock properties and the significantly different dimensions of the clastic dikes at the three localities into account, the seismo-tectonic epicentre was likely located north of the Biberach area. This renders a seismic source in the northern Alps that could be responsible for the formation of the dikes in the study area less likely. The only volcanically active region in the Middle Miocene north of the study area is the ~ 18 to 14 Ma phreatomagmatic Urach-Kirchheim volcanic field consisting of more than 350 tuffaceous and olivine-melilititic maar-diatreme complexes 15 . Due to the relatively low seismic efficiency of phreatomagmatic volcanism, intense and long-distance seismic effects of that volcanism are also unlikely 15 (see discussion and references therein). This suggests the Steinheim impact, which seemingly has the right position and approximate age, may have been the trigger of the post-Ries seismic event 15 .
Supporting arguments for a major post-Ries seismic event come from sediments of the lake inside the Ries crater itself. A ~ 314 m-thick sequence of crater lake deposits was drilled in the scientific drilling project 1973. This sediment sequence, deposited in a lake that lasted for ~ 1 Myr 43,44 , contains olistoliths and sediments with intense slumping and convolute bedding 44 . Somewhat surprisingly, the slumped deposits do not occur at the basis of the lake deposits, which would have been favored by the steep relief of the newly formed, precipitous impact crater; but soft-sediment deformation appears to be dominant in the middle of the sedimentary succession. The slumps and convolute bedding within the Ries crater lake could well represent a long-distance effect of a strong earthquake some hundred kyr after the Ries impact, potentially triggered by the Steinheim impact only some 40 km SW of the Ries crater.
The two major paleoseismic events recorded at various sites across the North Alpine Foreland Basin seem to have occurred close in time in the Miocene, yet during markedly different climatic and paleoenvironmental  In the past decade, many of the seemingly well-established terrestrial impact crater doublets and chains were discredited despite the seemingly low calculated likelihood of two separate impacts spatially close to one another [50][51][52] . 40 Ar/ 39 Ar dating results for several impact structures 51-54 contradict the hypothesis that planet Earth experienced the formation of a giant 'impact crater chain' during a major Late Triassic multiple impact event 50 . Recent work, moreover, revealed that apparent crater pairs, for instance the partly overlapping East and West Clearwater Lake impact structures (Québéc, Canada) 51 or the two Suvasvesi impact structures (Finland) 52 , are not the crater doublets they seem. To date, the only terrestrial crater pair that survived closer inspection is the Lockne-Målingen pair in Middle Sweden 36 , which was produced during an active period of Mid-to Late Ordovician asteroid bombardment of the Earth 53,54 .
Assuming two spatially and temporally separate impact events, the occurrence of the distinct and wellpreserved Ries-related seismite topped by primary distal ejecta near Biberach, Ravensburg, and Bernhardzell is explained as follows: 1. Thick, fine-grained, and homogenous sandy deposits intercalated with clays 15 promoted water-saturation within the Upper Freshwater Molasse in the study area, facilitating dewatering processes and soft-sediment deformation 15 triggered by the Ries impact. 2. Distal Ries ejecta blanketed the Ries seismite, was locally preserved in situ, and presently crops out in ravines and a river bank. 3. As an additional feature, clastic dikes 15,32,55 cutting through the Ries-related seismite-ejecta unit appear to have been caused by a second highmagnitude earthquake presumably linked to the Steinheim impact some kyr after the Ries impact event 5,15 . The occurrences of the seismite near Biberach, Ochsenhausen, Ravensburg, and Bernhardzell are the first reported deposits in which evidence for earthquake-induced soft-sediment deformation structures caused by the Ries impact has been documented. To our knowledge, this is also the first known occurrence of a primary continental seismite-ejecta couplet exposed in situ.

Magnitudes of impact-earthquakes. The magnitude of earthquakes induced by meteorite impacts is
still somewhat uncertain, and the seismic efficiency (i.e., the portion of the impactor's kinetic energy transformed into seismic energy) is only constrained within two orders of magnitude (for the theoretical background and calculations see "Methods" section) 15,30 . Accordingly, taking into account global-scale seismic effects linked (tentatively) with terrestrial impacts 2,3,14,20,22,23,30,31,33,56 , calculated magnitudes may, in some cases, be too conservative 15 . Applying widely used equations, the magnitude of the 'Chicxulub earthquake' was probably approximately M W 10-11.5 20 (and references therein). Endogenic (tectonic) earthquakes may not reach such an extraordinary magnitude 57,58 , and the strongest earthquakes ever recorded correspond to a magnitude M W 9.2 to 9.5 (e.g., the Alaska earthquake (USA) or the Great Chilean (Valdivia) earthquake [59][60][61] ; see Supplementary  Table 1).
An earthquake of a moment magnitude of M W 6.5 or higher is required for the formation of seismites 15,32 . The systematic relation between specific styles of crustal deformation (e.g., clastic dikes and soft-sediment deformation) and radial distance from the seismic source depending on the earthquake magnitude was studied for many regions on Earth 55,59,60 and takes into account the decrease of energy of seismic waves with time and rock volume traveled. Liquefaction and the concomitant formation of seismites caused by impact-induced earthquakes is preserved in the sedimentary record at a number of localities worldwide and summarized in a comprehensive database 15,17,20,22,23,25,31,33,34,62,63 . However, the earthquake magnitude-distance relationship for liquefaction effects is currently still underexplored and needs to be evaluated from the perspective of geologically younger major earthquakes.
For the impact that formed the 24 km-diameter Ries crater in southern Germany (impact energy ~ 5 × 10 23 J; equivalent to ~ 120,000 megatons of TNT), an earthquake of moment magnitude M W ~ 8.5 was calculated 30 (Supplementary Table 1 Table 1). The most distal seismites in the form of soft-sediment deformation and clastic dikes presumably linked with the Steinheim impact earthquake occur within a radial distance of at least 150 km from the source crater. While ground failure due to earthquakes of M W ≥ 7.8 may occur within a radial distance of 100 km or more, the outer limit for the occurrence of seismogenic clastic dikes dramatically decreases for earthquakes of M W < 7.8 59,60 . The most distal ground effects of an earthquake with M W 7.1 (Supplementary Table 1), for instance, reach radial distances of only ~ 23 km from the epicentre 59,60 . The formation of clastic dikes at a radial distance of 150 km, therefore, requires a palaeo-earthquake of the magnitude M W ~ 8.5 or higher. From this point of view, we speculate whether the magnitude of the postulated 'Steinheim earthquake' , assuming a genetic link, may have been (significantly) higher than M W 6.6 15,30 . A remaining caveat is that precise and accurate calculations of the seismic intensity of impact events are not straightforward, because the knowledge about the near-surface propagation of seismic waves following impact events is rather limited 15,30 and the seismic efficiency factor (determined within an uncertainty of three orders of magnitude 15,30 ) is not well constrained.
Environmental effects of the Ries and Steinheim events. The Ries impact caused a series of events ( Table 1) that affected the wider surroundings of the crater within a minimum radial distance of 180 km [2][3][4][9][10][11][15][16][17][18]38,49 . Some of the effects overlap and initiated the near-complete destruction of the near-surface environment within this radial distance. The impact-induced earthquake immediately followed the impact event when P-waves reached radial distances of 110 km from the crater centre ~ 15 s after the impact. The earthquake would have lasted for ~ 45 s until P-and S-waves passed this damage zone 57,58 (Table 1). The seismic energy would have caused intense slumping, soft-sediment deformation, and locally clastic dikes in the upper metres of the water-saturated Upper Freshwater Molasse (Figs. 2, 3, 4, 5, Supplementary Figs. 1 and 2). Approximately 2 min after the impact event, a fire ball and a subsequent air blast 64 reached the study area blowing off woods, soil, and the upper portions of the slumps and deformed soft-sediments (Table 1). A typical feature of the DREL is that it commonly lies on deformed Upper Freshwater Molasse sediments that are sometimes truncated at the top and exhibit an almost perfectly flat paleosurface (Fig. 4), thereby forming an eye-catching discordance (Fig. 7). This 'disaster topography' does not correspond with the original, unaffected palaeolandscape that was dominated by rivers, lakes, and damp forests 5,15,49 . Charred wood, reported for instance from the Unterneul sandpit 18 , suggests high temperatures of the fireball. Within three to five minutes (Table 1), an episode of bom- Table 1. List of the environmental effects of the Ries event from seconds to days after impact affecting the wider surroundings of the impact structure as observed in the study area 100 to 180 km from the centre of the crater. Single cobbles and boulders mainly of Upper Jurassic limestones (some shatterconed) landed on top of the seismite-hosting deposits, forming a distint discordance (Fig. 7) 170-300 s Fall-out from impact plume Mean velocity of vapour plume may exceed escape velocity 2,3 ; hot plume velocity of 7-10 km/s 2,3 ; collapse starts ~ 2 min. after impact event 2,3 ; velocity of ejecta curtain 0.5 km/s 5 km from crater rim 2,3 Quartz-rich loose sands (sometimes fining-upward succession) forming cm-to dm-thick horizons of distal Ries ejecta from impact plume fallout; sand contains some single shocked quartz grains  2,3,10,11,15,16 . The ballistically transported components stem from the uppermost tens of metres of the Ries target rocks 2,10 . They directly overlie the seismite in Upper Freshwater Molasse deposits and sometimes penetrate these sediments by a few cm or dm, thereby forming small funnel-like depressions (Fig. 4). Accordingly, these features can be described as small-scale secondary impact pits (i.e., formed by ejecta projectiles), an impact-related feature rarely seen on Earth 11,15,20 . The ejected material temporarily reached a height of ~ 50 to 100 km above the land surface 10 . In contrast to the coarser ejecta fragments, the highly shocked quartz grains were not ballistically transported, but are more likely part of the fallout from the Ries impact plume that began to collapse roughly two minutes after the impact 2,3,10 . Fallout from the impact plume may have rained down for minutes to hours 2,3 . Similar to crustal materials dispersed during volcanic eruptions 65,66 , small airborne ejecta particles and ash from the impact plume probably reached the higher troposphere and stratosphere and caused havy rainfall for days (and possibly for weeks or months due to the atmospheric disturbance) after the impact event.
The Ries impact event was, hence, followed by heavy rainfall and flashfloods (Table 1), as known from volcanic eruptions 65,66 . Fluvial channels were incised into the seismite-bearing Upper Freshwater Molasse in the study area (Fig. 3) and now contain a mix of reworked DREL and locally-derived rock material that can be correlated across several exposures within the North Alpine Foreland Basin. The reworked layers sometimes lack obvious sorting or grading and clasts are matrix-supported. These debritic layers show similarities to lahars to a certain degree. Most of the reworked layers, however, show indistinct sorting, and rounding and imbrication of clasts indicate transport and deposition in fast-flowing, high-energy flood streams (Fig. 3). Logs and pieces of wood up to 2.6 m in length 67 , relics of the impact-blasted wet forest 67 , are abundant in the reworked fluvial deposits. Moreover, well-preserved skeletal remains of the Miocene rhinoceros Brachypotherium brachypus were reported in flash flood deposits near Ravensburg 67 . It can be speculated wheter this impressive animal was killed by the hot airblast, struck to death by incoming Ries ejecta boulders, or whether it drowned in the 'tsunamilike' continental flashflood following the impact event. In the Biberach and the Ravensburg area, the primary DREL resembles a bone bed owing to the high concentration of fossil wood, remnants of amphibians, reptiles  Fig. 4 exhibiting a distinct slump fold with convolute layering (bottom; hammer in that unit) sharply truncated at its top thereby forming an eye-catching discordance and draped by coarse-grained distal Ries ejecta (pebble right of centre). The rare case of a DREL overlaying a near-perfect unconformity probably reflects a situation where slight elevations of the pre-Ries land surface were cut by the destructive airblast. The DREL shows an internal fining upward trend starting with coarser grained components at its base, overlain by fine sands, and a clayey horizon at its top. It is, in turn, overlain by undisturbed post-Ries deposits characterized by horizontal layering. This exposure of a continental seismite-ejecta couplet highlights the distal environmental effects of the Ries earthquake, ejecta deposition, and the impact-induced air blast in the Mid-Miocene (compare Table 1 www.nature.com/scientificreports/ (e.g., turtles, small alligators), and mammals amongst other bones and teeth of rhinoceroses, peccaries, deers (Fig. 4d), water chevrotains, and other hoof animals 67 . The intact nature of bones and teeth document that these fossils were not significantly reworked and that the finding situation is more or less in situ. Some 500 kyr later, the same region was affected by a second set of catastrophic effects, presumably induced by the Steinheim impact event, that produced large dikes cutting through the Ries seismite-ejecta couplet and the overlaying layers of Upper Freshwater Molasse. With the Ries and Steinheim impacts as an extraterrestrial one-two punch, Southern Germany seems to have witnessed a veritable double disaster in the Middle Miocene.

Methods
Field studies. In the last three decades, the DREL 10,1115-18 was systematically investigated in the North Alpine Foreland Basin. We paid particular attention to ravines in the areas of Biberach and Ravensburg in SW Germany and Bernhardzell (St. Gallen, Switzerland). After heavy rainfall in the Biberach and Ravensburg area in spring 2019, deposits with soft-sediment deformation structures and clastic dikes were partially exposed below and above the distal ejecta horizon along the valley sides of the ravines. The structures were excavated during eight field campaigns from spring to winter 2019. We excavated the sandy foreland basin deposits over a vertical extension of 15 m along the flank of the 'Tobel Oelhalde-Nord' (Biberach) and over tens of metres laterally along the flanks of the ravines 'Tobel Oelhalde-Nord and -Süd' (Biberach) and Kleintobel (Ravensburg).
Petrography. Samples of the dike's infills were taken, stabilized by synthetic resin, and processed to polished thin sections. Thin sections of the dike's infill were analyzed for their petrographic properties using a polarization microscope. Additional unconsolidated samples of the infill were investigated by reflected-light microscopy to assess their fossil content (e.g., Miocene mammal bones, invertebrates, and plant remnants).

Shock metamorphism.
Mineral grains separated from the distal Ries ejecta horizon from the Tobel Oelhalde-Nord south of Biberach and Kleintobel near Ravensburg were mounted in epoxy blocks from which thin sections were prepared, then studied using a four-axis universal stage mounted on an optical microscope. Planar deformation feature (PDF) planes in quartz grains and their crystallographic orientation were determined using the universal stage microscope 68,69 . The resulting PDF orientations are indicative of shock pressures that affected the impacted bedrock 68,69 . However, this method requires the detailed analysis of a large number of shocked quartz grains. Due to their rare nature in the distal Ries ejecta horizon, this study does not provide systematic PDF statistics.
Estimated magnitude of impact earthquakes. Seismic efficiency (i.e., the fraction of the impactor's kinetic energy that is transformed into seismic wave energy) is thought to range between 10 −5 and 10 −3 . Using a mean value of 10 −4 for that efficiency 30,56,57 (and references therein), an equation that correlates the impact energy with the resultant seismic magnitude (M L ) was derived: where M is the local (Richter) magnitude and E is the kinetic energy of the incoming projectile (E = half the projectile mass multiplied with the projectile's velocity squared, in Joules) 30 . Earthquake magnitudes calculated using that equation are only (geologically reasonable) approximations. Applying Eq. (1), the giant Chicxulub impact, for instance, (impact energy ~ 3.7 × 10 23 J) that caused the mass extinction event at the K-Pg boundary generated a seismic pulse roughly equivalent to a moment magnitude M W 10-11.5 earthquake 20 . The causal relation between the magnitude-distance relation of the formation of seismites in the form of clastic dikes and soft-sediment deformation caused by intense earthquake activity was reported for many regions on Earth 32,37,55,60 . Liquefaction and concomitant formation of seismites caused by meteoritic impact-induced earthquakes is preserved in the sedimentary record 15,17,20,22,23,31,32 and can help to evaluate intensity of other impact-induced earthquakes. However, the impact earthquake magnitude-distance relationship for liquefaction effects in sediments has to be evaluated mainly from more recent large seismically-induced earthquakes and their distal dewatering effects reported in the literature 59 www.nature.com/scientificreports/