Journal of Marine Science and Engineering

Article Tsunami Boulders on the Rocky Coasts of and ()

Francesc Xavier Roig-Munar 1, Antonio Rodríguez-Perea 2, José Angel Martín-Prieto 1,2, Bernadi Gelabert 3,* and Joan Manuel Vilaplana 4 1 QU4TRE Consultoría Ambiental, C/Carritxaret 18-apt. 6, , 07749 , ; [email protected] (F.X.R.-M.); [email protected] (J.A.M.-P.) 2 Departamento de Geografía, Universitat de les Illes Balears, Palma de , Carretera de km 7,5, 07122 , Spain; [email protected] 3 Departamento de Biología, Universitat de les Illes Balears, Palma de Mallorca, Carretera de Valldemossa, km 7,5, 07122 Palma de Mallorca, Spain 4 Dpto.de Dinàmica de la Terra i de l’Oceà, Grupo RISKNAT, Geomodels, Universitat de Barcelona, Martí i Franquès, s/n. 08028 Barcelona, Spain; [email protected] * Correspondence: [email protected]; Tel.: +34-97117237

 Received: 5 June 2019; Accepted: 6 September 2019; Published: 20 September 2019 

Abstract: Large boulders have been found in marine cliffs from 7 study sites on Ibiza and Formentera Islands (Balearic Islands, Western Mediterranean). These large boulders of up to 43 t are located on platforms that form the rocky coastline of Ibiza and Formentera, several tens of meters from the edge of the cliff, up to 11 m above sea level and several kilometers away from any inland escarpment. Despite than storm wave height and energy are higher from the northern direction, the largest boulders are located in the southern part of the islands. The boulders are located in the places where numerical models of tsunami simulation from submarine earthquakes on the North African coast predict tsunami impact on these two islands. According to radiocarbon data and rate of growth of dissolution pans, the ages of the boulders range between 1750 AD and 1870 AD. Documentary sources also confirm a huge tsunami affecting the SE coast of Majorca (the largest Balearic Island) in 1756. The distribution of the boulders sites along the islands, the direction of imbrication and the run-up necessary for their placement suggest that they were transported from northern African tsunami waves that hit the coastline of Ibiza and Formentera Islands.

Keywords: tsunami boulders; coastal cliff; Ibiza; Formentera

1. Introduction There is evidence that rocky coasts are sensitive to high-energy events such as storms [1], hurricanes, typhoons, or cyclones [2] and tsunamis [3]. One of the main effects of the tsunamis on rocky shores is represented by the presence of mega boulders displaced inland [4]. The identification of these boulders transported by tsunamis or storms is essential for the recognition of the occurrence of events produced in the past [5], as well as to estimate the hydraulic properties that have given rise to these [6]. The distinction of boulders associated with tsunamis is based on a set of sedimentological, morphological, chronological, stratigraphic, and organizational criteria that can be analyzed in detail. Being the deposits of boulders imbricated and aligned along the coast, they show clear transport indicators associated with tsunamis [7]. In the last decade, the debate regarding on the transport of boulders to discern their origin between tsunamis and large storms has forced to researchers to further consider in more detail the role of storms on the rocky coasts [8]. Some equations have been developed to estimate the over-elevation by lift or run-up necessary on a block, under three assumptions: submerged boulders, subaerial boulders, and boulders delimited by joints or fractures [9,10].

J. Mar. Sci. Eng. 2019, 7, 327; doi:10.3390/jmse7100327 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2019, 7, 327 2 of 19

In the Western Mediterranean, documented examples of boulders displaced on rocky shores by historical tsunamis are numerous and have been compiled by [11,12], and expanded by [13,14]. These are boulders of metric order, plucked from the edge of the cliff and transported inland, presenting geomorphological, orientation and imbrication characteristics that allow them to be differentiated from those related to other sedimentary environments. The presence of boulders on the rocky coasts of Majorca (the largest of the Balearic Islands) was studied by [11,15,16]. Reference [17,18] analyzed boulders on the coasts of Minorca and Majorca (see Supplementary Materials), applying different equations to distinguish between the boulders associated with storms and boulders associated with tsunamis, and outlining its relation with the trajectories of tsunamis from the N of Africa [19]. In this paper we document, for the first time, the presence of large boulders on the coasts of Ibiza Island (located at the S of the Balearic Islands). The main goal of this article is to demonstrate that some of these boulders, located close to the coastal cliffs of Ibiza and Formentera Islands, were transported and deposited by tsunamis that occurred in the recent past and mostly originated from submarine earthquakes at the Algerian coast.

1.1. Geological Framework The island of Ibiza is located in the south-western and is the third-largest (571 km2) and most Westerly Island of the Balearic Islands (Figure1). Geological structure of the island is composed of a series of thrust sheets (mainly of Middle Triassic to Middle Miocene carbonate deposits) formed during the Alpine compression (Upper Oligocene to Middle Miocene) and trending NE-SW [20]. These thrust sheets correspond to the northeasterly continuation of the Subbetic Ranges in the southern Iberian Peninsula. Bedrock lithology of Ibiza is composed mainly of Miocene and Mesozoic carbonate rocks [21]. Muschelkalk limestone and dolomite, as well as Keuper marls and clays, constitute the Triassic materials of the island, whereas Jurassic limestone and dolomites and Cretaceous to Middle Miocene limestone overlie the Triassic materials and constitute the significant reliefs of the island. Quaternary fluvial, alluvial and colluvial sediments fill the central basins, whereas Pleistocene coastal successions characterized by shallow-marine to coastal aeolian and colluvial deposits crop out J.patchily Mar. Sci. Eng. along 2019 the, 7, x cli FORffed PEER coasts REVIEW [22]. 3 of 20

FigureFigure 1. 1. SettingSetting and and geological geological framework framework of of Ibiza Ibiza an andd Formentera Formentera Islands. Islands. Red Red and and yellow yellow dots dots correspondcorrespond to to the the boulder boulder outcrops outcrops analyzed. analyzed.

In Formentera island, boulders remain in the areas of Punta Prima, in the E of the island, and Punta de sa Gavina, in the W (Figure 2) [24,25]. These two areas, formed by Miocene calcareous materials, stand out forpresenting metric size boulders at distances tens of meters away from the cliff edge and with heights higher than 11 m a.s.l. The sites are associated with several littoral terraces with heights between 5 and 15 m a.s.l.

1.2. Wave Climate The Mediterranean basin is characterized by a highly indented coastline that creates some small and well-defined sub-basins, where wave energy is conditioned by wind speed and limited fetches [26]. In the western Mediterranean, the most intense waves come from the NE [27], although the NW also generates strong waves between the Balearics, Corsica, and Sardinia as well [28]. Tidal regime observed at Harbors of Formentera and Ibiza is about 0.41 m [29]; hence, the coastal area subjected to this study can be considered micro-tidal and low and high pressures can be considered responsible of some more significant oscillations. The wave data correspond, on the one hand, to the Puertos del Estado digital buoy system; it is formed by time series of wind and wave parameters, at some points, from numerical modelling (called SIMAR points) and, on the other, to the analysis of wave data carried out by [30]. In the first case, these figures are average values for the four SIMAR points used. According to the analysis of Puertos del Estado, the distribution chosen to describe the average wave series regime is that of Weibull, Hs is the average height of the highest third of waves, while Tp is the period of the group of waves with more energy. Data from SIMAR points 2099108 and 2106108 (placed in the WandE, respectively) for the period 1958–2018 with the reliability of 99.68% [29] were analyzed (Figure 2, Table 1). The SIMAR data set consists of a time series of wind and wave parameters obtained from numerical modeling [29].

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Table 1. Wave data from SIMAR points (Figure 2). Fetch in kilometers; Hs, significant wave height in Inmeters; Ibiza, Tp, the wave main period outcrops in seconds are found (www.puertos.es on the west coast,); Hs50, west significant of Sant wave Antoni, height and for on 50 the years’ northeast coast,return close period to Santa according Eularia to [30] (Figures (for location1 and2 see). WestFigure of 2). Sant Antoni, analyzed boulders are set in two different locations: first, above Punta Pedrera, a small peninsula 16.5 m a.s.l (above sea level) Fetch formedSIMAR by Pleistocene Location colluvial andWater alluvial Depth sediments, Fetch and secondly, in aTp coastal Hs ditch twoHs50 meters Direction a.s.l. (Sant Antoni) formed by Pleistocene aeolianites. Northeast of Santa Eularia, analyzed boulders 2099108 1.25 E–39.00 N 95 m 180 NW 10.99 5.17 11 are also2106108 located in 1.83 three E–39.00 settings: N Ses Eres 150 m Roges shows 920 boulders E on Pleistocene 10.46 aeolianites, 5.83 11 in Pou des Lle2099105ó the materials 1.25 E–37.75 are Middle N Triassic 108 m limestones 500 and in PuntaSW Arab 11.33í boulders 6.04 are formed 7 by Cretaceous2104105 limestones. 1.67 E–38.75 N 325 m 900 E 10.71 5.83 11

Figure 2.2. WaveWave fetch fetch a ffaffectingecting Ibiza Ibiza and and Formentera Formentera Islands. Islands. Roses Roses of wave of wave directions directions and wave and heightwave frequenciesheight frequencies for each for SIMAR each SIMAR points. points. Red points Red correspondpoints correspond to boulder to boul outcropsder outcrops analyzed. analyzed.

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Physiographically, the island of Formentera is very different from Ibiza: Formentera constitutes a graben, whereas Ibiza is the corresponding horst. Formentera is constituted of four domains (Figure1). At its eastern and western ends rise two promontories, meanwhile, between them, there is a dune ridge NW-SE, which is less than 2 km wide. The eastern promontory, La Mola, reaches an altitude of 197 m on a gently undulating tabular platform, with cliffs that surpass 100 m. The western promontory, of Barbaria, tilted towards the NNE, reaches 108 m of altitude at its extreme SSW. Geologically, the island is constituted by a carbonate set of reef origin deposited during the Tortonian, on which alluvial deposits, soils and wind accumulations are superimposed. A fracture under an extensive regime gave rise to a network of normal faults, the result of which was the individualization of the promontories of La Mola and Barbaria [23]. The Miocene materials of the Tortonian are found in a part of the coast, little deformed, where the clays, sands, breccias, and limestones constitute a heterogeneous group. Several islands and islets insinuate the connection between the northern dune ridge and Ibiza, constituting the intermediate archipelago between both islands, which is composed of the remains emerged from a partially submerged threshold and whose depth does not reach 10 m. In Formentera island, boulders remain in the areas of Punta Prima, in the E of the island, and Punta de sa Gavina, in the W (Figure2)[ 24,25]. These two areas, formed by Miocene calcareous materials, stand out for presenting metric size boulders at distances tens of meters away from the cliff edge and with heights higher than 11 m a.s.l. The sites are associated with several littoral terraces with heights between 5 and 15 m a.s.l.

1.2. Wave Climate The Mediterranean basin is characterized by a highly indented coastline that creates some small and well-defined sub-basins, where wave energy is conditioned by wind speed and limited fetches [26]. In the western Mediterranean, the most intense waves come from the NE [27], although the NW also generates strong waves between the Balearics, Corsica, and Sardinia as well [28]. Tidal regime observed at Harbors of Formentera and Ibiza is about 0.41 m [29]; hence, the coastal area subjected to this study can be considered micro-tidal and low and high pressures can be considered responsible of some more significant oscillations. The wave data correspond, on the one hand, to the Puertos del Estado digital buoy system; it is formed by time series of wind and wave parameters, at some points, from numerical modelling (called SIMAR points) and, on the other, to the analysis of wave data carried out by [30]. In the first case, these figures are average values for the four SIMAR points used. According to the analysis of Puertos del Estado, the distribution chosen to describe the average wave series regime is that of Weibull, Hs is the average height of the highest third of waves, while Tp is the period of the group of waves with more energy. Data from SIMAR points 2099108 and 2106108 (placed in the W and E, respectively) for the period 1958–2018 with the reliability of 99.68% [29] were analyzed (Figure2, Table1). The SIMAR data set consists of a time series of wind and wave parameters obtained from numerical modeling [29].

Table 1. Wave data from SIMAR points (Figure2). Fetch in kilometers; Hs, significant wave height in meters; Tp, wave period in seconds (www.puertos.es); Hs50, significant wave height for 50 years’ return period according to [30] (for location see Figure2).

SIMAR Location Water Depth Fetch Fetch Direction Tp Hs Hs50 2099108 1.25 E–39.00 N 95 m 180 NW 10.99 5.17 11 2106108 1.83 E–39.00 N 150 m 920 E 10.46 5.83 11 2099105 1.25 E–37.75 N 108 m 500 SW 11.33 6.04 7 2104105 1.67 E–38.75 N 325 m 900 E 10.71 5.83 11

The wave climate of Ibiza differs from one coast to the other, mainly in the length of the fetch. The shorter corresponds to the W with a maximum of 180 km to the NNW, and the swell is characterized by a significant wave (Hs) where 86.02% is lower than 1 m, and only 0.006% is higher than 6 m, the J. Mar. Sci. Eng. 2019, 7, 327 5 of 19

87.26% of the peak period (Tp) is inferior to 7 s. The main component direction is from NNW, with a frequency of 24%. The East sector of Ibiza has the biggest fetch to the E with 920 km. It is characterized by an Hs, where 72.56% is lower than 1 m. Concerning the peak period, 87.2% is lower than 7 s, and only 0.55% of the record exceeds 10 s. The main component direction is from the ESE and E, with a frequency of 18% and 16%, respectively. In Formentera, the maritime climate has similar characteristics to the neighbor Ibiza. On the western coast, the maximum fetch is 500 km towards the SW, and the swell is characterized by a significant wave height (Hs) with a frequency of 83.8% less than 1 m, and a peak period of 73.7% less than 6 s, where only the Hs exceeds 6 m by 0.20%. The main component of its address is SW, with a frequency that reaches 25%. Its eastern coast has a maximum fetch of 900 km towards the E, with an Hs less than 1 m in 75.2% of cases, where only 0.11% of the time exceeds 6 m. The peak period is characterized by 63.4% less than 6 s, and the main component of its direction is from E, with a frequency of 28%. Reference [30] made an estimate of the spatial variability of the recurrence of 50 years for the significant wave height of the Balearic Sea, obtaining estimates around 11 m in the eastern sector (for both islands) and 7 m in the western of Formentera and 11 in western Ibiza (Table1).

1.3. Tsunamis in Ibiza and Formentera According to [31], the primary tsunamigenic source in the Western Mediterranean is located offshore at the north of Algeria (Figure3), which is characterized by compressive tectonics (the North Algerian fold and thrust belt). Another minor tsunamigenic area is the Alboran Basin, characterized by transcurrent and transpressive tectonics. The last tsunami registered affecting the Balearic Islands was in 2003 (May 21). This tsunami was due to an earthquake, generated by a reverse fault, with a magnitude of 6.9 in Zemmouri (Algeria). Despite being a moderate magnitude earthquake, it generated a tsunami observed on the coasts of Algeria, Spain, France, and Italy. The maximum lift by run-up measured in the Balearic Islands was 3 m in Sant Antoni (Ibiza), and material damage occurred in the ports of Majorca, Minorca, and Ibiza. The propagation of this 2003 tsunami was modeled by [19,32–34], including in these study data of wave trajectories, location of tsunami impact areas, wave travel times and wave elevation (Figure3). Thus, there is currently seismic activity at the bottom of the Algerian Basin that gives rise to tsunamis affecting the coast of the Balearic Islands. In the recent past, in the last 500 years, there have been tsunamis affecting the Balearic Islands (Table2). Among the historical records of massive wave phenomena that have affected the Balearic Islands, some episodes can be attributed to tsunamis. In 1856, the chronicles were written by [35] record an extraordinary sea rise in the Port of Maó (Minorca Island, Figure1) that destroys several moorings. In 1918, a new ‘seismic wave’ floods the Port of Ma ó, following an earthquake offshore the Algerian coast [35]. There are also historical records reporting a flooding event with a run-in up to 2 km inland and a run-up up to 45 m at the east coast of Majorca (the largest of the Balearic Islands) in 1756 [35]. J. Mar. Sci. Eng. 2019, 7, 327 6 of 19 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 6 of 20

Figure 3. Modeling estimated estimated travel travel time time and and impact impact area areass based based on on the the tsunami tsunami records records of of 21 21 May, May, 2003 [34]. [34]. Blue dots record background seismicityseismicity from 1998–2005 (CSEM-EMSC).(CSEM-EMSC). Green rectangles record tide gauges with precise sampling rates.

Table 2.2. Historical tsunamis phenomena were were impacting in in the the Balearic Balearic Islands, Islands, modified modified from from [36]. [36]. Information sources (IS): (1) [[35]35] and (2) [[37,38].37,38].

Data Data AffectedAff Areaected Area PhenomenonPhenomenon IS IS 1660 Majorca,1660 Palma, Majorca, Campos Palma, Campos Earthquake Earthquake and and tsunami tsunami 1 1 1721 Balearic1721 Islands Balearic Islands EarthquakeEarthquake and and seawater seawater withdrawal withdrawal 1 1 1756 Majorca, Santanyí Tsunami and big waves 1 1756 Majorca, Santanyí Tsunami and big waves 1 1756 Balearic Islands Tsunami and flooded coasts 2 1756 Balearic1790 Islands Alboran Sea Tsunami Tsunami and flooded coasts 2 2 1790 Alboran1804 Sea Alboran Sea Tsunami Tsunami 2 2 1804 Alboran1856 Sea Minorca, Maó TsunamiTsunami and seismic wave 1 2 1856 Minorca,1856 Maó Algeria Tsunami Tsunami and seismic wave 2 1 1885 Algeria Sea level changes 2 1856 Algeria Tsunami 2 1891 Algeria Tsunami 2 1885 Algeria1918 Minorca, Maó SeaSeismic level changes wave 1 2 1891 Algeria2003 Algeria Tsunami Earthquake (7.0) and tsunami 2 2 1918 Minorca, Maó Seismic wave 1 2003Reference Algeria [33 ] modeled the tsunami-related Earthquake with the(7.0) 1856 and otsunamiffshore Djijelli (Algeria) earthquake, 2 with particular attention towards its impact on the Balearic Islands. The study concludes that the wave arrivalsReference in the Balearic[33] modeled Islands the concerning tsunami-related the 2003 with tsunami the 1856 are offshore reported Djijelli in the (Algeria) same areas earthquake, than for withthe modeled particular 1856 attention results, towards highlighting its impact the highest on th exposuree Balearic of Islands. the southeastern The study coasts concludes of the that Balearic the waveIslands arrivals to tsunamis in the comingBalearic fromIslands central concerning and eastern the 2003 Algeria. tsunami are reported in the same areas than for theReference modeled [19 1856] used results,highlighting 22 tsunamigenic seismicthe high sourcesest exposure to estimate of the the southeastern tsunami threat coasts over of the BalearicSpanish MediterraneanIslands to tsunamis coast coming of the Iberian from central Peninsula and and eastern the Balearic Algeria. Islands. They modeled tsunamis generatedReference from [19] seismic used sources 22 tsunamigenic of N Africa, seismic from the sour Alborances to Seaestimate to N ofthe Algeria. tsunami According threat over to [19the], Spanishthe sources Mediterranean of the N of Algeriacoast of S-1 the and Iberian S-2 (Figure Peninsula4) are and those the that Balearic most aIslands.ffect the They coasts modeled of Ibiza tsunamisand Formentera generated and from have seismic maximum sources wave of N height Africa values, from the of more Alboran than Sea 2 mto inNof the Algeria. S of both According islands, toespecially [19], the Ssources of Formentera, of the N whereof Algeria values S-1 higher and S-2 than (Figure 4 m reach4) are thethose Cap that de most Barbaria. affect In the addition coasts of to Ibiza and Formentera and have maximum wave height values of more than 2 m in the S of both islands, especially Sof Formentera, where values higher than 4 m reach the Cap de Barbaria. In

J. Mar. Sci. Eng. 2019, 7, 327 7 of 19 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 7 of 20 theseaddition two to principal these two sources, principal sources sources, S-3, S-4,sources and S-3, S-6 canS-4, alsoand generateS-6 can also wave generate elevations wave close elevations to 2 m. Theclose seismic to 2 m. sources The seismic S-0 to sources S-9 are S-0 located to S-9 Nare of locat Algeriaed N (S-0 of Algeria to the west(S-0 to and, the progressively,west and, progressively, S-9 to the east,S-9 to Figure the east,4). TheFigure model 4). The considers model considers a 7.3 earthquake a 7.3 earthquake magnitude ma andgnitude the seismic and the sources seismic S-0sources to S-9 S- consists0 to S-9 ofconsists low-angle of low-angle reverse faults, reverse 55 faults, km in 55 length, km in verging length, towardsverging thetowards N and the NW. N and NW.

FigureFigure 4.4.Maps Maps ofof maximum maximum wave wave elevation elevation and and estimated estimated travel travel times times of of the the tsunami tsunami in thein the islands islands of Ibiza and Formentera, according to the three of the tsunami sources defined by [19]. Below, seismic of Ibiza and Formentera, according to the three of the tsunami sources defined by [19]. Below, seismic sources modelled as probable tsunamigenic worst cases for the westernmost Mediterranean coast sources modelled as probable tsunamigenic worst cases for the westernmost Mediterranean coast (taken from [13]). The thick lines are the surface trace of the faults and the focal mechanisms represent (taken from [13]). The thick lines are the surface trace of the faults and the focal mechanisms represent the rupture characteristics. The black line of each double couple is the fault plane. the rupture characteristics. The black line of each double couple is the fault plane. 2. Methods 2. Methods For each area the following tasks have been carried out: For each area the following tasks have been carried out: 1. Geomorphological map of the coastal areas at a 1:1000 scale. 2.1. TopographicGeomorphological and bathymetric map of the profiles coastal perpendicular areas at a 1:1000 to the scale. coast were made for each area. Profiles 2. wereTopographic prepared and from bathymetric the 30 m isobaths profiles to perpendicular the start of the terrestrialto the coast vegetation were made cover. for Topographic each area. − dataProfiles from were [39] prepared and the bathymetric from the −30 data m fromisobaths [40] to were the used.start of the terrestrial vegetation cover. 3. TheTopographic dimensions data of from the boulders [39] and werethe ba measuredthymetric(a, data b, cfrom axis [40] on behalf were used. of the long, intermediate, 3. andThe dimensions short axis, respectively).of the boulders According were measured to [10 (a,], theb, c volumeaxis on behalf of a boulder of the long, that intermediate, is based on aand multiplication short axis, respectively). of the central According axis (Vabc) to overestimates [10], the volume the actualof a boulder volume that and is produces based on an a overestimationmultiplication of thethe wavecentral energy axis and(Vabc) wave over heightsestimates needed the foractual their volume transport. and Those produces authors, an throughoverestimation a complex of the process wave ofenergy digital and photography, wave heights [10 needed] estimate for their the real transport. volume Those as 49% authors, of the Vabc.through To a estimate complex that process percentage of digital for ourphotography, measured volumes,[10] estimate we didthe areal test volume on several as 49% boulders of the throughVabc. To decomposing estimate that thepercentage volume for of theour block measur ined measurable volumes, parallelepipedswe did a test on thatseveral by additionboulders through decomposing the volume of the block in measurable parallelepipeds, that by addition

J. Mar. Sci. Eng. 2019, 7, 327 8 of 19

represent more accurately the real volume of the block. On average, the volume by triangulation was 68% of the Vabc. This percentage has been applied to all of the analyzed blocks. 4. The height above mean sea level of the boulders, and their distance from the edge of the cliff were also measured as well. Their orientation and imbrication were considered, and the geomorphological context in which they were found. Isolated boulders, an imbricated group of boulders or ridges of imbricate boulders, were also registered.

Other qualitative observations were taken into account:

(a) The relation of the boulders with its source area (based on bed thickness, facies, and lithology), and the presence of fractures that can promote detachment of the boulders, (b) The presence of encrusted marine fauna indicating the origin of the boulder before its displacement, (c) The presence of pre-detachment and post-detachment solution pans which have been used as age indicators for boulder emplacement, (d) The degree of rounding of the boulders, presence or absence of another type of sediment as well as the presence of abrasion surfaces due to boulder quarrying and transport, (e) The presence of flow-outs, areas with denudated beds forming channels over the cliff, favoring the entry and acceleration of the water flows and leaving a boulder ridge at its front.

To have an approximate hydrodynamic value of storm or tsunami for quarrying, transport, and deposition of the boulders, equations of [5,10] were applied under three different pre-settings: submerged, subaerial and joint-bounded boulders. The Transport Figure values of [11] were calculated (Table3). Because most of the observed boulders were detached from the edge of the cli ff joint-bounded and subaerial scenarios must be considered. Two boulders showed features (incrusted marine fauna or notch fragments) indicating that they were submerged in their origin.

3 Table 3. Equations used in the analysis of Ibiza and Formentera boulders. ρs = 1.9 g/cm for Quaternary 3 2 boulders and 2.3 g/cm for Jurassic boulders, ρw = 1.027 g/mL, Cd = 2, Cl = 0.178, Cm = 2, ü = 1 m/s , µ = 1, q = 0.73. Coefficient values according to [10].

Ht Hs 2 2 submerged Ht = [0,25(ρs ρw/ρw) 2a]/[(C (ac/b )+ C ] Hs = [(ρs ρw/ρw) 2a]/[(C (ac/b )+ C ] − d l − d l Nott (2003) [9] Ht = [0,25 (ρs ρw/ρw) [2a Cm (a/b) Hs = [(ρs ρw/ρw) [2a 4Cm (a/b) (ü/g)] subaerial − 2 − − 2− (ü/g)]/[Cd (ac/b )+ Cl] ]/[Cd (ac/b )+ Cl] joint-bounded boulder Ht = [0,25 (ρs ρw/ρw) a]/C Hs = [(ρs ρw/ρw) a]/C − l − l subaerial Ht = 0,5 µ V ρ /C (a c q) ρw Hs = 2 µ V ρ /C (a c q) ρw Engel and May · · · b D· · · · · · · b D· · · · Ht = (ρ ρw) V (cosθ + µ sin Hs =(ρ ρw) V (cos θ + µ sin θ)/0.5 (2012) [10] joint-bounded boulder b − · · · b − · · · · θ)/2 ρw.C a b q ρw.C a b q · L· · · L· · · tsunami the large axis of the Ht a C coefficient of drag height boulder d storm the medium axis of Hs wave b C coefficient of lift the boulder l height boulder the short axis of the ρ c C coefficient of mass s density boulder m seawater the speed of water ρ g force of gravity ü w density flow vol. abc of boulder area V the q θ clifftop steepness coefficient boulder coefficient µ of friction

Ref. [41] proposes a new equation to obtain the minimum tsunami height (HT) at the coastline which can move a joint-bounded boulder (JBB). This Nott-derived equation differs from the original concerning the relevance of the c-axis, which indicates the thickness of the boulder directly exposed to the wave impact. Ref. [42] also revised Nott’s equation, rearranging the lift area of the boulders in the subaerial and submerged scenarios and taking into account the effect of the slope at the pre-transport location for the joint-bounded scenario. The differences between the results obtained from Nott’s J. Mar. Sci. Eng. 2019, 7, 327 9 of 19 equations and the revised equations of [42] were that the minimum flow velocity required to initiate J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 9 of 20 the transport was reduced up to 56% for submerged boulders and up to 65% for joint-bounded blocks. approximateReference value, [10] reconsidereven just an Nott’s order equationsof magnitud throughe, for the a moreheight accurate of the waves volume required and density for the measurementboulder transport. and established equations to derive the minimum wave height of a tsunami (HT) or storm wave (HS) which is required to dislodge a particular subaerial or JBB boulder (Table3).

Finally,Table 3. we Equations also used used the Transportin the analysis Figure of (TF)Ibiza equation and Formentera of [11]. TFboulders. equation ρs is= the1.9 productg/cm3 for of the heightQuaternary (H, in meters) boulders of the and boulder 2.3 g/cm above3 for Jurassic sea level, boulders, its distance ρw = 1.027 (D, ing/mL, meters) Cd = from2, Cl = the0.178, edge Cm of= 2, the ü cliff and its= 1 mass m/s2, (M,μ = 1, in q tons) = 0.73. Coefficient values according to [10].

Ht Hs Ht = [0,25(TFρs =− ρMw/ρDw) 2a]/[(CH.d (ac/b2)+ (1) submerged · · Hs = [(ρs − ρw/ρw) 2a]/[(Cd (ac/b2)+ Cl] Cl] TransportNott (2003) figure is a simple, useful and essential formula because it is an indirect approach for Ht = [0,25 (ρs − ρw/ρw) [2a − Cm (a/b) Hs = [(ρs − ρw/ρw) [2a − 4Cm (a/b) [9] subaerial establishing the energy required for the transport(ü/g)]/[C ofd (ac/b the boulders:2)+ Cl] the heavier(ü/g)] the boulders,]/[Cd (ac/b2)+ the Cl] higher its elevation abovejoint-bounded sea level boulder and the farther Ht = its [0,25 distance (ρs − ρw/ toρw) the a]/C clil ff, the higher Hs the = [( energyρs − ρw/ρw required) a]/Cl for itsEngel transport. and Ref. [11subaerial] used the TF values Ht in = the 0,5· southernμ·V·ρb/CD·(a·c·q) and northern·ρw sector Hs of = 2· Majorcaμ·V·ρb/CD for·(a·c·q) discerning ·ρw May (2012) Ht = (ρb − ρw)·V·(cosθ + μ· sin Hs =(ρb − ρw)·V·(cos θ + μ· sin θ)/0.5· the storm or tsunamijoint-bounded origin boulder of the boulders. According to these authors, TF < 250 corresponds to [10] θ)/2·ρw.CL·a·b·q ρw.CL·a·b·q boulders transported by storms and TF > 250 matches to boulders transported by tsunamis. In this Ht tsunami height a the large axis of the boulder Cd coefficient of drag work, and in orderHs storm to fall wave on height the side b of safety, the medium it has axis been of the estimated boulder that Cl a TF > 1000 coefficient is indicative of lift of tsunami. It is fourρs times boulder the density considered c value the short by previous axis of the authors,boulder even Cm when applyingcoefficient a of significant mass ρw seawater density g force of gravity ü the speed of water flow reduction (32% of Vabc) in calculating the volume of the boulders. vol. abc of the We are awareV than mathematicalq models boulder are stillarea coefficient in their initial stagesθ andclifftop that the steepness equations boulder are under constant reviewcoefficient and of improvement. In selecting [5,10,11] formulas, we search to obtain an μ approximate value, evenfriction just an order of magnitude, for the height of the waves required for the boulder transport. 3. Results 3. Results 3.1. Ibiza: Punta Pedrera 3.1. Ibiza: Punta Pedrera Boulders are located on a small peninsula formed by a Pleistocene tabular platform slightly tilted Boulders are located on a small peninsula formed by a Pleistocene tabular platform slightly tilted to the east (Figure 5). The cliff has a vertical profile that continues below the sea, followed by a gentle to the east (Figure5). The cli ff has a vertical profile that continues below the sea, followed by a gentle bathymetry. Boulders are distributed individually along with the tabular platform, although there bathymetry. Boulders are distributed individually along with the tabular platform, although there are are small groups of 3 to 4imbricated boulders of small dimensions. Boulders do not show evidence small groups of 3 to 4imbricated boulders of small dimensions. Boulders do not show evidence of of reworking. The average weight of the boulders is 8.4 t, and they are located at an average distance reworking. The average weight of the boulders is 8.4 t, and they are located at an average distance of of 66 m from the cornice and at an average height of 10 m a.s.l. Maxim values of these figures are 43.2 66 m from the cornice and at an average height of 10 m a.s.l. Maxim values of these figures are 43.2 t of t of weight, 11 m a.s.l., and 77 m from the cliff edge. Average orientation of the boulders is towards weight, 11 m a.s.l., and 77 m from the cliff edge. Average orientation of the boulders is towards the theNNW, while the dominant swell comes mainly fromNE. NNW, while the dominant swell comes mainly from NE.

B

3 m A

Figure 5. Cont.

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J.J. Mar. Mar. Sci. Sci. Eng. Eng. 20192019, ,77, ,x 327 FOR PEER REVIEW 1010 of of 20 19 C

C

1 m

1 m Figure 5. (A) Geomorphological scheme of the Punta Pedrera area. Roses show the prevailing wave direction. (B) Large coastal boulder located 10 m a.s.l. (C) Boulder ridge at Punta Pedrera. Notice the Figureperson 5. in(A the) Geomorphological cercle. scheme of the Punta Pedrera area. Roses show the prevailing wave Figure 5. (A) Geomorphological scheme of the Punta Pedrera area. Roses show the prevailing wave direction. (B) Large coastal boulder located 10 m a.s.l. (C) Boulder ridge at Punta Pedrera. Notice the direction. (B) Large coastal boulder located 10 m a.s.l. (C) Boulder ridge at Punta Pedrera. Notice the 3.2. personIbiza: Sant in the Antoni circle. person in the cercle. 3.2. Ibiza:The Santboulders Antoni westward of Sant Antoni are located over a low-lying littoral terrace build on 3.2.Pleistocene Ibiza: Sant aeloanites Antoni (Figure 6). That terrace shows a gentle stratification towards the sea, which allowsThe the boulders progressive westward dismantling of Sant of Antoni strata to are form located boulders. over The a low-lying bathymetry littoral is shallow terrace and build follows on The boulders westward of Sant Antoni are located over a low-lying littoral terrace build on Pleistocenethe slope of aeloanites the terrace. (Figure The height6). That of terracethe terrace shows in the a gentle highest stratification places does towards not exceed the sea,3 m. which a.s.l. In Pleistocene aeloanites (Figure 6). That terrace shows a gentle stratification towards the sea, which allowsthe immediate the progressive submerged dismantling area, a oflarge strata number to form of boulders. fractured Theboulders bathymetry have been is shallow observed, and followssome of allows the progressive dismantling of strata to form boulders. The bathymetry is shallow and follows thethem slope with of themarine terrace. fauna. The Just height one ofboulder the terrace has a in TF the > 1000: highest its places weight does is 17.6 not t, exceed it is located 3 m. a.s.l. 2.1 m In a.s.l., the the slope of the terrace. The height of the terrace in the highest places does not exceed 3 m. a.s.l. In immediateand a distance submerged from the area, edge a largeof the number cliff of 30.5 of fractured m. The rest boulders of the haveboulders been have observed, an average some weight of them of the immediate submerged area, a large number of fractured boulders have been observed, some of with11 t marineand, on fauna. average, Just are one located boulder 1.4 has m a a.s.l., TF > and1000: 11.3 its weightm inland is 17.6from t, itthe is cliff located edge. 2.1 Some m a.s.l., boulders and a them with marine fauna. Just one boulder has a TF > 1000: its weight is 17.6 t, it is located 2.1 m a.s.l., distanceshow new from impact the edge features of the and cliff ofone 30.5 of m.them, The with rest ofincrusted the boulders fauna, have have an been average used weight for C14 of 11 age t and a distance from the edge of the cliff of 30.5 m. The rest of the boulders have an average weight of and,analysis. on average, The orientation are located of all 1.4 the m a.s.l.,boulders and is 11.3 towards m inland NNE, from while the the cliff dominantedge. Some swell boulders comes mainly show 11 t and, on average, are located 1.4 m a.s.l., and 11.3 m inland from the cliff edge. Some boulders newfrom impact NE. features and one of them, with incrusted fauna, have been used for C14 age analysis. The showorientation new impact of all the features boulders and is towardsone of them, NNE, with while incrusted the dominant fauna, swell have comes been mainly used for from C14 NE. age analysis. The orientation of all the boulders is towards NNE, while the dominant swell comes mainly from NE.

2 m B A

2 m B A C

C

2 m

2 m FigureFigure 6. 6.( A(A)) Geomorphological Geomorphological scheme scheme of of the the Sant Sant Antoni Antoni area. area. Roses Roses show show the the dominant dominant orientation orientation ofof boulders boulders (left (left) and) and the the prevailing prevailing waves waves (right (right). ().B (,CB) Ridgesand (C) of Ridges boulders of boulders very close very to seaclose level to atsea Santlevel Antoni. at Sant Antoni. Figure 6. (A) Geomorphological scheme of the Sant Antoni area. Roses show the dominant orientation

of boulders (left) and the prevailing waves (right). (B) and (C) Ridges of boulders very close to sea level at Sant Antoni.

J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 11 of 20

3.3. Ibiza: Ses Eres Roges The outcropping boulders in Ses Eres Roges are located on a low-lying terrace, corresponding to fossil dunes and clay levels that give rise to a sloping coastline characterized by processes of differentialJ. Mar. Sci. Eng. dismantling 2019, 7, x FOR thatPEER favor REVIEW the presence of boulders (Figure 7). We can differentiate clusters 11 of 20 J. Mar. Sci. Eng. 2019, 7, 327 11 of 19 of imbricated boulders, isolated boulders, and boulder ridges in the upper areas of the outcrop. The 3.3. Ibiza: Ses Eres Roges bathymetry in the area is quite gentle and, there is a large number of isolated boulders in the 3.3.shoreface. Ibiza:The outcropping Ses Eres Roges boulders in Ses Eres Roges are located on a low-lying terrace, corresponding to fossilAs well dunes as inand Sant clay Antoni, levels just that one give boulder rise to has a slopinga TF > 1000: coastline its weight characterized is 14.5 t, andby processes it is located of The outcropping boulders in Ses Eres Roges are located on a low-lying terrace, corresponding to 3.5differential m a.s.l. anddismantling a distance that from favor the the edge presence of the ofcliff boulders of 25 m. (Figure Rest of 7). the We boulders can differentiate have an averageclusters fossil dunes and clay levels that give rise to a sloping coastline characterized by processes of differential weightof imbricated of 2.3 t,boulders, are located isolated 3.1 m boulders, a.s.l., and and 21.4 boulder m inland ridges from in the the cliffupper edge. areas Some of the boulders outcrop. show The dismantling that favor the presence of boulders (Figure7). We can di fferentiate clusters of imbricated newbathymetry impact featuresin the area and isone quite of them,gentle with and, incrus thereted is fauna,a large have number been ofused isolated for C14 boulders age analysis. in the boulders, isolated boulders, and boulder ridges in the upper areas of the outcrop. The bathymetry in Averageshoreface. orientation of all the boulders is towardsENE, while the dominant swell comes mainly from the area is quite gentle and, there is a large number of isolated boulders in the shoreface. theNE.As well as in Sant Antoni, just one boulder has a TF > 1000: its weight is 14.5 t, and it is located 3.5 m a.s.l. and a distance from the edge of the cliff of 25 m. Rest of the boulders have an average weight of 2.3 t, are located 3.1 m a.s.l., and 21.4 m inland from the cliff edge. Some boulders show new impact features and one of them, with incrusted fauna, have been used for C14 age analysis. Average orientation of all the boulders is towardsENE, while the dominant swell comes mainly from theNE.

Figure 7.7. Geomorphological scheme of the Ses EresEres RogesRoges area.area. Roses show the prevailingprevailing waveswaves ((rightright)) andand dominantdominant orientationorientation ofof bouldersboulders ((leftleft).).

3.4. Ibiza:As well Pou as des in Lleó Sant Antoni, just one boulder has a TF > 1000: its weight is 14.5 t, and it is located 3.5 m a.s.l. and a distance from the edge of the cliff of 25 m. Rest of the boulders have an average The boulders of this site are placed over a littoral platform at an average altitude of 12 m a.s.l. weight of 2.3 t, are located 3.1 m a.s.l., and 21.4 m inland from the cliff edge. Some boulders show new (FigureFigure 8). The 7. Geomorphological slope of the platform scheme reaches of the 6.4°.Ses Eres The Ro studyges area. area Rosesshows show two theunits prevailing with the waves presence impact(right features) and dominant and one oforientation them, with of boulders incrusted (left fauna,). have been used for C14 age analysis. Average of boulders and is separated by a small sea entrance. The materials are Middle Triassic limestone, orientation of all the boulders is towards ENE, while the dominant swell comes mainly from the NE. and the presence of boulders is quite conditioned by the degree of fracturing present in the area. Both 3.4. Ibiza: Pou des Lleó 3.4.units Ibiza: show Pou ridges des Lle ofó boulders of metric size. The average weight of boulders is 8.5 t with a maximum of 28 Thet. Average boulders distance of this from site arethe placedcliff edge over is a38.6 littoral m with platform a maximum at an average of 46 m. altitude The dominant of 12 m swell a.s.l. of(Figure thisThe zone 8). boulders The comes slope of from thisof the siteNE, platform arewhile placed thereaches dominant over 6.4°. a littoral The direction study platform areaof the at shows animbricated average two units altitudeboulders with ofthe is 12 presencenot m a.s.l.well (Figuredefined.of boulders8). The and slope is separated of the platform by a reachessmall sea 6.4 entrance.◦. The study The areamaterials shows are two Middle units with Triassic the presence limestone, of bouldersand the presence and is separated of boulders by a is small quite sea conditioned entrance. Theby the materials degree areof fracturing Middle Triassic present limestone, in the area. and Both the presenceunits show of bouldersridges of boulders is quite conditioned of metric size. by The the degreeaverage of weight fracturing of boulders present is in 8.5 the t with area. a Bothmaximum units showof 28 ridgest. Average of boulders distance of from metric the size. cliff The edge average is 38.6 weightm with of a bouldersmaximum is of 8.5 46 t with m. The a maximum dominant of swell 28 t. Averageof this zone distance comes from from the NE, cliff whileedge isthe 38.6 dominant m with adirection maximum of ofthe 46 imbricated m. The dominant boulders swell is not of well this zonedefined. comes from NE, while the dominant direction of the imbricated boulders is not well defined.

Figure 8. Geomorphological scheme of the Pou des Lleó area. Roses show the dominant orientation of boulders (picture on the right) and the prevailing waves.

FigureFigure 8.8. GeomorphologicalGeomorphological scheme scheme of of the the Pou Pou des des Lle Lleóó area. area. Roses Roses show show the the dominant dominant orientation orientation of bouldersof boulders (picture (picture on theon the right) right) and and the the prevailing prevailing waves. waves.

J.J.J. Mar.Mar. Mar. Sci.Sci. Sci. Eng.Eng. Eng. 20192019 2019,, ,77 7,, , 327x x FOR FOR PEER PEER REVIEW REVIEW 1212 12 of of 19 20 20

3.5.3.5. Ibiza:Ibiza: PuntaPunta ArabíArabí 3.5. Ibiza: Punta Arabí TheThe bouldersboulders areare locatedlocated overover aa smallsmall peninsulapeninsula ofof CretaceousCretaceous marlymarly limestoneslimestones atat anan averageaverage altitudealtitudeThe of bouldersof 14.514.5 mm (Figureare(Figure located 9).9). TheThe over bouldersboulders a small peninsula areare distributeddistributed of Cretaceous inin severalseveral marly ridgesridges limestones andand scatteredscattered at an groupsgroups average ofof altitudeboulders.boulders. of The 14.5The boulders mboulders (Figure dodo9). notnot The prpr bouldersesentesent anyany are reworking;reworking; distributed neitherneither in several impactimpact ridges marksmarks and areare scattered observed.observed. groups WeightWeight of boulders.averageaverage ofof The thethe bouldersboulders doisis 4.6 4.6 not tt with presentwith aa maximummaximum any reworking; ofof 7.3 7.3 t,t, neither andand thethe impact averageaverage marks distance distance are observed.fromfrom thethe cliffcliff Weight edgeedge averageisis 35 35 m. m. ofThe The the dominant dominant boulders swell swell is 4.6 for tfor with this this a area area maximum is is from from of ENE, ENE, 7.3t, while while and thethe the averagedominant dominant distance direction direction from of ofthe the thecli imbricated imbricatedff edge is 35bouldersboulders m. The isis dominant SESE andand somesome swell ofof for themthem this areare area imbricated.imbricated. is from ENE, while the dominant direction of the imbricated boulders is SE and some of them are imbricated.

FigureFigureFigure 9. 9.9. Geomorphological GeomorphologicalGeomorphological schemescheme scheme of ofof the thethe PuntaPunta Punta Arab ArabíArabíí area. area.area. RosesRoses showshow thethe prevailing prevailingprevailing waveswaves waves ( (left(leftleft))) andandand dominantdominant dominant orientationorientation orientation ofof of bouldersboulders boulders (( right(rightright).).).

3.6.3.6.3.6. Formentera: Formentera:Formentera: PuntaPunta PrimaPrima TheTheThe boulders bouldersboulders of ofof Punta PuntaPunta Prima PrimaPrima are areare located locatedlocated on onon small smallsmall peninsula peninsulapeninsula East EastEast of of Formenteraof FormenteraFormentera that thatthat conforms conformsconforms to atoto littoral aa littorallittoral platform platformplatform from fromfrom 5to 55 to15to 15 m15 m a.s.l.m a.s.l.a.s.l. (Figure (Figure(Figure 10 10).).10). The TheThe boulders bouldersboulders are areare situated situatedsituated in inin the thethe central centralcentral part partpart of ofof thethethe platform platformplatform at atat an anan average averageaverage altitudealtitude ofof 11.711.7 m m a.s.l. a.s.l.a.s.l. The The averageaverage weightweight ofof of thethe the bouldersboulders boulders isis is 8.78.7 8.7 t,t, t, withwith with aa amaximummaximum maximum ofof of 31.531.5 31.5 t,t, t, andand and theirtheir their averageaverage distancedistance fromfrom the the edge edge of ofof the the cliff clicliffff isisis 838383 m. m.m. SomeSomeSome groups groupsgroups of ofof imbricatedimbricatedimbricated boulders boulders boulders exist, exist, exist, and and and a a a ridgeridge ridge inin in thethe the centralcentra centrall partpart part waswas was set.set. set. The The maximummaximu maximumm recorded recorded wavewave wave heightheight height forforfor this thisthis area areaarea is isis 9 99 m; m;m; meanwhile meanwhilemeanwhile the thethe dominant dominantdominant swell swellswell presents presentspresents an anan orientation orientationorientation from fromfrom ENE, ENE,ENE, the thethe dominant dominantdominant directiondirectiondirection of ofof the thethe imbricated imbricatedimbricated boulders bouldersboulders is is towardsis towardstowards the thethe E. E. TheE. TheThe short shortshort axes axesaxes of the ofof the bouldersthe bouldersboulders correspond correspondcorrespond to the toto stratathethe stratastrata thickness thicknessthickness of the ofof denudation thethe denudatidenudati areasonon areasareas of the ofof coastal thethe coastalcoastal terraces. terraces.terraces.

AA BB

Figure 10. Cont.

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C D C D

2 m 2 m

Figure 10.10.( A(A) Geomorphological)Geomorphological scheme scheme of theof Puntathe Punta Prima Prima area. Roses area. show Roses the show dominant the orientationdominant Figureoforientation boulders 10. ( andofA)Geomorphological boulders the prevailing and the waves. prevailingscheme (B) Cli of ffwaves. onthe whichPunta (B) the CliffPrima analyzed on area.which boulders Roses the analyzed show are located. the boulders dominant (C) Large are orientationblocklocated. located (C )of Large atboulders 11.5 block m a.s.l., andlocated andthe at datedprevailing 11.5 inm thea.sl., waves. year and 1792 dated (B BC.) Cliff in ( Dthe )on Block year which 1792 ridge the BC. located analyzed (D) Block 115 m boulders ridge from thelocated are cliff located.edge,115 m andfrom (C) 12.9 Large the m cliff a.s.l.block edge, located and 12.9 at 11.5 m a.s.l. m a.sl., and dated in the year 1792 BC. (D) Block ridge located 115 m from the cliff edge, and 12.9 m a.s.l. 3.7. Formentera: Punta Punta de de sa sa Gavina Gavina 3.7. Formentera: Punta de sa Gavina The geomorphological scheme of Punta de sa Gavina (Figure 11)11) reflects reflects the the presence presence of of different different bouldersThe geomorphological ridges. The The boulders boulders scheme have have of an anPunta average average de sa weight weightGavina of of(Figure 10.7 10.7 t; they t; 11) they reflects are are at atan the anaverage presence average distance of distance different of 59 of boulders59m, m,and and an ridges. anaverage average The height boulders height of of11.3 have 11.3 m. m.an This Thisaverage area area has weight has also also largeof large 10.7 boulders boulderst; they are partially partially at an average covered covered distance by by an an aeolian of 59 m,mantle, and an and average with dominantheight of 11.3 orientations m. This area and has imbrications also large boulders of 254,254,similar similar partially to to the thecovered boulders by an analyzed. aeolian mantle,These partially and with buried dominant boulders orientations are located and 217 imbrications m from the of cliff cli 254,similarff ledge and to onthe a boulders tabulartabular platform analyzed. at These11.5 m partially a.s.l. No buried impact boulders marks are are observed. located 217 m from the cliff ledge and on a tabular platform at 11.5 m a.s.l. No impact marks are observed.

A A

1 m 1 m

C 1 m C 1 m

Figure 11. (A) Geomorphological scheme of the Punta de sa GavinaGavina area.area. Roses show the dominant Figurewave windswinds 11. (A ()(left leftGeomorphological)) andand thethe dominant dominant scheme block block orientationof orientation the Punta (right (deright sa). ).Gavina (B (B) Groups) Groups area. of ofRoses imbricated imbricated show bouldersthe boulders dominant at 7at m 7 wavea.s.l.,m a.s.l., winds and and 25 ( mleft25 from )m and from the the clithe dominantff ledge.cliff ledge. (blockC) Imbricate (C orientation) Imbricate boulders ( rightboulders of). large(B) ofGroups dimensionslarge ofdimensions imbricated 37 m from 37 boulders m the from cornice, at the 7 mandcornice, a.s.l., 8.5 mandand a.s.l. 258.5 (mmD )froma.s.l. Boulders (theD) Boulderscliff deposited ledge. deposited more(C) Imbricate than more 85 m thanboulders from 85 them frof cliom largeff ledge,the dimensionscliff and ledge, 9.5 m and 37 a.s.l. m9.5 from m a.s.l. the cornice, and 8.5 m a.s.l. (D) Boulders deposited more than 85 m from the cliff ledge, and 9.5 m a.s.l.

J. Mar. Sci. Eng. 2019, 7, 327 14 of 19

The maximum recorded wave height in this area is 8 m. The dominant swell is from SW, while the dominant direction of the boulders analyzed is WSW.

3.8. Application of Hydrodynamic Equations The first approach to discriminate storms from tsunamis in the formation of these large boulders is to test the equations which model boulder quarrying by waves. The equations of [9,10] were employed to discriminating between tsunami and storm waves. In Table4, results of applying Engel and May’s equation are presented for joint-bounded boulders (JBB), and subaerial boulders (SAB) of the seven outcrops studied. Hs (minimum wave height of a swell wave able to move the boulder at sea level) is, in almost all the areas, approximately three times Ht (minimum tsunami water column height needed to move a boulder at sea level). Because Hs is higher to Hmax (the maximum wave height recorded) and Hsw for T50 (significant wave height for a 50-year return period), in all the study sites (excepting Ses Eres Roges and Sant Antoni)storms on Ibiza and Formentera cannot move any boulders with TF > 1000, not even the boulders located at sea level. This point agrees with our observations in the field, where the most significant storm waves ever recorded in the Ibiza and Formentera moved none of the boulders we marked in advance (work in progress).

Table 4. Main characteristics of the boulders with TF > 1000 from the different study areas. (Alt., average altitude of the boulders, Dist., the average distance from the cliff edge, JBB, joint bounded boulders, Rs—run-up for storm waves, Rt, run-up for the tsunami). In grey, locations dominated by storm-waves action.

Subaerial Transport Study Area Alt. Dist. Weight Hc Hs50 JBB Run-up Run-up Figure Hs Ht Rs Rt Rs Rt Punta Pedrera 10.0 66.0 8.4 9 11 10.5 3.4 19.5 12.4 11.9 10.4 5319 Sant Antoni 2.1 30.5 17.6 0.5 11 7.8 1.6 8.3 2.1 10.4 3.2 1126 Ses Eres Roges 3.5 25.0 14.5 1 11 6.5 0.9 7.5 1.9 4.9 2.8 172 Pou des Lleó 9.4 38.6 8.5 5.5 11 15 6.5 20.5 12.0 11.6 9.9 3230 Punta Arabí 14.5 35.0 4.6 10 11 11.4 6.2 21.4 16.2 17.6 15.1 2353 Punta Prima 11.7 83.0 8.7 9.5 7 12.2 4.7 21.7 14.2 13.5 12.1 8365 Punta de sa Gavina 11.3 59.0 10.7 9.5 11 12.6 4.5 22.1 14.0 13.1 11.7 7005

On the other hand, tsunami waves with heights less than 6.5 m in Ibiza or less than 4.7 m in Formentera, can move boulders with TF > 1000 at sea level. The run-up values given in the text are the sum of Hs (minimum storm water column height) and Alt (the average altitude of boulders), for storm run-ups (Rs) and the sum of Ht (minimum tsunami water column height) and Alt for tsunami run-ups (Rt). In Formentera (Punta Prima, Punta de sa Gavina), for joint bounded boulders, storm run-ups of 22 m are required to explain the position of the boulders, while 14 m tsunami run-ups can explain the same positions. Results in Ibiza requires tsunamis run-ups of 12 m high and or storm run-ups of 20 m. According to these results, a tsunami appears to be a more likely mechanism for transportation and deposition of the boulder field than storm waves. The run-up of tsunamis on vertical cliffs is several times higher than that occurring on low coastal areas [43]. The run-up is also enhanced due to several factors [44]: (1) by the distance from the tsunami generation area (only 300 km, in our case), (2) the narrowness of the continental shelf (as in Ibiza and Formentera), (3) the fact that the tsunami propagation vector is almost perpendicular to the main shoreline direction, and (4) land morphology, characterized by vertical cliffs with entrances (calas). For these reasons, we think than run-up heights for the Ibiza and Formentera cliffs would have been several times higher than tsunami wave heights. Recent examples in the Balearic Islands confirm the last statement: the tsunami of 2003 had an offshore wave height of 30–40 cm (according to simulations) and reached the western part of Ibiza with a run-up of 3 m, which indicates a multiplying factor of 10. × J. Mar. Sci. Eng. 2019, 7, 327 15 of 19

3.9. Dating of the Boulders Just some boulders of Sant Antoni outcrops have incrusted fauna able to be aged by C14 isotope. We sampled a boulder and Conventional age is 310 +/ 30 BP, and Calibrated date is 1874–1950 AD with − 95.4% probability (High Probability Density Range Method (HPD): MARINE13 from Beta Analytic). The boulders without incrusted fauna are dated by measuring the karst dissolution features after the block transport. The depth of dissolution pans has been used for an approximate dating of the boulder detachment and transport. Some boulders show the existence of both pre-transport and post-transport dissolution pans. The pre-transport dissolution pans were formed when the boulder formed part of a horizontal bed of the Upper Miocene Reefal Unit. After the transport, the boulder has been tilted, together with the dissolution pan, usually more than 30 degrees due to imbrication. After imbrication, a new dissolution pan develops at an approximate 30 degrees angle concerning the pre-transport dissolution pan. To ensure that it is a real post-transported pan, the existence of an angle of discordance between the stratification of the block, almost horizontal before being ripped, and the surface of the pan, has been verified. Thus, calculating how much time took the post-transport dissolution pan to develop, the age of the boulder transport would be known According to [45,46] the average value of dissolution rate in the Balearic Islands for dissolution pans is 0.3 mm/yr. Applying this average value of dissolution rate to the mean depth of the dissolution pans (6.8 cm), results in a time-lapse of 227 years, obtaining an age of 1792 AD for Formentera boulders emplacement [47]. This dating shows similar age than the documentary sources of a tsunami registered in 1756 [35] in the municipality of Santanyí (SE Majorca) and with the data analyzed in boulders by C14 on the coast of Minorca [17].

3.10. Discussion The record of earthquakes offshore from the Algerian coast are extensive (Figure3). Most of them may generate tsunami waves which reach the southern coasts of the Balearic Islands and, in particular, the Ibiza and Formentera shores. The last event took place in May 2003. Modeled directions by [18] from the N of Africa, corresponding to trajectories S-1 and S-2 (Figure4), match to the outcrops of boulders analyzed in Ibiza and Formentera Islands. According to the hydrodynamic equations, two of them, Sant Antoni and Ses Eres Roges, are clearly within reach of swell, while the other five are far out of reach. The existence of tsunamis reaching the coasts of Ibiza and Formentera is unquestionable, because there is recent and also historical evidence. If we prove the existence of boulders transported by tsunamis in the most unfavorable situations for an interpretation of transport by storm waves, it is evident that the boulders deposited in low coast may have a mixed origin: tsunamis and storm waves. Therefore, we must focus the discussion on the characteristics of the boulders identified in Punta Pedrera, Pou des Lleo, Punta Arabí in Ibiza, and Punta Prima and Punta de sa Gavina in Formentera. The boulders of these outcrops are at average altitudes between 9.4 and 14.5 m a.s.l., at medium distances from the edge of the cliff between 66 and 217 m, and average weights range between 8.4 t and 10.7 t (Table2). When the equations of Engel and May [ 10] are applied to these boulders, we get run-ups of around 20 m for the quarry and transport by storm waves of boulders delimited by joints (JBB). For the transport of subaerial boulders, previously uprooted, the run-up values of waves are between 11.6 and 17.6 m. These results are almost impossible to reach with the available data of the wave regime of this area. Alternatively, the results of the Engel and May [10] formulas (Table2) for tsunami flows are between 12 and 16.2 m of run-up for boulders delimited by joints (JBB) and between 9.9 and 15.1 m for subaerial boulders. To understand how a tsunami impacts on a cliff, we must know how this flow works. When the tsunami flow hit vertical cliffs, the flow rises progressively until it overtops the cliff and creates fields of boulders plucked from its cornice. The results of the tsunami run-up (Rt) here obtained are adjusted to the models of the water column required for the displacement of each block described by [48]. The deposits analyzed show well-imbricated boulders (Figure 11B) J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 16 of 20

to the criteria of [42],which argue that this type of imbricated organization is attributable to tsunami J. Mar.events. Sci. Eng. Thus,2019 the, 7, 327 boulders show the result of significant flow events associated with tsunamis,16 of 19 providing evidence of individual and/or multiple events over the same area, with a clear correlation with the tsunami propagation models (Figure 3), and ratified by the application of hydrodynamic whereequations the average to establish directions the water of the columns boulders (run coincide-up) necessary with tsunami for the model transport directions, and start adjusting-up of their them disposition(Table 2). to the criteria of [42], which argue that this type of imbricated organization is attributable to tsunamiA events.more integral Thus, theway boulders of establishing show the the result energy of significant needed to flowstart events and transport associated the with boulders tsunamis, is the providingformula evidenceof Scheffers of individual and Kelletal and [11]/or, multiplethat multiplies events over the height the same of area,the block, with a the clear distance correlation to the withcoastline the tsunami and its propagationweight (Transport models Figure). (Figure This3), and equation ratified allows, by the according application to its of hydrodynamicauthors, to better equationsdefine the to difference establish thebetween water the columns energy (run-up)of the storm necessary surge an ford thetsunami transport flows. and Ref start-up. [16] determine of them a (Tablethreshold2). of TF > 250 for tsunami boulders in Majorca. In our work, for safety, only TF for the biggest bouldersA more (TF integral > 1000) wayhave of been establishing used. The the boulders energy analyzed needed toshow start TF and values transport between the 2353 boulders and 8365 is thein formulathe highest of Sche cliffs,ffers while and for Kelletal the lowest, [11], that the multipliesTF values therange height between of the 172 block, and the1126 distance (Figure to12 the and coastlineTable 2). and its weight (Transport Figure). This equation allows, according to its authors, to better defineAs the shown difference in Figure between 1, most the energy of the outcrops of the storm of the surge boulders and tsunami in the Balearic flows. Ref. Islands, [16] determineare found aon thresholdits southern of TF coasts,> 250 fororiented tsunami towards boulders the in Algerian Majorca. coasts. In our Howeve work, forr, safety,both in only Minorca TF for theand biggest in Ibiza bouldersthere are (TF some> 1000) outcrops have on been itsused. northern The coasts boulders, but analyzed not in Majorca. show TF In values the case between of Ibiza, 2353 this and situation 8365 inis the explained highest clibyff thes, while diffraction for the of lowest, the tsunami the TF, valuesas happened range betweenin the event 172 andof 2003 1126 (Figure (Figure 3) 12, whichand Tableproduced2). a maximum elevation in the port of Sant Antoni.

FigureFigure 12. 12.Average Average values values of of the the Transport Transport Figures Figures for for the the boulders boulders with with TF TF> 1000.> 1000 (PD,. (PD Punta, Punta Pedrera,Pedrera ST,, ST Sant, Sant Antoni, Antoni ER,, ER ses, ses Eres Eres Roges, Roges PL,, PL Pou, Pou desLle desLleòò, PA,, PA Punta, Punta Arab Arabíí, FT,, Punta FT, Punta Prima, Prima PG, , PuntaPG, Punta Gavina). Gavina).

As shown in Figure1, most of the outcrops of the boulders in the Balearic Islands, are found on its southern coasts, oriented towards the Algerian coasts. However, both in Minorca and in Ibiza there are some outcrops on its northern coasts, but not in Majorca. In the case of Ibiza, this situation is explained by the diffraction of the tsunami, as happened in the event of 2003 (Figure3), which produced a maximum elevation in the port of Sant Antoni. J. Mar. Sci. Eng. 2019, 7, 327 17 of 19

4. Conclusions The tsunami waves that impact on the Balearic Islands come from the activity of reverse faults on the northern Algeria shelf. There have been tsunami events recently (May 2003), and there is also historical evidence of tsunamis in the past. As a result of the impact of these tsunami waves, both isolated boulders and ridges of boulders of metric size have been deposited at the rocky coasts of Ibiza and Formentera Islands. The radiocarbon dating of the fauna incrusted in some boulders records an event around 1874 (95.4%). Measures of the deepness of post-transport kamenitzas (dissolution basin pools) in Formentera boulders give an age of 1792 AD. Five littoral boulders outcrops have been analyzed in the island of Ibiza and two more in the island of Formentera. Disposal of the boulders, ten of meters inland from the cliff edge and well away from any source of gravitational origin, restrain their transport from moving inland from the seashore. Lithology and facies are coincident with the ones laying on the upper beds forming the cliffs. In this way, most of the boulders have been quarried and transported inland from the cliff edge. Just very few boulders have incrusted fauna. One of them has been used for radiocarbon dating. The wave regime of Ibiza and Formentera is characterized by a limited fetch from the northern and southern winds, a 500 km fetch from the SW, and 900 km fetch from the ESE. Wave altitudes reach up to 11 m (Hs50) according to deep water digital buoys data set. Boulders of five of the outcrops (Punta Pedrera, Pou des Lleó and Punta Arabí in Ibiza and Punta Prima and Punta Gavina in Formentera) are located 12 m a.s.l. on average, at distances between 35 and 217 m from the cliff edge, and have weights between 5 and 10 t (Table2). Hydrodynamic equations require storm wave heights of 20 m for quarrying the boulders and around 13 m for storm waves to move subaerial boulders already plucked. Transport Figure [11] confirm a tsunami interpretation for the origin of this boulders. Values of TF from two to eight thousand ratify the requirement for a tsunami flow to start and transfer those boulders to their current position andeven for their imbrication. Two outcrops of Ibiza (Sant Antoni and Ses Eres Roges) show boulders between 2 and 3 m a.s.l., 25 to 30 m inland from the sea-shore. Although their weights on average are 17.6 and 14.5 t, respectively, their position could be reached by storm waves. Nevertheless, the tsunami origin of the rest of outcrops obliges to consider a mixed origin for these deposits. As a conclusion, most of the boulders of the analyzed outcrops are quarried from the cliff edge by tsunami flows. They come from the activity of the faults on the northern Algeria shelf. They hit the Balearic Islands, and, in this case, Ibiza and Formentera coasts.

Supplementary Materials: The following are available online at http://hdl.handle.net/2445/103318 (last access: June 11, 2019). Author Contributions: Conceptualization and Methodology, F.X.R.-M., A.R.-P., J.A.M.-P., B.G., and J.M.V.; Fieldwork F.X.R.-M.; Investigation, F.X.R.-M., A.R.-P., J.A.M.-P., B.G., and J.M.V.; Writing—original draft preparation, A.R.P.; Writing—review and editing, B.G.; Visualization, J.A.M.-P. Funding: This study was supported by the projects CGL2013-48441-P, the CGL2016-79246-P (AEI/FEDER, UE), the CHARMA project (MINECO, ref. CGL2013-40828-R), the PROMONTEC project (MINEICO, ref. 444CGL2017-84720-R) and the CSO20015-64468-P (MINECO/FEDER) project. Acknowledgments: The authors would like to acknowledge to the staff of the d’Eivissa and Formentera Natural Park: Núria Valverde and Vicent Forteza, for the authorizations to access Punta Gavina. Conflicts of Interest: The authors declare no conflict of interest.

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