Numerical modelling of the September 8, 1905 Calabrian (southern Italy) tsunami

Transcription

1 Geophys. J. Int. (2002) 150, Numerical modelling of the September 8, 1905 Calabrian (southern Italy) tsunami Alessio Piatanesi and Stefano Tinti Dipartimento di Fisica, settore di Geofisica, Viale Berti Pichat, 8, Bologna, Italy. Accepted 2002 February 13. Received 2002 February 13; in original form 2001 March 22 1 INTRODUCTION Calabria and Sicily are the two Italian regions most exposed to earthquake and tsunami risk. During the last few centuries the largest and most catastrophic tsunamigenic earthquakes that ever hit the Italian peninsula occurred here: e.g. the 1693 eastern Sicily (Piatanesi & Tinti 1998; Tinti et al. 2001), the 1783 southern Calabria (Tinti & Piatanesi 1996) and the 1908 Messina Strait (Piatanesi et al. 1999; Tinti et al. 1999) earthquakes, all reaching the epicentral intensity XI Now at: Istituto Nazionale di Geofisica e Vulcanologia, Via di Murata 605, Roma, Italy. piatanesi@ingv.it SUMMARY This paper presents a study of the tsunami following the disastrous earthquake that occurred on the 8th of September 1905 in Calabria, southern Italy. The shock caused devastation in many towns and villages leading to more than 500 victims. According to coeval sources the tsunami was not catastrophic, but was large enough to inundate low lying lands in several coastal segments and to affect boats. No specific study was ever devoted to this tsunami in the literature. Our analysis is carried out by means of numerical modelling and aims at filling this gap. Since the source fault of the earthquake has not yet been identified, we study three tsunamis produced by likely potential sources, according to macroseismic data and the seismotectonic knowledge of the region, namely the Capo Vaticano (CV) fault, the Vibo Valentia (VV) fault and the Lamezia (LA) fault. We compute tsunami waves under the hypotheses that the sea floor deformation is caused by a shear double-couple dislocation taking place over a rectangular fault and that sea waves propagate according to the shallow water approximation. The three tsunamis cause either a pure initial depression (VV and LA) or a predominant initial depression (CV) of the sea surface in the gulf of St. Eufemia. One very relevant finding is that tsunami energy is trapped within a narrow channel along the Calabrian coast to the north of the source with the consequence that wave amplitudes computed here are much larger than the values expected in the case of an ordinary energy decay law with distance; energy trapping along southern coastal segments is less efficient. Only a small fraction of tsunami energy penetrates the Straits of Messina to the south. Propagation to the west is affected by the Aeolian islands that produce a quasi-shadow zone on the side opposite to the tsunami impact. The LA tsunami is found to be too weak to be compatible with observations. A sensitivity analysis concerning some parameters of the faults (namely length, width and slip magnitude) has been performed in order to explore their influence on the tsunami features. The main result of this paper is that we cannot discriminate between the CV and VV sources: both are in agreement with some historical observations, whilst they do not match others. We believe that a better tuning of the source mechanism over these faults can improve the agreement between model computations and historical observations. Key words: earthquakes, fault models, seismology, seismotectonics, tsunami. of the MCS (Mercalli Cancani Sieberg) scale. The tsunami considered in this work was due to an earthquake striking southern Calabria on September 8, 1905 at around 01:43 a.m. local time. The towns and villages most damaged by the shock were those located toward the Tyrrhenian side of Calabria, from Capo Suvero to Capo Vaticano (see Fig. 1), where the destruction was almost total. Some damage was also reported in the Aeolian Islands and in several Sicilian villages belonging to the Messina district. The final earthquake toll was 557 dead, more than 2000 injured and about 300,000 homeless. The tsunami generated by the main shock was not catastrophic, but it was observed both in the open sea and along the coast, and its effects were described, though very succinctly, by several authors C 2002 RAS 271

2 272 A. Piatanesi and S. Tinti Figure 1. Map of the region affected by the 1905 earthquake and tsunami. Contour lines are isoseismals in the Mercalli-Cancani-Sieberg scale (data from Boschi et al. 1995). Inverted triangles mark the positions of coastal villages where information on tsunami effect is available and where we compute synthetic tide-gauge records. in coeval reports and studies (Baratta 1906; Mercalli 1906; Rizzo 1907; Platania 1907), as may be found in the catalogue of the Italian tsunamis (Tinti & Maramai 1996). Offshore the tsunami was reported by eyewitnesses, who at the time of the earthquake were sailing a few tens of km from the coast and were awakened by an anomalous shaking of the boats. On the coasts of the epicentral area a lot of fish were found on the beach (at Briatico and Pizzo) and inundation by some tens of metres was reported in several villages with fishing boats carried inland (at Briatico, Pizzo, Bivona). Flooding and fishing boats carried inland were also documented at Scalea about 100 km to the north of the epicentre. Some tide-gauges recorded the signal associated with tsunami waves. The tsunami was also seen on the coasts of Sicily. The harbour office of Milazzo reported that the sea rose and fell every 30 min with an amplitude of 80 cm. At Messina, located at the mouth of the homonymous strait between Calabria and Sicily, the main shock broke the clock of the tide-gauge recorder: a few hours later, when repaired, the recorded mareogram still showed tsunami oscillations with an amplitude of 10 cm and a period of 8 min. The tsunami propagated in the Tyrrhenian sea to large distances from the source region. At Naples and Ischia, located some hundreds of kilometres further north along the Tyrrhenian coast of Campania, and at Civitavecchia, even farther north, the tsunami left a quite clear signal in tide-gauge records: they all show an initial negative wave followed by a larger positive wave, with peak-to-peak amplitudes ranging from 10 to 18 cm and periods of about min. The main goal of this paper is to carry out a scientific investigation of this tsunami, because no such study can be found in the literature. The only existing analyses (see e.g. Platania 1907) date back to the immediate post-event times and are precious phenomenological reconstructions, rather than studies in the modern sense, being inadequate according to the present views, needs and standards of earthquake and tsunami research. The chief tool we use in the paper is numerical modelling of the tsunami, by means of which we intend (1) to highlight the main features of tsunami propagation and (2) to evaluate the impact of the waves on the coast. In the next section we will give a synthetic description of the main tectonic features of southern Calabria and we will indicate the source faults used in this work. In Section 3 the numerical model will be briefly described while in Section 4 the numerical simulations carried out in this work will be presented. Discussion of results will be made in Section 5, where moreover a sensitivity study on the dependence of the tsunami features on the geometrical parameters of the faults (basically length and width) as well as the amount of slip will be exposed. Conclusions will be drawn in Section 6. 2 TECTONIC SETTING AND SOURCE FAULTS The Calabrian arc is a structure belonging to the Mediterranean orogenic belt, and connecting the Maghrebides to the Appennines. This arc and the associated southern Tyrrhenian subduction zone originated from the collision between the African and the European plates, due to N S to NNW SSE-directed convergence acting over the past 70 Myr. The geodynamical evolution of this region is complex and controversial: recently Wortel & Spakman (2000), on the basis of seismic tomography models, suggested that a process of slab detachment came to an end in Calabria only in very recent times after having reached full completion in the central-southern Apennines. On the other hand, the hypocentral distribution of accurately located seismic events reveals a seismic slab 200 km wide and km thick with no clear evidence of detachment: it is subducting with a dip of 70 degrees in a NW direction, with the top of the slab at a depth of a few tens of km under the Calabrian arc, and is sinking down to 400 km and to 500 km under the Aeolian Islands and the Marsili Basin, respectively (Selvaggi & Chiarabba 1995; Frepoli et al. 1996). Geological and geophysical data suggest that in the last 0.7 Myr the geodynamic evolution of the Calabrian arc is dominated by strong vertical motion (Westaway 1993). The focal mechanisms of recent and historical earthquakes show an extensional mode of deformation, both parallel and perpendicular to the arc (Selvaggi 1998; Frepoli & Amato 2000); geological data also indicate that extension has acted along NE SW and NW SE faults since the middle Pleistocene, modelling graben-like structures trending both NE SW and NW SE (Tortorici et al. 1995; Argnani 2000). The main tectonic feature of this region is represented by a normal fault that runs along the inner side of the arc for a total length of about 180 km (Fig. 2). The fault is segmented into several fault systems striking, from north to south, N S (Crati Valley fault system), NE SW (Serre and Cittanova faults), then ENE WSW and finally NE SW (Reggio Calabria fault) (Tortorici et al. 1995; Monaco & Tortorici 2000). Also present are faults striking E W, namely the Crati Valley and the Lamezia grabens (Argnani 2000). Looking at the isoseismal map relative to the 1905 September 8 earthquake (Fig. 1) we can see that most damage was concentrated along and near the coast (from Capo Vaticano to Capo Suvero) and that all the isoseismals are open lines, with an ideal continuation in the sea, which is suggestive of an epicentre close to the coast. There are mainly two active fault segments that can be considered as a good candidate for the source of both earthquake and tsunami,

3 The 1905 Calabrian tsunami 273 Figure 2. Seismotectonic map of southern Calabria. Seismological data from Boschi & Gruppo di Lavoro CPTI (1999). Fault segments from Monaco & Tortorici (2000) and Argnani (2000): (1) Crati Valley graben, (2) Crati Valley fault system, (3) Serre fault, (4) Cittanova fault, (5) Reggio Calabria fault. Hachures in the fault segments indicate the downthrown blocks. Faults in bold are the tsunami sources used in the numerical simulations: (CV) Capo Vaticano, (VV) Vibo Valentia and (LA) Lamezia faults. SEP: Santa Eufemia Plain, SEG: Santa Eufemia Gulf. namely the Capo Vaticano (CV) and the Vibo Valentia (VV) faults, intersecting the epicentral area. For the sake of completeness, we also add to these the Lamezia (LA) fault, which is located slightly to the north. All faults are shown as bold segments in Fig. 2, whilst the geometrical parameters we used in this work are reported in Table 1. We consider that each fault has a width of 20 km, a total length of 30 km and a uniform slip of 2.5 m: with the above parameters, and assuming a lithospheric rigidity µ = Nm 2, the associated earthquake has a seismic moment M 0 = N m and a magnitude M S = 7, in accordance with the estimation done on the basis of macroseismic data (Boschi et al. 1995). Fault CV separates the Tyrrhenian offshore from the Capo Vaticano peninsula, which is marked by a series of Quaternary marine terraces. It is characterised by westward normal faulting: the footwall uplift rate, estimated on the basis of age determination of several marine terrace deposits, is about 1.5 mm yr 1 (Monaco & Tortorici 2000). In the present work this fault is modelled as a single plane striking 245, dipping almost vertically at 80 with a rake of 270 : rupturing of this fault produces a co-seismic displacement field involving both subsidence and uplifting of the sea bottom (see Fig. 3). The VV fault is made up of two non-overlapping planes, striking 235 and 240 respectively, while dip and rake angles are assumed to be the same as the CV fault: in this case the associated vertical displacement determines a large subsidence of the sea bottom and minor uplift south of Capo Vaticano. The third source, i.e. the LA fault, consists of three nonoverlapping subfaults of various length (see Table 1) striking, from

4 274 A. Piatanesi and S. Tinti Table 1. Fault parameters of the tsunamigenic sources used in this study. Fault Strike Dip Rake Slip Length Width Depth of (deg) (deg) (deg) (m) (km) (km) the upper border (km) CV VV VV La La La EtoW,110,90 and 160, dip and rake angles being equal to the above discussed faults. The first two segments are part of a grabenlike structure that is able to model efficiently the St. Eufemia Plain. However, from a tsunamigenic point of view they are scarcely efficient, since they produce only minor deformation of the sea bottom. For this reason we suppose the complementary activation of the third segment to the west, that is close to the sea, strikes with a direction almost parallel to the coast and contributes to most of the sea bottom subsidence associated with the LA fault (see Fig. 3). 3 TSUNAMI MODELLING Tsunamis propagate in the sea as gravity waves and obey the classical laws of hydrodynamics. Since their wavelength is much larger than the sea depth, tsunamis are considered as long waves propagating in shallow waters, and therefore the equations governing their propagation can be written as: { t ζ = [(h + ζ )v] (1) t v = g ζ v v In eqs (1) ζ represents the water elevation above the mean sea, h the water depth in a still ocean, v the depth-averaged horizontal velocity vector, and g the gravity acceleration. System (1) is completed by suitable boundary conditions, which are that pure wave reflection occurs at a solid boundary (coastlines) and that full wave transmission occurs at the open boundary (open sea): v n = 0 on the solid boundary (2a) v n = 2(c 1 c 0 ) on the open boundary (2b) Here n is a unitary vector normal to the boundary and oriented outwards, c 1 = g(h + ζ ) 1/2 represents the local phase velocity and c 0 = (gh) 1/2 is the phase velocity of the linear wave. Eqs (1) and (2) are solved by means of a finite-element method that was developed specifically for tsunami modelling (Tinti et al. 1994). In the model the initial sea water elevation ζ (x, y, t = 0) in any point P of the computational domain with coordinates (x, y) is assumed to be equal to the total vertical co-seismic displacement of the sea bottom. If the sea floor is displaced from the pre-event position z = h(x, y, t = 0 ) to the post-event place z + = h(x + u x, y + u y, t = 0 + ) + u z, with u = (u x, u y, u z ) being the co-seismic displacement vector, then the initial sea surface elevation results from two distinct contributions, according to the expression: ζ (x, y, t = 0) = z + z = u z (x, y) + u h (x, y) h(x, y) (3) The first term is exactly the vertical component of the co-seismic displacement, and is usually predominant. The latter takes into account the horizontal movement of the sea bottom, and cannot be neglected when we are dealing with relevant bathymetric structures and/or with large horizontal displacement fields (Tinti & Armigliato 1998). In our case the latter term has some significance due to the ocean depth changes found in the source region, especially corresponding Figure 3. Co-seismic vertical displacement of the sea bottom (labels are in cm), produced by the source faults shown in Fig. 2 with parameters listed in Table 1.

5 to Capo Vaticano. The co-seismic displacement produced by the fault dislocation is here computed through Okada s analytical model (Okada 1992), dealing with a rectangular rupture surface with shearmode slip embedded in a homogeneous half-space. The initial field velocity is assumed to be identically null: this assumption is adequate since fault rupture time ( 10 s) is much smaller than typical tsunami periods ( s), allowing us to consider a static co-seismic deformation. The computational domain embraces the part of the southern Tyrrhenian sea and of the Straits of Messina between latitude N and to the east of longitude E, and is discretised with a FE mesh consisting of nodes and triangular elements. As may be appreciated from Fig. 1, it includes the source region, the entire Tyrrhenian coast of Calabria, the northeast corner of Sicily and the archipelago of the Aeolian islands, namely all the places where information on tsunami effects are available. Its size is large enough to allow the investigation of the near-field behaviour of the excited waves as well as the main features of the tsunami propagation, and is therefore adequate for the purposes of this study. It is to be noticed, however, that it does not comprehend the far field, and does not enable us to compare the computed waves with the available tide-gauge records of Ischia, Naples and Civitavecchia. This aspect has been left for future investigations, mainly for reasons related to computer costs. Indeed, enlarging the FE grid with no loss of space resolution would imply the need of computer resources that are not prohibitive, but do exceed what is presently available to the authors. On the other hand, reducing resolution by making use of a much coarser grid to extend the mesh size would have resulted in degraded computations, with excessive smoothing of the shorter wavelengths, thereby making the comparison with recorded mareograms almost useless. The basin bathymetry is given in Fig. 2. It may be seen that it is quite far from being uniform. To the north of Capo Vaticano typically an east west transect would exhibit a sequence of five characteristic regions: (1) a narrow strip of shallow water close to the coast, followed by (2) a steep slope connecting it to (3) a wide region of milder gradient with depth from 500 m to 1000 m, and extending from km offshore. A further steep slope (4) leads irregularly to the (5) abyssal Tyrrhenian plain at a depth of more than 3000 m. To the south of Capo Vaticano a SE NW transect would pass more gradually from shallow waters to abyssal depths, but the bathymetry here is made very irregular by the marine cones of the Aeolian archipelago that may be grouped into two distinct alignments, one NE SW, including the smallest islands (Stromboli, Panarea, etc.), and the other NW SE with the larger islands of Salina, Lipari and Vulcano. This complex bathymetric pattern is expected to influence remarkably the propagation of tsunamis, as will be seen in the next section. 4 NUMERICAL SIMULATIONS We performed numerical simulations of three tsunamis, each associated with one of the faults discussed in Section 2. The final computation time is 85 min, and is sufficiently long to take into account the main waves at all the coastal stations considered in the simulations. The initial water elevation fields, that are calculated through Okada s double-couple source model, are shown in Fig. 3. It is immediately noticeable that there is a basic distinctive difference between faults that are fully inland (i.e. VV and LA faults) and the CV fault that is partially offshore: the former faults give rise to a unipolar sea level displacement (in our case pure subsidence), whilst the latter produces positive as well as negative sea-surface The 1905 Calabrian tsunami 275 displacements. This difference of the initial perturbation fields is also reflected in the subsequent propagation: unipolar fields usually show a comparatively weaker content of small-scale features, resulting in tide gauge records characterised by oscillations of longer period. In order to compare the main characteristics of the computed waves, six panels are displayed in Fig. 4, each panel referring to a given coastal site (see the map in Fig. 1) and showing the calculated local tide-gauge records corresponding to the three faults. We stress that each calculated record of the panels is computed as the difference between the instantaneous water elevation ζ (x, y, t) and the initial elevation value ζ (x, y, t = 0), since the tide-gauge itself is assumed to be affected by the tectonic dislocation produced by the earthquake. Therefore within the source region the final sea level tends to a post-seismic value that is ζ (x, y, t = 0): this means that in subsided coastal segments the new post-event still sea level is higher than the pre-event level by an amount exactly equal to the amount of subsidence, as is trivially to be expected. This fact is evident in the mareograms computed at Pizzo, Bivona and Briatico, which are located in the source area. We mention that in the above localities coeval observations report an initial inundation of the shore followed by a withdrawal of the sea. This feature is not correctly reproduced by the VV fault which produces oscillations mainly above the previous sea level, nor by the LA fault, which generates only minor sea level fluctuations with the wrong first wave polarity. It is weakly satisfied by the CV fault, that causes a small inundation followed by a large withdrawal. At Scalea, which is located in the northern part of the mesh, far from the source area, all faults produce a small negative wave as first arrival, followed by a larger positive wave. This is indeed a common feature of all the examined stations that are located outside the source area (see also the mareograms computed at Milazzo and Messina). It is worth recalling that this is in agreement with the polarity of the first arrivals recorded by the tide-gauges of Naples, Ischia and Civitavecchia, located some hundreds of km north of the source (outside our domain of computation). An interesting result concerns the computed waveform at Scalea for the CV fault: here a later arrival, around 75 min after the initiation, features an amplitude larger than that of the primary wave. This is probably due to edge waves that propagate slowly on the continental shelf and is suggestive of tsunami-energy coastal trapping as will be discussed in more detail in the next section. 4.1 Maximum energy density fields One goal of the present work is to study the main pattern of tsunami propagation and to identify the coastal segments of Calabria and north-eastern Sicily that are most exposed to the tsunami attack. For each tsunami we computed the fields of maximum density of tsunami energy which are shown in Fig. 5. They are simply obtained by plotting, for each node of the domain, the highest value of the total wave energy per unit area computed during the simulation run, with the energy density of the wave ε being defined as usual by: ε = 1 2 ρ(gζ 2 + hv v) where ρ is the density of the water and all other symbols were already defined in Section 3, with no correction made for the co-seismic displacement ζ (x, y, t = 0). It is straightforward to note that the CV fault is the most energetic source among the three considered in this work, followed by faults VV and LA. All graphs serve to highlight the features of the tsunami radiation that is mainly governed by the bathymetry. It is evident that the largest perturbation is found in the source region, but it is equally evident that the coastal shallow

6 276 A. Piatanesi and S. Tinti Figure 4. Computed tide-gauge records at the coastal sites shown in Fig. 1. Each panel includes three curves, corresponding to the CV, VV and LA source faults with details given in Table 1. All curves start from a zero-level because coastal tide-gauges experience the same co-seismic vertical displacement as the water surface. The straight lines in Pizzo, Bivona and Briatico represent the post-tsunami still water level.

7 The 1905 Calabrian tsunami 277 Figure 5. Maximum total energy density fields computed over the whole propagation time (85 min) for the three reference fault sources. Isoline labels are in KJ m 2. The sea region with energy levels above 100 KJ m 2 is black. waters, especially to the north, are quite efficient at trapping and channelling tsunami waves, irrespective of the orientation of the parent fault, which means that bathymetric features predominate here over source directivity in determining the radiation pattern. In the case of the CV fault, wave trapping is quite manifest also along the southern coasts of the grid, that is the Calabria coast to the south of the cape, the mouth of the Straits of Messina and north-eastern Sicily. This southward wave radiation may be easily explained by the fact that the initial field produced by this fault extends to the south beyond Capo Vaticano (see Fig. 3). To the north, in addition to the wave trapping discussed above that is confined to the very-shallowwater belt, a second milder case of wave trapping may be identified more offshore for the CV source: it involves a larger space scale and is produced by the interaction of the tsunami with the steep offshore slope connecting the intermediate-depth (around m) sea floor down to the Tyrrhenian abyssal plain. One more interesting feature is that the Aeolian islands are able to screen tsunami propagation efficiently, giving rise to a characteristic energy drop in the lee of each island cone (see e.g. the Capo Vaticano case in Fig. 5). 4.2 Maximum water elevation (MWE) along the coast The energy density fields graphed in Fig. 5 give only large-scale information and are certainly useful to delineate the main features of the tsunami propagation. However, to evaluate the impact of the tsunami more precisely and quantitatively, the water elevation has to be analysed on all coastal nodes. The maximum water elevation (hereafter MWE) reached by the waves over the entire computation time interval (85 min) along the coastal segments of Calabria and Sicily is shown in Fig. 6. As already noted in discussing the tide-gauge records at the beginning of this section, the analysis of coastal node elevation within the source region needs to account for the co-seismic vertical displacement experienced by the shore. Let us focus once more on this point by means of Fig. 7, where the MWE produced by the VV fault along the coast of Calabria is shown. Here, the dashed curve is computed by ignoring the co-seismic lowering of the coast due to faulting, and represents the effect of pure hydrodynamic propagation, being defined as MWE(x, y) = max[ζ (x, y, t)]. On the other hand, the solid curve is calculated as MWE(x, y) = max[ζ (x, y, t) ζ (x, y, t = 0)], and illustrates the joint action of hydrodynamics and tectonics. It is evident that in the source region (the shaded area), where the co-seismic subsidence is a relevant effect, water elevations are much larger, whilst as we go further off, the two MWEs become identical. In Fig. 6(a) we plot the MWE along the coast of Calabria, computed taking into account the co-seismic vertical displacement of the coast: owing to this latter contribution, in several places belonging to the source area, the MWEs relative to the CV and VV faults are of the same order, in spite of the fact that from the energy pattern displayed in Fig. 5 the former appears to be largely the more energetic source. Indeed, the co-seismic uplift produced along the coast by fault CV (see Fig. 3) mitigates the effects of the associated tsunami. Also the LA fault, at least along a short segment belonging to the source area, produces MWEs of the order of 1 m, rapidly decreasing as soon as we go away from that area. The MWEs computed along the coast of Sicily (see Fig. 6b) are relevant only for the tsunami generated by the CV fault, for which they exceed 60 cm in some localities; the other two sources produce only minor effects, not exceeding 15 cm. Along the coast of Sicily in the Straits of Messina the tsunami effects are negligible, especially for the VV and LA sources: this is probably due to the small cross-section of the northern mouth of the Straits of Messina which permits only a weak transmission of the tsunami wavelengths, and to the V-shape configuration of the basin causing a rapid decay of the waves.

8 278 A. Piatanesi and S. Tinti Figure 6. MWE computed along the coast of (a) Calabria and (b) Sicily for the three source fault sketched in Fig. 2. MWE is computed by taking into account the co-seismic vertical displacement of the shore due to faulting (see Fig. 3).

9 The 1905 Calabrian tsunami 279 Figure 7. MWE along the coast of Calabria computed by ignoring (solid line) and by taking into account (dashed line) the co-seismic vertical displacement of the shore due to rupturing of the VV fault. The shaded area indicates the source region. 5 DISCUSSION The main objective of this work was the study of the tsunami ensuing from the 1905 September 8 Calabrian earthquake. This was carried out by using a forward modelling approach, that is by running numerical tsunami simulations relative to different genetic mechanisms that seem plausible on the basis of the present knowledge of the seismotectonics of the region: we have selected three possible faults (CV, VV and LA faults) depicted in Fig. 2 with fault parameters listed in Table 1. What we have learned from the simulations can be summarised in the following remarks. The three faults we use fulfil the constraint of similar seismic moment and magnitude. Consequently they produce Earth-surface deformation fields that have common features (bipolar fields with almost the same extension of subsiding and uplifting elliptical lobes), but they have quite different tsunamigenic potential since they induce very diverse displacements of the sea floor, owing to the different strike and position relative to the coastline (see Fig. 3). Initially, the main effect of the sea floor displacement is to cause a change of the sea surface level, which is chiefly determined by the tectonic displacement, but which is also influenced by the sea bottom bathymetric slopes within the source region. The largest initial sea surface perturbation is caused by the CV source, and the weakest by the LA source. The main difference however concerns the sign of the perturbation: it is a pure negative sea level depression for VV and LA sources, whilst it is bipolar, with depression dominating on uplift, for the CV source (see Fig. 3). The initial energy of the tsunami is merely potential energy since the initial velocity field can be assumed to be null, while in the course of the propagation the waves tend to reach the usual dynamic equipartition between potential and kinetic energy forms. Wave propagation is strongly determined by sea bottom topography that is quite complex in the southern Tyrrhenian basin and is found to have a dominant influence on source directivity. In a flat basin bathymetry would have caused the wave fronts to travel mostly along paths normal to the fault strike, but this is not what is found in our simulations, which result in being strongly trapped in a narrow near-coast channel along northern Calabria for all sources (see Fig. 5). In the case of the CV source energy trapping can be observed also along the southern coasts of Calabria and northeast Sicily: this can be explained by noting that this is the only source producing an initial sea level disturbance extending south of Capo Vaticano. It can be stated also in a complementary way: local sources affecting only the gulf of St. Eufemia, north of the promontory of Capo Vaticano are not able to radiate much energy toward the coasts south of the cape, since the cape itself acts as a protecting shield (reducing wave height by about 50 per cent see Fig. 6). The computed tsunami penetrates weakly in the Straits of Messina: during its southward path along the channel it decays quite fast down to 20 per cent of the values it has at the entrance to the strait, due to the characteristic V-shape of the strait morphology (see Figs 5 and 6). In the south Tyrrhenian basin, tsunami amplitude decreases in passing from shallow to deep waters, as expected. The Aeolian islands are attacked by the deep-ocean small-amplitude front of the tsunami. All the large-size islands of the group are able to act as screens against tsunami propagation, with a shadow zone forming in the lee of the islands, preventing substantial wave propagation to the west (see evidence in the leftmost panel of Fig. 5). The features of the tsunami radiation are reflected in the computed tide-gauge records and in the MWE of the waves on the coasts. It has been noticed that these are determined only by hydrodynamic wave propagation outside the source region, while within it they result from the combined effects of propagation and tectonic dislocation. The consequence is

10 280 A. Piatanesi and S. Tinti that in the far field, tsunamis keep the hydrodynamic signature of their initial field. From the mareograms computed at the far-field stations of Scalea, Milazzo and Messina it can be observed that: (1) since initially water is mainly down-going for all tsunami cases, gauge stations are excited by a leading front attacking either as a deep trough (Scalea and Milazzo) or as a small crest followed by a larger-amplitude trough (Messina); and (2) the rank of the tsunamis based on the amplitude of the tide-gauge oscillations is the same as the rank deduced from their initial potential energy: for example, the CV tsunami has the largest potential wave energy and accordingly produces the largest waves (compare Figs 3 and 4). In the near field, however, coastal wave heights measured with respect to the preevent shoreline level are affected by tectonic displacements: coastal subsidence enhances the effect of the tsunami inundation, while coastal uplift tends to counteract it. Bearing this in mind, the VV fault tsunami produces waves of similar penetration and flooding capability as the CV fault tsunami, in the southern coasts of the St. Eufemia gulf (see mareograms of Pizzo, Bivona and Briatico in Fig. 4), since these localities are respectively downlifted and uplifted by the former and latter events. The dominant periods of the tsunamis visible on the mareograms depend both on the source and on the local features of the area of the receiver gauges. Unipolar sources (see fault VV) generate longer-period waves than the bipolar source (i.e. CV fault): min against 8 12 min. Observe that the sea surface adjustment from the old to the new level affects the first oscillations much more than the others: with the CV fault the first sea withdrawal from the shoreline is two three times greater than the following ones. In a sense it can be stated that after the first sea retreat the effect of the adjustment is almost exhausted and then it is replaced by the trail of tsunami fluctuations around the new sea level. 5.1 Trade-off between fault dimensions and slip The fault sources used in the present work are based on the assessment of the earthquake magnitude M S = 7 from the catalogue of Boschi & Gruppo di Lavoro CPTI (1999). This M S is then interpreted in terms of the seismic moment M 0 = µlw u = N m, where µ is the rigidity of the lithosphere and L, W and u are respectively the length, the width and the slip of the fault. Finally, assuming a rigidity µ = Nm 2, M 0 is used to construct a model for L, W and u. However, with no additional information available, only the product LW u is constrained by M 0,or, at the best, W u if the length can be estimated from morphotectonic studies. In other words, a range of trade-offs between fault dimensions (L, W ) and slip u are possible and should be considered in order to evaluate correctly the impact on the coast due to the tsunami generated by the source fault responsible for the 1905 Calabrian earthquake. Since the LA fault has proved to have slight tsunami potential, we focus our efforts on the CV and VV faults and suppose that their fault planes are affected by some degree of uncertainty in the length and/or in the width. As to the VV fault, we observe that it lies completely beneath dry land and its signature is visible on the ground surface: therefore, we consider that its length is a well constrained parameter. For this reason, in addition to the reference case (see Table 1), we consider two supplementary fault sources, that are characterised by the same parameters as the reference fault but with a width that is varied by ±5 km. Furthermore, since we want the corresponding seismic moment M 0 to remain unchanged, we modify the slip allowed on the faults accordingly (see Table 2). On the other hand, since the surface signature of fault CV is difficult to detect because it lies largely beneath the seafloor, we Table 2. Trade offs between L, W and slip for the CV and VV faults; grey highlight marks the reference source faults. Fault Slip Length Width (m) (km) (km) CV L30W CV L30W CV L30W CV L 25W CV L35W VV L30W VV L30W VV L30W consider that both the length and the width are not well constrained. Owing to this, four supplementary source faults are studied, with parameters listed in Table 2, that are representative of both (L, u) and (W, u) trade-offs. To provide a synthetic result of the influence of perturbing fault parameters on tsunami generation, we proceed as follows. For each source we run a tsunami simulation and compute the MWE at each point belonging to the coastline, just as we did in the previous section for the reference source faults. Then, for each point and for each group of source faults (see Table 2) we compute the mean and the standard deviation of the MWE. In Figs 8(a) and (b) we show the results relative to the CV source faults obtained along the coast of Calabria and Sicily respectively. We found that the mean values µ are quite similar to the values associated with the reference case (compare with Figs 6a and b). The standard deviation σ is almost uniformly distributed over the coastline, taking values in the range of per cent of µ: only in those locations where µ is very small, i.e. less than 5 cm, which occurs in a few places in the source region, the relative standard deviation σ/µ may become quite large (even exceeding 200 per cent). This may be easily explained bearing in mind that the faults of the CV group cause both uplift and subsidence of the coast, but with patterns that are slightly different from each other (i.e. some coastal points are displaced downward with one fault and upward with another). Under these circumstances, as already pointed out in Section 4.2, the joint effect of hydrodynamics and tectonics may shift the positions of the minimum values of the computed MWE. Corresponding to these minima, which can be seen to the north and south of Capo Vaticano (see Fig. 8a), the highest values of the ratio σ/µ are found. However, it should be noted that the standard deviation has absolute values typically around cm that only exceptionally increase up to 40 cm. Also for the VV group of faults (see Fig. 9) we find that perturbing the fault width does affect the computed MWE, but without altering the general MWE pattern of the reference VV fault. The relative standard deviation σ/µis generally in the range per cent along the central and northern coasts of Calabria, and tends to increase to per cent along the south Calabrian coasts and in Sicily, where the mean MWE values are smaller. The absence of sharp high peaks in the ratio σ/µ is due to the fact that the VV faults lie completely on dry land and induce a unipolar co-seismic displacement (subsidence) of the sea floor. In addition to the above experiments where the fault size was changed and the slip was correspondingly changed to keep the seismic moment M 0 constant, we have also explored the effect of varying M 0 under the constraint of unchanged fault dimensions. It is known that in the far-field M 0 is the main parameter controlling the tsunami amplitude, while small modifications of the geometric parameters are considered to produce minor effects (see Okal 1988, for a review). To estimate to what extent a perturbation of the seismic moment M 0

11 The 1905 Calabrian tsunami 281 Figure 8. MWE along the coasts of (a) Calabria and (b) Sicily relative to the group of the CV faults (see Table 2). The mean µ (solid circles) together with the ±σ bars are shown for each coastal point using the faults with source parameters listed in Table 2. Open circles are σ/µ values (in per cent).

12 282 A. Piatanesi and S. Tinti Figure 9. MWE for the group of VV faults (see Table 2). See caption of Fig. 8 for symbols explanation.

13 The 1905 Calabrian tsunami 283 Figure 10. MWE along the coast of Calabria for the CV fault with ±25 per cent perturbation on the seismic moment M 0. See the caption of Fig. 8 for symbols explanation. affects the local MWE, let us analyse the results shown in Fig. 10. Here we consider the CV reference fault (see Table 1) and we fix all the parameters except for the seismic moment M 0, which is modified by ±25 per cent, by changing the co-seismic slip by an equal amount. We found that the perturbation of M 0 produces, as expected, variations of the computed MWE. The mean MWE value µ is quite close to the MWE of the reference case (Fig. 6a) and to that shown in Fig. 8(a). What is remarkable is that the relative standard deviation σ/µ is almost constant around 20 per cent over the entire coastline. In summary, the sensitivity study clarifies the result that the basic cases studied in Section 4 provide sensible results and are adequate to provide a portrait of the basic effects of the tsunami. 6 CONCLUSIONS Comparison of the numerical results with the available historical observations does not provide an unequivocal picture, due also to scarcity of data. The tsunami was not catastrophic, but was large enough to transport boats inland and to flood low lands in several coastal villages, to produce oscillations in the range of min the far field (within the computational mesh: Scalea and Milazzo) and to be seen in tide-gauge records hundreds of kilometres away from the source (Naples, Ischia and Civitavecchia). Given the tsunami size, an LA source causes a sea floor dislocation too weak and consequently a tsunami too small to be compatible with observations. Identifying which one of the remaining two sources is to be preferred is not objectively easy since they show both pros and cons. The CV tsunami is more energetic and of comparatively higher frequency than the VV tsunami, hence explaining better the experimental far-field wave heights and periods (e.g. flooding at Scalea, wave amplitude at Milazzo, wave period in Messina, and plausibly wave periods of the distant tide-stations outside the computational domain). However, the VV tsunami may explain better the observations in the source region, namely the sea flooding that occurred at Pizzo, Bivona and Briatico. In the light of the above results, one could argue that since none of the sources respects all the observational constraints, all have to be rejected and that the source fault has to be found elsewhere. Strictly speaking this is correct. However, all other main faults of the Calabria region depicted in Fig. 2 should be ruled out since they would cause seismic shaking too incompatible with the estimated isoseismal pattern (Fig. 1) and sea bottom displacements either too small or too far from the St. Eufemia gulf that is the area with the major tsunami effects. Therefore, our idea is that the agreement with observations is not complete, yet it is satisfactory, and that the parent fault characteristics, namely geometry, position and source mechanism, cannot be too diverse from the properties of the two sources, CV and VV, that we have considered here. We believe that through a better tuning of these sources (for example concerning fault dip and slip rake, etc.) and by using more detailed bathymetric databases (especially in the near-shore band) the discrepancies with observations could be reduced. There is a further remark that is worthy of attention. All faults taken into account in the present study would produce a permanent change of the shoreline level (either a regression or ingression of the sea) of the order of tens of cm: but there is no trace of this variation in the historical coeval sources. Since the Calabrian population affected by the earthquake and tsunami was quite familiar with the sea

14 284 A. Piatanesi and S. Tinti (fishermen, seamen,...), it seems strange that this change passed unnoticed. One possibility is that it was noticed, but it was considered an irrelevant detail, not worthy of mention in the reports. This possibility is not remote. For example, the disastrous tsunamigenic Messina earthquake that hit Sicily and Calabria three years later (1908 December 28) caused the subsidence of both coastlines of the Straits of Messina as is documented by levelling campaigns carried out before and after the event (Loperfido 1909), but no mention of the lateral shift of the shoreline can be found in the numerous accounts of eye-witnesses. We conclude this paper with a final remark, that can also be taken as the formulation of an alternative hypothesis. We cannot exclude the possibility that the responsible source is a fault with similar strike, dip and surface size as CV and VV, but somewhat displaced toward the west, about km offshore. Such a fault would produce a bipolar sea surface displacement, a large subsidence offshore (like fault CV), a milder coastal uplift (but quite a lot smaller than the CV fault). We do not know if such a hypothetical fault exists, since the present knowledge of the seismotectonics of the region is rather incomplete in the offshore coastal zone, but it is not in contrast with what is known. We are conscious that this hypothesis needs verification. It can be tested by an extensive programme of more accurate tsunami simulations, which we intend to perform in future work, but it also requires the undertaking of specific geological and geophysical investigation of the zone off Capo Vaticano and St. Eufemia Plane, which we hope and wish can be performed in the coming years. ACKNOWLEDGMENTS This research was carried out with funds from the Gruppo Nazionale di Difesa dai Terremoti (GNDT) within the Istituto Nazionale di Geofisica e Vulcanologia (INGV) and from the Ministero dell Università e della Ricerca Scientifica e Tecnologica (MURST). REFERENCES Argnani, A., The Southern Tyrrhenian subduction system: recent evolution and neotectonic implications, Ann. Geofis., 43, Baratta, M., Il grande terremoto calabro dell 8 settembre 1905, Atti della Società Toscana di Scienze Naturali, Memorie, 22 (in Italian). Boschi, E. & Gruppo di Lavoro CPTI, Catalogo parametrico dei terremoti italiani, ING, GNDT, SGA, SSN, Bologna (in Italian). Web site: Boschi, E., Ferrari, G., Gasperini, P., Guidoboni, E., Smriglio, G. & Valensise, G., Catalogo dei forti terremoti in Italia dal 461 a.c. al 1980, Istituto Nazionale di Geofisica, Roma, Italy (in Italian). Web site: Frepoli, A. & Amato, A., Spatial variation in stresses in peninsular Italy and Sicily from background seismicity, Tectonophysics, 317, Frepoli, A., Selvaggi, G., Chiarabba, C. & Amato, A., State of stress in the Southern Tyrrhenian subduction zone from fault-plane solutions, Geophys. J. Int., 125, Loperfido, A., Livellazione geometrica di precisione eseguita dall Istituto Geografico Militare sulla costa orientale della Sicilia, da Messina a Catania, a Gesso ed a Faro Peloro e sulla costa occidentale della Calabria da Gioia Tauro a Melito di Porto Salvo, per incarico del Ministro dell Agricoltura, Industria e Commercio, Relazione Commissione Regia, Roma, (in Italian). Mercalli, G., Alcuni risultati ottenuti dallo studio del terremoto calabrese dell 8 settembre 1905, Atti dell Accademia Pontoniana di Napoli, 36 (in Italian). Monaco, C. & Tortorici, L., Active faulting in the Calabrian arc and eastern Sicily, J. Geodyn., 29, Okada, Y., Internal deformation due to shear and tensile faults in a half-space, Bull. seism. Soc. Am., 82, Okal, E.A., Seismic parameters controlling far-field tsunami amplitudes: a review, Natural Hazards, 1, Piatanesi, A. & Tinti, S., A revision of the 1693 eastern Sicily earthquake and tsunami, J. geophys. Res., 103, Piatanesi, A., Tinti, S. & Bortolucci, E., Finite-element simulations of the 28 December 1908 Messina Straits (southern Italy) tsunami, J. Phys. Chem. Earth, 24, Platania, G., I fenomeni in mare durante il terremoto di Calabria del 1905, Boll. Soc. Sism. Ital., 12, (in Italian). Rizzo, G.B., Contributo allo studio del terremoto della Calabria del giorno 8 settembre 1905, Regia Accademia Peloritana, 22 (in Italian). Selvaggi, G., Spatial distribution of horizontal seismic strain in Apennines from historical earthquakes, Ann. Geofis., 41, Selvaggi, G. & Chiarabba, C., Seismicity and P-wave image of the Southern Tyrrhenian subduction zone, Geophys. J. Int., 121, Tinti, S. & Armigliato, A., Seismic displacement of non-flat sea floor in tsunami generation: application to the 1693 case in Sicily, Italy, Proc. Internat. Conf. Tsunamis, Paris, France, May 26 28, Tinti, S. & Maramai, A., Catalogue of tsunamis generated in Italy and in Côte d Azur, France: a step toward a unified catalogue of tsunami in Europe, Ann. Geofis., 39, (Corrections, Ann. Geofis., 40, 781, 1997.) Tinti, S. & Piatanesi, A., Finite-element simulations of the 5 February 1783 Calabrian tsunami, J. Phys. Chem. Earth, 12, Tinti, S., Gavagni, I. & Piatanesi, A., A finite-element numerical approach for modelling tsunamis, Ann. Geofis., 37, Tinti, S., Armigliato, A., Bortolucci, E. & Piatanesi, A., Identification of the source fault of the 1908 Messina earthquake through tsunami modelling. Is it a possible task?, J. Phys. Chem. Earth, 24, B, Tinti, S., Armigliato, A. & Bortolucci, E., Contribution of tsunami data analysis to constrain the seismic source: the case of the 1693 eastern Sicily earthquake, J. Seismol., 51, Tortorici, L., Monaco, C., Tansi, C. & Cocina, O., Recent and active tectonics in the Calabrian arc (Southern Italy), Tectonophysics, 243, Westaway, R., Quaternary uplift of Southern Italy, J. geophys. Res., 98, Wortel, M.J.R. & Spakman, W., Subduction and slab detachment in the Mediterranean-Carpathian region, Science, 290,