A variable slip fault model for the 1908 Messina Straits (Italy) earthquake, by inversion of levelling data

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1 Geophys. 1. Inr. (1991) 104, A variable slip fault model for the 1908 Messina Straits (Italy) earthquake, by inversion of levelling data Giuseppe De Natale and Folco Pingue Osservatorio Vesuuiano, Via Manzoni 249, Napoli Italy Accepted 1990 July 18. Received 1990 July 18; in original form 1989 February 21 INTRODUCTION The Messina Straits is located in the southern part of the Calabrian Arc (Fig. la). Most of the strongest Italian earthquakes have occurred in this area. The 1908 December 28 Messina earthquake is the largest event which occurred in Italy during the last century, and in the Calabrian Arc since It was a very catastrophic event, killing more than 6OOOO people and causing extensive damage. The main shock was followed by a tsunami, which produced waves up to 12 m high, reaching more than 200 m inland (Baratta 1910). Seismotectonic activity in the southern part of the Calabrian Arc is characterized by normal faulting, leading to the formation of graben structures. These features are mainly connected to the lateral stretching of the crust, due to the strong curvature of the arc in this area, also reflected at depth by a spoon-shaped Benioff zone (Gasparini et af. 1982; Iannaccone, Scarcella & Scarpa 1985). Several strong earthquakes, with magnitude exceeding I, have occurred in the southermost segment of the arc, between Catanzaro and Messina, in 1905, 1908, and in February-March 1783 within a sequence of five large earthquakes. The 1905 earthquake was also followed by a tsunami; this event probably occurred at sea, along the SUMMARY A variable slip fault model is presented for the 1908 December 28 Messina (Italy) earthquake. It has been obtained by inversion of levelling data, using a gradient method. Fault location and mechanism are consistent with an approximately N-S orientation and normal faulting on a low-angle plane dipping 39", with about 45" of strike-slip component. The main difference from a homogeneous slip model is represented by a higher slip area. (up to 3 m), located close to the city of Reggio Calabria. It is interpretable as a major asperity, which is related to the main fracture episode. This is in agreement with some macroseismic evidence and the same structure could be responsible for the nearby recent seismic activity. The area which effectively slipped is all confined within the Messina straits. This result differs from the homogeneous slip model recently proposed by Capuano et al. (1988). Key words: fault, inversion, Messina earthquake, slip. westward continuation of the Mesima graben (Barbano et al. 1980), as indicated by the isoseismal patterns (Fig. lb). The 1783 sequence occurred further south, probably along the easternmost structures of the same graben (Tortorici, Taponnier & Winter 1986). The 1908 earthquake was recorded by 110 worldwide distributed seismic stations. It has been located in the Messina Straits, according to the distribution of major damages, showing intensities up to XI Mercalli degrees on both sides of the Straits. For this event, several kinds of data exist. 23 seismic records could be used to obtain a reliable focal mechanism by first pulse polarities, indicating normal faulting with a considerable strike-slip component (Martini & Scarpa 1983). Tide gauge data in the Messina harbour were also collected from 1897 to 1908, and from 1912 to They show land subsidence with a rate of 2.8 mm yr-' from 1900 to 1906, 22.7 mm yr-' from 1906 till 1908, and 24mmyr-' from 1912 to 1916 (Mulargia & Boschi 1983). Precision levelling surveys were carried out just after the mainshock along several lines located both on the Calabrian coast and on the Sicilian side of the Straits. Previous levellings on the same lines had been performed just one year before the earthquake in Calabria, and few years before in Sicily. The vertical deformations computed by comparing these consecutive sets of measurements can therefore be reasonably considered as coseismic, providing a 73

2 74 G. De Natale and F. Pingue, $4, f Figure 1. (a) Schematic seismotectonic map of Calabrian Arc: (1) foundered peri-tyrrhenian basin and downfaulted peri-tyrrhenian margins; (2) tectonic troughs opened within the axial part of chain; (3) external Pliocene-Pleistocene basin; (4) main systems of normal faults; (5) fault system offsets in Middle Pliocene times and normal activity in Pleistocene times. (b) Intensity distributions for the largest earthquakes which occurred in this region. high-quality data set to study details of the rupture mechanism of this earthquake. These data have already been used by Capuano et al. (1988) to infer the geometry of the fault model for the 1908 earthquake. Although they found an overall good fit of the data by using simple homogeneous slip fault models, some features of the observed deformation field remained unmodelled, calling for a slightly more complex slip pattern. Moreover, their preferred model, namely a single normal fault, showed a fault plane which largely extends to the north, well beyond the Straits; this contrasts with the distribution of maximum damage, due to both the earthquake and the tsunami, which appeared mainly localized within the Straits. In particular, as shown in the next sections, the fault extension to the north is an effect of constraining the slip distribution to be homogeneous. This arbitrary constraint may be not justified, especially in the case of large earthquakes, when complex rupture patterns are expected. In order to account for this apparent complexity we use a variable slip fault model for interpreting the levelling data of the 1908 Messina earthquake. The inferred model also gives new insight into the rupture process associated with this event, whose understanding is of fundamental importance for a correct interpretation of seismotectonics and seismic hazard in this important part of the Mediterranean area. LEVELLING DATA AVAILABLE FOR THE 1908 EARTHQUAKE The 1908 earthquake was accompanied by visible ground cracks (Baratta 1910). The coastline road close to Messina showed a graben-type collapse, with fractures up to 100m long and slip around 0.6 m. Vertical displacement data are relative to three double-run surveys performed during in Sicily, in Calabria and March 1909 in Sicily and Calabria. The standard errors of these measurements are 1.74~ x and 1.32a x m for the first surveys in Sicily and Calabria, respectively, and 1.69t/;i X lop3 m for the 1909 survey (d is the distance in km). Since the interval between these measurements is rather short, the observed displacements can be reliably interpreted as coseismic movements. The measured pre-seismic and post-seismic movements at Messina harbour, through tide gauge data, gave values of the order of several mm yr-. The reference bench mark for the Calabrian levelling line was located at Gioia Tauro (Fig. 2), which is far from the seismic area. The smaller distances from the ruptured area spanned by the levelling lines located in Sicily made the choice of a reference bench mark difficult. For these lines, the data set is represented by the measured changes in

3 The 1908 Messina Straits earthquake T Y R R H E N I A N '" REGGIO CALABRIA C , ~ast coo-dizate UTM Figure 2. Levelling network (dots). The Symbols 'x' indicate numbered bench marks; some displacements (in cm) are also reported (in brackets), corresponding to bench marks indicated by '@I,. (After Capuano et nl. 1988). differential elevations between consecutive bench marks, which made the use of a reference point unnecessary. METHOD OF ANALYSIS When fault location and mechanism are assumed known, finding a variable slip fault model from inversion of ground deformation data can be posed as a linear problem. Several examples can be found in literature on this subject (Ward & Barrientos 1986; Harris & Segall 1987). The slip distribution on the fault plane can be described in several ways, depending on the parametrization used. The most common approach is to subdivide the fault area in several elements; the inverse problem consists, in this case, of determining the slip distribution on the elements, providing synthetic data that will give the best fit to the observed data. An alternative method is to parametrize the slip distribution as the sum of a complete set of orthogonal functions of the position on the fault (see, for example, Vasco, Johnson & Goldstein 1988). When using the first (Krnl - a 1 method, it is important to use a fine parametrization of the structure (with respect to the average spacing of the measurements) (Menke 1984), to avoid arbitrary constraints on the slip distribution. In this case, the inverse problem is effectively underdetermined. The most general form of the constitutive equations linking the data to the model parameters, in the framework of the linear elasticity theory, is N uk(~;) =,=1 Ak(xi, q,,)q(xoj) (i = 1, M: j = 1, N: k = 1, 3). In (1) uk(xi) is the displacement at (xi), along the kth coordinate direction. The functional forms of q(q,) and A,(x,, xi, q,,) depend on the parametrization for the slip distribution and on the adopted mathematical formalism. Choosing a parametrization in terms of point-sources, q(qj) represents the seismic moment of the source at q,,, whereas it can represent the dislocation on the jth element if finite dimension elements

4 76 G. De Natale and F. Pingue are chosen. A,(x,, bj) (k = 1, 3) is completely determined from the fault geometry and mechanism, once q(q,) is specified. In order to find an unique solution for the underdetermined inverse problem, some kind of 'a priori' information must be added to the data. This 'a priori' information can be chosen in order to satisfy our physical intuition, or to test the performance of particular models. As an example, one could be interested in testing the statistical significance of a variable slip model against an uniform one. In this case it is convenient to find a slip distribution as close as possible to a homogeneous one, and test its performance against the uniform slip model; for such an application, constraints of 'minimum roughness' or 'minimum norm' could be used (see Harris & Segal 1987). We use a point-source parametrization for the slip distribution. The mathematical formulation follows that used by Ward & Barrientos (1986). Referring to equation (I), we have, for the vertical component of A,(x, x,)): 8niuA3(x7%) = (Mil + M22)G(r, X0-J + 2M3,CXrt XoJ with +2(MI3 cos 8 + Mz3 sin O)fl(r, xg3) (2) +[2M,,sin28+ (M,, -Mz2)~~~20]Z2(r,xo3), fi(rp ~03) = 6(x0J2r/R5, 4(r, xo3) = [P(R-xod2(2 +xojr)i/[(a + P )~'R~] - 3(x0-J2r2/R5, G(r, Xoj) =Xo3/R3[-(A + 2P)/(A + P) -t 3(~o3)~/R'], I&, xg3) = xo3/k3[a/(a + P) - ~ (x,,)~/r~i. q(&,)=m(x,,j) is the scalar seismic moment at on the fault plane; M,](i, j = 1, 3) is the moment tensor; R = I(x - %I(, r2 = R2 - (x,j2 and 8 = tan-' [u(x - x,j/v(x - q,)];the xj axis is positive downward and u and v represent unit vectors at the surface. The problem is to determine the values of m(x,,]) (j = 1, N) on a grid, simulating the fault plane. The constraint m(xoj) > 0 (j = 1, N) is used, which physically corresponds to unidirectional slip for any point on the fault plane. This constraint represents a kind of 'a priori' information based on a physically reasonable assumption. Using the positivity constraint for m(qj), the set of exact solutions to (1) drops from infinite to possibly null and least-squares solutions must be searched for. In order to invert (1) we use a gradient technique (see also De Natale & Pingue 1987). The update of the model at the kth iteration is sketched as follows; the function we want to minimize is: E2b) = IlA,m - u311 where u3 is the observed data and A,m corresponds to the synthetic data. We first compute the gradient: -VE2(m) = 2A3(u3 -A+) then update our model:.20,,,.,,,,,,,.,.,,,,,. where Amk+' is the factor which, multiplied by -VE2(mk), determines the magnitude of the correction applied to mk. At any iteration, if some m, values become less than zero, they are automatically zeroed, in order to satisfy the constraint of unidirectional slip (m, > 0 for all j's). The process is repeated until a stable minimum is found for E2(m). This method differs from the one used by Ward & Barrientos (1986) for the computation of the correction to apply to m, (j = 1,..., N) at any iteration. In fact, they used only the sign of -VE2(mk), multiplied by Am*+'. In doing so, however, an arbitrary value of slip is assigned to sources on the fault which weakly contribute to the displacement field at the measured bench marks (VE2(mk) << max [VE'(m,)]). The present method, on the contrary, simulates the computation of a 'minimum norm' solution, i.e. the one for which the slip values of point-sources which do not contribute to the observed displacements are left unchanged with respect to the starting values I. ' ' I ' l * ' * ' ' ' ' I " * SO BO Banchmarka Figure 3. Distribution of residuals computed from the homogeneous fault model by Capuano er al. (1988) reported in Table 1. The broken lines enclose the 95 per cent confidence level of the measurements. The sum of squared residuals EEom = 0.24 mz.

5 DATA ANALYSIS 1 Variable slip fault model The residuals obtained on the basis of the Capuano et al. (1988) model (homogeneous slip) are shown in Fig. 3. As it is clear, residuals show some systematic patterns (e.g. benchmarks numbered 65 to 75 or 85 to 100) and they are not uniformly distributed along all the lines, showing a marked increase between bench marks These observations call for a slightly more complex model. Vertical deformation data obtained from the IGMI levellings have therefore been inverted, using the gradient method described previously, in order to find a model of slip distribution on the fault plane associated with the earthquake. As a reference model (geometry and mechanism of the fault plane) we used the one obtained from the uniform slip model of Capuano et al. (1988), which is in substantial The 1908 Messina Straits earthquake 77 Table 1. Source parameters of the uniform slip model (Capuano.. el al. 1988) used as reference model. Model parameters Dislocation (m) 1.s Dip angle (deg) 39 Slip angle (deg) 133 Fault width (km) 19 Fault depth (km) 1 Fault length (km) 57 Fault strike (deg) 176 agreement with the focal mechanism computed by seismic data, to within the error bounds of its determination (see Capuano et al. 1988). Also, several tests performed using different fault locations and mechanism did not show improvements in fit with respect to the reference model of Li95.L I I I I cc , East coordinate UTY (K711 Figure 4. Total allowed fault plane for the variable slip model. The smaller area encloses the maximum extension of the effectively slipped area, for the final model resulting by data inversion. Locations and focal mechanisms of the 1908 and 1975 earthquakes are also shown.

6 78 G. De Natale and F. Pingue 2, -.91 I SO n. of bench mark Figure 5. (a) Variable slip model resulting by inversion of levelling data. Contours are in units of 10" N m; 1 m of dislocation corresponds to 3.0 x 10"N m. (b) Fit of theoretical to experimental data. Capuano et al. (1988). Faults parameters are shown in Table 1. The total area of the fault structure has been enlarged with respect to the reference model, giving it a length of 70 km and a width of 30 km (Fig. 4). The best-fitting model is shown in Fig. 5a; it is characterized by broad maxima of slip (2-3m) in a 50 km x 20 km zone, with a global maximum (about 3 m) located close to the city of Reggio Calabria at a depth of about 8 km. Lame's constants p = 3.12 X 10" N m-' and h= 3.75 x 10'0Nm-2 have been used. In Fig. 5(b), a comparison of observed and theoretical data is shown. Data on the Sicilian side of the Straits have been arbitrary referenced to the bench mark located at Gesso (no. 21), which is the farthest from the fault, only for purpose of comparison. Another striking feature of the inferred solution is the high patch of dislocation in the zone of the fault crossing the city of Messina. This is due to the high gradient of displacement observed along the levelling lines which cross the city. However, since these data can be questionable by some points of view, as discussed in the next section, this feature of the solution cannot be assessed unequivocally. Figure 6 shows the residuals associated to individual bench marks computed on the basis of the variable slip model. One should note that, as will be quantatitively assessed in the next section, they do not show clear systematic effects and are more uniformly distributed all over the levelling lines, as compared to those computed by the homogeneous slip model. 2 Model variance A general problem when dealing with inversion of experimental data, is to compute appropriate statistics to assess the reliability of results, such as model parameter errors and resolution. In order to compute errors in the model parameters due to errors in the data, the simplest procedure is to invert many sets of data with noise, so to obtain a significant set of possible solutions. To obtain different noised data sets, random realizations of Gaussian noise have been consecutively added to the data. Errors in the solution have been estimated using two different assumptions for the data variance. In the first assumption, the data variance has been considered to come from intrinsic survey errors. For the bench marks located on

7 The 1908 Messina Straits earthquake I 10 o BO. eo. loo. iio. 120 bmnchrnsrkm Figure 6. Distribution of residuals computed for the variable slip model of Fig. 5. For bench marks 1-20, residuals on absolute displacements are shown, obtained by assuming bench mark 21 (Gesso) as zero level. The broken lines enclose the 95 per cent confidence limits of the measurements. The sum of squared residuals is E:a, = 0.08 m2. the Sicilian side of the Straits errors in the changes in differential elevations have been computed by the standard deviation (u = 2.43fi m) where d is the distance (in km) between the two consecutive bench marks considered. For the Calabrian bench marks (where a reference datum has been assumed) a random height error En at the nth station is generated by the formula En = ~(0,) is a zero mean random variable with standard deviation a, = 2.14 a. m. 100 realizations of Gaussian noise generated in this way have been consecutively added to the data and inverted. The standard deviations of computed 7 2 ' where ~(0,) N4OW 70Km source slip, over 100 inversions, are shown in Fig. 7(a). As it can be seen, maximum errors are of the order of about 0.3 X 10l6 N m (corresponding to about 0.10 m in terms of dislocation), about 30 times smaller than the slip values in the same zones. However, in the general case, errors in the data come not only from the intrinsic levelling errors, but also from unmodelled features of the physical model; in our case, a source of errors can be the unmodelled heterogeneities in the elastic parameters of the medium, or slight deviations from the assumption of a perfectly planar fault. For this reason, it is a common procedure to consider the 'a posteriori' variance instead of the intrinsic measurement errors, to compute errors on the model parameters. The total squared residual for the computed model is Eta, = 0.08 m2; using this value (which is assumed constant for the whole data set) instead of the intrinsic levelling error to compute model errors gives, after 100 inversions of data with noise, the results shown in Fig. 7(b). Errors for the fault slip are higher, of the order of about 0.6 x 1016N m (or about ) in the zones where moment value is about 5-10 x 1OI6 N m. These errors are certainly more realistic, because they take into account, in the assumption of a Gaussian distribution of errors, all the possible sources of misfit to the data. Figure 7. (a) Standard deviations for the moment distributions computed from the inversion of 100 noisy data sets generated using intrinsic levelling errors (see text). (b) The same as in (a), but using the variance of residuals based on the theoretical model of Fig. 5 for generating noisy data sets (see text). / 3 Model resolution Errors of the model computed this way are not able to give a complete description of the reliability of the solution, because of the correlation existing among point-sources on the fault. Moreover, points on the fault which are not constrained by the data are practically fixed to zero, so that the estimated error also vanishes. The most appropriate approach to examine the degree of correlation among source points is to compute the resolution, defined for a linear problem Ax=y, as the matrix R = A;' A (A;' stands for a generalized inverse of

8 80 G. De Natale and F. Pingue (a) Figure 8. Contours of resolution (in per cent of the maximum) computed for four selected source points (stars), by inverting data generated for a de\ta-like slip distribution (see text). The maximum resolution (R) and the percentage of total moment recovered over all the fault by inversion (TMR) are: (a) R = 0.82 and TMR = 2.5. (b) R = 0.02 and TMR = 1.7, (c) R = 0.07 and TMR = 2.4, (d) R = and TMR = 0.7. A). Since the approach followed for the inversion is based on a gradient method, giving no explicit computation for A;', the resolution can be alternatively computed as the solution given by the inverse method for a delta-like slip distribution on the fault. In practice, to compute the resolution associated with the ith point on the fault, synthetic data are generated for a slip distribution given by unitary moment on the ith point and zero elsewhere. Synthetic data are hence inverted, the final solution giving the resolution associated with the ith point. Figure 8 shows the resolution computed for four selected points. For well-resolved points, the resolution is singly peaked around the sample point, so that only neighbouring points are correlated (a, b and c of Fig. 8). The spreading of the resolution is a function of the distance of the source point from the closest bench marks. In zones not constrained by the data, the resolution is practically zero (see d in Fig. 8). This means that we cannot precisely resolve slip on single source points, which is obvious, but we can resolve patches of given sizes, since the resolution is generally peaked around the sample source point. In order to estimate the size of slip features we can resolve on each part of the fault, it is better to consider a quantity which also accounts for the effects of random errors on the data. We can choose as a criterion for slip on a given part of the fault to be resolved, the condition for which it produces a total signal over the measurement network greater than the noise amplitude. This condition can be formulated as uru = mtatam 2 E2 where E2 represents the total square noise amplitude over the measurement network. Considering the relation mj = pl2sj, where sj is the slip of jth source, the following expression is obtained (Ward & Valensise 1989): with In conclusion, Lm'" is the searched minimum resolvable scale length of slip Fn, for data with assigned mean error E = E ~/M. We have used the standard deviation of the residuals as the noise amplitude in order to take into account model errors as well as data errors, for calculating the quantity Lmin over the fault. Fig. 9 shows the minimum dimensions of slip features which can be resolved over the noise, as a function of position on the fault. We can see that the S4'E Figure 9. Contours of the minimum resolution length L"'" (in km) for 1 m of fault slip (see text). (4)

9 minimum size of patches of fault slip which can be resolved over the noise level is generally 3-4 km. Only in a small area around Messina, where the levelling line crosses the fault, is the minimum resolvable size smaller than 1 km. The lateral extent of the highly slipped area of the fault close to Messina, however, is not well controlled by the data, as can be inferred by the very sharp change of the resolution away from the shallowest zone, increasing the minimum resolvable patch size for 1 m of slip to more than 10 km at a distance of 2-3 km north and south of Messina. Because of the lack of bench marks close to the fault trace, sources shallower than 3-4 km are practically not resolved, away from Messina. 4 Statistical significance of the variable slip fault model The total square residual for the best variable model is Eta, = 0.08 m'. The improvement over the best homogeneous fault (E~,,=0.24m2) is 66 per cent. This improvement is difficult to test with a classical test of hypothesis, because the number of degrees of freedom for the variable slip model is not computable. This is due to the presence of the positivity constraints and to the correlation between neighbouring points on the fault, which implies that at each bench mark, only the total contribution of finite sizes of slip patches is seen, not the single source points. The most practical approach to test the significance of the heterogeneous model versus the homogeneous one is to perform numerical tests assuming that the residuals for the homogeneous model are random and looking at the probability of obtaining a residual improvement as the observed one by fitting synthetic data by a variable slip model. In practice, synthetic data are generated for the best homogeneous model, adding random errors with Gaussian distribution having the variance E2/M of data. 100 such data sets have been inverted by the variable slip model. The average variance improvement was 20 per cent, with a maximum of 32 per cent; 63 out of 100 inversions showed a variance improvement of less than 25 per cent. This means that a 66 per cent variance improvement has a negligible probability in presence of random noise. It implies that the misfit to the homogeneous model is systematic, not random, and hence has physical meaning. In this sense, the variable slip fault model is significant at a probability level higher than 99 per cent. 5 The effect of excluding the bench marks at the Messina harbour The four bench marks located at the Messina harbour (nos 1-4), showing more than m of subsidence, are often thought to be more associated to local slumping than to elastic deformation. This is because of the observed graben type collapse, which make the use of these bench marks in the framework of the elastic theory questionable. Although there is no concrete evidence for rejecting these data, the possibility that they can be misinterpreted cannot be rejected. We therefore performed some tests to investigate the effect on the solution of excluding such data. Since for the proposed fault plane, as already observed, these data only constrain the very shallow slip around Messina, the only variation in the proposed solution is the The 1908 Messina Straits earthquake Km SIP 390 Figure 10. Variable slip model obtained by inversion of levelling data, excluding Messina bench marks. disappearance of the shallow slip patch in this zone (see Fig. 10). However, since the large displacement gradient of these points represents the strongest constraint on the northernmost fault location, their exclusion causes a larger uncertainty in the location and strike direction. We have performed several inversions by varying the strike of the fault in steps of 10" and the location of the point F1 in Fig. 11 in the E-W direction, in steps of 2 km. We have shown in Fig. 11 the limits for the orientation and x location of the fault planes as defined by the 25 per cent of maximum increase of total square residuals. It is important to stress that, despite the variations in strike and location, all the feasible models show the higher slip patch on the part of the fault located close to Reggio Calabria, which then represents a feature strongly constrained by geodetic data. DISCUSSION Several observations can be made from the variable slip model obtained by inversion of levelling data. First, the overall shape of the fault slip is mainly controlled by the data resolution, because of the minimum norm assumption (see Fig. 9). The extension of the fault, except in the northernmost part, is however well constrained by the data. The higher slip zone (about 3 m of dislocation, located close to the town of Reggio Calabria), also appears well resolved. Dislocations in this area are significantly higher than in the neighbouring areas. This patch is likely to represent the main fracture episode. This area was already indicated (Omori 1909; Schick 1977) as the one which generated the most destructive effects, on the basis of macroseismic observations. Unfortunately, the epicentre location from seismic data is not accurate enough to allow for a comparison with the location obtained from geodetic data. This is because most of recording seismic stations were very far from the epicentral area and the few close ones were damaged by the earthquake. However, the resulting location is in the neighbourhood of the higher slip area (see Fig. 4). More significantly, the most energetic event occurring after the 1908 sequence, namely the 1975 January 16,,U, = 4.7 earthquake, was located in this zone (Bottari & Lo Giudice 1975). It showed a mostly strike-slip mechanism, with strike direction consistent with that of the 1908 earthquake (see Fig. 4). It represented, perhaps, a minor episode of reactivation of this part of the fault. Another strongly slipped zone is represented by the very localized patch crossing the city of Messina. Maximum dislocation in this area is about 3 m, and it is very shallow,

10 82 G. De Natale and F. Pingue GIOIA TAURO T Y R R H E N I A N S E A -> Y r c, m ~4226 r( U L 3 0 u K c, ;4216. Z A2C6. / CASTAN - 2 0, 0, S. GrOVANNI a REGGIO CALABRIA I I East coordinate UTM m a -J a MELrro or P. SALV~ Figure 11. Uncertainty of the location (Fl) and direction of fault as obtained excluding the Messina bench marks. The models shown have a maximum increase of variance of 25 per cent, with respect to the best model (see text). reaching the surface with a dislocation of about 2.5 m. The lack of very shallow slip in other parts of the fault is obviously due to the general poor resolution of the data on shallow features, because bench marks are generally far from the fault trace. The area close to the city of Messina, however, is the most constrained by the data, because the fault trace in this zone crosses the bench marks (see Fig. 2). The main constraints for the fault location in this area come from the strong subsidence of the bench marks numbered 1 to 4 (up to m), and the high gradient of displacement observed going from bench mark 4 to the ones on the Sicilian side. Special care must be taken when interpreting the measurements at bench marks located in this area. Loperfido (1909) reported the observation of ground cracks on the road, although he never mentioned damages to the bench marks. If the data located at Messina harbour are excluded, however, because they are suspected to be influenced by local slumping, this feature of the solution disappears and shallow slip is no longer required on the (Km) fault. Moreover, the strike and location of the fault are less constrained and a variation of strike within about 20" and of the location of point F1 (see Fig. 11) within about 6 km is still compatible with the data. All these models are equally compatible with the focal mechanism obtained by seismic P-wave polarities, within the error intrinsic to its determination (see Bottari et al. 1989). The important feature of these models is that they all show the higher slip patch in front of Reggio Calabria, which is then well constrained by data. However, further support to the existence of fault structures close to the city of Messina comes from recent vertical deformation data measured along several levelling lines located on the Sicilian side of the straits, analysed by Mulargia et al. (1984). They found that the overall pattern of vertical deformations in the period was in substantial agreement with about 0.04m of dislocation on a normal fault located in Sicily, close to Messina. Other important information about land movements at

11 The 1908 Messina Straits earthquake 83 Messina, associated to some extent with the 1908 earthquake, comes from the tide gauge data. They indicate subsidence of the Messina harbour of more than 2 cm yr- in the periods and (Baldi, Achilli & Mulargia 1983). No data exist in the period , because of damage due to the main shock. Significantly, tidal data from the Palermo harbour (about 300 km away) in the same period (Baldi et al. 1983) do not show such a trend, indicating that subsidence of Messina was a local event. This pre-seismic subsidence may indicate that aseismic slip on the main fault had been occurring since 1906, whereas the subsidence in the period could be associated with fault slip episodes as well as with viscoelastic effects following the main shock. As a final remark, we must point out that such a fault model, namely a low-angle fault located on the Sicilian side, produces a general subsidence of the straits and a modest elevation of both the Sicilian and Calabrian inlands. This is, qualitatively, the same kind of deformation which would be produced by a graben model and in fact the Messina Straits is generally recognized as a graben structure (Ghisetti 1984). The essential features of the morphology of the Messina Straits can be then thought of as being controlled by the occurrence of repeated earthquakes on this fault structure, in the form of characteristic earthquakes (Schwartz & Coppersmith 1984) and do not necessarily require a graben structure. This observation can shed new light on the seismotectonic interpretation of the Messina Straits area. CONCLUSIONS It is important to point out the advantages of using a variable slip fault model. Firstly, it should be noted that slip release from large earthquakes is generally far from being homogeneous, as directly inferred from geological evidence, as well as by results obtained from seismological studies. Therefore, constraining the slip to be homogeneous can give biased estimates of other fault parameters. In the present case, in particular, the assumption of a uniform slip model led to a considerably larger length of the fault in the north direction well beyond the Messina Straits (Capuano et al. 1988). The variable slip model, on the contrary, shows that the faulting process did not necessarily extend far north of Messina. The best homogeneous model found by Capuano et al. (1988) gave a total square residual E&,=0.24m2; the improvement obtained with the variable slip model is about 66 per cent (E~,,=0.08m2). It has been shown that this improvement is significant to more than 99 per cent confidence limits. The main feature of the model which is enlightened by the use of a variable slip model is the high slip patch close Reggio Calabria, which seems to represent a major asperity on the fault plane, susceptible to partial reactivation, as in the case of the 1975 earthquake, generating large to moderate earthquakes. ACKNOWLEDGMENTS We acknowledge S. Ward for useful discussions. We also thank two anonymous referees whose suggestions significantly improved the quality of the paper. A. Zollo and M. Noble are acknowledged for carefully reading manuscript. REFERENCES Baldi, P., Achilli, V. & Mulargia, F., Geodetic surveys in Messina Strait area, Bull. Geod., 57, Baratta, M., La Catastrofe Sismica Calabra-Messinese (28 Dicembre 1908), Rel. SOC. Geogr. It., Rome (in Italian). Barbano, M. S., Cosentino, M., Lombardo, G. & Patane, G., Isoseismal maps of Calabria and Sicily earthquake, Prog. Fin. Geodinamica, Gruppo di Lavoro Catalog0 dei terremoti, Pub. no. 341, CNR, Rome. 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