High spatial resolution DInSAR data for the Umbria Marche 1997 seismic sequence are exploited by relaxing constraints derived from datasets of different nature, such as seismologically derived fault dimensions. DInSAR data are thus inverted for a realistic slip distribution over the faults, in terms of depth distribution and roughness, which allows us to relocate the main faults and to minimize the misfit between the vertical displacement pattern derived from DInSAR and model predictions. Our analysis reveals that slip affected not only the shallowest part of the fault system but also its deepest part, rupturing the whole seismogenic layer of the crust down to 10 km, reaching slip values up to 30 cm at the base of the seismogenic layer. Misfit is reduced by a factor of two with respect to previous analyses based on a smaller number of digitized fringe points.
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 Various models, differing mainly in terms of geographical fault location, fault dimension and slip distribution, have been proposed for the Umbria-Marche (1997) seismic sequence. Differently from previous analyses, such as Hernandez et al. [2004, hereinafter referred to as HE04], we make use of a large number of DInSAR points and, with respect to Crippa et al. [2006, hereinafter referred to as CR06], we afford a more realistic inversion, relaxing constraints such as limited fault dimension and fixed geographical location. This new approach makes it possible to derive a more realistic slip distribution in depth, to relocate the fault and to perform the analysis of earthquake triggering in terms of Coulomb stress failure, based on a large number DInSAR points, as never accomplished for that seismic sequence.
 The coseismic displacement field observed at surface is based on a 35-day coseismic interferogram, obtained from two ERS2 images acquired before (7 Sept. 1997) and after (12 Oct. 1997) the two main shocks of the seismic sequence (average satellite angle 23°). We have applied the classical DInSAR procedure consisting in co-registration of images, creation of the differential interferogram, unwrapping and removal of atmospheric effects (CR06). We make the choice of focusing on the better determined DInSAR displacement component which is the vertical one. Although based on the same DInSAR dataset of CR06, the inversion procedure differs from that preliminary analysis in terms of development of a new algorithm based on the smoothing method as described by deGroot-Hedlin and Constable  for linear problems, as in our case of surface displacement due to slip sources at depth. A penalty function for model roughness is taken into account when evaluating the misfit. Differently form CR06, based on limited fault dimensions, which impose strict constraints on slip pattern at depth, the down-dip extension is now chosen sufficiently wide to avoid edge effects. Another important difference with respect to CR06 is that our inversion searches for the best position of the two faults, both along strike and perpendicular to it.
 The two main faults of the 1997 Umbria-Marche seismic sequence, F1 and F2 in Table 1, are modeled by means of 1 km × 1 km patches and Green functions (i.e. the surface displacement calculated at observation points for a unit dislocation over the patch) are obtained from Okada's theory as implemented by EDGRN-EDCMP by Wang et al.  for a homogeneous half space, characterized by μ = 2.6 × 1010 Pa, λ = 3.2 × 1010 Pa and ρ = 2.8 × 103 Kg/m3, as used by HE04 for the layer embedding the hypocenters. The high spatial resolution in the slip pattern is made possible by the inverse problem being overdetermined, with 8909 DInSAR points at high spatial density and 375 unknowns, which are the slip amplitudes over the patches of the two faults. The geographical location for the initial guess is taken accordingly to Salvi et al.  and then displaced by intervals of 0.5 km along and orthogonally to the strike. Rake is -80° for both faults, while strike is 152° for F1 and 154° for F2 and dip angles are 46° and 42° for F1 and F2, in accordance with seismological solutions.
Table 1. Faults with Mw ≥ 5 Considered in This Papera
 Instead of fixing the width of the fault in depth, as done in most of previous geodetic analyses which limit the width of the faults at about 8 km, we increase this parameter to 15 km for both faults, in such a way to avoid possible edge effects on inverted slip distribution. The lengths of F1 and F2 are 10 km and 15 km.
 The inversion procedure, known as the Occam's smoothing scheme, penalizes complexities in such a way that model characteristics deviate from the simplest model the least but sufficiently to match observations; we thus introduce the roughness parameter ρ representing the average gradient of the dislocation over the rupture area, following Jónsson et al. . The most appropriate roughness parameter is chosen in such a way that any further reduction with respect to this value does not provide any significant reduction in the χ2 value. From various tests, ρ is fixed at 0.02 m/km.
3. Discussion of the Results
 Independently on the ρ value, moving both faults by 1 km in the NE direction orthogonally to the strike, leads to a substantial lowering of the χrid2 value to 1.5, with respect to χrid2 = 1.9 corresponding to the starting model, represented by the dashed rectangle in Figure 1 portraying the surface projections of the two faults.
Figure 2 shows the DInSAR displacement pattern (Figure 2a), the modeled one (Figure 2b), corresponding to the best-fit solution after relocation of F1 and F2 orthogonally to the strike only, and the misfit (Figure 2c). Within the frame of a generally good agreement, we note in Figure 2c that negative misfit values, of 2–2.5 cm, are uniformly distributed, while positive ones show the tendency to cluster in the SW with respect to F1, possibly due to model limitations or to regions of low coherence in the data. We note that the whole displacement pattern is well reproduced, as the broad subsidence overprinting the projected fault area, including the smooth uplift NE with respect to the fault system. Moving F1 with respect to F2 to the NE by 1–2 km, as proposed by Capuano et al. , would produce an unrealistic increase of the positive residuals and an increase in the χ2 value, which leads us to prefer alignment of the two faults.
Figure 3 shows the slip over the F1 and F2 faults, for the best fit relocated model of Figure 2. For F1, the largest slip occurs at 7–8 km along the fault plane, or 5.0–5.8 in depth, including the 5.7 km hypocenter by Nostro et al. ; important slip values, ranging from 40 to 77 cm, are located in the NW part of the fault, from 4 to 13 km along the fault plane, extending for about 4 km along strike. The depth of the top of the patch undergoing significant dislocation, green in the figure corresponding to about 30 cm of slip, agrees with findings from Salvi et al. , HE04 and CR06, while the extension of the pattern at depth is larger in our analysis. Concerning F2, the largest slip zone over F2 is located in the SE part of the fault, close to F1, and a second small slip patch up to 30 cm is located in the NW part, close to the Earth's surface, at about 2 km along the fault. Even in the absence of clear evidences of surface ruptures, this patch of slip shows that the top of the fault is very shallow, at least in the NW part of F2, in agreement with previous findings by Salvi et al. , HE04, and CR06. Except for this NW slip patch, the largest part of the dislocation is concentrated between 4 and 11 km along the fault plane, or between 3 and 8 km depth, in agreement with Capuano et al.  from seismological data. The largest slip of 85 cm is found at 7 km along fault, or 4.7 km in depth, 1.1 km shallower than the hypocenter by Nostro et al. , but in agreement with Capuano et al. . With respect to previous studies, a notable amount of slip over F1 and F2 reaches greater depths, suggesting that the whole seismogenic crust of about 10 km is ruptured by the two major shocks.
 Relocating only orthogonally to the strike, as done in this Figure 3, the seismic moment partitioning is not in accordance with the seismological one, since it is 0.58 × 1018Nm for F1 and 0.86 × 1018Nm for F2, compared to 0.4 × 1018Nm and 1.2 × 1018Nm [Ekstrom et al., 1998]. Since DInSAR inversion is rather insensitive to relocation along strike, a closer agreement with the partitioning from seismology can be obtained by translating the two faults parallel to the strike. From the initial position we let the two faults move, indipendently from each other, by steps of 0.5 km up to 2.5 km in SE and NW direction, interval in which the χ2 is uniform. Moving F1 and F2 by 1 and 2 km in the SE direction, in fact, makes the ratio between the F1 and F2 seismic moments, 0.39 × 1018Nm and 1.01 × 1018Nm respectively, in closer agreement with the seismological one. Residuals of this along strike-translated model does not differ substantially from Figure 2, and are distributed accordingly to a Gaussian PDF, with standard deviation of 1.2 cm, close to the 1 cm DInSAR data error, and a factor of two smaller than the standard deviation obtained by HE04, the latter based on a smaller amount of DInSAR fringe points.
Figure 4 shows the slip over F1 and F2 for the fully relocated model. Moving F2 to SE causes, as expected, the displacement of the patches of large slip to the left over the fault plane with respect to Figure 3. Slip is substantially reduced in F1, at 50 cm at the most, but even over F2 slip is lowered from 85 cm to 60–70 cm and slip patterns over the two faults are smooth, once compared with HE04, unaffected by edge effects at the bottom. The highest slip zone over F2 is now well correlated with the seismologically retrieved hypocenter by Capuano et al. . Over both F1 and F2 the dimensions of the starting model, expecially along dip, are sufficient to include all the slip zones of 30 cm, green zones, in distinct contrast with CR06, with artificially limited fault dimensions. In Figure 4, the almost perfect closure of the slip isolines at the F1 and F2 facing edges supports the concept that the two faults belong to the same tectonic lineament, segmented by foreshocks. A major finding of our DInSAR inversion is that the whole seismogenic layer is ruptured by the major events, since a conspicuous slip of 30 cm is obtained at 14 km along dip or 10 km in depth, corresponding to the thickness of the whole seismogenic crust, as shown by seismic reflection results [Pialli et al., 1998]. With respect to Figure 3, relocation of the fault along strike allows the slip vanishing at the bottom of the fault. Although the general shape of slip patterns over F1 and F2 of previous DInSAR slip patterns portrays a general agreement with ours at middle and shallow depths, we obtain an important amount of slip also at the base of the seismogenic layer at 10 km, compared to the maximum fault depth of 6.5 km allowed by HE04. Peak values of 0.6–0.7 m of slip as in Figure 4 are lower than those of at least 0.8 m for F2 obtained by HE04, being our slip distributed over a wider area.
Figure 5 shows the ΔCFF (Colulomb Failure Function) projected over the six faults, Mw ≥ 5, activated after the major shock F1 of 26 September 1997, each including the effects due to all previous shocks. The ΔCFF patterns over the faults reflect the complexities of both DInSAR retrieved slip distribution over F1 and F2 and the geographical location of the faults. The largest positive ΔCFF values over F2 coincide with the hypocenter, as obtained by Chiaraluce et al. , as indicated by the star, which reinforces previous suggestions of F2 being triggered by F1 [Nostro et al., 2005]. F3 is the only case in which the hypocenter at 4.81 km of depth, as obtained by Chiaraluce et al. , lays in a shadow zone, as shown in Figure 5 and in agreement with the findings by Nostro et al. , whereas the hypocenter of F4 could be compatible with a positive ΔCFF zone, taking into account uncertainties in hypocenter location. The close agreement of positive ΔCFF zone with the actual location of seismic main events, particularly evident for the main aftershock at Sellano (F7), shows that this stress related quantity can be used as an indicator of stress changes and built up in complex seismogenic zones, although it may not be the only controlling factor for earthquake triggering [Miller et al., 2004].
 By increasing the faults dimension in depth, we obtain a slip distribution which is not biased by edge effects at the bottom of the faults, which allows us to exploit all the potentials of dense DInSAR data treatment, in particular for inferring the maximum depth of slip distribution. Our findings show that previous DInSAR and GPS analyses based on seismologically constrained fault dimensions overestimated the amplitude of the slip, since the same surface displacement had to be accommodated by a larger amount of slip occurring within artificially small fault surfaces. Our DInSAR analysis shows that the two major events of the Umbria-Marche 1997 seismic sequence ruptured the whole elastic seismogenic upper crust. These achievements are made possible by the use of large numbers of DInSAR points, so that to improve, with respect to previous studies based on a smaller number of DInSAR fringe points, the details of slip over the two major faults at higher spatial resolution. We can thus relax constraints on fault dimensions derived from purely seismological analyses and not completely consistent with DInSAR ones.
 This work is supported by the project SISMA (Seismic Information System for Monitoring and Alert) of the Italian Space Agency and by the P.R.I.N. 2006 project of M.I.U.R.: “Dynamics of the northern Apennine, Po plain and Alpine system”. We thank Bruno Hernandez and an anonymous reviewer for important suggestions.