TRANSITION CRUSTAL ZONE VS MANTLE RELAXATION: POSTSEISMIC DEFORMATIONS FOR SHALLOW NORMAL FAULTING EARTHQUAKES

IC/99/80 United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM 1NTKRNATIONAL CENTRE FOR THEORETICAL PHYSICS TRANSITION CRUSTAL ZONE VS MANTLE RELAXATION: POSTSEISMIC DEFORMATIONS FOR SHALLOW NORMAL FAULTING EARTHQUAKES R. Riva 1 Dipartimento di Scienze della Terra, Sezione Geofisica, Universita di Milano, via L. Cicognara 7, 1-20129 Milano, Italy, A. Aoudia 2 Dipartimento di Scienze delta Terra, Universita di Trieste, via E. Weiss 1, 1-3^127, Trieste, Italy and The Abdus Salam International Centre for Theoretical Physics, SAND Group. Trieste, Italy, L.L.A. Vermeersen 3 DEOS, Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, NL-2629 HS Delft, The Netherlands, R. Sabadini 4 Dipartimento di Scienze della Term, Sezione Geofisica, Universita di Milano, via L. Cicognara 7, 1-20129 Milano, Italy and G.F. Panza 5 Dipartimento di Scienze della Terra, Universita di Trieste, via /;'. Weiss 1, 1-34127, Trieste, Italy and The Abdus Salam International Centre for Theoretical Physics, SAND Group, Trieste, Italy. MIRAMARE - TRIESTE July 1999 'E-mail: nccardo@sabadini.geofisica.unimi.it 2 E-mail: aoudia@geokuno.univ.lrieste.it 3 E-mail: b.vermeerseu@lr.tudclft.nl 4 E-mail: bob@sabadini.geofisica.un.imi.it 6 E-mail: panza gcosuno.univ.trieste.it

Abstract. Following a normal mode approach for a stratified viscoelastic Earth, we investigate the efrects induced by shallow normal faulting earthquakes on surface postseismic deformation rates, when stress relaxation occurs in the transition zone of the crust or in the asthenosphere. We focus on the Central Apennines (Italy), where the 1997 Umbria-Marche earthquake sequence took place. The layered viscoelastic structure of the crust and mantle imposes a pattern and scale on the observed coseismic and postseismic deformations with a major contribution from the transition crustal zone. Vertical rates of deformation, for viscosity values ranging between 10 18 and 10 19 Pa s in the crustal transition zone, vary between 0.7 to a few millimeters per year, lasting for several years after the earthquake.

Introduction The calculation of postseismic deformation requires the assumption of a layered viscoelastic Earth model. Nearly all viscoelastic relaxation studies [e.g. Ma and Kuznir, 1995; Pollitz et ai, 1998] assume a three-layer model schematizing the brittle upper crust (UC), the lower crust (LC) and the mantle. Seismological and geological observations from regions of active faulting suggest that the seismogenic UC is likely to be separated from the LC by a transition zone (TZ) where both brittle and ductile processes can occur [e.g. Sibson, 1982; Meissner and Strehlau, 1982; Chen and Molnar, 1983; Sibson. 1989; Scholz, 1990]. These observations are more frequent in regions of active continental extension [Jackson and White, 1989] and suggest that the thickness of such crustal layering imposes a pattern and a scale on the observed coseismic and postseismic deformation. We investigate the effects of the stress relaxation in the TZ of the crust and its interplay with the mantle on the surface vertical deformation that follows shallow normal faulting earthquakes. The modeling approach we use, based on normal mode theory, is the fully analytical one described by Vermeersen and Sabadini [1997] and Sabadini and Vermeersen [1997], and it allows us to deal with some of the complexities of the real Earth, such as crust and mantle viscoelastic layering, sphericity and self-gravitation. However, other possible aspects like lateral variations, non-linear rheologies and non-hydrostatic pre-stresses that might occur in the region are not considered. Since a large amount of data may be brought to bear on this issue, we focus on the part of Central Italy, undergoing continental extension, that experienced the recent moderate Umbria-Marche 1997 normal faulting earthquake sequence [e.g. Amato et ai, 1998; Ekstrom et al, 1998; Meghraoui et ai., 1999; Hunstad et at, 1999]. The recent CROP03 seismic reflection profile [Pialli et al., 1998], aimed to the study of the deep crust in the Northern Apennines, imaged the top of the LC using regional high-amplitude reflectors, e.g. K-Horizon: thermal and phase boundary at 450 C [Cameli ei al. 7 1998].

Below the Umbria-Marche extensional belt, the top of the LC is about 20 km deep, with a Moho around 30 km [Coli, 1998], Cattaneo et al. [1999] show an abrupt cutoff of the 1997 aftershock sequence at about 9 km of depth. Thus the seismic activity is largely restricted to the upper one third of the deforming continental crust and leaves room for a 10 km thick TZ (Fig. 1). We assume that the TZ acts as a low-viscosity layer which decouples the UC from the LC. Accordingly, in our modeling we use a five layer Earth model (Fig. 1). This 5-layer model assures that saturated continuum limits are obtained for the deformation [Sabadini and Vermeersen, 1997], The relevant stratification is consistent with the range of regional velocity models estimated through the analysis of surface-wave dispersion [Calcagnile and Panza, 1981; Du et al., 1998] and regional gravity and heat flow anomalies [Delia Vedova et a/., 1991; Marson et al, 1995]. Modeling and Results We consider the strongest earthquake of the Umbria-Marche sequence that took place on the 26.09.1997 at 9:40 (Ms = 6.0). We use the moment solution of Sarao et al. [1998] retrieved by broad-band waveform inversion, in good agreement with the CMT [Ekstrom et al, 1998], Since in this first approach to the problem we are not interested in the details of the deformation pattern, we do not consider all the complexities of the earthquake. We focus on the global characteristics of crustal deformation and on a first order estimate of the expected vertical velocities. To illustrate the sensitivity of the results on the depth of the source, we neglect the flniteness of the source in the vertical direction, and besides the source depth of 7 km [Sarao et al, 1998] we consider another case where the source is embedded at a depth of 3 km, to simulate the effects of a fault nearly reaching the surface. We thus distribute the seismic moment not over a plane but along a line of dislocations, whose length along strike is 10 km; in order to resolve the deformation produced by this fault, we summed 4500 normal modes, which ensures convergence of the solution. We limit our description to the vertical deformation, most

relevant to normal faults, evaluated at the surface along a line perpendicular to the strike of the fault, crossing its center. In the whole set of panels, the fault is dipping to the left, and the distance is measured from the intersection of the upward prolongation of the fault with the Earth surface. In Fig. 2, the depth is fixed at 7 km. Fig. 2a portrays the coseistnic and postseismic vertical deformation, measured at the surface. The cosetsmic component (solid line) shows the deformation pattern characteristic of normal faulting, with an uplifted, localized footwall and a broad subsidence in the hanging wall. The postseismic component (dashed line), that includes the coseismic one plus the extra deformation resulting from the relaxation in the TZ, is responsible for a broadening of the subsidence, that affects now also the footwall. The largest coseismic displacement is 8 cm at 10 km from the fault. Due to the relaxation in the TZ, the maximum displacement increases to 13 cm, and a broad area, that remained at rest during the coseismic deformation, is now subject to subsidence, at distances of tens of kilometers. This effect is due to the decoupling of the uppermost part of the crust with respect to the lower layers. After stress relaxation in the TZ, all the deformation is elastically supported by the UC, which is now partially free to bend being decoupled from the LC. The occurrence of normal faulting and the extension at the bottom of the UC, below the neutral plane, is responsible for the downflexure of this layer, visible in the broad subsidence of Fig. 2a. Fig. 2b provides another perspective to this physics, with the rates of vertical deformation, expected at different times after the earthquake. The wide region of negative velocity marks the broad downflexure of the UC. The two regions of positive velocity represent the peripheral response of the layer to the subsidence, and disappear a very long time after the earthquake, eventually reversing to negative values. Another interesting characteristic of Fig. 2b is the short wavelength feature at the center of the subsiding area, that follows the pattern of the coseismic displacement. We can recognize the relative maximum corresponding to the footwall, and the largest subsidence of the hanging wall, within a generalized subsidence. The

highest velocity is -0.7 mm/yr, in the hanging wall, immediately after the earthquake, at t = 0. Due to the relatively high viscosity of the TZ (10 19 Pa s) this velocity shows a minor reduction after 10 yr, and after 50 yr there is still a visible signal of 0.1 mm/yr. With a single viscoelastic layer, the rate of the vertical deformation scales inversely with the viscosity; if, for the TZ, we consider a viscosity of 10 18 Pa s, the highest velocity increases by one order of magnitude to -7 mm/yr. Since the viscosity of the TZ is largely uncertain, probably ranging between 10 18 and 10 19 Pa s, it is likely that the largest subsidence rates in the highly deforming area of the hanging wall vary in the range that we have estimated. Comparison between the ongoing GPS campaigns and model predictions will be crucial to estimate the effective viscosity of the TZ. In Fig. 2c we describe the effects of the inclusion of the stress relaxation in the mantle, where the viscosity is lowered to 10 19 Pa s, with the same sampling time of Fig. 2b. Both features of normal faulting being maintained, the striking differences with respect to Fig. 2b are: (1) the disappearance of the global subsidence responsible for the high negative velocity, (2) the persistence of the 0.4 rnm/yr difference between the footwall and the fast subsiding part of the hanging wall. The reason for the disappearance of the downflexure of the UC stands on the reduced effectiveness of the TZ, a large amount of deformation being absorbed by the relaxation in the mantle. The bending of the UC is thus substantially reduced with respect to Fig. 2b. Fig. 2d deals with stress relaxation limited to the mantle, with sampling times increased with respect to the previous cases. The characteristic deformation pattern due to normal faulting is broadened, since stress relaxation involves a larger portion of the Earth. The global subsidence disappears because the whole crust is now coupled. The amplitude of the deformation rates in the earthquake area is substantially reduced, since the whole planet is now involved in the deformation, as indicated by the slow decay with increasing distance from the epicentral area and longer relaxation times with respect to Figs.2b and c. Figs. 2b and d show that for shallow normal faulting, the TZ plays a major role in comparison with the

stress relaxation in the mantle. In Fig. 3 the source is embedded at a depth of 3 km, in the top half part of the UC. In comparison with Fig. 2, the pattern of both coseismic and postseismic displacement in Fig. 3a becomes sharper, and the largest coseismic subsidence in the hanging wait is increased by a factor of two. The uplift in the footwall, with respect to Fig. 2, is subject to a larger increase by a factor of three. This increase in the amplitude of the displacement and sharpening of its pattern is attributable to the decrease of the wavelength, caused by the shallower source depth in comparison with Fig. 2. The most interesting difference with respect to Fig. 2 stands on the upward migration of the postseismic displacement pattern with respect to the coseismic one. An extensional source located above the neutral plane of the UC causes a bending moment opposite to the one induced by the deeper source of Fig. 2, and the Earth surface is thus subject to a general uplift, rather than subsidence. From Fig. 2a and 3a we thus obtain that, due to the location of the source beneath or above the neutral plane, the postseismic curves lie completely above or below the coseismic one. The findings differ from those by Ma and Kuznir [1995] where, due to the finiteness of the source in the vertical direction, the fault cuts the whole UC through its neutral plane, which causes the crossing of the curves depicting the postseismic and coseismic vertical displacement. The difference between the highest uplift in the footwall and subsidence in the hanging wall is doubled with respect to Fig. 2. This doubling impacts also the difference in the rates of vertical displacement between these two regions in Fig. 3b, now 0.6 mm/yr in comparison with the 0.4 mm/yr of Fig. 2b. The global subsidence, caused by the deep source, disappears in the velocity pattern of Fig. 3b, in agreement with the previous observations on the flexural properties of the UC. This tendency of a general upwarping is visible also in Fig. 3c, where relaxation involves both the TZ and the mantle. In comparison with Fig. 2c, we notice also here the increase in the difference in the velocity between the footwall and the hanging wall, with an increase in the uplift rates to 0.4 mm/yr, in comparison to the 0.1 mm/yr, t =0 yr, of Fig. 2c. If

relaxation is limited to the mantle (Fig. 3d) the same observations made about Fig. 2d can be done, except that now the uplift of the footwall is enhanced with respect to the subsidence in the hanging wall. The rates of the vertical deformation cannot be compared with observations yet, surveying being under way. Our results can thus be compared only with the observed coseismic displacement, but with caution, since for our purposes we are not interested in modeling the details of the source [Hunstad et al, 1999] but rather in the physics of the expected process of postseismic deformation. If we consider the results for the shallow source, we obtain a coseismic displacement, from the footwall to the hanging wall of 20 cm, comparable with the one observed from SAR interferometry [Stramondo et al., 1999], Our results, reproducing the coseismic signal, provide a first estimate of the expected rates of vertical postseismic deformation in the Umbria-Marche epicentral area. Conclusions For shallow normal faulting earthquakes the stress relaxation in the TZ plays a major role in the pattern of the postseismic deformation, in comparison with the relaxation in the mantle. This is due to the proximity of the source to the rheological discontinuity between the elastic UC and soft TZ, which decouples the UC in such a way that its bending properties become crucial to determine the deformation pattern. An appropriate test area for studying the effects of the TZ is the central Apennines, Italy, where a clear cutoff in the depth distribution of earthquakes indicates that the seismogenic layer is limited to the first ten kilometers of the crust, and a well-developed TZ lies below this depth. Depending on the effective viscosity of this layer, postseismic vertical velocities ranging between 0.7 to a few millimeters per year are expected for several years after the earthquake, for viscosities ranging between 10 18 and 10 19 Pa s. Acknowledgments. This work is supported by the Active deformation project - AC-DEF - (Italian Ministry of Research).

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FIGURE CAPTIONS Figure 1. Earth model and viscosity parameters used in this study. Figure 2. Coseismic and postseismic vertical surface displacements and rates calculated for a 7 km deep normal faulting line-source. The profiles are across the center of the fault (x = 0 km) and perpendicular to its strike. The fault is dipping to the left and is buried in the upper layer of Fig. 1. (a) Coseismic (solid line) and postseismic (dashed line) displacements, (b) Postseismic rates due to relaxation in the TZ expected at different times after the earthquake, with t = 0, 10, 20, 50 yr, solid, dashed, dash-dotted and dotted respectively, (c) same as in (b) including the effects of relaxation in the mantle, (d) Postseismic rates due to relaxation in the mantle expected at t= 0, 100, 500, 1000 yr, solid, dashed, dash-dotted and dotted respectively after the earthquake. Figure 3. Coseismic and postseismic vertical surface displacements and rates calculated for a 3 km deep normal faulting line-source. Terminology as in Fig. 2 11

^^_ ^ ^^ Surface Elastic upper crust (UC) Transition zone: v = 10 (TZ) Pa s 10 km. 10 1 ' Pas 20 km 2 1 Lower crust (LC): v = 10 Pa s Asthenosphere: v= 10 Pa s Inviscid core I 10 1 ' Pas 30 km 2891 km 6371 km Fig-1 12

Rate of vertical displacement (mm/yr) Vertical displacement (mm) oo

Rate of vertical displacement (mm/yr) Vertical displacement (mm) o b