Control of pore fluid pressure diffusion on fault failure mode: Insights from the 2009 L Aquila seismic sequence

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2011jb008911, 2012 Control of pore fluid pressure diffusion on fault failure mode: Insights from the 2009 L Aquila seismic sequence Luca Malagnini, 1 Francesco Pio Lucente, 2 Pasquale De Gori, 2 Aybige Akinci, 1 and Irene Munafo 1 Received 5 October 2011; revised 12 March 2012; accepted 14 March 2012; published 9 May [1] The M W 6.13 L Aquila earthquake ruptured the Paganica fault on 2009/04/06 at 01:32 UTC, and started a strong sequence of aftershocks. For the first four days, the region north of the hypocenter of the main quake was shaken by three large events (M W 5.0) that ruptured different patches of the Monti della Laga fault (hereafter Campotosto ). In our hypothesis, these aftershocks were induced by a dramatic reduction in the fault s shear strength due to a pulse of pore fluid pressure released after the L Aquila main earthquake. Here we model the time evolution of the pore fluid pressure northward from the main hypocenter. We show that, during the sequence, the Campotosto fault failed in multiple episodes, when the specific patches/asperities underwent fluid pressure-related strength reductions of 7 10 MPa. Although such drops in strength are very large in amplitude, the contribution of other weakening mechanisms (perturbations of the Coulomb shear stress, and/or dynamic stresses induced by passing seismic waves) cannot be ruled out by our observations. However, the Coulomb shear stress variations either had negative amplitudes down to 0.2 MPa (i.e., tended to inhibit further seismic activity), or had very small positive amplitudes (<0.05 MPa). Paleoseismological evidence supports the hypothesis that larger events (M W 6.5 7) have occurred on the Paganica fault [EMERGEO Working Group, 2009], whereas Lucente et al. [2010] concluded that an important migration of pore fluids characterized the preparatory phase of the L Aquila main shock. Consequently, the M W 6.13 L Aquila earthquake may be analogous, at a larger scale, to one of the three Campotosto largest aftershocks. The complex behavior observed for the L Aquila-Campotosto fault system seems to be common to other seismogenic structures in the Central Apennines (e.g., the Umbria-Marche fault system), and need to be taken into consideration for the assessment of seismic hazard. Citation: Malagnini, L., F. P. Lucente, P. De Gori, A. Akinci, and I. Munafo (2012), Control of pore fluid pressure diffusion on fault failure mode: Insights from the 2009 L Aquila seismic sequence, J. Geophys. Res., 117,, doi: /2011jb Introduction [2] On April 6, 2009, an M W 6.13 earthquake struck Central Italy [Herrmann et al., 2011], nucleating right underneath the town of L Aquila. Although the earthquake was of a moderate size, it caused extensive damage. This region of the Central Apennines is characterized by one of the highest values of seismic hazard in Italy [Akinci et al., 2009; 2010], and experienced three significant earthquakes in 1349, 1461, and 1703 (XI-X MCS) [Working Group CPTI, 2004]. 1 Sezione di Roma, Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy. 2 Centro Nazionale Terremoti, Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy. Corresponding author: L. Malagnini, Sezione di Roma, Istituto Nazionale di Geofisica e Vulcanologia, I Rome, Italy. (malagnini@ingv.it) Copyright 2012 by the American Geophysical Union /12/2011JB [3] The earthquake ruptured a NW-trending, SW-dipping normal fault (the Paganica fault) [Boncio et al., 2004], about 20 km-long along-strike [Chiarabba et al., 2009] (Figure 1). The main shock was preceded by a 6 months-long foreshock sequence [Lucente et al., 2010], whose analysis suggested the existence of over-pressurized pore fluid around the fault before failure, leading various authors to hypothesize a strong role of fluids in the earthquake nucleation [Lucente, et al., 2010; Terakawa, et al., 2010; Di Luccio, et al., 2010]. [4] The main shock started a vigorous aftershock sequence that, within the first twenty-four hours, began spreading over a secondary structure north of L Aquila, the Monti della Laga fault (hereafter, the Campotosto fault) [Basili et al., 2008; Galadini and Galli, 2003], where four events with M W 5 nucleated within a short time window following the main earthquake. The Campotosto and the Paganica faults share similar geometry and kinematics, delineating an en-echelon system about 40 km-long (Figure 1). 1of15

2 Figure 1. Map of the L Aquila seismic sequence, up to 31/12/2009. Aftershocks are sized and colorcoded by magnitude according to the scale on bottom. The red beach ball indicates the main shock, and it is located at its hypocenter. The two boxes (dashed) approximately outline the Paganica and the Campotosto faults. The same boxes are projected on the cross-sections to the right, where topographic profiles are also indicated. Largest aftershocks (ML 5) in all plots are indicated with their focal solutions (green beach balls). All solutions are taken from Herrmann et al. [2011]. [5] In a scenario where the rock volume around the main rupture contains over-pressured compartments, the diffusion of fluids released during the main shock could have modulated the subsequent failure process on the adjacent Campotosto fault. Our working hypothesis is twofold: i) the Paganica fault, when ruptured by the main shock, suddenly became a preferential diffusion direction for the pressurized fluids released during the fault-valve action of the earthquake; ii) the Campotosto fault was hydraulically connected to the main rupture, and represented some sort of a pipeline through which the fluid flow took place as a diffusion front that rapidly marched toward N-NW from the northernmost edge of the Paganica fault. reduced by the counteracting effect of the fluid pressure [Terzaghi, 1923]: s n ¼ sn ap; ð1þ thus reducing the fault strength, t = ms (sn ap), where sn is the effective stress, P is the pore fluid pressure, and a is the Biot-Willis coefficient (see, for example, Wang and Manga [2010]). For simplicity, hereafter we will use a = 1.0. [7] In order to compute the normal and the shear stresses (sn and t, respectively) on a specific fault plane, in a specific tectonic environment, and in the general case of non-optimally oriented faults (at an angle q with the direction of maximum compression, s1) we need to solve the following system: 2. Pore Fluid Pressure and Fault Strength [6] It is well known that pulses of pore fluid pressure may trigger seismic failure by reducing a fault s shear strength. The mechanism is that the effective fault-normal stress is 2 of 15 8 t ¼ m s ðs n P Þ < s1 s3 sinð2 qþ t¼ 2 : sn ¼ s1 þ s3 s1 s3 cosð2 qþ 2 2 ð2þ

3 the gradient transition depth z GT and the pore fluid pressure coefficient l f ¼ P r r gz for an arbitrary depth of 10 km, and an arbitrary rock density r r = kg/m 3 (gabbro). Using a worldwide collection of data, Hunt [1990] observed that 3 km is the clustering depth for changes in the pore fluid pressure gradient. [11] Following Malagnini et al. [2010], the normal and the shear stresses at failure, relative to a normal fault above and below the gradient transition depth, may be written as: 8 < s z z GT : n ¼ gzr ð r r w ÞsinðÞ q m cosðþþsin q ðþ q : t ¼ m s s n 8 < s z z GT : n ¼ gz GT ðr r r w ÞsinðÞ q m s cosðþþsin q ðþ q : ð5þ : t ¼ m s s n Figure 2. Ratio of pore fluid pressure to lithostatic load l f ¼ P f rgz as a function of the gradient transition depth, Z GT [Suppe, 2010]. The value l f = 0.8 corresponds to Z GT = 3000 m, if r = 2990 kg/m 3 (gabbro), a depth where the upper seals of overpressure compartments seem to cluster worldwide [Hunt, 1990]. s 3 is the minimum compressional stress. In the hypothesis of Andersonian faulting [Anderson, 1905], one of the principal stresses is vertical. [8] Byerlee [1978] showed that the coefficient of static friction (m s ) is independent of the sliding materials. Also, for an effective normal stress s n 200 MPa (a threshold much higher than the effective normal stress in hydrostatic conditions estimated at 7 km depth for a normal fault oriented at an angle q =30 from the maximum compressional stress s 1 ), he found that m s = He observed m s = 0.6 beyond the 200 MPa effective normal stress threshold. Finally, since the pressure increase is kept constant, lesser values of the friction coefficient result in lesser values of pressure-induced fault weakening, the latter being defined as: Dt ¼ m s ½ðs n P FINAL Þ ðs n P INITIAL ÞŠ ¼ m s DP ; ð3þ DP ¼ P INITIAL P FINAL where P FINAL P INITIAL = P HYDROSTATIC, and DP <0. [9] For our calculations, we use an intermediate value of the static coefficient of friction, m s = [10] Pore fluid pressure at depth may be quantified by using the simple model of the pore fluid pressure gradient transition depth, z GT [Suppe and Yue, 2008], according to the following profile: P ¼ r wgz z z GT ð4þ r w gz GT þ r r gz ð z GT Þ z z GT where r w and r r are the densities of water and rock, respectively. Figure 2 shows the correspondence between The shear stress t in equations (2) and (5) represents the strength of the specific normal fault under consideration. From equation (2) it is clear that the strength of any fault is maximum at the lowest possible pore fluid pressure. In nature, dry conditions at depth are unrealistic, and the largest possible strength must be reached closely to the hydrostatic case. We hereby postulate that the volume in which the aftershocks take place was originally in hydrostatic conditions and that, now following Lucente et al. [2010], an overpressurized crustal compartment was located right below the nucleation depth. [12] For the case of the L Aquila main shock, a substantial overpressure was hypothesized around the Paganica fault [Lucente, et al., 2010; Terakawa, et al., 2010; Di Luccio, et al.; 2010]. In particular, Di Luccio, et al. [2010] proposed a pore fluid pressure coefficient 0.6 l f 0.8 for the pressurized volume that was affected by the main shock. The existence of overpressure at depth in the Central Apennines has been documented in the deep boreholes of San Donato and Santo Stefano, where over-pressured CO 2 at 85% of the litho-static load was found, respectively, at depths of 4.8 km and 3.7 km [Chiaraluce et al., 2007], within the Triassic evaporates at depth [Collettini et al.,2008]. Finally, overpressure-induced effects have been inferred for the Umbria-Marche seismic sequence of 1997 [Miller et al., 2004]. In the present study, following Chiaraluce et al. [2007], we adopted the pore fluid pressure coefficient, l f = Pore Fluid Flow, Migration of Earthquakes, and Aftershock Decay Rate [13] In order to quantify the effects of a pore fluid pressure perturbation on the aftershock sequence, we build upon the work by Nur and Booker [1972] who solved the problem of aftershock rates due to the pore fluid fluxes induced by a large dislocation occurring in a porous medium. They postulated that, in the hypothesis that all aftershocks are induced by decreasing fracture strength due to increase in pore fluid pressure: dn dt ¼ 1 W Z V P t dv; ð6þ 3of15

4 where dn dt is the aftershock decay rate; P t is the temporal derivative of pore fluid pressure, and W is a normalization constant with the physical dimensions of pressure times volume. [14] Using equation (6), Nur and Booker showed that the fluid flow induced by a large shallow event (no external pressure source) can produce a rapid transient signal on the aftershock decay rate computed in some volume V near the main shock. Such a transient pressure pulse induces secondary events (aftershocks), whose rate must be characteristic of a diffusion process. That is, dn dt p 1 ffi t, where N(t) is the cumulative number of aftershocks that occurred in the volume V. [15] If an external source of pressure does not supply a pressurized fluid flow, the transient signal is rapidly obliterated infavor of a regular Omori-like decay rate [Utsu, dn 1961], dt 1 ðc þ tþ ; p 1. p [16] In the case of the 1966 Parkfield-Cholame earthquake, the diffusion effect induced by the mere redistribution of pore fluids between compressional and extensional quadrants lasted slightly less than 24 h [see Nur and Booker, 1972, Figure 2]. The L Aquila earthquake of April 6, 2009 has a comparable moment magnitude (M W = 6.13) [see Herrmann et al., 2011] to the 1966 Parkfield event (M W = 6.0), thus a comparable time scale may be expected for the dislocation-induced fluid migration. [17] Different cases are the ones characterized by fault-valve behavior [e.g., Sibson, 2009], in which the fluid flow induced by the dislocation-induced compressions and dilatations becomes negligible when compared to the fluid flow due to an earthquake-activated, external pressure source. Faultvalve behaviors seem to be typical for Central Apennines, as demonstrated for the Umbria-Marche sequence of 1997 [Miller et al., 2004;Lombardi et al., 2010], as well as for the L Aquila foreshock-main shock-aftershock sequence [Lucente et al., 2010]. Following Lucente et al. [2010], the most important portion of the L Aquila seismic sequence started with a foreshock of M W 4 that occurred on March 30, 2009, which is likely to have injected pressurized fluids in the main fault plane, consequently reducing its strength. A fluid-driven cascade of failures culminated with the M W 6.13 main shock of April 6, 2009; in Sibson s [2009] terms, the L Aquila main shock was preceded, at least in the final stage of its precursory sequence, by hydrofracture dilatancy Short-Term Magnitude Completeness of the L Aquila Aftershocks Catalog [18] Before starting the analysis of the L Aquila aftershock sequence, we need to assess the level of consistency of our data set. In particular, a critical issue to be addressed is the magnitude completeness of the aftershock catalog in the first hours after the main shock. This issue arises from the under-reporting of short-term aftershocks, especially smaller ones in earthquake catalogs [Kagan and Houston, 2005; Enescu et al., 2007]. Therefore, we compute the frequencymagnitude distribution of the aftershocks for subsequent time intervals after the main shock, modeling the aftershock occurrence through the standard relation of Gutenberg and Richter [1944]. [19] We determine the magnitude of completeness (Mc) as the magnitude at which 90% of the data can be modeled by a power law fit [Wiemer and Wyss, 2000]. The b value in each case is obtained using a maximum likelihood procedure [Aki, 1965], considering only the earthquakes with magnitudes M Mc. As shown in Figure 3, six hours after the main shock the completeness threshold of our aftershock catalog is Mc = 2.1. We take this value as the cut-off threshold for the computation of the aftershock rates in the analysis described in the following paragraphs. It is clear that, in the first six hours after the main shock, many aftershocks of magnitude well above the completeness magnitude Mc = 2.1 were lost Spatiotemporal Distributions of the L Aquila Aftershocks [20] The spatiotemporal distribution of the aftershocks of the L Aquila main earthquake was analyzed by mapping all the events with M Mc = 2.1 that occurred on the Paganica-Campotosto fault system. The activated region was arbitrarily divided into two subsections, marked NW and SE in Figure 4: northwest and southeast, respectively, of a line oriented S45W-N45E passing through the location of the main hypocenter. [21] We observe that, in the first few days after the main shock, the spread of the along-strike seismicity takes place with different patterns in the sectors labeled NW and SE : time-distance plots of the events in Figure 4 clearly demonstrate the existence of a migration process in the N-NW direction from the main hypocenter, and the activation of the Campotosto fault seems to be modulated by a diffusion process. A noteworthy feature of the sequence is that, between 1 and 4 days after the main earthquake, three M w 5.0 events struck along the Campotosto fault (stars in Figure 4), where the Coulomb stress was practically unaffected by the occurrence of the main shock (see section 4.2 of this paper). SE from the main hypocenter, on the contrary, no ruptures on adjacent structures were triggered, and the entire volume around the Paganica fault was activated almost instantaneously at the occurrence of the main shock Evaluating Aftershock Decay Rates [22] In order to investigate the effects of pore fluid pressure on the aftershock activity rates we plot the number of aftershocks/day as a function of the time for the NW and SE sectors of Figure 4 (Figures 5a and 5b). Uncertainties on the rates were calculated by bootstrapping the data sets with 100 realizations, and indicated with vertical bars at each data point in Figure 5c. [23] In the NW sector, the two-line fit shown in Figure 5a is statistically more significant than a single-slope Omorilike behavior (not shown). The first part of the NW-sector fit dn (Figure 5) was forced to be diffusion-like dt t 1 = 2,as required by equation (11), whereas the slope of its second part was free to vary. In contrast, in the SE sector (Figure 5b), a single-slope Omori-like behavior characterized the sequence since its beginning. Both plots, for the NW and SE sectors, were made after a thorough completeness analysis of the seismic catalog, which indicated a completeness magnitude Ml 2.1 for the second bin. The catalog is complete to a lower 4of15

5 Figure 3. Frequency-magnitude distribution of aftershocks for different time windows elapsed from the L Aquila main event (entire sequence): (a) first 6 h; (b) 6 18 h; (c) h; (d) h. The cumulative and non-cumulative numbers of earthquakes are shown by solid and open circles, respectively. The solid lines represent maximum likelihood fits to the data, for magnitudes above the magnitude of completeness, Mc (the magnitude at which 90% of the data can be modeled by a power law [Wiemer and Wyss, 2000]). Mc, and for the two parameters, a and b, are indicated in each time window. The same analysis was also performed separately on the NW - and SE -labeled subsets indicated in Figure 4, yielding the same results. magnitude level for the bins to the right, but it must be clear that only events with Ml 2.1 are included in the analyzed data set. The first point represents the first bin (the first 6 h after the main shock, for which a higher completeness magnitude was found), which was not included in the regressions. [24] In the entire NW sector (see Figure 5a), the first 4 5 days after the main shock were characterized by a dif- fusive behavior. After 2009/04/10, the after- dn dt t 1 = 2 shock rate shows a steeper decay, indicating the onset of a regular, Omori-like behavior. In the SE sector (Figure 5b), no diffusion-like aftershock rate characterizes the sequence, and the aftershock decay rate was Omori-like. We calculated the misfit function for the two-line fit (Figure 5a): Figure 5c indicates the transition time that yields the minimum misfit Evaluating Coulomb Stress Perturbations on the Campotosto Fault [25] After the L Aquila main shock, two other mechanisms could have triggered earthquakes on the Campotosto fault: perturbations of the static Coulomb stress [e.g., Stein, 1999; Toda et al., 2005], and dynamic fluctuation of the shear stress across the fault plane induced by elastic waves radiated by the main shock [e.g., Hill et al., 1993; Brodsky and Prejean, 2005; Gomberg and Felzer, 2008]. A specific analysis (Figure 6) shows that it is either that the maximum Coulomb stress variation is very small on the Campotosto fault, or the different fault patches are in the stress shadow of previous events, including the main one. [26] Positive variations, corresponding to stress conditions more favorable to failure, have amplitudes <0.05 MPa, whereas negative variations (zones of stress shadow) in the order of 0.2 MPa affect the Campotosto fault patches in most cases. Dynamic excitation, not computed here, was obviously not enough to trigger the Campotosto fault failure immediately after the L Aquila earthquake occurrence. Nevertheless, dynamic excitation may be responsible of delayed earthquake triggering [Velasco et al., 2008], and cannot be ruled out. [27] Clearly, since both the cited mechanisms are thought to induce seismic events even days after the passage of stress waves, we have no evidence that can rule them out from the evolution of the Campotosto seismic sequence. Nevertheless, the magnitude of the weakening action due to pore fluid pressure increase, as computed in the following subsections, suggests such an effect to be the dominant one. We are aware that other physical mechanisms may be invoked to describe diffusion-like migration of earthquakes (e.g., stress corrosion) [Das and Scholz, 1981; Freund, 1990], but our interpretation of the observed patterns in the seismicity, in terms of migration of pressurized pore fluids, may be equally valid Modeling Pore Fluid Diffusion and Aftershocks Occurrence [28] As a first step in the modeling of the aftershock migration, in the hypothesis described by equation (6), we need to define the geometry of the problem to correctly estimate the diffusion coefficient D from the expansion of the aftershock area [Talwani and Acree, 1984], which in our 5of15

6 Figure 4. (left) Map of the events occurring close to the Paganica and Campotosto faults (whole catalog, see Figure 1). Red star indicates the main shock hypocenter. The line going through the red star, oriented S45W-N45E divides the area in two subregions marked NW (blue and green hypocentral locations, and four yellow stars including the three aftershocks that occurred on the Campotosto fault with M w 5), and SE (purple hypocenters and one yellow star, corresponding to the deeper event of April , M w 5). (right) Time-distance plots of the events in the map. Data points are projected to the distance axes at the same scale used in the seismicity map. Only earthquakes with magnitude equal or above the cut-off threshold of 2.1 are plotted. All data points in the slanted upper frame to the right are plotted in gray because we are interested in the overall behavior of the NW-labeled region. case occurs only toward northwest. Another method for the computation of the hydraulic diffusivity using only the observed seismicity rate and the estimate of the activated seismogenic volume is that by Parotidis and Shapiro [2004]. Beyond a spherical geometry, which is obviously too simple for our case, the simplest approximation that can be used to represent our problem is 1-D, along a northerly direction where the migration of earthquakes is the fastest. In such a geometrical setting, the origin (x = 0 in Figure 4, and in the equations that will follow) must be taken at the northernmost edge of the Paganica fault, to the portions of the Campotosto fault ruptured by the largest aftershocks (M w 5, Figure 4). [29] As for the boundary and initial condition, our hypothesis is that the fluid flow starts right after the occurrence of the main shock, from a source that we suppose to be steady-state, at least for the first few days after the main event. Moreover, in agreement with Chiaraluce et al. [2007], we use l f = 0.8. Finally, computations are performed at the depth of nucleation of the three largest aftershocks of the Campotosto fault, whose centroid depths were well-constrained at around 7 km by Herrmann et al. [2011]. 6of15

7 Figure 5. (a) Number of aftershocks/day as a function of the time elapsed from the main shock, in the NW-labeled portion of the seismic sequence (see maps in Figures 1 and 4). (b) Number of aftershocks/ day as a function of time elapsed from the main shock, for the SE-labeled portion of the seismic sequence. The dashed lines connect points for which the completeness magnitude is larger than M L 2.1 (the value used in the calculations, relative to the second point from the left in Figures 5a and 5b). The slope of the shallow line in the upper-left frame (t 0.5 ) is the characteristic decay rate (equation (7)) of a diffusion-like phenomenon, whereas steeper slopes agree with a regular Omori-like decay rate. For the NW data set, he two-slope model is statistically better (with a likelihood of 99%) than a single-slope Omori-like behavior, whereas a single line t describes the southeastern data set. (c) misfit functions for the two-line fit relative to the northwestern data set (Figure 5a). The vertical dashed lines indicate, for each side of the figure, the time of the minimum misfit. [30] The presented results are obtained by using a simplified pressure field with only two possible gradients: hydrostatic and lithostatic, because rock pores are either interconnected up to the free surface, or they belong to isolated volumes. The first situation produces a hydrostatic pressure field, whereas overburden increments would increase the pore fluid pressure of isolated volumes at a lithostatic rate. Over-pressured compartments in the area of active extension of the Central Apennines [Collettini et al., 2008] are probably due to upwelling CO 2 of mantle origin [Chiodini et al., 1999, 2000, 2004], which gets trapped by impermeable formations (sealing caps) like the layers of Triassic evaporites found at the deep boreholes of San Donato and Santo Stefano Steady-State Source of Pressure [31] Given the relatively simple geometry of the earthquakes diffusion toward N-NW (Figure 4), we further simplified the problem and formulated it in 1-D: a steady state source of pressure applied at x = 0 (the red star in Figure 4), and the pressure field at depth moves along the direction indicated by the arrow in Figure 2. Initial and boundary conditions are the following: Px¼ ð 0; t 0Þ ¼ P 0 ¼ l f r r gz ð7þ Px ð 0; t ¼ 0Þ ¼ P 1 ¼ r w gz (z is source depth) [e.g., Turcotte and Schubert, 1982]. [32] The 1-D diffusion problem has the solution: x Px; ð tþ ¼ ðp 0 P 1 Þerfc p 2 ffiffiffiffiffi þ P 1 ; Dt in which erfc(y) =1 erf(y) is the complementary error function, erf(y) is the error function, and D is a diffusion coefficient that may be estimated in Figure 7 (top left), using: p x P ¼ 2:32 ffiffiffiffiffi Dt ; ð9þ ð8þ 7of15

8 Figure 6. Coulomb stress perturbations due to the occurrence of the L Aquila main event (indicated as MS, and by the large rectangular fault plane [Atzori et al., 2009]). White and red boxes indicate, respectively, the faults responsible for the stress perturbations, and the receiver faults. (a c) Effects of the main event (MS) on the three Campotosto fault patches ruptured by the three largest aftershocks (AS1, AS2 and AS3). (d) cumulated effect of two events (MS and AS1) on AS2. (e) cumulative effects of MS, AS1, and AS2 on AS3. The amplitudes of the largest perturbations are around 0.2 MPa. where the coefficient 2.32 in (9) defines the thickness of the x pressure boundary, x p, given by: p ffiffiffiffi ¼ erfc 1 ð0:1þ ¼ 2 Dt 1:16 [Turcotte and Schubert, 1982, equation 4 114]. [33] From (6) we can write: dn dt ¼ 1 ðp 0 P 1 Þ p a 2 ffiffiffiffiffiffiffiffiffiffi pdt 3 Z 0 x exp x2 ð dx ¼ P 0 P 1 Þ p 4Dt W ffiffiffi p p ffiffiffiffi D 1 p ffiffit ð10þ 8of15

9 Figure 7. (right) Map of the events that occurred to the L Aquila (Paganica) and Campotosto (Monti della Laga) faults. On this map the whole aftershock catalog, up to the end of 2009, is shown. The red star indicates the location of the main shock hypocenter. (left) The set of events on the NW sector of the map in the center is plotted in two distance-time plots, where only the earthquakes with magnitude equal or above the cut-off threshold of 2.1 are included. Distances in the top frame are relative to the light-blue events in the map, plus the four yellow stars. Distances are epicenters projected onto the line with the arrow, and then measured from the dashed line. In Figure 7 (bottom left), distances are calculated along the projection on the S-ward pointing arrow, from the same horizontal dashed line in the map. The diffusion coefficient is calculated using equation (8). Figure 7 (top left) also shows the sensitivity of the curve to the diffusion coefficient, D, which is given as 70, 60, and 50 m 2 /sec. That is: dn dt p 1 ffiffi t ð11þ The trend (11) was observed by Nur and Booker [1972] on the first 24 h of the aftershock rate after the Parkfield-Cholame (1966) earthquake, and was interpreted as generated by the short-lived, dislocation-induced fluid diffusion. Parotidis et al. (2003) also described similar results for the triggering of an earthquake swarm in Vogtland/NW-Bohemia, in the year 2000, due to ascending magmatic fluids. [34] The corrected Akaike criterion was applied to the results shown in Figure 5, in order to understand, for both the NW and SE subsets, whether the diffusion-omori (double slope) model is significantly better, in a statistical sense, than a simple Omori-like (single slope) model. On the one hand, for the northwestern data set described in Figure 5a, the modified Akaike criterion indicates that, with a 99% likelihood, a two-slope model is significantly better, in a statistical sense, than a single-slope Omori model. For the southeastern data set, on the other hand (Figure 5b), the corrected Akaike criterion indicated that, with an 85% likelihood, a singleslope non-diffusive model (i.e., a pure Omori-like behavior) is the option to choose in order to describe the seismic sequence since its beginning Nonsteady-State Source of Pressure [35] Initial and boundary conditions (7) describe the diffusion of pore fluid pressure away from a steady-state source, where the pore fluid pressure does not significantly change within the time window of the observed phenomenon. In contrast, if the pressurized compartment (a half-space in our approximation) does significantly deflate within the time window of the diffusion phenomenon (a few days), a lower bound model is that of two half-spaces of equal diffusivity in contact, separated by an impermeable barrier that is suddenly removed at the onset of the main shock. In such a setting, the initial and boundary conditions would be: Px ð 0; t ¼ 0Þ ¼ P 0 ¼ l f r r gz Px ð 0; t ¼ 0Þ ¼ P 1 ¼ r w gz ; ð12þ 9of15

10 i.e., the net increase in pressure in the initially hydrostatic half-space (x 0, t 0) would be one-half than what indicated in equation (8): Px; ð tþ ¼ P ð 0 P 1 Þ x erfc p 2 2 ffiffiffiffiffi þ P 1 : ð13þ Dt We note that the activation of the first 8 km from the hypocenter of the main shock, in the N-NW direction is instantaneous (see Figure 7). In the hypothesis that the aftershocks are driven only by pore fluid pressure changes, the co-seismic activation indicates a region where the faulting processes induce a very high diffusivity (infinite, for our practical purposes), and thus permeability. The region where the diffusion process is observed, on the contrary, is characterized by a finite diffusivity: higher than that of undisturbed rocks, yet much lower than that of the volume that closely surrounds the main fault. We conclude that, for the length of the time window in which aftershocks diffuse on the Campotosto fault (i.e., a few days), equation (8) and boundary/ initial conditions (7) describe a realistic approximation. [36] Instead of a functional form like equation (11), the Omori law prescribes aftershock rates of the form: dnðþ t ¼ a dt b þ t ; ð14þ in which both a and b contain the rate-related parameter of the rate-and-state constitutive law [Dieterich, 1994]. Equation (14) was derived by Dieterich [1994] for a step-like increase of stress, and describes a mechanism of aftershock generation due to after-slip propagation. 4. Diffusion of Pore Fluids and Multiple Failures of the Campotosto Fault [37] In the hypothesis that all the events that occurred on the Campotosto fault were induced by decreasing fracture strength due to increasing pore fluid pressure, we can evaluate the time history of the Campotosto fault s shear strength by using equations (1), (5), (8), and (9). The depth at which all the calculations took place was determined using the best fit centroid depths of the moment tensors of the three largest events on the Campotosto fault, shown in Figure 1 (event depths were all at 7 km) [see Herrmann et al., 2011]. [38] The first step of our analysis of fault strength was the estimation of the diffusion coefficient, D, to be used in equation (8). A pretty simple task to accomplish, once the 1-D geometry of the diffusion process was defined, and the spatiotemporal evolution of the seismicity away from the Paganica fault suggested that the fastest propagation of the leading front of the migrating earthquakes was in a northward direction. The migration process started from the northernmost corner of the Paganica fault: a location identified from the visual inspection of the distance-time diagrams of Figure 7. Starting point and diffusion direction are indicated in Figure 7, respectively, by the thick horizontal segment used to separate the two portions of the NW-labeled data set analyzed in the two left frames, and by the arrow pointing toward North in its central frame. [39] The diffusion coefficient, D, indicated in equation (9), was quantified by fitting the leading edge of the seismicity in the time-distance diagram in Figure 7 (top left). The analysis yielded D =60m 2 /sec. In order to show the sensitivity of the curve to the diffusion coefficient, time-distance diffusion curves are also given using values of 70 m 2 /sec and 50 m 2 /sec for the diffusion coefficient (Figure 7). [40] Using D =60m 2 /sec, we calculated the decrease in shear strength following equations (1), (5), (7) and (8), due to the increase in pore fluid pressure that affected the Campotosto fault plane. Note that, although we imply that CO 2 is the most likely fluid to cause the changes in pore pressure, the calculations of the pressure cannot distinguish between fluids of different nature. [41] The necessary parameters needed for the calculation are: [42] i) the angles q =90 d between the fault plane and the maximum compressional stress s 1, where d is the fault dip angle from the focal mechanisms computed by Herrmann et al. [2011] (in the studied events, we have: d =50,40, and 45 ); [43] ii) the diffusion coefficient D =60m 2 /sec; [44] iii) the two values of the pore fluid pressure, P 0 and P 1 in equation (8): P 0 is the overpressure (l f = 0.8), and P 1 is the hydrostatic pressure field (l f = 0.4). [45] The time series relative to the Campotosto fault strength at the locations of the three largest events of the sequence (M w 5) are shown in Figure 8. The three individual frames show, for each location (i.e., diffusion distance, from the source of pressure in the northward direction, see Figure 7), the 5-day predicted time history of the pore fluid pressure (dashed increasing curves) and of the effective shear strength (dotted decreasing curves). Hydrostatic pore fluid pressure (horizontal solid line), and maximum (hydrostatic) fault shear strength (dashed horizontal line) are also indicated at each location. Time scales represent-days elapsed from the L Aquila main shock. [46] The times of failure, indicated by the long vertical arrows, correspond in all cases to a 7 10 MPa drop in the effective fault strength (Figure 8). Absolute values of fault strength on the same fault range roughly between 57 MPa (evt. 2009/04/09 19:38) and 67 MPa (evt. 2009/04/06 23:15). Such variations are mainly due to differences in dip angle between the different events (d =50,40, and 45 ). Within the error bars of the dip angles, the differences in absolute fault strength between the three different fault areas are not to be considered significant Sensitivity Analysis [47] Figure 9 shows the time histories of pore fluid pressure (short-dashed lines) and effective shear strength (dotted lines) computed on the patch of the Campotosto fault responsible for the M W 4.90 aftershock that occurred at 23:15 GMT on April (see also Figure 8, top left). Three curves are indicated for the pore fluid pressure as a function of time, obtained with a coefficient of hydraulic diffusion D = 50, 60, and 70 m 2 /sec. Two sets of three curves indicate, for two coefficients of static friction (m S = 0.6 and m S = 0.75) and the three values given above for the hydraulic diffusion. This study yields that, at failure, the possible strength reduction of the specific patch of the Campotosto fault is in the range between 7 MPa (obtained with m S = 0.6 and D =50m 2 /sec) and 12 MPa (obtained with m S = 0.75 and D =70m 2 /sec). Similar results can be obtained for the 10 of 15

11 Figure 8. Five days time evolution of the pore fluid pressure (short-dashed lines), in the N direction from the main hypocenter, together with the effective fault shear strengths (dotted lines) computed for the portion of the Campotosto fault responsible for the events of April 7 and 9, 2009 (d =50,40, and 45 ; diffusion distance, 4 km, 7 km and 9 km respectively). Strengths were calculated using a coefficient of friction, m S = 0.75, and a diffusion coefficient D =60m 2 /sec. We assume that the fault strength before the main shock of April 6, 2009 was hydrostatic (long-dashed horizontal lines). other two patches of Figure 8, indicating that the strength reduction remains substantial for variations of the main parameters, when the latter stay within a range of plausible values A Minor Role for the Coulomb Stress Changes? [48] Before proceeding further, we need to spend a few words to explain why we think the Coulomb stress perturbations of Figure 6 played a minor role in triggering the large events on the Campotosto fault. First, we observe that 0.05 MPa stress changes are very small when compared to the 7 12 MPa strength decrease of the Campotosto fault at the time of failure, as calculated for the incremented pore fluid pressure. Actually, Coulomb stress changes as low as 0.01 MPa are thought to be large enough to trigger earthquakes [see Harris, 1998, and references therein]. Moreover, several prior studies have in fact concluded that the aftershocks on the Campotosto fault could have been triggered by Coulomb stress changes [e.g., Serpelloni et al., 2012; De Natale et al., 2011]. [49] Although it must be clear that we cannot rule out the Coulomb stress perturbation as a plausible mechanism for the triggering of the seismic activity on the Campotosto fault, we simply stress the difference between the amplitudes of the pressure-induced strength reduction of the Campotosto fault (up to 12 MPa), and the fact that the receiver fault patches in Figure 6 are either within the stress shadow (where earthquakes on the receiver faults are inhibited), or in almost neutral locations where a positive Coulomb stress increase on receiver faults is less than 0.05 MPa. 5. Diffusivity and Permeability of the Campotosto Fault System [50] Spatial and temporal distributions of earthquakes during seismic swarms have often been used to determine 11 of 15

12 Figure 9. Variability of the quantities plotted in the upper-left frame of Figure 8, induced by varying both the coefficients of static friction and hydraulic diffusivity (see main text for details). various material properties of the crustal rocks, via the evaluation of the diffusion coefficient D of equations (8) (10), and (13). For example, Antonioli et al. (2005) used a spherical geometry in order to calculate a permeability value for the fault system of the Umbria-Marche seismic sequence of k = m 2. [51] In our 1-D geometry, we used Townend and Zoback (2000, equation 3) to compute the rock permeability along the Campotosto fault and fracture system. For a rock compressibility b r = Pa 1, a fluid compressibility b f = Pa 1, using a porosity f = 0.05, a viscosity h = Pa-s, and a diffusion coefficient D in the range between 50 m 2 /sec and 70 m 2 /sec (from the results shown in Figure 7), we estimated the rock permeability along the fault system to be in the range between m 2 and m 2. [52] The estimates given above consider water moving along a non-critically stressed fault such as the Campotosto structure, where we expect the permeability to lie in an intermediate range of values, between undamaged upper crust (typically between m 2, and m 2 )[Townend and Zoback, 2000], and a fresh main shock rupture zone with a much higher permeability. An example of the latter case is the Dobi extensional earthquake sequence in Central Afar, where Noir et al. [1997] found a permeability k 10 8 m 2. Finally, the Campotosto estimate of permeability is consistent with measurements carried out on rough fractures in granite and marble at low effective normal stress (k ) [see Lee and Cho, 2002]. [53] Even though we assume that CO 2 is most likely the fluid that migrates along faults and fractures of the Central Apennines, we used water parameters in our calculations. We do so after Miller et al. [2004], who assumed that the flow properties of supercritical CO 2 (the phase of CO 2 at the source depth) are the same as for water because CO 2 at the P T conditions encountered at hypocentral depth similar to the ones used here is ten times more compressible than water, but it is of the same order less viscous, resulting in similar flow properties. [54] Recently, Chiodini et al. [2011] showed that the regional aquifers located in the epicentral area of the 2009 L Aquila earthquakes are affected by the influx of deeply derived, CO 2 -rich gases. Their results suggest that pressurized compartments of CO 2 exist at depth, and they may stimulate the seismicity before entering the groundwater circulation. [55] An interesting question is about the reason why fluid migration, with the resulting earthquake triggering, is observed only to the North of the main hypocenter, and does not take place symmetrically South of it. Our hypothesis is that the location of the valve of the high-pressure fluid reservoir is likely to be coincident with the location of the main hypocenter, very close to the southern tip of the Campotosto fault. [56] Due to the described configuration, post-seismic fluid flow to the NW likely occurred through a pipeline with intermediate values of permeability: much larger than undamaged crustal rocks, and yet much smaller than a fresh fracture. In contrast, the high permeability of the main rupture may have allowed the pressurized fluids to instantaneously flood the entire volume around the Paganica fault. Within such a volume, diffusion-like phenomena would be too fast to be recognized on plots like the ones of Figures 5 and Implications for the Hazard Assessment in the Central Apennines [57] We found observational ground to support the hypothesis that the Campotosto fault failure was induced by a dramatic reduction in the fault s shear strength, due to the 12 of 15

13 pore fluid pressure field that was diffusing away from the northwestern edge of the Paganica fault, where the L Aquila main shock took place. Most interestingly, fluid diffusion processes seem to have modulated the rupture on the Campotosto fault through the subsequent failure of different fault patches, once they were reached by the pressure perturbation. The recognition of such an activation mechanism for a fault has obvious outcomes in terms of the probabilistic forecast that can be issued during an ongoing seismic sequence, when the seismogenic structures in a region are known. [58] Moreover, we can put our results into a broader perspective: Lucente et al. [2010] demonstrated the strong role played by the pore fluids in the late dilatancy stages that preceded the L Aquila main shock. Following their conclusions, the results by Terakawa et al. [2010], and the previous comments on the Campotosto fault failure mode, it is possible that the Paganica fault was also activated, while in a non-critical state, by fluid injection. As a consequence, the rupture that occurred on April 6, 2009 may not represent the full seismogenic potential of the activated structure. In fact, evidence of larger surface offsets, up to 0.8 m, were observed in a trench for a paleoseismic study on the same fault by Cinti et al. [2011], as opposed to the maximum surface offsets of 0.1 m observed along the surface expression of the Paganica fault rupture of April 6, [59] The two most recent events on the Paganica fault (M w 6, surface offsets of m) experienced a return period of 500 years [Cinti et al., 2011]. The three older events recognized on the same fault were probably larger (M w , surface offsets m), and spaced in time by years. If an advance (Dt) in the fault s clock is to be expected by pressure-induced weakening, it is likely that: Dt = years. Thus: ð Dt ¼ l L þ 2m L Þ 2 _ɛdt sinð2qþ ð15þ For a fault angle q = 30 with respect to the maximum compressional stress, with current estimates of the extensional strain rate, _ɛ ¼ nstrain/year [D Agostino et al., 2011], and with l L = m = Pa, the strength reduction Dt corresponding to a clock advance Dt = years is: 1 Dt 6 MPa, as opposed to our estimates of 7 10 MPa. In order to reconcile our previous estimates (obtained using equations (1), (2), (4), (5), (7), (8) with the one obtain with equation (15), we would need a lower coefficient of friction for the Paganica fault, like: m S ¼ 0:3; ð16þ as suggested by Collettini et al. [2008] for faults in the Northern Apennines, or a lower level of pore fluid pressure increase, as predicted by the non-constant source of pressure described by the initial and boundary conditions (12), and by equation (13). For the Paganica fault, however, a regular coefficient of friction m S = 0.6 is to be expected (C. Collettini, personal communication, 2011). A third possibility that may reduce the effective increase of pore fluid pressure may be a Biot-Willis coefficient a < 1.0 (see equation (1)). Whatever solution we choose in order to solve the issue, it is quite striking that a crude estimate like that obtained using equation (15) is within a factor of 2 3 of the 7 10 MPa obtained after modeling the diffusion process. [60] If an offset 10 times larger than that of the main shock of April 6, 2009 is to be expected on the Paganica fault, and if we want to keep the stress drop within a realistic upper bound for normal faults (say, Ds Brune 20 MPa), we need to activate a much larger fault area, probably capable of earthquakes of M W 7. [61] The latter statements may produce a substantial impact on the estimates of seismic hazard in the area. On the one hand, the pore fluid pressure pulse described here contributed to the discharge of strain energy in a relatively wide area, thus strongly impacting the time-dependent estimates of seismic hazard. On the other hand, although the faults in the area may be capable of large earthquakes, we argue that a physical mechanism of early discharge for the stored strain energy may reduce the frequency of occurrence of the large events. [62] The occurrence of large and small earthquakes on the same fault indicates that: i) the inhibition mechanism does not always activate; ii) the characteristic earthquake model fails. Both conclusions need to be taken into account by the seismic hazard community. 7. Reconciling Apparent Discrepancies With Results From the ETAS Model [63] The L Aquila seismic sequence was studied by means of other approaches, and apparent discrepancies are evident between our results of Figure 5, and the pure Omori-like behavior described by the ETAS model [Kagan and Knopoff, 1981; Ogata, 1988; Kagan, 1991; Ogata, 1998] shown in the study by Marzocchi and Lombardi [2009]. [64] The ETAS model, which does not include fluid pressure effects, does include secondary earthquake triggering, in addition to the Omori decay following the main shock. The apparent discrepancy between our results and those by Marzocchi and Lombardi [2009, Figure 3] is because the ETAS calculation, which does not use the spatial information associated with the events of the sequence, is carried out over the entire available data. Figure 5 shows two independent calculations made over two non-overlapping data sets, arbitrarily separated by a line striking N45E passing through the main epicentral location. It is important to mention that the completeness analysis has been carried out separately over the two non-overlapping catalogs marked NW and SE in Figure 5, yielding the same completeness magnitude that was calculated for the entire data set. [65] In the southeastern half of the seismic data set (marked SE in Figure 5), the number of aftershocks/day in the first day is much larger than its counterpart in the northwestern half (marked NW in Figure 5). When we compare the absolute number of aftershocks/day that were recorded between 18 and 75 h after the main quake (i.e., between the third and the fourth data point in the diagrams of Figure 5), we see that the SE data set contains roughly 2.5 times the aftershocks/day that are contained in the NW data set. Due to such difference in population, when the aftershocks decay rate is computed over the entire set of earthquakes (as done by Marzocchi and Lombardi [2009]), the diffusion signal seen to the NW gets wiped out by the regular Omori-like behavior that dominates the SE-marked frame of Figure 5. Due to the strong diffusion phenomenon that dominated the seismicity on the Campotosto fault for the first six-eight days, if we were to run the ETAS model over 13 of 15

14 the NW part of the data set (ETAS does not incorporate diffusion terms), we expect the results to be problematic in the first day of the sequence (W. Marzocchi, personal communication, 2011). [66] For completeness, the analysis of the aftershock decay rate was also run over the entire catalog of aftershocks at once. Results (not shown) indicate a hint (74% likelihood) for a diffusion process dominating at least the first three days of the entire sequence. Consequently, a likelihood of 26% characterizes a single-slope Omori-like aftershock decay rate (no diffusion) on the entire data set. 8. Conclusions [67] From the results of the analysis, as summarized by Figures 5 and 8, we conclude that the Campotosto fault experienced a strong reduction in shear strength due to the increasing pore fluid pressure started by the fault-valve action of the L Aquila main event. In fact, three earthquakes of M w 5 nucleated on adjacent patches of the Campotosto fault within the first four days of activation. At failure, on 2009/04/07, we estimated that the shear strength of the first patch, 4 km from the open valve, decreased about 10 MPa from its hydrostatic value (see Figures 7 and 8). Two subsequent events occurred on 2009/04/09 (00:53 and 19:38, 7 and 9 km from the open valve) on two patches of the fault plane that underwent, respectively, strength reductions of 10 and 7 MPa from their hydrostatic levels. Our calculation shows that the strength of the Campotosto fault was dominated for at least six days after the L Aquila main shock by the effects of the migrating pore fluid pressure field, which lead the structure to multiple failures. [68] On the Paganica fault, Lucente et al. [2010] documented the important role played by pore fluids during the preparatory phase of the April 6, 2009 L Aquila earthquake. Specifically, the M w 4 foreshock that occurred on March 30, 2009 started the migration of pressurized pore fluid that may have significantly lessened the strength of the Paganica fault plane. Moreover, on the same Paganica fault, the EMERGEO Working Group [2009] found evidence of slip episodes much larger than the one that occurred on April 6, As a consequence, the L Aquila earthquake may represent a relatively minor failure of the Paganica fault, occurred way before reaching the fault s hydrostatic strength. In turn, large events may be the ones that occur when the hydraulic weakening does not take place, letting the Paganica fault fail at its hydrostatic strength. Keeping in mind that similar phenomena of fluid-earthquake interaction were documented also by Miller et al. [2004] in the Central Apennines during the Umbria-Marche seismic sequence of , a corollary of the latter statements is that the characteristic earthquake model fails to describe the behavior of faults in the Central Apennines. [69] The effects of the increase in pore fluid pressure could be mitigated by at least three factors: a lesser Biot-Willis coefficient in equation (1), a lesser overpressure parameter l f, and a fast decaying pore fluid pressure source. Moreover, we neglected other competing effects (e.g., perturbations in the Coulomb stress field, or dynamic excitation due to passing stress waves radiated during the main shock) that may have affected the seismic sequence on the Campotosto structure. In any case, for many days after the main shock, a diffusive phenomenon is observed to dominate the entire section to the NW with respect to the hypocenter of the main shock. [70] The simplicity of our calculations can, in principle, provide the seismological community with an important tool that can be integrated within the real-time procedures for the calculation of space-time forecasts of aftershock occurrence that are already used in forecasting the short-time evolution of seismic sequences [e.g., Lombardi et al., 2010]. We strongly suggest that the likelihood of the occurrence of transient phenomena affecting the strength of seismogenic faults are to be taken into account in hazard calculations. [71] Finally, future work is required to answer the following open question: what is the maximum M W that can occur on the Campotosto fault? In other words: can it actually fail as a whole? [72] Acknowledgments. We thank the editor Robert Nowack, Martha Savage and an anonymous reviewer for the constructive reviews and comments, which allowed us to strongly improve the readability of this manuscript. 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