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Strain rates in northwestern Italy from spatiallysmoothed seismicity

Simone Barani,1 Davide Scafidi,1 and Claudio Eva1

Received 22 May 2009; revised 14 January 2010; accepted 25 February 2010; published 10 July 2010.

[1] This work presents seismic strain rate maps for the Western Alps and NorthernApennines (northern Italy) as derived from an earthquake catalog collecting both historicaland instrumental data. Strain rates are calculated on the basis of the rate of seismic momentrelease using the Anderson method. Unlike previous applications, which determined thetotal strain rate associated with specific seismogenic sources, we have employed aninnovative zoneless approach based on a spatially smoothed seismicity method. In addition,a Monte Carlo simulation procedure is applied to allow for uncertainty in the input data(e.g., magnitude to moment conversion, seismogenic thickness, maximum earthquakemagnitude). Strain rate maps are developed by summing the moments of the earthquakesreported in the catalog and by using two different earthquake recurrence relations. Ourresults indicate that deformation rates are quite high, ranging from about 2 to 12 × 10−9 yr−1

in the Northern Apennines and from 0.5 to 6 × 10−9 yr−1 in the Western Alps. Thesevalues, however, are ∼1 order less than those derived from Global Positioning Systemmeasurements, suggesting that a portion of the recent deformation in northwestern Italy isrelated to aseismic processes. The discrepancies between seismic and geodetic strain ratesmay also indicate that the record of seismicity may not provide a sufficient time windowfor assessment of secular rates of moment release (or secular deformation rates) and ratesof recurrence of large magnitude earthquakes in the study area.

Citation: Barani, S., D. Scafidi, and C. Eva (2010), Strain rates in northwestern Italy from spatially smoothed seismicity,J. Geophys. Res., 115, B07302, doi:10.1029/2009JB006637.

1. Introduction

[2] Understanding the nature of earthquakes in a region andevaluating the associated hazard requires a detailed knowl-edge of the geodynamic and tectonic processes relative to thatarea (see Text S1 in the auxiliary material).1 Hence, seismicstrain rate and moment rate evaluations are of great impor-tance for a more complete understanding of the earth-quake process and for the development of finer seismichazard source models [e.g.,Chen andMolnar, 1977;Molnar,1979; Wesnousky et al., 1982; Hyndman and Weichert,1983; Anderson, 1986; Field et al., 1999; Jenny et al., 2004;Mazzotti and Adams, 2005].[3] The earthquake source model, which describes the

spatial and temporal distribution of earthquakes in a region(or on a fault), is of central importance in seismic hazardanalyses based on a probabilistic approach [e.g., Cornell,1968]. Its definition involves the evaluation of the sizes ofearthquakes that the region can be expected to generate. Inother words, defining a model of seismicity for a given sourceinvolves specifying an earthquake recurrence relation, indi-cating the frequency with which various magnitude levels are

exceeded over a given period. The choice of a recurrencerelation is not an easy task as different relations may berepresentative of the earthquake distribution in the area.In addition, various forms of data (seismologic, geological,geophysical) and/or alternative methods can be employed toestimate the values of the parameters of a recurrence relation.For example, earthquake recurrence parameters (i.e., b valueof the log linear Gutenberg and Richter relation [Gutenbergand Richter, 1944], earthquake occurrence rate above aminimum threshold magnitude) are generally evaluated onthe basis of historical seismicity while maximum magnitudevalues can be determined from geologic data and geophys-ical data or simply by increasing the maximum observedmagnitude by an amount based on professional judgment.Therefore, a seismicity model should be analyzed to ensurethat it is consistent with all available data. To this end, it maybe useful to express earthquake size in terms of seismicmoment,M0, a measure of the energy release during a seismicevent. Thus, it is possible to compare seismic moment rates(or strain rates) with independent estimates derived fromgeology or geodetic measurements [e.g., Wesnousky et al.,1982; Field et al., 1999; Jenny et al., 2004; Pancha et al.,2006].[4] In this study, strain rates for the Western Alps and

Northern Apennines (northern Italy) are calculated from1Dipartimento per lo Studio del Territorio e delle sue Risorse,

University of Genoa, Genoa, Italy.

Copyright 2010 by the American Geophysical Union.0148‐0227/10/2009JB006637

1Auxiliary materials are available in the HTML. doi:10.1029/2009JB006637.

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, B07302, doi:10.1029/2009JB006637, 2010

B07302 1 of 16

historical and instrumental seismicity using the Andersonmethod [Anderson, 1979], which estimates the average rateof deformation, _", as a function of the moment rate, _Mo

Important applications of this method are reported byHyndman and Weichert [1983], Anderson [1986], Rao[2000], Mazzotti and Hyndman [2002], and Hyndman et al.[2003, 2005]. Unlike these studies, the purpose of thispaper is not the calculation of strain rates for specific seis-mogenic sources but the production of maps outlining thegeographic distribution of _" based exclusively on the earth-quake catalog. This is achieved through the application ofa smoothed seismicity approach similar to that proposed byFrankel [1995] for the seismic hazard assessment of thecentral and eastern United States. This procedure does notrequire the delineation of area or fault sources but implicitlyincorporates them through the seismic catalog. The methodconsists of calculating _Mo for each cell of a homogeneousgrid covering the entire study area. A smoothing function isthen applied to the gridded _Mo values.[5] As noted by various authors [e.g., Anderson, 1986;

Field et al., 1999; Jenny et al., 2004; Mazzotti and Adams,2005], strain rate estimates are affected by a significantdegree of uncertainty that derives from input data uncertainty.Different statistical approaches can be adopted to allowfor parameter uncertainties in strain rate calculations. Forexample, Mazzotti and Adams [2005] applied the logic treeformalism to allow for the uncertainty related to magnitudeto moment conversion and uncertainty in the values of thesource zone parameters (e.g., earthquake recurrence param-eters, maximum magnitude, seismogenic thickness, sourcelength). In this study we have chosen to adopt a Monte Carloapproach that consists of randomly varying earthquake mag-nitude, maximum magnitude, and thickness of the seismo-genetic layer.

[6] Following a description of the seismotectonic setting ofthe area in question, we present the earthquake catalog and themethod used to estimate _Mo and _". Strain rate maps detailingthe geographical distribution of _" mean values and relativeuncertainty (expressed in terms of standard deviation, s

_") are

then presented and discussed. Finally, the sensitivity of strainrate estimates to the uncertainty in earthquake magnitude,maximum magnitude, seismogenic thickness, and to thechoice of the recurrence relation is investigated.

2. Seismotectonic Setting and Stress Regime

[7] Seismic strain rate evaluations based on the Andersonmethod [Anderson, 1979] demand that the area under inves-tigation is homogeneous with respect to the stress field. Basedon an analysis of various geophysical data, including focalmechanism solutions, we divided the study area into sixmacro‐zones with uniform tectonic pattern (Figure 1), termedas “seismotectonic provinces” (SPs). It is worth specifyingthat the moment tensor solutions in Figure 1 are those used tocalibrate the regional stress field coefficient needed for thecalculation of _" (for details, see equation (2) and Appendix B)and are not representative of the prevalent tectonic style of theprovinces. This latter feature, along with the SP geometry,was defined based on a larger data set of focal mechanisms,including those presented byFrepoli andAmato [1997],EvaandSolarino [1998], Vannucci and Gasperini [2004], Delacou etal. [2004], and Eva et al. [2005]. The ZS9 seismogeniczonation [Meletti et al., 2008] and data published in theDatabase of Individual Seismogenic Sources (DISS) [Basiliet al., 2008] were also kept into account. SP 01 and SP 02correspond to the internal and external sectors of the WesternAlps. The former is a continuous zone of extension that fol-lows the topographic crest line of the Alpine arc. The area is

Figure 1. Seismotectonic provinces and moment tensor solutions from the Italian centroid moment tensordata set [Pondrelli et al., 2006].

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characterized by low‐to‐moderate but relatively frequentearthquakes (see Figure 2). The largest events are located inthe western Swiss Alps (the strongest earthquakes occurredon 9 December 1755 with moment magnitude Mw = 5.9[Gisler et al., 2004] and 25 January 1946 with Mw = 6.1)where extension is associated with a notable present‐dayuplift [e.g., Kahle et al., 1997]. On the basis of an analysis offocal mechanism solutions and Global Positioning System(GPS) data, several authors [e.g., Eva et al., 1998; Eva andSolarino, 1998; Calais et al., 2002; Nocquet and Calais,2003, 2004] show that extension (i.e., T axes) is virtuallyperpendicular to the structural trend of the Alps, followinga radial pattern [e.g., Frechet, 1978; Nicolas et al., 1990;Champagnac et al., 2004;Delacou et al., 2004]. The externalsector (SP 02), which is located at the Po Plain border, ischaracterized by a compressive‐transpressive regime. Focalmechanism solutions indicate that the direction of maximumcompression (i.e., P axes) rotates counterclockwise fromnorth (where P axes are ENE‐WSWoriented) to south (wherethey are approximately N‐S directed) following the contourof the Alpine belt [Delacou et al., 2004]. Earthquakes aremainly concentrated in the western part of the province wherethe Alps transitions from a compressive sector to an internalextensional one (see Figure 2). Aswith SP 01, events are quitefrequent and present low to moderate magnitudes (up toMw =5.7). SP 03 corresponds to thewestern part of the Ligurian Seawhere a compressive stress field overprints a previousextensional regime [Béthoux et al., 1992; Eva and Solarino,1998]. The majority of offshore seismic activity is associ-ated with the fault system that characterizes the continentalslope [Augliera et al., 1994; Eva et al., 1999; Barani et al.,2007a] where magnitudes rarely exceeded 5.0. The stron-gest events were recorded on 19 July 1963 (Mw = 5.9) and23 February 1887 (Mw = 6.3). SP 04 represents a transitionzone between the Alps and Apennines. This area is charac-

terized by a low seismic activity that is mainly concentrated inthe southern part of the province (see Figure 2) where, of late,two significant seismic sequences have occurred, in August2000 [Massa et al., 2006] and April 2003 with main shocksof magnitude Mw = 5.0 and Mw = 5.3. The small number offocal mechanism solutions suggests that a strike‐slip regimeprevails. SP 05 and SP 06 correspond to the inner and outersectors of the Northern Apennines, an area where bothshortening and extension coexist [e.g., Anderson and Jackson,1987; Carmignani and Kligfield, 1990; Frepoli and Amato,1997]. The inner part (SP 05) is dominated by a crustalextension of ∼2.5 mm yr−1 [Hunstad et al., 2003] that issuperimposed on a previous compressive Oligocene‐Tortoniandeformation [Boccaletti et al., 1985; Boccaletti and Sani,1998; Finetti et al., 2001]. Although focal mechanisms donot suggest a homogeneous orientation of the extensionaldeformation, an E‐W direction appears to prevail [Frepoliand Amato, 1997]. The strongest events have occurredalong the eastern border of the province with magnitudes ofup to 6.5 (7 September 1920 earthquake). SP 06 is charac-terized by a compressive regimewhere compression is roughlyperpendicular to the NW‐SE Apennine trend [Frepoli andAmato, 1997]. As with SP 05, seismic activity is moderateto high, with the largest event occurred on 24 April 1741 withMw = 6.1.

3. Earthquake Catalog

[8] A seismic catalog collecting both historical and instru-mentally recorded earthquakes has been suitably compiledfor the purposes of strain rate assessment. Earthquake data(e.g., time and location of earthquakes, magnitude) werecollected from different primary data sets. With the exceptionof four strong earthquakes that occurred in western Liguria(northwestern Italy) during the 19th century, for which the

Figure 2. Geographical distribution of earthquake epicenters within the seismotectonic provinces(Figure 1).

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epicentral parameters proposed by Barani et al. [2007a] areconsidered, historical events (from 217 B.C. to 1980) arebased on the CPTI04 catalog [Gruppo di Lavoro CPTI,2004]. Instrumental data, from 1981 to 2006, are selectedfrom two data sets: the CSI catalog [Castello et al., 2007] andthe bulletin of the RSNI seismic network (Regional SeismicNetwork of Northwestern Italy, University of Genoa).[9] Instrumental data were screened for reliability and

events with highly uncertain locations were rejected. Spe-cifically, all earthquakes with root mean square value of traveltime residuals RMS � 3.0 s, gap in azimuth coverage (i.e.,maximum azimuthal distance between two nearby‐distanceseismic stations) GAP � 220°, horizontal and vertical loca-tion error <20 km, and at least six P and/or S phase picks arereported in the final catalog. Furthermore, given that the twoinstrumental catalogs overlap both in space and time, theywere analyzed to identify duplicate events. The identificationof duplicates was based on comparison of occurrence time,epicentral coordinates (latitude and longitude), and magni-tude. When analogous events were identified, those charac-terized by a lower location error were retained.[10] Given that the instrumental data are not homogeneous

with respect to magnitude scale, a uniform magnitude mea-sure was estimated for each event. In this study, momentmagnitude (Mw) is taken as the reference scale. The proce-dure adopted to covert magnitudes to Mw is presented inAppendix A.[11] Once Mw is determined, seismic moment, M0 (N m),

is calculated using the Hanks and Kanamori [1979] relation

M0 ¼ 10cMwþd ð1Þ

where c = 1.5 and d = 9.101.[12] As observed by Pancha et al. [2006], values of the

coefficient d different from 9.101 are reported in literature.These discrepancies result from rounding of the coefficientsused in the original Kanamori [1977] equation. Since thevalue of d has a nonnegligible effect on the final strain rateestimates [Field et al., 1999], we rounded this coefficient tothree decimal places.[13] In order to achieve an instrumental data set that, as for

the historical section of the catalog, reports independentevents only, earthquake clusters (i.e., sequence or swarms)are identified and foreshocks and aftershocks removed.Indeed, the CPTI04 catalog [Gruppo di Lavoro CPTI, 2004],compiled for standard seismic hazard assessments based onthe Poisson occurrence model [Cornell, 1968], does notinclude dependent events. It should be noted that althoughseismic sequences could be considered for strain rate eva-luations, the contribution from low‐magnitude events, suchas aftershocks and foreshocks (whose magnitude rarelyexceeds 4.0, at least in the area investigated in this study), is

negligible when compared to that from main shocks [Scholz,1972;Chen andMolnar, 1977;McGuire, 2004]. In this study,dependent events are identified using a new technique basedon the windowing approach proposed by Gardner andKnopoff [1974] and the cluster link method by Reasenberg[1985]. Specifically, an event is considered part of a clusterif it is located within D(Mm) kilometers from the main shock(as in the Gardner and Knopoff [1974] method) and occurredwithin a period of t days from the last earthquake in thecluster (as in the Reasenberg [1985] approach). The values ofD(Mm) are defined as a function of themain shockmagnitude,Mm, and increase along with Mm, while the look‐aheadtime, t (i.e., the waiting time to be reasonably confident ofobserving the next earthquake in the cluster), is derivedfrom a stochastic model of aftershock sequences based on theOmori law [Reasenberg, 1985; Barani et al., 2007b]. Thevalues of D(Mm) used in this study are those proposed byGardner and Knopoff [1974] for southern California. Theapplication of these values was proved to be appropriate in theidentification of earthquake clusters in northwestern Italy byBarani et al. [2007b]. In the same article, the authors describehow t is calibrated for the same area [see also Barani, 2007].Compared to the Gardner and Knopoff method, the applica-tion of this new hybrid approach results in a declusteredcatalog that is drawn by the Poisson distribution with aslightly higher degree of confidence (as verified through achi‐square test).[14] The final catalog includes 744 earthquakes of magni-

tudeMw greater than or equal to 4.0, extending from 217 B.C.to 2006 (Figure 2). It should be noted that the catalog pro-vides an estimate of the magnitude uncertainty, quantified bysMw

. The values of sMware indicated in equations (A2)–(A4)

(Appendix A) with the exception of those events whosemoment magnitude value was already provided by the sourcecatalog. In these cases, we have assumed sMw

= 0.37 (cal-culated as the weighted average of the values of sMw

reportedin the intensity to magnitude conversion table developed byGruppo di Lavoro CPTI [2004]) and sMw

= 0.1 for historicaland instrumental earthquakes, respectively.[15] Given that moment rates are calculated based on his-

torical data, estimates vary with the degree of completeness ofthe earthquake catalog. A quantitative estimate of the catalogcompleteness is obtained by applying the Mulargia et al.[1987] method that as the original approach proposed byStepp [1972], is based on the assumption that seismicity issteady over time. The catalog completeness for differentmagnitude ranges is summarized in Table 1.

4. Methodology

[16] The Anderson method [Anderson, 1979], whichderives from the Kostrov formula [Kostrov, 1974] relating themean rate of seismic strain and the sum of the moment tensorcomponents, calculates the average strain rate _" (yr−1) withina volume V as

_" ¼_M0

ð2=kÞ�V ð2Þ

where _Mo (N m yr−1) is the average rate of seismic momentrelease, k is an empirical constant (Table 2) that depends onthe regional stress field (the calibration of this parameter is

Table 1. Catalogue Completeness

Magnitude Interval Year of CompletenessCompleteness Period

(years)

[4.0, 4.5) 1985 22[4.5, 5.0) 1885 122[5.0, 5.5) 1825 182[5.5, 6.0) 1740 267�6.0 1350 657

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described in Appendix B), m is the shear modulus (taken as3.6 × 1010 N m−2), V = Ah, A (m2) is the area of a seismogenicsource (when a smoothing approach is applied as in this study,A indicates the area of a grid cell; further details about thesmoothing procedure are given below), and h (m) is thethickness of the seismogenic layer, defined as the depthinterval that produces the largest number of earthquakes in aseismotectonic province [Meletti et al., 2008].[17] For each seismotectonic province, the thickness of

the seismogenic layer, h, is estimated based on the statisticaldistribution of the hypocentral depth. For this purpose, a moreextensive earthquake data set comprising all the instrumentalevents that comply with the selection criteria described insection 3 but with magnitudeM1� 2.0 and hypocentral depthlower than or equal to 50 km is considered. We define theseismogenic thickness as the depth range to include 68% ofthe earthquakes. The depth of the upper and lower boundariesof the seismogenic layer corresponds to the 16th and 84thpercentiles of the hypocentral depth distribution. A largerconfidence interval is not considered, as it would implyunrealistic thickness values due to the uncertainty in earth-quake depths. The values calculated using this statisticalapproach are consistent with those of Chiarabba et al. [2005]and with the distribution of the Moho discontinuity at depth[Finetti, 2005]. For each seismotectonic province, the valuesof h are summarized in Table 2 along with other parameters orfeatures (k value, b value of the log linear Gutenberg andRichter recurrence relation, maximum observed magnitudemmaxobs , tectonic regime).[18] As stated in section 1, the Anderson method is gen-

erally applied to determine the mean strain rate associatedwith the seismic activity of individual fault or area sources.This requires that a specific value of _Mo is computed for eachseismogenic source. In this study, however, a smoothedseismicity approach is employed. _Mo is calculated for eachcell of a homogeneous grid of 0.05° spacing in latitudeand longitude by summing the moments of all events thatoccurred within each cell during a given time period and byusing two alternative forms of the doubly truncated Gutenbergand Richter (hereinafter GR) recurrence relation. In the firstinstance, following the calculation of moment rates, a two‐dimensional (elliptical) Gaussian kernel oriented by anangle � (measured counterclockwise from east) is applied toobtain smoothed _Mo values, ~_Mo. The use of an ellipticalkernel was introduced in seismic hazard studies by Lapajneet al. [2003] to account for the orientations of seismogenicfaults in regions where data are insufficient to define a direct

relationship between epicenter distribution and knownfaults. Unlike this earlier approach, in which the ellipticalkernel is applied within a two‐step smoothing procedure,this study applies a one‐stage technique with an ellipticalGaussian function with the major axis that lies in the directionof the seismogenic faults within a seismotectonic province.Mathematically, it is expressed as follows:

~_Mo ¼

Pj

_Mo exp � Dij;�1�1

� �2þ Dij;�2

�2

� �2� �� �

Pjexp � Dij;�1

�1

� �2þ Dij;�2

�2

� �2� �� � ð3Þ

where t1 and t2 are the major and minor semiaxes of theellipse and Dij,t1 and Dij,t2 indicate the distance between theith and jth cells along the directions of t1 and t2. The sum istaken over cells j within distances 3t1 and 3t2 of cell i (inother words, only the jth cells within an ellipse centered on celli with semiaxes of length 3t1 and 3t2 are considered in thecalculations). If t1 equals t2, then equation (3) defines acircular Gaussian function as in the original approach byFrankel [1995].[19] Based on this approach, the elliptical smoothing

function allows for both the epicentral location error (quan-tified by t1 and t2) and the prevalent orientation of activefaults within a province (defined by the angle �). The valuesof t1, t2, and � are calibrated using the fault data reported inDISS [Basili et al., 2008], which collects information withrespect to known seismogenic faults in Italy. For both SP 05and SP 06, we assume t1 = 30 km and t2 = 20 km, whereas �is set to 136° and 151°, respectively. This latter parameter isdetermined by averaging the strike angle values of the faultsources within each province while t1 and t2 are defined afteranalyzing trial ~_M maps generated using different semiaxislengths. Note that Lapajne et al. [2003] suggest the adoptionof t1 and t2 values that are equal (or proportional) to the faultrupture length and width, respectively. The values adoptedfor SP 05 and SP 06 are approximately twice the length andwidth of the largest seismogenic fault in each province.Lower values are considered not conservative in that they areunable to capture the location error in the epicenters of his-torical earthquakes. Greater t1 and t2 values, however, tendto oversmooth the results, obscuring localized areas of higherrate of seismic moment release. For all the other provinces(SPs 01–04) we used a circular Gaussian kernel with t1 = t2 =25 km, given that seismogenic faults are unknown or data areinsufficient to correctly define an elliptical smoothing func-tion. The correlation distance of 25 km was suggested forItaly by Console and Murru [2001] and used by Akinci et al.[2004] in the evaluation of the seismic hazard map of Alpsand Apennines (Italy) and by Barani et al. [2007a] in theseismic hazard assessment of certain sites in western Liguria.[20] As previously stated, moment rates are also calculated

by employing two different forms of the doubly truncated GRrelation, specifically that presented by Field et al. [1999,equation 4] and that proposed by Cornell and Vanmarcke[1969] [see McGuire, 2004, equation 26]. We have alsoapplied these models, as they are two of the most widely usedin probabilistic seismic hazard analyses. _Mo is calculatedby integrating the moment contributions over magnitude (or,

Table 2. Seismotectonic Province Parametersa

SeismotectonicProvince

TectonicRegime

h(km) k mmax

obs u(mmin) b

SP 01 Extensional 13 0.86 6.1 1.239 1.093SP 02 Compressive 11 0.66 5.7 0.578 1.336SP 03 Compressive 19 0.66 6.3 0.239 0.985SP 04 Strike‐slip 18 0.50 5.7 0.284 1.149SP 05 Extensional 15 0.86 6.6 3.776 1.345SP 06 Compressive 24 0.66 6.1 2.793 1.143

aParameters are h, seismogenic thickness; k, stress field coefficient; mmaxobs ,

maximum observed magnitude; u(mmin), mean annual rate of earthquakeoccurrence above mmin = 4.0; b, slope of the log linear Gutenberg andRichter recurrence relation. The prevalent stress regime is also indicated.

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over seismic moment) in the recurrence law. Considering themodel presented by Field et al. [1999], _Mo is calculated as[Field et al., 1999]

_M0 ¼Zmmax

mmin

nðmÞM0dm¼ �ðmminÞ10 bmminþdð Þ

ðc� bÞ lnð10Þ 10ðc�bÞmmax �10ðc�bÞmmin

h i

ð4Þ

where n(m) is the incremental rate of an earthquake ofmagnitude m, u(mmin) is the annual rate of earthquakeoccurrence above a minimum threshold magnitude mmin, cand d are the coefficients in equation (1), and mmax is theupper bound magnitude.[21] From the Cornell and Vanmarcke [1969] relation one

obtains [McGuire, 2004]

_M0 ¼ZM0;max

M0;min

M0�ðmminÞfM0ðM0ÞdM0

¼ �ðmminÞ�e� mminþd=cð Þ

1� e�� mmax�mminð Þ½ � �� �ð Þ M1��=�0;max �M 1��=�

0;min

� �ð5Þ

where fM0(M0) is the probability density function for seis-

mic moment, b = bln(10), c and d are the coefficients inequation (1), l = c 1n(10), and M0,min and M0,max are thelower and upper bound seismic moments corresponding tommin and mmax.[22] When equations (4) and (5) are used, gridded activ-

ity rates, u(mmin), are calculated by counting the numberof earthquakes in each cell of the homogeneous grid usedin the calculations and then dividing the earthquake rate bythe completeness time to obtain the rate per year. Subse-quently, smoothed activity rates, ~�(mmin), are calculatedusing equation (3) where _Mo is replaced by u(mmin). Thevalue of the coefficient b in equations (4) and (5) is estimatedfor each seismotectonic province by applying a least squaresapproach while mmax is assumed to vary between the maxi-mum observed value, mmax

obs , and mmaxobs + 0.5 (for details, see

section 5). This latter assumption is consistent with thehypothesis that the earthquake catalog may be affected by theincompleteness of large potential earthquakes. It is worthnoting that theWeichert [1980] maximum likelihood approachwas initially used to calculate the value of b. In general, thisapproach may be preferable to a least squares fitting methodas it accounts for zero observations (i.e., empty magnitudebins) and, when applied to incremental data, does not violatethe assumption of independent observations [e.g., McGuire,2004]. However, it has the disadvantage that a priori knowl-edge ofmmax (along with an estimate of its recurrence period)is required. As a consequence, the least squares method maybe more suitable in studies that, like this, uses a Monte Carloapproach to allows for the mmax variability and, contrary toprobabilistic seismic hazard analyses, do not require anyparticular assumption about event independency.

5. Treatment of Uncertainties

[23] As stated in section 1, the uncertainty in strain rateestimates results from various contributory factors. Excludinguncertainty in the seismogenic source geometry, which is not

considered in this study as a zoneless approach is used, themain contributory factors to the overall _" uncertainty areseismogenic thickness, maximum magnitude, and, particu-larly, the error affectingM0 values due to conversion betweendifferent magnitude scales. Other factors that contribute to the_" uncertainty are the catalog completeness and the valueof the coefficient b of the GR relation. In this study, theuncertainty in the input parameters is considered via a MonteCarlo simulation procedure that consists of randomly varyingthe magnitude of earthquakes, M, the maximum magnitudevalue, mmax, and the seismogenic thickness, h. Note that,contrary to b, which is uniform throughout the provinces,mmax and h are considered to vary randomly from a grid cell toanother. Except formmax, which is assumed to vary uniformlyfrom mmax

obs to mmaxobs + 0.5, the other random variables (RVs)

are considered to be normally distributed with a given meanand standard deviation, sRV. Specifically, for each event inthe seismic catalog, we assume sM = sMw

, where sMwis

defined as in Appendix A1, while sh is assumed to be equal to2 km. Distributions are truncated at ±2sRV to prevent unre-alistic parameter values. Following this procedure, the mag-nitude variability is reflected in the values of mmax

obs (and,consequently, in those of mmax), M0, M0,max, u(mmin), and b,that are determined automatically during each run of theMonte Carlo simulation. According to the maximum mag-nitude values proposed by DISS [Basili et al., 2008] andbased on a conservative criterion, the randomized value ofmmaxobs is assumed not to be lower than the maximum value

observed in each province. Finally, note that the complete-ness periods (Table 1) are assumed as constant within eachsimulation run.

6. Strain Rate Maps

[24] Figures 3 and 4 show the geographical distribution ofthe mean strain rate (and its standard deviation, s

_") within the

study area as obtained from 1,000 Monte Carlo randomiza-tions. Specifically, mean strain rate values in Figure 3a arecalculated from the total moment derived from the earthquakecatalog while those in Figure 4a are calculated by averagingresults obtained applying equations (4) and (5) (averagingthese mathematical models is like to assume that they areequally likely, at least in principle; separate maps are pre-sented in Figure 7 and discussed in section 7). These twoapproaches provide similar strain rate distributions withlower values in the second case, when _Mo is based on theapplication of two alternative earthquake recurrence rela-tions. The reason for this may be related to the form of therecurrence relations used, particularly near the maximummagnitude. The impact of these relations on _"will be assessedin section 7. Here, our discussion is confined to the strain ratemaps in Figures 3 and 4. Before discussing these maps, itshould be observed that _" values are somewhere affected byhigh uncertainty (up to 80%), as indicated by the values ofstandard deviation (Figures 3b and 4b). A detailed analysis ofuncertainties will be presented in section 7.[25] The highest strain rate values in the study area roughly

follow the crest line of the Apennine belt. In particular, theyare concentrated along the Etrurian Fault System (EFS), aPlio‐Pleistocene fault array that consists of east dipping low‐angle normal faults extending for about 350 km from northernTuscany to southernUmbria [Boncio et al., 2000]. Strain rates

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are at their highest in the northernmost part of the EFS(Lunigiana‐Garfagnana basin, LG) where they range up toapproximately 12 × 10−9 yr−1 (Figure 3a) or 6.5 × 10−9 yr−1

(Figure 4a) according to the approach used to estimate _Mo.These deformation rates can be related to the activity oftwo major NW‐SE normal faults, Garfagnana North Faultand Garfagnana South Fault [Basili et al., 2008], that werethe sources of destructive earthquakes, including that of7 September 1920 (Mw = 6.5). High strain rate values (up toapproximately 8.5 × 10−9yr−1 and 5.5 × 10−9yr−1 as derivedfrom Figures 3a and 4a) are also observed in the central part ofthe EFS where faults in the Casentino basin (CS) and in the

northern part of the eastern Tiber basin (TB) generate seismicactivity in eastern Tuscany and northern Umbria. This area ischaracterized by moderate‐ to high‐magnitude events, suchas the destructive and frightening Gubbio earthquake of29 April 1984 (Mw = 6.0). Northeast of the Casentino basin,the EFS continues with the Mugello basin (MG). This basincan be clearly identified in Figure 3a but not in Figure 4awhere it corresponds to an area of lower deformation rates,in contrast with actual seismicity. Here, seismic activity and,consequently, deformation rates ( _" ≈ 6.0 − 7.0 × 10−9 yr−1

from Figure 3a) are controlled mainly by the Mugello EastFault and Mugello West Fault [Basili et al., 2008]. The

Figure 3. (a) Strain rate map (mean values of _") as obtained by summing the moments of the events col-lected in the seismic catalog and (b) uncertainty map showing the geographical distribution of the values ofthe strain rate standard deviation, s

_". ST, Saorge‐Taggia fault; OP, Orciano Pisano fault; LG, Lunigiana

Garfagnana basin; MG, Mugello basin; CS, Casentino basin; TB, eastern Tiber basin.

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former was responsible for the Mugello earthquake thatoccurred on 29 June 1919 withMw = 6.2. Again in Figure 3a,we clearly see a zone characterized by lower strain rates( _" ≈ 2.5 − 3.5 × 10−9 yr−1) between the Mugello andGarfagnana basins. This area has been interpreted as anactive E‐W transfer zone, reactivating a left‐lateral crustaldiscontinuity that remains from aMiocene compressive phase[Lavecchia, 1988;Meletti et al., 2000]. Again with referenceto the inner sector of the Northern Apennines (SP 05),Figure 4a displays a small area of enhanced deformation( _" ≈ 3.0 × 10−9 yr−1) that extends offshore and along the

Tuscany coast near Livorno to the west of the Orciano PisanoFault (OP). This area is characterized by moderate seismicitythat tends to be clustered in a region where seismic reflectionprofiles published by Fanucci et al. [1984] indicate thepresence of normal faults affecting the seafloor during thePlio‐Quaternary period and possibly in the Holocene.[26] In the Western Alps, the highest deformation rates

are concentrated in the Valais region (western Swiss Alps),where _" is approximately 3.5 to 6.0 × 10−9 yr−1 (Figure 3a).These strain rates coincide with pronounced seismic activityaccompanied by a significant surface uplift [Ustaszewski

Figure 4. (a) Strain rate map (mean values of _") as obtained from the application of both equations (4) and(5) and (b) uncertainty map showing the geographical distribution of s

_". ST, Saorge‐Taggia fault; OP,

Orciano Pisano fault; LG, Lunigiana Garfagnana basin; MG, Mugello basin; CS, Casentino basin; TB,eastern Tiber basin.

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and Pfiffner, 2008], with maximum uplift rates of around1.5 mm yr−1 [Kahle et al., 1997]. Another nucleus of quitehigh deformation ( _" ≈ 4.0 × 10−9 yr−1) is located in thesouthern part of the Western Alps along the western coastof Liguria (Figure 3a). Seismicity associated with theSaorge‐Taggia fault system (ST) [Giammarino et al., 1978;Spallarossa et al., 1997; Turino et al., 2009] and that con-centrated within the Ligurian Sea basin contribute to thestrain rates in this area. As various authors have noted [e.g.,Béthoux et al., 1992; Eva and Solarino, 1998], recent seis-micity and observed deformation rates may be related tothe reactivation in compression the basin. Here, the stressfield is attributable to the basin geometry and to high‐temperature conditions, indicating that the basin has not yetreached thermal equilibrium following the rifting process[Béthoux et al., 2008]. Just east of this area of enhanceddeformation, again with reference to the Ligurian Sea basin(SP 03), Figure 4a displays another nucleus of high strainrate values that may be partially attributed to the actualseismicity, but, more likely, results from the large impact ofthe uncertainty in the magnitude of earthquakes and mmax

(see Figure 6), and also from the assumption of a uniformb value throughout all of the seismotectonic province. Indeed,this area does not come out of Figure 3a. The portion of thewestern Alpine arc sited between the Valais region andwestern Liguria presents lower strain rate values ( _" < 2.0 ×10−9 yr−1, as seen in Figures 3a and 4a), with their minimaconcentrated in a zone just south of Valais. Moving fromthe crest of the chain toward the Po Plain, _" progressivelydecreases to zero. The observed seismic strain rate distri-bution and the current seismotectonic setting of the western

Alpine area could be related to counterclockwise rotation ofthe Adriatic plate around a pole in the Po Plain [Andersonand Jackson, 1987; Calais et al., 2002] and to the gravita-tional reequilibration of the belt from buoyancy forces [Sueet al., 1999; Delacou et al., 2004; Sue et al., 2007b], mostlikely enhanced by erosion [Champagnac et al., 2007].

7. Sensitivity and Uncertainty Analysis

[27] As prefaced in section 6, strain rate maps are affectedby high uncertainty. The values of s

_"displayed in Figures 3b

and 4b are extremely high, resulting in a pronounced dis-persion (measured by the coefficient of variation whichis defined as the ratio of s

_"to the mean _") in the _" value

(statistical) distribution. In high‐seismicity areas, such asnorthern Tuscany, this can be as high as 80%.[28] By randomizing the values of M, mmax, and h in

separate simulations, we can quantify the contribution ofthe uncertainty of each parameter to s

_". To evaluate this

contribution, we compare the values of the _" standard devi-ation obtained by randomizing M, s

_",M, and mmax, s _"mmax,

with those from the randomization of h, s_",h, which was found

to be the minor contributor to the total _" uncertainty. Spe-cifically, the comparison is based on the s

_",M /s _",h and s _"mmax/

s_",h ratios. Note that _" estimates derived by summing earth-

quake moments do not keep into account the variability ofmmax, as they are simply based on the seismic catalog. Thus,the sensitivity of _" to the mmax uncertainty can be onlyexamined when _Mo results from integration of earthquakerecurrence statistics (equations (4) and (5)). Figure 5 presentsthe geographical distribution of s

_",M /s _",h obtained by sum-ming earthquake moments while Figure 6 shows maps of

Figure 5. Geographical distribution of the s_";M/s _",h ratio based on the total moment derived from the earth-

quake catalog.

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s_",M /s

_",h and s _",mmax/s

_",h as derived by applying equations (4)and (5). Figures 5 and 6 use different color scales because ofthe large differences in the range of mapped values. Using thesame scale would not allow the reader to clearly distinguishbetween areas of low s

_"ratios and areas characterized by

higher values. Maps presented in Figures 5 and 6 show thatmost of the uncertainty affecting _" estimates is due to theconversion between different magnitude scales. As shown inFigure 5, indeed, the contribution of the magnitude variabilityto s

_"is at least twice that of h and can be as much as about ten

times greater. Integrating earthquake recurrence statistics(Figure 6) tends to smooth the impact of the uncertaintyassociated with M. In this case, indeed, s

_",M is no more thanthree times greater than s

_",h. Finally, the influence of themmax

variability on strain rate estimates can be almost twice that ofthe seismogenic thickness (Figure 6).[29] Besides the previous parameters, the form of the

earthquake recurrence relation may have a significant impacton seismic strain rate estimates. Figure 7 compares strain ratemaps obtained by applying the truncated models of Fieldet al. [1999] (i.e., equation (4) and Figure 7a) and Cornelland Vanmarcke [1969] (i.e., equation (5) and Figure 7b)separately. Again, these maps display average strain ratesfrom 1,000 Monte Carlo randomizations. The two recurrencemodels provide similar strain rate geographical distributionswith higher values, comparable to those obtained by sum-ming seismic moments (Figure 3a), when _Mo is based on theapplication of the Cornell and Vanmarcke [1969] relation.

Figure 6. Geographical distribution of the (a) s_";M/s _",h and (b) s

_",mmax/s

_",h ratios based on moment ratevalues derived from the application of equations (4) and (5).

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This suggests that this relation mimics best the observedseismicity. As confirmation of this, we compare magnitudedistributions resulting from the application of the Field et al.[1999] and Cornell and Vanmarcke [1969] models withthe observed annual activity rates (Figure 8) for each seis-motectonic province. Here, seismicity rates indicate thetotal number of earthquakes above a given magnitude (i.e.,cumulative GR distribution), N(m). Note, moreover, that themagnitude distributions presented in Figure 8 do not allow forthe uncertainty in M and are simply based on the seismic-ity parameter values estimated from the earthquake catalog(Table 2). As expected, Figure 8 indicates that the Cornelland Vanmarcke [1969] magnitude distribution is closer to

the observed rates, suggesting that it is more suitable forthe characterization of a hazard source model for the areainvestigated. The systematic discrepancy between observedactivity rates and rates predicted by the cumulative truncatedmodel of Field et al. [1999] may be ascribed to the func-tional shape and the approach adopted for truncating theGR distribution. In the case of the Cornell and Vanmarcke[1969] relation, the frequency density function for mag-nitude is truncated and then renormalized (for details, seeMcGuire [2004] or Youngs and Coppersmith [1985]). Inthe case of the Field et al. [1999] model, the Heavisidestep function is used to truncate the incremental magnitudedistribution [Field et al., 1999, equation 4] which is then

Figure 7. Strain rate maps as obtained from the application of (a) equation (4) and (b) equation (5).

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integrated to obtain its cumulative form [Field et al., 1999,equation 4].[30] As a further remark, the contribution of the uncertainty

in the selection of the earthquake recurrence relation to s_"is

almost the same as that of the seismogenic thickness.[31] Although results are not presented, it should be men-

tioned that the procedure used to calculate the coefficient b oftheGR relationwas found to have a significant influence on _".Indeed, comparing preliminary estimates based on the useof the Weichert [1980] maximum likelihood approach (toevaluate earthquake recurrence parameter values) and theassumption that mmax = mmax

obs with analogous estimates but

based on the application of the least squares approachevidences differences in strain rates of up to approximately35–40%.

8. Summary and Conclusions

[32] This paper has presented seismic strain rate maps foran area in northwestern Italy including the Western Alps andNorthern Apennines based on an innovative procedure thatintegrates the smoothed seismicity approach and the Andersonmethod [Anderson, 1979]. According to this procedure, strainrates are based exclusively on the epicenter distribution and

Figure 8. Comparison between observed annual activity rates (gray squares) and magnitude distributionsresulting from the application of the Field et al. [1999] (dashed line) and Cornell and Vanmarcke [1969](solid line) recurrence relations.

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are independent of any specific seismogenic source model.Strain rates were calculated from moment rates that, in turn,were estimated for each cell of a homogeneous grid bysumming the scalar moments collected in the earthquakecatalog and by applying two alternative earthquake recur-rence relations. Although these two approaches lead to similarresults, the former was found to provide a strain rate map thatmore accurately reflects the current seismotectonic settingand the geodynamics of the study area. A MonteCarlo simulation procedure was also adopted to considerthe uncertainty in earthquake magnitude values, maximumearthquake magnitude, and seismogenic thickness. This hasallowed us to quantify the uncertainty in the final strain rateestimates.[33] Seismic strain rates in the study area are quite high,

with mean values ranging between 2 × 10−10 yr−1 and 12 ×10−9 yr−1. Although affected by a high level of uncertainty,the highest deformation rates are observed along the EtrurianFault System in the Northern Apennines, where _" takes val-ues as high as 12 × 10−9 yr−1, corresponding to maximummoment rates of approximately 3.5 × 1014 N m yr−1. Inthe Western Alps, strain rates are at their highest in theValais region ( _" ≈ 6 × 10−9 yr−1) and in western Liguria ( _" ≈4 × 10−9 yr−1) where moment rates are up to approximately1.5 × 1014 N m yr−1.[34] A further objective of this paper was the quantification

of the uncertainty in the strain rate estimates via the appli-cation of a Monte Carlo simulation procedure. As previouslyobserved by various authors [e.g., Anderson, 1986; Mazzottiand Adams, 2005], strain rate values are affected by a sig-nificant uncertainty, mainly due to conversion between dif-ferent magnitude scales. The impact of the uncertainty in themagnitude values was found to be up to 10 times greater thanthe impact of the uncertainty in the seismogenic thickness(Figure 5), which, in turn, is comparable to that in the choiceof the earthquake recurrence relation but is almost half theinfluence of the maximum magnitude variability. In thispaper, we evaluated the influence of two truncated models,proposed by Field et al. [1999] and Cornell and Vanmarcke[1969]. The latter was found to represent more effectively theobserved seismicity, providing deformation rates that werecloser to the those obtained by summing earthquakemomentsand to published geodetic strain rate estimates (see below).Hence, this recurrence relation was deemed most suitablefor the characterization of a seismic source model for thearea investigated. Note that analogous results (not presentedhere) were obtained by setting M0,min = 0 in equation (5) toaccount for events withmagnitude lower thanmmin [McGuire,2004]. This indicates that, as expected, the contributionfrom low‐magnitude earthquakes is negligible in strain rateassessments.[35] Comparing our results with deformation rates obtained

using GPS networks [e.g., Serpelloni et al., 2005; Delacouet al., 2008; D’Agostino et al., 2008] shows that the seismicdeformation explains only a small percentage of the totalgeodetic deformation. With the exception of northernTuscany, where seismic and geodetic strain rates are com-parable, the rate of seismic strain release, indeed, is of∼1 order less than that derived fromGPS data. The significantdiscrepancy between seismic and geodetic strain rates hasalready been documented by other authors [e.g., Hunstadet al., 2003; D’Agostino et al., 2008; Sue et al. 2000, 2007a],

raising the hypothesis of aseismic deformation in theWesternAlps and Northern Apennines. For example, the high geodeticstrain rate values (≈5 × 10−8 yr−1) measured by D’Agostinoet al. [2008] in the southernmost part of the Northern Apen-nines near Gubbio may be related to aseismic slip on the Alto‐Tiberina fault system [Chiaraluce et al., 2007]. In the WesternAlps, the difference between seismic strain rates calculated inthis study and geodetic rates (≈2 − 5 × 10−8 yr−1 [Delacouet al., 2008]) confirms observations by Sue et al. [2000,2007a], indicating that most of the recent Alpine deformationis attributable to aseismic processes, such as the accumula-tion of elastic energy on locked faults, creep on faults, and/orductile‐style deformation in the Earth’s crust [Sue et al.,2000, 2007a]. Furthermore, the discrepancies between seis-mic and geodetic strain rates may also suggest that the recordof seismicity, while extending back over ∼2000 years, maynot provide a sufficient time window for assessment of sec-ular rates of moment release and rates of recurrence of largemagnitude earthquakes. Hence, future research focused onthe estimation of geologic slip rates on Quaternary faultsappears of paramount importance in constraining earthquakeoccurrence rates and estimating the rate of seismic strainrelease with a high level of accuracy.

Appendix A: Magnitude Conversion

[36] As stated in section 3, a uniform magnitude measurewas estimated for each event. Specifically, magnitudes areconverted to Mw, which is taken as the reference scale.[37] Magnitudes in the RSNI bulletin are expressed in

terms of duration (Md) or local (Ml) magnitude [Spallarossaet al., 2002; Bindi et al., 2005] while the CSI catalogindicates the Ml value for most events (moment magnitude,Mw, and body wave magnitude, mb, values are at timesreported instead of Ml). Md values in the RSNI bulletin arefirst converted to Ml using the following equation that wascalibrated within the framework of this study using the leastsquares method:

Ml ¼ 1:251Md � 1:248 ð3:0 � Md � 5:2;�Ml ¼ 0:33Þ ðA1Þ

where sM1indicates the residual standard deviation of the

model.[38] ForMl values lower than 5.8,Mw is estimated using the

conversion equation byCastello et al. [2007], while for largermagnitudes the relationship by Gruppo di Lavoro CPTI[2004] is applied:

Mw ¼ 0:79Ml þ 1:20Mw ¼ 0:812Ml þ 1:145

� ð3:5 � Ml � 5:8;�Mw ¼ 0:20ÞðMl > 5:8;�Mw ¼ 0:25Þ ðA2Þ

Note that when Ml is estimated from Md, uncertainty inMw, sMw

, has to allow for the effect of error propagation.Mathematically, this is expressed as

�Mw;tot ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�2Mw

þ @Mw

@Ml

2

�2Ml

sðA3Þ

As a consequence, sMwincreases from 0.20 to 0.33 for 3.5 �

M1 � 5.8 and from 0.25 to 0.37 for M1 � 5.8.

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[39] For a number of events with magnitude expressed interms of mb, Mw is estimated as follows [Gruppo di LavoroCPTI, 2004]:

Mw ¼ 0:972mb þ 0:265 ð3:0 < mb � 5:5;�Mw ¼ 0:31Þ ðA4Þ

Appendix B: Determination of Coefficient k

[40] The coefficient k in equation (2) is an empiricalconstant which expresses the relationship between the totalseismic moment tensor, Mij

T, along the principle axes ofextension (i = j = 1) and compression (i = j = 2) and the totalscalar moment, M0

T [Chen and Molnar, 1977]:

MTij ¼ kMT

0 ðB1Þ

where MijT = ∑Mij and M0

T = ∑M0. The sum is taken overall seismic events in a catalog of moment tensor solutions.[41] For each seismotectonic province with the exception

of SP 04, the value of k is calculated using the moment tensorsolutions reported in the Italian centroid moment tensor cat-alog [Pondrelli et al., 2006]. Given the limited quantity ofdata for certain provinces, fault plane solutions are groupedinto two distinct data sets, one for the provinces characterizedby a prevalent extensional tectonics (SP 01 and SP 05) andone for those with a compressive regime (SP 02, SP 03,and SP 06). Summing the moment tensors for extensive andcompressive provinces gives

MTij ¼

�4:2 2:3 �1:02:3 1:1 �2:3�1:0 �2:3 3:0

24

35� 1017 N m ðB2Þ

MTij ¼

3:3 0:5 �0:70:5 �3:1 �0:6�0:7 �0:6 �0:2

24

35� 1017 N m ðB3Þ

respectively. Diagonalizing matrix B2, we find that alongthe principle axes of extension and compression M11

T =5.13 × 1017 N m and M22

T = −5.05 × 1017 N m. Analogously,from matrix (B3), we obtain M11

T = 3.49 × 1017 N m andM22

T = −3.18 × 1017 N m. Finally, dividing M11T and M22

T byM0

T (M0T = 5.91 × 1017 N m and M0

T = 5.02 × 1017 N m forextensive and compressive provinces, respectively) gives

MT11 ¼ 0:87MT

0 ðB4Þ

MT22 ¼ �0:85MT

0 ðB5Þ

for the provinces where an extensional tectonics dominatesand

MT11 ¼ 0:69MT

0 ðB6Þ

MT22 ¼ �0:63MT

0 ðB7Þ

for the provinces characterized by a prevalent compressiveregime.[42] Hence, an average values of k equal to 0.86 has been

adopted for SP 01 and SP 05 while a value of 0.66 has been

used for SP 02, SP 03, and SP 06. For SP 04, where only threemoment tensor solutions are available, we have assumed k =0.5 as indicated byMazzotti and Hyndman [2002] for regionswhere strike‐slip rupture mechanisms prevail.

[43] Acknowledgments. This study was developed within the frame-work of the PRIN (Programmi di Ricerca di Rilevante Interesse Nazionale)Project “Dinamica del Sistema Costituito dagli Appennini Settentrionali,dalla Pianura Padana e dalle Alpi” coordinated by R. Sabadini (Universityof Milan) and funded by MIUR (Ministero dell’Istruzione, dell’Universitàe della Ricerca). We thank two anonymous reviewers and the AssociateEditor Rodolfo Console for their thorough review and helpful comments.We are grateful to B. Castello (Istituto Nazionale di Geofisica e Vulcanolo-gia) for providing us with the values of the residual standard deviation of theregression model in equation (A2). We are also grateful to C. H. Scholz andD. Spallarossa for their suggestions and fruitful discussions. We acknowl-edge the use of the Generic Mapping Tools software package byWessel andSmith [1991] to produce most of the figures in this paper.

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S. Barani, C. Eva, and D. Scafidi, Dipartimento per lo Studio delTerritorio e delle sue Risorse, University of Genoa, Viale Benedetto XV 5,I‐16132 Genoa, Italy. (barani@dipteris.unige.it; eva@dipteris.unige.it;scafidi@dipteris.unige.it)

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