viscoelastic relaxation and long-lasting after-slip following the 1997 umbria-marche (central italy)...

Geophys. J. Int. (2007) 169, 534–546 doi: 10.1111/j.1365-246X.2007.03315.xG

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Viscoelastic relaxation and long-lasting after-slip following the 1997Umbria-Marche (Central Italy) earthquakes

R. E. M. Riva,1,∗ A. Borghi,2 A. Aoudia,1,3 R. Barzaghi,2 R. Sabadini4 and G. F. Panza1,3

1Department of Earth Sciences, University of Trieste, Italy. E-mail: [email protected] - Politecnico di Milano, Italy3Abdus Salam International Centre for Theoretical Physics, SAND Group, Trieste, Italy4Geophysics Section, Department of Earth Sciences ‘A. Desio’, University of Milan, Italy

Accepted 2006 November 27. Received 2006 November 15; in original form 2006 July 13

S U M M A R YWe combine Global Positioning System (GPS) measurements with forward modelling of vis-coelastic relaxation and after-slip to study the post-seismic deformation of the 1997 Umbria-Marche (Central Apennines) moderate shallow earthquake sequence. Campaign GPS mea-surements spanning the time period 1999–2003 are depicting a clear post-seismic deformationsignal. Our results favour a normal faulting rupture model where most of the slip is locatedin the lower part of the seismogenic upper crust, consistent with the rupture models obtainedfrom the inversion of strong motion data. The preferred rheological model, obtained fromviscoelastic relaxation modelling, consists of an elastic upper crust, underlain by a transitionzone with a viscosity of 1018 Pa s, while the rheology of deeper layers is not relevant for theobserved time-span. Shallow fault creep and after-slip at the base of the seismogenic uppercrust are the first order processes behind the observed post-seismic deformation. The deepafter-slip, below the fault zone at about 8 km depth, acting as a basal shear through localizedtime-dependent deformation, identifies a rheological discontinuity decoupling the seismogenicupper crust from the low-viscosity transition zone.

Key words: crustal deformation, earthquakes, Global Positioning System (GPS), rheology.

1 I N T RO D U C T I O N

The 1997 Umbria-Marche seismic events represent the strongest

earthquake sequence in Italy in the last two decades.

The Umbria-Marche region, part of the Central Apennines, is

within a complex plate boundary between the Tyrrhenian and the

Adriatic in Central Italy. The regional structural setting is charac-

terized by the presence of normal faults cutting the upper crust, re-

lated to the backarc extension of the west directed Adriatic subduc-

tion with a compressional front progressively migrating eastward

(Pialli et al. 1998; Doglioni et al. 1999). The post-orogenic ex-

tension has been accompanied by thinning of the crust, volcanic

activity and high heat flow (Miocene to Plio-Pleistocene) towards

the Tyrrhenian (Pialli et al. 1998, and references therein). In Plio-

Pleistocene, extension affected the Apennines, where graben-like

structures trending NW–SE overprint the compressional features.

On the Adriatic margin, in contrast, the outer front of the belt still

exhibits thrust faulting (Meletti et al. 2000).

∗Now at: Geophysics Section, Department of Earth Sciences ‘A. Desio’,

University of Milan, Italy.

Two moderate size crustal earthquakes struck the Umbria-Marche

area on September 26: the first event (M w 5.7, 0:33 UTC) was fol-

lowed by a nearby second large shock (M w 6.0, 9:40 UTC). A third

major event took place on October 14 (M w 5.6) at 15 km SE of the

September events. All the mentioned events, together with several

aftershocks (including three with M w ≥ 5.0), exhibited NW trending

normal fault focal mechanisms and relatively shallow hypocentral

depths (less than 7 km) (Amato et al. 1998; Chimera et al. 2003). Fo-

cal mechanisms and epicentral locations of the three largest events

are displayed in Fig. 1.

In 1999 we set-up a first network of six campaign Global Posi-

tioning System (GPS) sites distributed along a 30-km-long transect

crossing the fault responsible of the largest normal faulting earth-

quake (1997 September 26, 9:40, M w 6.0). This network was first

occupied in 1999 October and in 2000 September.

The results of the first two campaigns were published by Aoudia

et al. (2003). The authors showed that relaxation in the crust explains

part of the observed post-seismic deformation. They argued that the

localized deformation may require other processes such as after-slip

or poro-elastic relaxation.

The existing network was extended in 2000, with the addition

of a second transect of four sites crossing the neighbouring fault,

534 C© 2007 The Authors

Journal compilation C© 2007 RAS

Post-seismic deformation in Central Italy 535

12˚36' 12˚48' 13˚00' 13˚12'

42˚48'

43˚00'

43˚12'

0 10 20

km

SEFR

MONT

CERE

COLLVALL

SPEL

RASI

POPO

DIGNCENT

CAME

Mw 5.7 (26/09/97, 0:33)

Mw 6.0 (26/09/97, 9:40)

Mw 5.6 (14/10/97, 15:23)

Tr.A

Tr.B

Figure 1. GPS network, focal mechanisms for the three main earthquakes (from Capuano et al. 2000) and topography of the area. Rectangles represent the

surface projections of the faults, dipping SW, as described in Section 3 (solid blue line for Zollo FM, dashed red line for Salvi FM). Campaign GPS sites are

indicated by circles and diamonds, respectively belonging to the first transect (Tr.A) or the second transect (Tr.B). The continuous station of CAME is indicated

by a full square.

responsible of the first event of 1997 September 26 (0:33, M w 5.7).

The network extension was preceded by the installation of a nearby

continuous GPS station at Camerino (CAME), as a support to cam-

paign measurements. During the 2000 September campaign, we oc-

cupied the network extension for the first time; later, we remeasured

the whole network in 2001 September and 2003 May.

In this paper, we extend the results of Aoudia et al. (2003) by

means of a larger geodetic data set and a refined modelling of the

post-seismic deformation. For the geodetic measurements we ex-

tend the GPS data set with the addition of two GPS campaigns

and the continuous GPS station of CAME. Therefore, we move a

step forward with respect to the 1-D baseline approach adopted

by Aoudia et al. (2003) and we describe deformations in terms of

2-D (planimetric) displacements. For the modelling of post-seismic

deformation, further to viscoelastic relaxation, we explore the con-

tribution of after-slip and poro-elastic processes.

We test the statistical significance of the measurements and com-

pare them with the predictions of several deformation models. Ac-

cordingly, we propose a viscosity structure for the crust and discuss

different published coseismic fault rupture models.

2 S E I S M O T E C T O N I C S E T T I N G

The main active faults of the Umbria-Marche fault zone have been

reported by the GNDT working group (Galadini et al. 2000), and

those recognized as seismogenic are extending along a NW–SE

trend, in an echelon distribution, from Gualdo Tadino to the north up

to Norcia to the south, crossing the Colfiorito basin where the large

1997 September 26 events are located. These faults, dipping towards

the southwest, define a half-graben structure and form a series of

intermontane basins, which alternate with NW–SE trending ranges.

At the southernmost edge of the fault system that has been

reactivated during the 1997 earthquake sequence, Meghraoui et al.(1999) reported NE–SW trending fold axes. The Umbria-Marche

fold and thrust belt is, therefore, likely to be segmented into three

main structural bodies that could explain the interplay between the

last three moderate earthquake sequences in the region: Colfiorito

in 1997, Norcia to the south in 1979 (MS = 5.8; Deschamps et al.1984) and Gubbio to the north in 1984 (MS = 5.2; Haessler et al.1988).

At the scale of the 1997 reactivated fault system, the moment

tensor inversions of the two large September 26 and October 14

events show dominantly normal faulting mechanisms, whereas se-

lected aftershocks (magnitude in the range between 2.7 and 4.4)

within the Colfiorito basin, reveal that the prevailing deformation at

the step-over is of strike-slip faulting type (Chimera et al. 2003).

According to Cello et al. (2000), this step-over zone is marked by

pre-existing transverse faults. Furthermore, within the same area,

Cinti et al. (2000) report several differently oriented cracks inter-

preted as the surface effect of minor displacements along transverse

structures that are likely to be oriented N–S and may correspond to

western edge of the Colfiorito basin. Therefore, it is likely that the

step-over between the 1997 reactivated fault fragments (Meghraoui

et al. 1999), collocated between the rupture areas of the two Septem-

ber 26 events, is of strike-slip type and could have controlled the

lateral propagation of slip.

Shear wave velocity sections across the zone of the 1997 normal

faulting earthquake sequence show that the reactivated SW dip-

ping fault zone, delineated by the earthquake foci of the September

earthquakes, displays a typical thrust fault geometry (Chimera et al.2003). Therefore, the 1997 Umbria-Marche normal fault zone can

be interpreted as an inversion of pre-existing thrust faults, where

structural changes in the upper crust seem to control the present

fault characteristics such as: rupture geometry, pattern of deforma-

tion and emergence towards the surface.

C© 2007 The Authors, GJI, 169, 534–546


536 R. E. M. Riva et al.

Table 1. Fault rupture models for the three largest earthquakes.

Earthquake fault Strike Dip Rake M 0 L W Zmin

model (Nm) (km) (km) (km)

26/9/97, 0:33

Zollo 148◦ 36◦ −106◦ 0.40 × 1018 6 6 3.5

Basili updip ext. 80◦ 0.15 × 1018 3.6 0.4

Salvi 154◦ 46◦ −77◦ 0.48 × 1018 6 7 1.98

26/9/97, 9:40

Zollo 152◦ 38◦ −118◦ 1.00 × 1018 12 7.5 3.5

Basili updip ext. 80◦ 0.29 × 1018 3.6 0.4

Salvi 138◦ 45◦ −75◦ 0.98 × 1018 10 8 0.05

14/10/97, 15:23

Capuano 160◦ 40◦ −105◦ 0.35 × 1018 7 5 4.8

Salvi 135◦ 45◦ 90◦ 0.69 × 1018 8 5.5 2.42

3 FAU LT M O D E L S

A number of papers have been published based on regional and local

seismic networks that estimate the source parameters and discuss

the tectonic significance of the 1997–1998 earthquake sequence

(e.g. Amato et al. 1998; Ekstrom et al. 1998; Meghraoui et al. 1999;

Barba & Basili 2000; Amato & Cocco 2000, and papers therein;

Chiarabba & Amato 2003; Chiaraluce et al. 2003; Chimera et al.2003).

Other papers provide fault rupture models using strong motion

and geodetic data sets. Zollo et al. (1999) propose a rupture model

for the two events on 1997 September 29 by inverting strong motion

data recorded at near-source distances, later updated by Capuano

et al. (2000) with the addition of the 1997 October 14 earthquake.

A number of authors (e.g. Hunstad et al. 1999; Stramondo et al.1999; Salvi et al. 2000; Lundgren & Stramondo 2002; Belardinelli

et al. 2003; Crippa et al. 2006) used GPS and DInSAR data. Basili

& Meghraoui (2001) and De Martini et al. (2003) use levelling

profiles.

The noticeable differences in the various fault rupture models

(Table 1) stands between the strong motion and the geodetic models.

Therefore, we decided to make use of the results published by Salvi

et al. (2000) as far as a geodetic model is concerned (hereafter

defined as Salvi FM), while we took the models published by Zollo

et al. (1999) and Capuano et al. (2000) as reference seismological

model (hereafter defined as Zollo FM). The refinement of Zollo’s

model proposed by Basili & Meghraoui (2001) (hereafter defined

as Zollo-Basili FM), consisting in a high-angle updip extension of

the rupture (Table 1), is also considered.

4 G P S N E T W O R K A N D

M E A S U R E M E N T S

Fig. 1 shows the GPS network covering the study area. The mon-

umentation of each site was carefully performed to ensure a sub-

millimetre centring. At each station point, a 25 cm long still rod

was fixed in solid rock and a properly designed steel pillar holding

the antenna was centred on this ground part. During all campaigns,

data were collected over a period of four consecutive days, with

daily sessions of 8 hr, contemporaneously for all sites. Data analysis

was performed with the Bernese software (Hugenobler et al. 2004),

where the Quasi Iono Free strategy for ambiguity fixing was selected,

among the other possible options. Due to the high ionospheric activ-

Table 2. Formal and re-estimated errors (mm) of the GPS

solutions.

Formal errors Re-estimated errors

2000 1.4 3.9

2001 1.6 4.2

2003 1.4 2.8

ity, mainly in 2001 and 2002, global ionospheric models estimated

by CODE (Hugenobler et al. 2000) were used in the L1 and L2 ambi-

guity estimation step. Tropospheric parameters were estimated on a

two-hourly basis and wet zenith delays were modelled as stochastic

parameters. Observations were first analysed on a daily basis with

multibase approach, yielding full network solutions; subsequently,

the daily network normal equations were combined into multiday

solutions for each year using the ADDNEQ program of the Bernese

software. In order to have realistic errors, formal sigmas, intrinsi-

cally small, have been multiplied by a factor ∼3 as inferred from

the analysis of the daily coordinate solutions repeatability (Table 2).

4.1 Antenna phase-centre variations and reference frames

In Aoudia et al. (2003) the results of the first two GPS campaigns for

the first transect were presented. The measurements at all sites were

in good agreement with model predictions, except for site MONT.

The anomalous behaviour of MONT revealed to be caused by an-

tenna mixing during the first two campaigns. Only at MONT, in fact,

two different antennas have been used in 1999 and in 2000, namely

a TRM22020.00+GP and a TRM33429.00+GP, respectively. All

the other sites have always been measured with the same antennas.

In order to verify if antenna mixing could justify the behaviour

of MONT, proper tests have been performed by Barzaghi & Borghi

(2004). The results of these tests show that antenna mixing using rel-

ative Phase-Centre Variation (PCV) parameters is critical in terms of

repeatability. By processing the data with relative PCV parameters,

differences in the height component up to 7 mm were estimated. On

the contrary, submillimetre coordinates differences were obtained

by processing the same data with the absolute PCV parameters pro-

vided by the German company GEO++ GmbH (Menge et al. 1998).

The reprocessing of the GPS data published by Aoudia et al.(2003) using these absolute PCV calibration led to an estimate in

the MONT baseline variation which amounts to 5 mm (instead of

8 mm obtained with the relative parameters provided by the US

National Geodetic Survey). This new result is in better agreement

with the model predictions of Aoudia et al. (2003).

Consequently, all the GPS campaigns (1999 October and 2000

September) and the new campaigns (2001 September and 2003 May)

have been processed (or reprocessed) using the absolute GEO++PCV parameters. Furthermore a new continuous station, established

in Camerino (CAME), has been added to the 10 points of our cam-

paign network. CAME has been set up in 2000 April.

All the campaigns have been framed in the ITRF97 and ITRF00

(Altamimi et al. 2002) (ITRF97 for the first three campaigns and

ITRF00 for the last one, respectively), using the precise ephemerides

provided by the International GNSS Service (IGS) and the IGS

continuous stations MEDI and UNPG. Transformation parameters

between frames (ftp://lareg.ensg.ign.fr/pub/itrf/ITRF.TP) have been

applied to allow the comparison between all campaigns. However,

as we are dealing with a local network, any slight mismodelling in

the transformation parameters has a negligible impact on relative

displacements (computed with respect to CAME).

C© 2007 The Authors, GJI, 169, 534–546



In fact, if we consider the general transformation formula between

frames

�X 2(P) = �X 1(P) + �T + (DI + δR) · �X 1(P), (1)

where �X1(P) and �X2(P) are the coordinates into two different frames

(in our case, ITRF97 and ITRF00, respectively); �T is the translation

vector computed at the actual epoch, taking into account its rate

from the reference epoch 1997.0; δR is the rotation matrix for small

rotation angles (r 1, r 2 and r 3) and is given by

δR =∣∣∣∣∣∣

0 −r3 r2

r3 0 −r1

−r2 r1 0

∣∣∣∣∣∣ (2)

D is the scaling factor; we have, for relative displacements,

δ �Xi j2 (P) = �X j

2 − �Xi2 = δ �Xi j

1 (P) + D · δ �Xi j1 (P) + δR · δ �Xi j

1 (P).

(3)

As the rotation angles r 1, r 2 and r 3 between the ITRF00 and

ITRF97 and their rates are very small (the only non-zero term is

the rate of r3 with a value of 0.02 millisecondarc yr−1), the term

δR · δ �Xi j1 (P) is negligible because in our network the maximum

distance is about 39 km (baseline SPEL—CAME). The same holds

for the term D · δ �Xi j1 (P), as the factor (D) and its rate are 1.55

and 0.01 ppb, respectively. So, the relative displacement vector has,

at first order, the same components in the two different reference

frames.

4.2 Displacement vectors for the whole network

Due to the availability of a larger network and of the CAME con-

tinuous station for the campaigns starting from year 2000, we de-

cided to proceed with vector displacements. In this way, even if

we neglect the 1999 campaign, we gain a realistic description of

the post-seismic deformation process. The baseline approach, in

fact, has major shortcomings: it neglects the component of motion

perpendicular to the baseline and is intrinsically biased by the low

accuracy of the vertical component. Nonetheless, for sake of com-

pleteness, at the end of Section 7 we shortly show and discuss rates

of post-seismic deformation along a profile.

12˚ 36' 12˚ 48' 13˚ 00' 13˚ 12'

43˚ 00'

43˚ 12'

SEFR

MONT

CERE COLLVALL

SPEL

RASI

POPO

DIGN

CENT

CAME

2003-2000

0 5 10

km

.

2001-2000

.

2003-2001

10 mm

Figure 2. GPS displacements with respect to CAME. Error ellipses represent 1σ . Surface fault projections are indicated with solid line rectangles for Zollo

FM and with dashed line rectangles for Salvi FM.

Campaign results are displayed in Fig. 2, separately for years

2001–2000, 2003–2001 and 2003–2000.

We see from Fig. 2 how the far-fault sites show a consistent mo-

tion through the years, while the near fault sites reveal a different

behaviour. The near fault sites CERE, COLL and MONT show an

inversion of the direction of motion between 2001–2000 and 2003–

2001. The near fault sites on the second transect, POPO, DIGN

and CENT, exhibit an almost 90◦ rotation between 2001–2000 and

2003–2001. RASI is the only site not showing any motion between

2001 and 2003.

The availability of uniformly measured and processed GPS data

clearly highlights a long-lasting control of the deformation lo-

calized around the fault, superimposed to a longer wavelength

deformation process, as exhibited by the difference in motion

of near fault sites (CERE, COLL, MONT and POPO, DIGN

and CENT) when compared to far-fault sites (SPEL, VALL and

SEFR).

4.3 Statistical comparison between geodetic and model

deformations

In order to compare the deformations from geodetic measurements

and those predicted using different geophysical models, we have

applied two different test statistics. The rationale for an accurate

characterization of the statistical tests, besides our belief that statis-

tics represents a powerful tool for the interpretation of any set of

measurements, lies in the fact that the magnitude of the displace-

ments that we are observing is challenging the capabilities of GPS

campaigns. Therefore, we have opted for a very accurate statistical

approach to the analysis of our data set, aiming to extract all the

information it might contain.

In the first case, after defining the vector d ξ as the GPS horizontal

displacements in the (N,E) coordinates between two epochs, that is,

d ξ = ξ (t2) − ξ (t1), and the corresponding dξM

coming from a

geophysical model, we want to test the hypothesis

H0 : d ξ = dξM

. (4)

C© 2007 The Authors, GJI, 169, 534–546



Assuming that the estimates are normally distributed, it can be shown

that

1

m(d ξ − dξ

M)+(N−1

1 + N−12 )−1(d ξ − dξ

M)

(n1 − m)σ 201 + (n2 − m)σ 2

02

n1 + n2 − 2m

= Fm,n1+n2−2m, (5)

where N 1 and N 2 are the normal matrices of the adjusted horizontal

(N,E) coordinates at epochs t1 and t2, propagated from the GPS geo-

centric coordinates covariance matrices; n1 and n2 are the number

of observations at epoch t1 and t2, respectively; m is the number of

estimated parameters; σ 201 and σ 2

02 are the solution variances.

Eq. (5) holds under the hypothesis

H0 : σ 201 = σ 2

02 (6)

which can be verified using the following test

σ 201

σ 202

=χ2

n1−m

n1 − mχ 2

n2−m

n2 − m

= Fsp ≤ Fn1−m,n2−m . (7)

In our case, this condition is verified for the 2000, 2001 and 2003

estimated variances at a significance level α = 10 per cent.

Eq. (5) is derived from the standard Fisher’s test on least squares

adjusted parameters that is commonly used in control problems

(Mikhail 1976). It can be applied to the whole displacement vector

(the entire network), on a part of it (e.g. one of the two transects) or

on a single point. Moreover, it has been generalized to allow distinct

normal matrices at epochs t1 and t2 and to be applied to horizontal

components only (see also Anzidei et al. 1996). In fact, in the stan-

dard Fisher’s test, the observation scheme and the stochastic model,

that is, the design matrices and the observation covariance matri-

ces, are supposed to be the same at the two control epochs. This

assumption is not realistic in case of GPS measurements, since at

least the satellite configuration is varying in time. Besides, as we

are mainly interested in the horizontal displacements coming from

the GPS network, we set up the test for the horizontal displacements

d ξ = (d N , d E), transforming the adjusted geocentric coordinates

(X , Y , Z) to local coordinates (N , E, U) and propagating their co-

variances.

Under the hypothesis (6), a second statistic can also be used in or-

der to rank the different model predictions versus the GPS estimated

displacements.

The quadratic form of the normalized horizontal residuals U is

chi-square distributed

U+C−1U = χ2m, (8)

where U is the difference between the horizontal GPS displace-

ments, d ξ = ξ (t2) − ξ (t1) and the horizontal geophysical model

displacements dξM

, C−1 is the inverse covariance matrix of the hor-

izontal displacement (N,E), propagated from the geocentric coordi-

nate covariance matrix. The lower is the χ2m value the better is the

agreement with the tested model.

In order to verify the statistical significance of the geodetic mea-

surements, the Fisher’s test is here applied to the null-displacement

model dξM

= 0. The hypothesis

H0 : d ξ = 0 (9)

has been tested according to eq. (5). At a significance level α =10 per cent, this hypothesis has been rejected both for the global

network and the two transects separately, as shown in Table 3 where

Table 3. Statistical significance of the GPS horizontal displacements. The

theoretical Fisher value Fth has been computed at significance level α =10 per cent. For each couple of campaigns, the first column stands for the

whole network (All), the second column for the transect through the main

fault (Tr.A, SPEL-SEFR) and the third column for the second transect (Tr.B,

RASI-CENT).

Campaigns All Tr.A Tr.B

Fsp Fth Fsp Fth Fsp Fth

2001–2000 16.30 1.48 11.90 1.64 15.78 1.80

2003–2001 21.61 1.48 16.24 1.64 28.32 1.80

2003–2000 21.06 1.48 27.33 1.59 20.85 1.72

Table 4. χ2 values for the null-displacement model.

Campaigns All Tr.A Tr.B

2001–2000 326 143 126

2003–2001 432 195 227

2003–2000 412 328 167

the values Fsp are much larger than the values Fth. Thus, the GPS

derived horizontal displacements are statistically different from zero

and it is meaningful to compare them with the predictions coming

from the geophysical models.

To be used as reference for the χ2m values listed in Sections 5 and

7, in Table 4 we list the χ 2 values for the null-displacement model,

where we have dropped the subscript m in the notation.

5 V I S C O E L A S T I C R E L A X AT I O N

The main purpose of this section is to test the effect of different fault

and earth models on the observed post-seismic deformation through

viscoelastic relaxation only. For this purpose, the three different fault

models (Table 1) are coupled to a number of candidate earth models

(Table 5).

Viscoelastic relaxation modelling is computed on the basis of up-

graded normal mode relaxation models with a Maxwell viscoelas-

tic rheology for a vertically stratified spherical Earth (Sabadini &

Vermeersen 1997; Riva & Vermeersen 2002).

Though aware of the importance of power-law rheologies in con-

trolling viscoelastic relaxation (e.g. Freed & Burgmann 2004), we

decided to model relaxation by means of a linear rheology due to

the characteristics of our data set:

(1) Sparse campaign data: the density of the network (only 10

sites) and the availability of yearly campaigns does not allow to

follow in detail the time-dependence of the relaxation process.

(2) Specific time-window covered by the observations: we have

at our disposal measurements between 2 and 5.5 yr after the

Table 5. Crustal earth models used in this study. UC: upper crust, TZ: crustal

transition zone, LC: lower crust.

Layer UC TZ LC

Model Thick. Visc. Thick. Visc. Thick. Visc.

(km) (Pa s) (km) (Pa s) (km) (Pa s)

LC17 8 ∞ 12 1018 15 1017

LC18 8 ∞ 12 1018 15 1018

TZ18 8 ∞ 12 1018 15 ∞TZ517 8 ∞ 12 5 × 1017 15 ∞TZ518 8 ∞ 12 5 × 1018 15 ∞d8-d13 8 ∞ 5 1018 22 ∞d10-d20 10 ∞ 10 1018 15 ∞

C© 2007 The Authors, GJI, 169, 534–546



12˚ 36' 12˚ 48' 13˚ 00' 13˚ 12'

43˚ 00'

43˚ 12'

SEFR

MONT

CERE COLLVALL

SPEL

RASI

POPO

DIGN

CENT

CAME

GPS (10 mm)

.

.

.

.

.

.

...

.

.

Zollo FM

.

.

.

.

.

.

...

.

.

Zollo-Basili FM

.

.

.

.

.

.

...

.

.

Salvi FM

Figure 3. 2003–2000 GPS and viscoelastic relaxation for model TZ18. Error ellipses represent the 98 per cent confidence level.

earthquakes, which do not cover either the early post-seismic part

(first 2 yr) or the relaxation occurring over time scales longer than

5 yr.

Moreover, the moderate size of the earthquakes can only lead to

relaxation rates in the order of a few millimetres per year, so that

measurement errors would partially mask qualitative differences in

the relaxation process. Therefore, our findings cannot exclude non-

linear or transient rheologies, although our viscosity values can be

interpreted as indicative of those attained by power-law rheologies

at various depths, in case non-linear flow is operative in the crust.

In Fig. 3, we show GPS displacements compared to one example

of viscoelastic relaxation for years 2003–2000, for the three different

fault models Zollo FM, Zollo-Basili FM and Salvi FM, with the

candidate earth model TZ18.

As far as the first transect, Tr.A (Fig. 1), is concerned, Zollo FM

provides a definitely better fit than the geodetic Salvi FM, especially

at the furthermost sites (SPEL, VALL and SEFR). The addition of

the shallow nearly vertical fault extension by Basili & Meghraoui

(2001) leads to a minor change in the fit, mostly effective at site

MONT. All fault models predict a similar motion at CERE, whereas

Salvi FM represents the best fit at COLL, even if all predictions fall

within the error ellipse.

For the second transect, Tr.B (Fig. 1), the situation is different,

because Zollo FM and Zollo-Basili FM better reproduce the two

northernmost sites DIGN and CENT, whereas Salvi FM provides a

better fit at POPO and RASI.

The general features of earth model TZ18 are maintained by the

other models listed in Table 5. For this reason, we will discuss the

performance of the various Earth and fault models on the basis

of the Chi-square values listed in Table 6, as the hypothesis H0 :

d ξ = dξM

is not verified for any viscoelastic relaxation model, both

globally and per transect.

Moreover, since the trend of all viscoelastic relaxation scenarios

remains rather constant in the time-span observed by our GPS mea-

surements, we have decided to compare viscoelastic models only

against the campaigns 2003–2000. We have thus neglected the par-

ticular year-to-year behaviour mainly marked by a clear twisting

in the vectors of the displacement field that cannot be reproduced

by any viscoelastic relaxation model. However, we have verified

that our χ2 analysis, listed in Table 6, is also representative of the

campaigns 2001–2000 and 2003–2001 when considered separately.

5.1 Sensitivity to TZ and LC viscosity

All listed earth models provide, for the seismological fault model

Zollo FM, an improvement with respect to the null-displacement

case (Table 4). In particular, a change in the LC viscosity has only

a small impact on the expected viscoelastic relaxation: almost no

difference is seen between a LC that is either elastic (mod.TZ18) or

with a viscosity of 1018 Pa s (mod.LC18), whereas a further lowering

of LC viscosity to 1017 Pa s (mod.LC17) leads to a worsening of the

fit. According to this result, in most earth models we have considered

an elastic LC, in order to isolate the effect of viscoelastic relaxation

in the TZ, which appears to be the main contributor to the observed

surface deformation. A change in TZ viscosity from the value of

1018 Pa s (mod. TZ517 and TZ518) leads to a gradual worsening of

the fit, due to a general reduction in the magnitude of viscoelastic

relaxation. In fact, a higher viscosity slows down the relaxation

process, whereas a lower viscosity shifts most of the displacement

to the first 3 yr after the earthquakes, thus prior to the considered

GPS campaigns.

The addition of a shallow and high-angle fault, as proposed in

Basili & Meghraoui (2001), produces a similar behaviour with re-

spect to changes in the earth models, but the weight of the two fault

Table 6. χ2 test for various Earth and fault models, for GPS campaigns

2003–2000.

Model Zollo Basili Salvi

All Tr. A Tr. B All Tr. A Tr. B All Tr. A Tr. B

LC17 323 230 133 357 268 107 429 298 150

LC18 298 197 125 322 230 100 440 298 161

TZ18 300 205 117 325 238 97 429 307 150

TZ517 325 237 127 361 281 101 374 281 124

TZ518 328 227 143 335 238 133 404 306 145

d8-d13 308 220 105 327 242 97 388 299 120

d10-d20 351 240 165 352 250 140 426 299 175

C© 2007 The Authors, GJI, 169, 534–546



segments changes. In fact, a general deterioration of the fit for the

first transect is accompanied by an improvement in the fit of the sec-

ond transect; nonetheless, the global fit is slightly worse than that

obtained with Zollo FM.

The situation is different for the geodetic model Salvi FM that

points to a TZ viscosity of 5 × 1017 Pa s. However, the agreement of

this fault model with the GPS measurements is generally worse than

that obtained with the seismological model, with χ 2 values mostly

close to the results of the null-displacement model (Table 4).

5.2 Sensitivity to TZ thickness and location

An important issue about the earth models is represented by the ac-

tual thickness and location of the TZ. From Section 5.1, we learned

that the most important contribution to the viscoelastic relaxation

is coming from the low-viscosity TZ, which has been so far rep-

resented by a 12-km-thick layer underlying an 8-km-thick elastic

upper crust (see Table 5). An important issue about the earth mod-

els is represented by the actual thickness and location of the TZ.

The hypothesis of an 8-km-thick UC is justified by a number of

arguments:

(1) The abrupt cut-off of the 1997 aftershock sequence (e.g.

Amato et al. 1998; Cattaneo et al. 2000).

(2) The shallow regional seismicity (Chiarabba et al. 2005).

(3) Results from deep crust reflection studies (Pialli et al. 1998)

and more recent shear wave velocity models (Chimera et al. 2003).

Nonetheless, it is worth analysing the effect of a slightly thicker

UC, as in model ‘d10–d20’: the result for the seismological fault

model is a marked reduction in the magnitude of deformation, with

the consequent deterioration of the global fit, whereas in the case of

the geodetic fault model it leads to an improvement of the fit for the

first transect and a deterioration for the second transect, leaving an

almost unchanged overall fit.

On the other side, the location of the boundary between the TZ and

the LC, so far fixed at 20 km depth, can reasonably be as shallow as

12˚36' 12˚48' 13˚00' 13˚12'

42˚48'

43˚00'

43˚12'

SEFR

MONT

CERE COLLVALL

SPEL

RASI

POPO

DIGN

CENT

CAME

GPS (10 mm)

0 5 10

km

Figure 4. 2003–2000 GPS (black arrows) and total poro-elastic relaxation (red arrows). Error ellipses represent the 98 per cent confidence level.

13 km, according to what is suggested by local seismic profiles Pialli

et al. (1998) and S-wave velocity profiles Chimera et al. (2003). The

earth model with a 5-km-thick TZ is labelled ‘d8–d13’: it provides

a small increase of the fit for Salvi FM, mainly due to a better

reproduction of the motion along the second transect, and a little

deterioration in the fit of the first transect for Zollo FM, while the

result of Zollo-Basili FM remains almost unvaried.

We can thus state that the thickness of the top elastic layer is a

crucial parameter to reproduce the observed motions by means of

viscoelastic relaxation, whereas the model is rather insensitive to

the actual thickness of the first viscoelastic layer.

In conclusion, the earth model for viscoelastic relaxation that

provides the best fit to the GPS measurements presents a low vis-

cosity layer (TZ, η = 1018 Pa s) located below a rather thin UC

(8 km thick). The thickness of the TZ (between 5 and 12 km) and the

viscosity of the LC have only a small impact on the modelled defor-

mation and are thus not sufficiently resolved by the data. Moreover,

the preferred fault model is represented by the solution published

by Zollo et al. (1999).

6 P O RO - E L A S T I C R E L A X AT I O N

Besides viscoelastic relaxation, another potentially important Post-

seismic process is represented by poro-elastic relaxation, due

to changes in pore-fluid pressure induced by the earthquakes

(e.g. Peltzer et al. 1998; Fialko 2004). We computed the fully re-

laxed poro-elastic signal by calculating the difference between the

elastic deformation induced by the earthquakes in undrained and

drained crustal rocks. In the attempt of maximizing the poro-elastic

response, we have chosen extreme values of Poisson’s ratio, namely

ν = 0.35 and ν = 0.20, to represent the undrained and drained elastic

moduli, respectively. The elastic deformation has been modelled by

means of an Okada (1985) half-space model (Feigl & Dupre 1998).

In Fig. 4, we show the resulting displacements vectors at the

GPS sites, together with the observed displacement for years 2003–

2000, for the case of Zollo FM. As we can see, the signal induced

C© 2007 The Authors, GJI, 169, 534–546



by poro-elastic relaxation is much smaller than the observed GPS

motion, and this result becomes even more clear when we consider

two important aspects:

(1) In the first place, the chosen Poisson’s ratios represent extreme

values, so that actual poro-elastic relaxation can easily be smaller

than what we have computed.

(2) Second and most important, our GPS motions concern a spe-

cific time-window, between 3 and 5.5 yr after the earthquakes, so

that we are not able to observe the large portion of poro-elastic re-

laxation that has probably taken place right after the earthquakes, as

also inferred from the rock properties of the UC derived from 3-D

tomography (Monna et al. 2003).

Considering those results, in the rest of our study we have de-

cided to regard poro-elastic relaxation as a second order process;

therefore, we have not included it further in our effort of modelling

the observed GPS motions.

7 A F T E R - S L I P

We have discussed how viscoelastic and poro-elastic relaxation are

largely underestimating the horizontal GPS displacements. More-

over, the measured displacements of the near fault sites, shown in

Fig. 2, present large variations in the motion directions between

campaigns 2001–2000 and 2003–2001 that are not reproduced by

any relaxation model. In order to account for the missing deforma-

12˚ 36' 12˚ 48' 13˚ 00'

43˚ 00'

43˚ 12'

CENT

DIGN

POPO

RASI

SEFR

MONT

COLLCEREVALL

SPEL

10 mm

(a)

12˚ 36' 12˚ 48' 13˚ 00'

43˚ 00'

43˚ 12'

CENT

DIGN

POPO

RASI

SEFR

MONT

COLLCEREVALL

SPEL

¿ g

(b)

12˚ 36' 12˚ 48' 13˚ 00'

43˚ 00'

43˚ 12'

CENT

DIGN

POPO

RASI

SEFR

MONT

COLLCEREVALL

SPEL

¿ g

(c)

12˚ 36' 12˚ 48' 13˚ 00'

43˚ 00'

43˚ 12'

CENT

DIGN

POPO

RASI

SEFR

MONT

COLLCEREVALL

SPEL

¿ g

(d)

Figure 5. 2001–2000 GPS (black arrows) and predicted displacements (coloured arrows) for Zollo FM. Error ellipses represent the 98 per cent confidence

level. Panel (a) represents viscoelastic relaxation for earth model TZ18; panel (b) after-slip on a 6-km-wide horizontal fault at the base of the UC, under the

footwall of the main fault; panel (c) after-slip on the updip extension of both faults, between 2 and 4 km depth; panel (d) the summation of the three contributions

from panels (a), (b) and (c).

tion, in this section we explore the contribution of after-slip, another

potentially important post-seismic process (e.g. Savage et al. 1994;

Pollitz et al. 1998). By after-slip we mean potentially either shallow

fault creep, aseismic slip below the fault zone, or both.

We have studied the effect of after-slip on separate segments for

different combinations of the two fault models (Zollo FM, Salvi FM)

for the two main shocks. The after-slip segments are as follows.

(1) Coseismic faults.

(2) Updip extensions of the faults, with the same dip.

(3) Vertical updip extension of the faults, as proposed by Basili

& Meghraoui (2001).

(4) Downdip extension of the faults.

(5) Horizontal faults at the base of the UC.

For each fault segment, we explore variable amount of slip, rake

and fault width. By means of a trial-and-error approach, minimizing

the misfit between measurements and model results, we search for

the best values for the above parameters.

Slip on the coseismic faults or on their downdip extentions does

not provide any satisfactory fit to the observed GPS motions. Our

tests have shown how the effect of accelerated creep on and below the

coseismic faults is only relevant for near-fault sites on the hanging

wall, but also in this case the impact is reduced to negligible values by

our trial and error minimization of the misfit with the measurements.

Differently, slip on shallow fault extensions, besides being con-

sistent with studies on the mechanics of after-slip (Marone et al.1991), provides an important contribution to the observed motions,

C© 2007 The Authors, GJI, 169, 534–546



in particular to the reversal of the near-fault displacement observed

after 2001, and will be discussed extensively.

We start our analysis with the displacements in the years 2001–

2000 for Zollo FM, shown in Fig. 5. It is evident from panel (a),

where GPS motions are compared with the predictions of viscoelas-

tic relaxation for earth model TZ18, that most of the deformation

remains unaccounted for, especially at the three sites closer to the

main fault (CERE, COLL and MONT). Large near-fault motions

are only reproduced by a rather shallow slip. Moreover, the direc-

tion of motion requires that slip occurs on a low angle fault, likely

corresponding with an updip extension of the main shock rupture.

The best-fitting model of shallow after-slip, shown in panel (c), al-

locates about 7 cm normal slip with a left-lateral component on the

updip extensions of both faults, between a depth of 2 and 4 km.

A better approximation to the motions observed at the furthermost

sites requires the addition normal slip on a horizontal fault plane

at the base of the UC. Keeping fixed the length of the horizontal

segment, equal to the length of the coseismic fault, we have tested

different locations, from the hanging wall to the footwall, and along-

dip dimensions, from 3 to 18 km: the best-fitting model, shown in

panel (b), presents 5 cm of normal slip on a 6-km-wide fault located

below the footwall of the main fault.

The three contributions, namely viscoelastic relaxation, slip on

the updip extension and deep horizontal after-slip, are summed to

provide the best-fitting model, represented in panel (d) of Fig. 5. We

clearly see that a good agreement between measured and modelled

displacements is reached at most sites, with the exception of those

sites that show a deviation from the general trend of motion. The

fact that we apply a homogeneous slip on the various fault segments

is likely the main reason for the trade-off between the different

contributions, that prevents us from obtaining a better fit at some

specific sites without a general deterioration of the fit for the rest

of the network. The improvement with respect to pure viscoelastic

relaxation is also demonstrated by the χ2 values listed in Table 7.

The effect of after-slip for Salvi FM is shown in Fig. 6. Differ-

ently from the previous case, the most important contribution comes

from 9 cm of normal slip on a 9-km-wide horizontal fault plane at

the base of the UC, displayed in panel (b). This segment has been

localized below the footwall, according to the same procedure pre-

viously discussed for Zollo FM. A further refinement comes from

the addition of 4 cm of normal slip on the upper segment of the main

fault, between a depth of 1.5 and 0.5 km, displayed in panel (c).

The χ 2 values listed in Table 7 show how the best model for Salvi

FM has a slightly worse overall fit that Zollo FM. In particular, Zollo

Table 7. χ2 test for the combined viscoelastic relaxation—after-slip models. Sites passing the Fisher test at significance level α = 1 per cent are also listed.

Model All Tr. A Tr. B Fisher Tr.A Fisher Tr.B

2001–2000, Zollo FM

Relax (TZ18) 295 123 154 SPEL, SEFR DIGN

After-slip 145 77 67 SPEL, VALL, COLL, MONT, SEFR POPO, DIGN, CENT

Relax + After-slip 141 68 68 SPEL, VALL, COLL, MONT, SEFR RASI, DIGN

2003–2001, Zollo FM

Relax (TZ18) 381 110 185 SPEL, MONT, SEFR RASI

After-slip 179 40 139 SPEL, VALL, CERE, COLL RASI, DIGN

Relax + After-slip 191 72 112 SPEL, VALL, CERE, COLL RASI, DIGN

2001–2000, Salvi FM

Relax (TZ18) 329 156 100 - CENT

Relax + After-slip 165 99 63 SPEL, VALL, MONT, SEFR POPO, CENT

2003–2001, Salvi FM

Relax (TZ18) 471 204 264 MONT RASI

Relax + After-slip 438 192 208 MONT -

FM has a better performance at COLL, POPO and DIGN, whereas

Salvi FM provides better results at RASI and CENT.

GPS motion vectors for the years 2003–2001, as already antici-

pated, present rather large differences with respect to years 2001–

2000: CERE, COLL and MONT invert the motion direction, while

POPO, DIGN and CENT are rotated by about 90◦ clockwise. Vec-

tors are displayed in Fig. 7, together with model results for Zollo

FM.

The motion of sites CERE, COLL and MONT can be grossly ex-

plained by 10 cm of after-slip on the almost vertical updip extension

proposed by Basili & Meghraoui (2001), here confined between a

depth of 4 and 2 km on the main fault, and shown in panel (c). Slip

on a horizontal fault at the basis of the UC becomes more important,

with the allocation of about 10 cm of normal slip on a 4 km-wide

fault below the hanging wall for both faults. It provides necessary

motion at sites SPEL, VALL, DIGN and CENT, and at the same

time contrasts the otherwise exceedingly large NE-motions at sites

MONT and SEFR, as shown in panel (b). Magnitudes and direc-

tions at SPEL, VALL and SEFR are similar to those of viscoelastic

relaxation, represented in panel (a). The summation of the three con-

tributions, displayed in panel (d) of Fig. 7, represents our best-fitting

model: part of the deformation remains unexplained, particularly at

MONT, where the two vectors are almost perpendicular, and POPO,

where the large measured displacement is completely unaccounted

for. Those two sites, however, are at the border of an abrupt change

in motion, namely the observed shortening of the baselines MONT-

SEFR and RASI-POPO, which represent a small scale behaviour

difficult to reproduce with our approach, where homogeneous slip

is applied on relatively large fault segments. Again, the significant

improvement with respect to pure viscoelastic relaxation is seen in

the χ2 values listed in Table 7.

It proves difficult to construct an adequate after-slip model for

2003–2001 starting from the coseismic rupture geometry of Salvi

FM. In this case, in fact, we miss the possibility of allocating slip

on a shallow and nearly vertical fault, since the results published

by Basili & Meghraoui (2001) have been obtained after using as

reference rupture model the deeper fault of Zollo et al. (1999).

From the χ 2 values listed in Table 7, we can see how only a minor

improvement to the fit of viscoelastic relaxation comes from the

addition of the best after-slip model for Salvi FM, represented by

3 cm of normal slip on the main fault between a depth of 3.5 and

1.5 km.

The rather good agreement between the GPS motions and the

predictions of the best post-seismic deformation models allows to

C© 2007 The Authors, GJI, 169, 534–546



12˚ 36' 12˚ 48' 13˚ 00'

43˚ 00'

43˚ 12'

CENT

DIGN

POPO

RASI

SEFR

MONT

COLLCEREVALL

SPEL

10 mm

(a)

12˚ 36' 12˚ 48' 13˚ 00'

43˚ 00'

43˚ 12'

CENT

DIGN

POPO

RASI

SEFR

MONT

COLLCEREVALL

SPEL

¿ g

(b)

12˚ 36' 12˚ 48' 13˚ 00'

43˚ 00'

43˚ 12'

CENT

DIGN

POPO

RASI

SEFR

MONT

COLLCEREVALL

SPEL

¿ g

(c)

12˚ 36' 12˚ 48' 13˚ 00'

43˚ 00'

43˚ 12'

CENT

DIGN

POPO

RASI

SEFR

MONT

COLLCEREVALL

SPEL

¿ g

(d)

Figure 6. 2001–2000 GPS (black arrows) and predicted displacements (coloured arrows) for Salvi FM. Panels (a) and (d): same as Fig. 5. Panel (b): after-slip

on a 9-km-wide horizontal fault at the base of the UC, under the footwall of the main fault; panel (c): after-slip on the upper segment of the main fault, between

0.5 and 1.5 km depth.

go beyond the χ2 values, which are only a measure of the misfit, and

discuss the statistical significance of the model predictions by means

of the Fisher’s test described in Section 4.3. In the right column of

Table 7, we list the sites for which the model predictions pass the

Fisher’s test at significance level α = 1 per cent.

In the case of the results for Zollo FM in years 2001–2000, we

see that viscoelastic relaxation alone provides a significant fit only

at sites SEFR, SPEL and DIGN. After-slip alone allows success-

ful predictions at five sites on Tr.A, missing CERE, and the same

result is obtained by the combined after-slip and relaxation model,

meaning that the two models are statistically equivalent. Larger dif-

ferences are present on Tr.B, because both models fit DIGN, but

after-slip alone fits also POPO and CENT, whereas the combined

after-slip and relaxation model fits RASI.

Salvi FM for years 2001–2000 provides similar results, further

missing only COLL on Tr.A and DIGN on Tr.B. Both sites are

situated directly above the two main faults according to Salvi et al.(2000): therefore, the observed misfit might be due to an erroneous

fault location either horizontally or in depth.

For the 2003–2001 campaigns only Zollo FM provides a statisti-

cally significant fit to the GPS data. Pure relaxation fits three sites

on Tr.A, SEFR, MONT and SPEL and RASI on Tr.B. After-slip

alone and the combined after-slip relaxation model are statistically

equivalent and fit the four southernmost sites of Tr.A, in addition

to RASI and DIGN on Tr.B. The degrading of the fit at MONT

and SEFR introduced by the after-slip model is due to the necessity

of fitting large and opposite motions at the remaining four sites of

Tr.A and could not be avoided. On Tr.B, only DIGN shows a motion

that is both significantly different from zero and reproduced by the

after-slip model.

In Fig. 8, we show rates of horizontal baseline variations along

Tr.A, with respect to the westernmost site SPEL. GPS results for

campaigns 2000–1999, represented by open stars joined by a dot-

ted line, have only a reference purpose because they have not been

used in the rest of the study. Model results are obtained by the joint

contribution of relaxation and after-slip for fault model Zollo FM.

The fit between measurements and model results is in most cases

well within the 68 per cent confidence level. In agreement with what

has already been largely discussed in the previous sections, also in

the baseline representation we can see how SPEL-VALL is always

shortening, at a rate decreasing after 2001, while the three sites near-

est to the fault are moving towards SPEL between 2000 and 2001

(green dots and squares) and in the opposite direction between 2001

and 2003 (red dots and diamonds). The baseline SPEL-SEFR is

not showing any significant motion between 1999 and 2003, while

model results give extention rates of 2–3 mm yr−1, but this discrep-

ancy is consistent with the expected measurement error. The large

variation in the direction of motion between 2000 and 2003 can only

be reproduced by after-slip, since viscoelastic relaxation alone gives

rise to a deformation pattern analogous to the one between 1999 and

2000, as reported by Aoudia et al. (2003).

8 D I S C U S S I O N

The study of deformation between 1999 and 2003 has clearly in-

dicated that long-lasting after-slip is the main post-seismic process

C© 2007 The Authors, GJI, 169, 534–546



12˚ 36' 12˚ 48' 13˚ 00'

43˚ 00'

43˚ 12'

CENT

DIGN

POPO

RASI

SEFR

MONT

COLLCEREVALL

SPEL

¿ g

10 mm

(a)

12˚ 36' 12˚ 48' 13˚ 00'

43˚ 00'

43˚ 12'

CENT

DIGN

POPO

RASI

SEFR

MONT

COLLCEREVALL

SPEL

¿ g

(b)

12˚ 36' 12˚ 48' 13˚ 00'

43˚ 00'

43˚ 12'

CENT

DIGN

POPO

RASI

SEFR

MONT

COLLCEREVALL

SPEL

¿ g

(c)

12˚ 36' 12˚ 48' 13˚ 00'

43˚ 00'

43˚ 12'

CENT

DIGN

POPO

RASI

SEFR

MONT

COLLCEREVALL

SPEL

¿ g

(d)

Figure 7. 2003–2001 GPS (black arrows) and predicted displacements (coloured arrows) for Zollo FM. Error ellipses represent the 98 per cent confidence

level. Panel (a) represents viscoelastic relaxation for earth model TZ18; panel (b) after-slip on a 4-km-wide horizontal fault at the base of the UC, under the

hanging wall of both faults; panel (c) after-slip on a nearly vertical updip extension the main fault, between 2 and 4 km depth; panel (d) the summation of the

three contributions from panels (a), (b) and (c).

0

3

6

9

12

Ba

se

line

va

ria

tio

n r

ate

s (

mm

/yr)

0 5 10 15 20 25

Baseline length (km)

GP

S

MO

DE

L

SEFRMONTCOLLCEREVALLSPEL FA

UL

T

Figure 8. Horizontal baseline variation rates along Tr.A. Model displacements represent the best-fitting result of combined relaxation and after-slip for Zollo

FM. Error bars represent the 68 per cent confidence level.

C© 2007 The Authors, GJI, 169, 534–546



responsible of the observed GPS motions, in terms of both magni-

tudes and directions. This conclusion is made possible by the ex-

tension of the GPS network from year 2000, which allows to obtain

reliable planar displacements, as testified by the positive Fisher’s

test values listed in Table 3.

The best results are obtained allowing various patches adjacent to

the two main faults to slip aseismically, using Zollo FM as preferred

coseismic model. In particular, we need shallow slip to match the

near fault sites and slip at depth to fit the far-fault sites.

The observed post-seismic deformation requires the contribution

of both faults, although the fault reactivated by the second large

event (9:40, M w 6.0) is the leading one. Regarding this later fault,

the main preferred coseismic model would require a rupture depth

as in Zollo FM that is deeper than Salvi FM. Moreover, the fact that

the preferred fault model ruptures the lower half of the seismogenic

UC is a key element to justify the activation of the nearly vertical

updip extension initially proposed by Basili & Meghraoui (2001),

and the occurrence of slip at the base of the UC itself. For the fault

reactivated by the first event (0:33, Mw 5.7), the main difference

between Zollo FM and Salvi FM stands in the location of the fault

projection at the surface, where Zollo FM is at about 4 km to the

NE with respect to Salvi FM. The fit between the observations and

model predictions for the pertinent transect as a whole (Tr.B) does

not allow us to choose between Salvi FM and Zollo FM. However,

the motion of the near fault sites (e.g. DIGN, Fig. 5d versus Fig. 6d)

gives more weight to Zollo FM.

Between 2000 and 2001, the shallow component is located on

the up-dip extension of both faults between a depth of 2 and 4 km

and accommodates about 7 cm of normal slip. At depth, we allow

the base of the footwall of the main fault to slip by 5 cm in normal

direction above the low-viscosity TZ. The required equivalent mo-

ment for this 1-yr period amounts to at least 12 per cent of the total

coseismic moment of the two events.

Between 2001 and 2003, the very different deformation pat-

tern for the near fault sites requires a considerable amount of

normal slip, about 10 cm, to be located on a nearly vertical up-

dip extension of the main fault, between a depth of 2 and 4 km.

At depth, the activated fault plane shifts SW under the hanging-

wall for both faults, allocating 10 cm of normal slip. The required

equivalent moment release for this 1.6-yr period amounts to at

least 15 per cent of the coseismic moment. Therefore, the rates

of after-slip on the faults are slightly decreasing from 2000 to

2003.

The last component of after-slip, allocated on a horizontal fault

at the base of the seismogenic layer, could be considered physically

analogous to viscous relaxation below the brittle-ductile transition.

However, a comparison between this contribution and the best model

of viscoelastic relaxation [panels (a) and (b) of Figs 5–7] shows how

the two processes affect the motion of the GPS sites in different ways.

Therefore, in the specific case, we do not regard the two processes

as being equivalent.

In spite of the important role of after-slip, the long-wavelength

deformation exhibited by the far-fault sites requires a contribution

of viscoelastic relaxation. The best results for viscoelastic relaxation

are obtained with Zollo FM, when a layer with viscosity of 1018 Pa s

(TZ) is located below an 8-km-thick upper crust. The observation

window of our GPS measurements spans between 2 and 5.6 yr after

the earthquakes. A much longer observation time would help to

detect the presence of any higher viscosity, while the effect of a

much lower viscosity has probably extinguished in the first year

after the earthquakes.

We have verified that another potentially active post-seismic de-

formation process, namely poro-elastic relaxation, is not capable of

affecting our GPS sites motions significantly.

9 C O N C L U S I O N S

We have shown that the campaign occupation of a small size GPS

network is capable of detecting deformation signals of the order of

a few millimetres per year, provided that accurate processing and

antenna positioning is realized.

The comparison between GPS measurements and displacement

predictions coming from different models of post-seismic deforma-

tion allows to put some constraints on the earth structure, the rupture

models and the specific post-seismic processes active in the area of

the 1997–1998 Umbria-Marche earthquake sequence.

The fit to the GPS motions is obtained when using the coseismic

fault model published by Zollo et al. (1999) and allowing various

patches adjacent to the two main faults to slip aseismically. The slip

on different shallow patches reflects an important on-going fault

creep, while the after-slip, at the base of the seismogenic UC, reflects

the presence of a possible discontinuity at 8 km. This discontinuity

is likely rheological, decoupling the seismogenic UC from the TZ,

and is the locus of a basal shear favouring localized time-dependent

deformation. The preferred rheological model, obtained from vis-

coelastic relaxation modelling, consist of an 8-km-thick elastic UC,

underlined by a 12-km-thick TZ with a viscosity of 1018 Pa s. Con-

tributions from deeper layers, LC and upper mantle, are negligible

for the time-span of the observations.

The first order process governing the observed post-seismic de-

formation following the Umbria-Marche earthquakes is controlled

by after-slip both above and below the fault zones.

A C K N O W L E D G M E N T S

This work is fully supported by the Italian MIUR-PRIN 2004

project: Active deformation at the northern boundary of Adria. We

thank the staff of Politecnico of Milan, University of Milan and Uni-

versity of Trieste for the help during the GPS campaigns. We would

also like to thank M. Crespi and M. Meghraoui for their comments

on this paper.

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