Geophys. J. Int. (1998) 135, 177–194
The instrumental seismicity of the western Alps: spatio–temporal
patterns analysed with the wavelet transform
Nicole Bethoux,1 Guy Ouillon2 and Marc Nicolas3
1 UMR Geosciences Azur, rue A. Einstein, Sophia-Antipolis, 06560 Valbonne, France
2 L aboratoire de Physique de la Matière Condensée, Université de Nice, Parc Valrose, 06108 Nice, cedex 2, France
3 L aboratoire de Détection et de Géophysique, L DG, BP 12, Bruyères le Châtel, France
Accepted 1998 April 22. Received 1998 April 20; in original form 1997 July 22
SU MM A RY
We perform a spatial and temporal analysis of the instrumental seismicity of the Western
Alps, between latitude 41°–48° N and longitude 5°–10° E, using a recently revised
catalogue available for the period 1962–1995 containing 7500 events in the magnitude
range 2–5.9. Taking into account the fact that the major difficulty of such an analysis in
an area of moderate seismicity is the long return period of the events and the diffusive
character of the seismic swarms, we first carry out a statistical analysis of the 3-D
distribution of the foci with the help of a 3-D wavelet transform. This smooths the
location errors, which are estimated to be 1 km in epicentral coordinates and 5 km for
the depth for recent years, whereas they are more than 10 km in epicentral coordinates
for the oldest events. The good agreement between the shape of the filtered volumes
and geological/tectonic features supports this new methodology for defining seismogenic
zones, which are outlined better than by simple observations of the seismicity map.
The study of seismic energy release shows the major heterogeneity in the mechanical
behaviour of these seismogenic zones. An evaluation of seismic deformation has been
carried out for some of these regions and compared with published geodetic results.
The cumulative slip estimated for the Durance fault is 0.01 mm yr−1 (1° per cent of
the geodetic estimation), and for the Vuache fault it is 0.19 mm yr−1, whereas historical
triangulation yields horizontal movements of up to 5 mm yr−1 in the neighbourhood
of the Vuache fault. In the Valais region, the ‘seismic’ shear strain rate has been
evaluated to be 5×10−4 mrad yr−1 (0.5 per cent of the geodetic deformation); in the
Ligurian Sea, the shortening rate deduced from seismological data is 1.1 mm yr−1
(20 per cent of the geodetic evaluation). The paradoxical result of this study is that areas
where instrumental seismicity is low correspond to the location of strong historical
seismicity or to regions of high geodetic deformation. Only two regions ( Valais and
the Ligurian Sea) seem to correspond in historical and present seismicity. These results
show the difficulty of predicting seismic activity in such areas. The discrepancy between
low seismic activity, high local deformation rate, and the moderate average velocity
between Africa and Europe in the western Alpine region needs to be explained by any
tectonic theory of the western Alps.
Key words: 3-D wavelet analysis, Alpine seismicity, seismic deformation, spatial
patterns, temporal patterns.
1
I NTR O D UC TIO N
The Alpine range results from the collision between the African
and European plates. The present-day convergence rate is
8 mm yr−1 in a NNW–SSE direction (DeMets et al. 1990).
This convergence involves seismic activity, which is known to
be nowadays generally weak and diffuse in the western part of
© 1998 RAS
the range, whereas in historical times some destructive events
occurred in the Alps, as well as in the surrounding regions.
Examples are the 1356 Basel earthquake, the 1564 Nissart
event, both of maximum intensity IX MSK, some destructive
earthquakes around Cuneo, and, in Switzerland, the Valais
earthquakes of 1755 and 1946 with epicentral intensities >VIII
(Pavoni 1977), the Imperia quake of 1887, with an estimated
177
178
N. Bethoux, G. Ouillon and M. Nicolas
magnitude of 6.4 (Capponi, Eva & Merlanti 1980), and the
events of the Durance and Rhone valleys, the most recent
being the 1909 shock of intensity IX (Levret, Bock & Cushing
1994). Geodetic data analysis (Reilly & Gubler 1990; Jouanne,
Menard & Jault 1994; Jouanne, Menard & Darmendrail 1995)
has shown that the Alpine massifs are subject to rather high
deformation rates, and that the most active areas in terms of
vertical or horizontal movements do not correspond to the
areas shown to be seismically active by instruments. Can we
gain a more accurate knowledge of the Alpine seismicity
behaviour from this apparent paradox? The first step to
understanding the role of seismic activity in the Alpine deformation is to perform a spatial and temporal analysis of the
instrumental seismicity. This seismicity is documented in many
reports, but most of them deal with regional and time-limited
studies. The western Alpine regions have had instruments for
a long time (Strasbourg as early as 1895, Trieste in 1911, Basel,
Chur and Zurich in 1912, Firenze in 1924), and the number
of seismological stations has increased considerably since 1976.
The present dense network has allowed important improvements in hypocentral determinations, even for low-magnitude
events. This improvement was a good opportunity to perform
a synthesis of 35 years of instrumental seismicity in the western
Alps (1962–1995) and to attempt to improve the location of
older (since 1950) events with the help of the more recent
locations. In the present paper, we use this new catalogue
(Nicolas & Bethoux 1995; Nicolas et al. 1998) to perform a
temporal analysis and a spatial analysis and to find criteria
concerning the seismic behaviour of the western Alps. Fig. 1
displays the region studied and the events in this catalogue,
limited to the period 1962 to 1995. Taking into account the
fact that the major difficulty of such an analysis in an area of
Figure 1. Seismicity map, superimposed on the structural map: AI, Internal Alps; AE, external Alps; GP, Grand Paradis; Ba, Brianconnais arc;
Pa, Piemontais arc; DF, Durance fault; VF, Vuache fault; V, Valais; A, Argentera; DR, Dora Maira; P, Pelvoux; B, Belledonne; AA, Aar; MB, Mont
Blanc; DB, Dent Blanche; LB, Ligurian basin. The location of the ECORS seismic profile (Roure et al. 1990) is displayed.
© 1998 RAS, GJI 135, 177–194
Instrumental seismicity of the western Alps
moderate seismicity is the long return period of the events and
the diffusive character of the seismic swarms, we first carry out
a statistical analysis of the 3-D distribution of the foci with
the help of a 3-D wavelet transform, in order to smooth the
location errors.
2
TH E CATA L O GU E US E D
In this section, we describe the most important characteristics of this new catalogue. The first stations of the French
network of the LDG/CEA (French Laboratoire de Détection
et Géophysique du Commissariat l’Energie Atomique) were
installed in 1957. We benefitted from the availability of all
seismograms of this network, which is important in revising
the arrival times as well as magnitude determinations. To build
the revised catalogue of Alpine seismicity we gathered together
all the data available in the ISC bulletins, but single and
regional station data were also added, which was especially
useful for locating the oldest events.
In recent years, the density of the network (Fig. 2a) covering
the geographical region we chose (5°E, 10°E; 41°N, 48°N)
was greatly increased. The main characteristics of the crustal
structure of the Alps have become known thanks to several
large profiles—EGT (Blundell, Freeman & Mueller 1992),
ECORS-CROP (Roure, Heitzmann & Polino 1990)—as well
as to more regional seismic lines frequently performed by the
Petroleum industry. Indirect seismological studies (Cattaneo,
Eva & Merlanti 1985; Guyoton 1991; Kissling, Solarino &
Cattaneo 1995) have also contributed to our knowledge. As a
result, we were able to relocate all events using local crustal
models that were developed by the different Alpine institutes
(IGG, LGIT, LDG1). For the recent seismicity (1990 to 1995),
the number of stations as well as the knowledge of crustal
structure generally allows 3-D locations with a precision of
1 km in epicentral coordinates and of 5 km for the depth.
Using these accurate locations, we performed relative location
for older events. What are the confidence intervals of these
new locations? Even though the results are correct in terms of
low rms and small confidence ellipses, it is known that this
computation may represent only the good statistical fit between
the data and the crustal model used. In order to test our results,
we first located artificial events (quarry shots, rock bursts,
navy shots); for natural events, we analysed the correlation of
epicentres with the faults recognized in the field. The coherence
in depth was compared with geological cross-sections (Nicolas
et al. 1998). As a result of this analysis, we concluded that,
while we are confident we have good 2-D locations for the
period 1980–1990, the accuracy of the focal depth is not
guaranteed for all the data. This is why we use a statistical
spatial analysis in order to smooth the depth errors by applying
a 3-D wavelet filter.
Fig. 2( b) displays the histograms of the number of events
versus the year. 1977 clearly shows a break in the number of
detected events, due to the network’s becoming denser, whereas
for magnitudes larger than 2.5 this evolution is smoothed.
Consequently, in order to guarantee the completeness of
the data used, we limited our spatial analysis to the period
1 IGG: Istituto Geofisico di Genova, Italy; LGIT: Laboratoire de
Geophysique Interne et Tectonique, Observatoire de Grenoble, France;
LDG: Laboratoire de Géophysique du Commissariat à l’Energie
Atomique, France.
© 1998 RAS, GJI 135, 177–194
179
1980–1995 and to magnitudes higher than 2.5; that is to say a
catalogue of 5464 events, whereas the whole catalogue available
for the period 1962–1995 contains 7500 events.
However, the analysis of seismic energy release requires the
use of all the events available; the histograms of Fig. 2( b) show
that major events occurred during the sixties. For the oldest
events, located with only a few arrival times, the errors of
location are estimated to be more than 10 km. Nevertheless,
we kept these events to make a complete study of energy
release during this very short period of instrumental seismicity,
even if the dramatic change of the seismological network
introduces some heterogeneity in the number of detected events
of low magnitude, since their contribution to the energy release
is negligible.
Another improvement is the revision of the magnitude
estimates. For older events, on analogue records, the signals
were often saturated, and consequently the magnitude was often
determinated using a duration time. A revision of the empirical
coefficients linking duration time and local magnitude was
performed. The magnitude was systematically recomputed from
1962 to 1995. Consequently, this catalogue has the advantage
of homogeneity of location techniques, including the local
magnitude determination.
3 FIR S T R E GI O NA L IZ ATI O N O F T HE
W ES TE R N A LP I NE S EI S M ICI TY
For each event our catalogue provides the evaluated magnitude, which is a convenient and fast way of estimating the
earthquake size from a seismogram. As a first approximation,
seismic energy (E ) can be related to the magnitude (M) by the
s
Gutenberg–Richter (1949) empirical relationship:
log(E )=1.5M+4.8 (E in Joules) .
s
s
Applying this relation, we obtain large differences between
the spatial distribution of the number of events (Fig. 3a) and
the corresponding distribution of energy (Fig. 3b). For comparison, we also show the historical earthquake map in
Fig. 3(c). Some areas are clearly defined by different behaviour
of the seismic activity:
(1) the Briançonnais and Piemont internal arcs, corresponding to the maximum numbers of events and a minimum of
energy (region IA in Fig. 1);
(2) western Switzerland, with numerous events and
corresponding high energy (region V in Fig. 1);
(3) the Ligurian Sea, which is the northeastern part of
the western Mediterranean basin, characterized by some large
shocks and historical activity and a low number of events
(region LB in Fig. 1);
(4) the Internal Jura, corresponding to recent low activity
(region J in Fig. 1);
(5) the Durance fault area, clearly recognized in the event
map, corresponding to historical activity contrasting with
low energy release during the period covered by instruments
(region DF in Fig. 1);
(6) seismic clusters located between the external crystalline
massifs, which are almost aseismic.
Comparison between the distribution of recent energy release
and the historical earthquake map shows the present-day gap
of seismicity in Provence and along the Durance fault. On
another timescale, major shocks were postulated to have a
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N. Bethoux, G. Ouillon and M. Nicolas
Figure 2. (a) Evolution of the seismological network available around the area studied, from 1982 to 1992. Dark triangles indicate stations
already installed in 1982 (corresponding to the installation of some regional networks); empty triangles indicate the supplementary stations
installed between 1982 and 1992. ( b) Histograms of the events recorded from 1962 to 1990: they enhance the step in the number of detected events,
around 1976.
© 1998 RAS, GJI 135, 177–194
Figure 3. (a) Number of events by pixels of 10 km2. (b) Corresponding energy density evaluated from the magnitude by the Gutenberg empirical formula. (c) The historical event map according to
data from Levret et al. (1994).
Instrumental seismicity of the western Alps
© 1998 RAS, GJI 135, 177–194
181
N. Bethoux, G. Ouillon and M. Nicolas
182
period of occurrence of 100 to 600 years, varying from area to
area (Hendrickx 1981; Beck et al. 1995). Clear discrepancies
observed between areas show either spatial heterogeneity of
the deformation, or a lag in the different cycles of seismic
energy release.
We must therefore analyse these seismogenic areas more
specifically. However, particularly in regions of diffuse seismicity,
it is very difficult to define the boundaries of seismogenic
volumes accurately.
4 S PAT IA L A N A LY SI S BY A N IS O T R O PI C
3- D WAVE LET M E TH O D
Some authors have studied the pattern of seismicity with depth
and have reached conclusions on the tectonics of the Alps
(Deichmann 1987; Cattaneo et al. 1987; Guyoton 1991).
However, the projection of the seismicity on vertical crosssections does not give a 3-D image of the seismicity. Another
method for studying earthquake distribution is statistical
analysis, which smooths the errors of locations and filters the
data in order to make major spatial tendencies evident. Some
authors have used a ‘distance method’, which computes the
distribution of distances between a pair of events (Kagan &
Knopoff 1980; Eneva & Hamburger 1989). If there exists
some interaction between points, the point distances should
present some characteristic distribution. This kind of analysis,
to which so-called fractal analysis belongs, only provides
certain global information about the spatial distribution of
events. Here we perform a spatial statistical analysis using a
3-D wavelet transform, which is a local analysis, as we explain
in the next section.
4.1
Methodology
The method is introduced in Ouillon, Sornette & Castaing
(1995). The aim of the wavelet analysis is to decompose a
signal into details of various scales using a battery of filters
called ‘wavelets’ derived from a single mother function y
(Grossmann & Morlet 1984). A frequently used wavelet is the
so-called Mexican hat, which is the second derivative of the
Gaussian function. Its analytical expression is
y(x, y, z)=[3−(x2+y2+z2)] exp
C
D
1
(x2+y2+z2) .
2
One can define a daughter wavelet, y (x, y, z)=y(x/a, y/a, z/a),
a
not necessarily orthogonal to the mother wavelet, where a is
the scale of analysis.
A wavelet coefficient is then defined at each point (x, y, z) of
the signal studied:
where k is the wavevector and y* the conjugate Fourier
transform of y.
If the event distribution is uniform, C(x, y, z, a) is equal to
zero everywhere. If C(x, y, z, a) is positive, then the point
(x, y, z) is located, at scale a, in a local cluster of events. If
C(x, y, z, a) is negative, the point is located in a gap of events.
The distribution obtained is therefore representative of the
degree of heterogeneity of the seismicity distribution. We will
only pay attention to points where C(x, y, z, a) is positive.
(These points will be denoted by a dark colour in the following
figures.) This set of points then defines a somewhat complex
3-D structure. The scale of these structures can be shown to
be equal to 2.2a (Ouillon et al. 1995). An objective criterion is
given by the value of the wavelet coefficient which characterizes
the degree of coherence of the spatial distribution. We will
only discuss structures with a sufficiently positive C(x, y, z, a).
For ease of interpretation of the spatial shape of our 3-D
structures, we have cut them into horizontal sections in steps
of 5 km depth, from 0 to 35 km, in Figs 4 to 9.
4.2 Results
First, we limited the area under study to between 6°E and 8°E
and between 43°N and 47°N. The data correspond to the
period 1980–1993 and to magnitudes >2.5, in order to be as
sure as possible of the completeness of the catalogue used in
this analysis.
The parameter a allows the wavelet to dilate ( high a) or to
contract (low a), corresponding to either a fine or a coarse
resolution: a corresponds to the size of the filter applied to the
signal. A complete wavelet analysis should include the scan of
all a values.
As a first step, we sampled numerous values of a to select
the most appropriate filter sizes for our data set. In our case,
our preliminary computations led us to choose a value of a of
5 km. This value seems the optimal scale to describe the 3-D
geometry of the seismogenic structures in the Alps because of
the range of location errors.
A value too low (a=2.5 km) does not sample the coherency
of the distribution pattern of the seismicity (see example in
Fig. 4). A value too high (a=10 km) samples too much of the
crust and thus provides information only for scales equal to
or larger than the thickness of the seismogenic crust (see
example in Fig. 5). In Figs 6(a) and 7(a), the structures obtained
with a=5 km will be analysed closely with the seismicity map,
corresponding to slices of 11 km thickness centred on the corresponding depth of the cross-section operated in the volume of
the 3-D computed wavelet (Figs 6b, 7b). It is worth noting
that the major characteristics of this spatial distribution of
earthquakes are found at every scale of analysis.
We now discuss some specific examples.
C(x, y, z, a)
NC
=1
K a−3/2
y
PPP
D
I(u, v, w)y (x−u, y−v, z−w) dudvdw .
a
C(x, t, z, a) is the convolution of the function I(x, y, z), the density
of seismicity around the point (x, y, z), with the analysing
wavelet y , with
a
K =
y
P
y*(k)3k−3 dk3 ,
4.2.1 Southern part of the area studied
(1) A minimum of seismicity occurs between 10 and 25 km,
dividing important shallow seismogenic volumes from some
smaller deep ones;
(2) the general trend of the structures follows the direction
of the western–southern end of the Alpine range (that is to
say, a NW–SE direction);
(3) a second direction, NE–SW, is found for the shallow
seismicity (0 up to 15 km);
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Instrumental seismicity of the western Alps
183
Figure 4. Southern part of the region: sections at depths z of 0, 5, 10, 15, 20, 25, 30 km of the volumes computed by 3-D wavelet analysis with
a=2.5 km.
(4) N–S structures are evidenced at depth, between the
Pelvoux and Dora Maira massifs (Fig. 6c) and following
the boundaries of this last massif (from 44°N to 45°N), and
there are some small E–W structures. It can be seen that the
‘wavelet structures’ outline these directions much better than
the non-filtered earthquake distribution (Fig. 6b).
In order to interpret the existence of these last two directions,
we compare these observations with the Moho map (Fig. 6d)
deduced from the EGT compilation (Blundell et al. 1992),
and we further analyse the area corresponding to the Ivrea
body (Fig. 6d), a zone where the Apulian crust overlaps the
© 1998 RAS, GJI 135, 177–194
European crust. In this area, the thrusts initiate on deep mantle
slices, assumed to be Apulian mantle (Ménard & Thouvenot
1984). From 10 km to 20 km depth, the structures we find are
parallel to the Moho lines of the Apulian domain, and this
depth range corresponds to the shallowest Ivrea body unit
(Ménard & Thouvenot 1984; Bayer et al. 1989). Below 20 km,
some structures trend parallel to the European Moho isobaths,
and the structural interpretation deduced from gravimetry and
seismic modelling (Bayer et al. 1989) allows us to conclude
that this depth range corresponds to the European crust. This
representation, therefore, seems to show that the seismicity
is mostly dominated by the Apulian thrusting and then by
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N. Bethoux, G. Ouillon and M. Nicolas
Figure 5. Southern part of the region: sections at depths z of 0, 5, 10, 15, 20, 25, 30 km of the volumes computed by 3-D wavelet analysis with
a=10 km.
the European domain. Unfortunately, the focal mechanisms
already computed for this region do not bring additional
information to this interpretation, because the biggest magnitudes correspond to shallow events (Madeddu, Bethoux &
Stephan 1996).
4.2.2
North part of the area studied
In Figs 7(a) and ( b) the direction N50° is more clearly observed
than on the seismicity map, where it is spoiled by the diffuse
character of this seismicity.
The coherence of deep events located between 45°N and
46°N and between 6°E and 7°E corresponds to the Alpine
frontal overthrust, elongated N50°. In Fig. 7(d), the seismicity
has been projected onto the interpretated seismic ECORSCROP profile (Truffert et al. 1990): the seismicity of this area
seems to be linked to the backthrusts (see the cluster near
point E), which could explain the discrete pattern of the
computed structures.
The 3-D structure elongated about N145° corresponds to
the Vuache fault (Fig. 7c), which seems to be restricted to the
upper crust (z=10 km).
© 1998 RAS, GJI 135, 177–194
Instrumental seismicity of the western Alps
185
Figure 6. Southern part of the region. (a) Sections at depth z (0, 5, 10, 15, 20, 25, 30, 35) in steps of 5 km of the volumes computed by 3-D wavelet
analysis, with a=5 km. ( b) Corresponding distribution of seismicity in slices 2.2 a thick centred on Z=z0 in steps of 5 km. The crystalline massifs
are superimposed. (c) Structural map of the Western Alps: A, Argentera; DR, Dora Maira; P, Pelvoux; M, Maures; L s, Ligurian sea. (d) Moho
isobaths deduced from EGT compilation (Blundell et al. 1992). The location of the Ivrea body is denoted by Ib in (c).
© 1998 RAS, GJI 135, 177–194
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N. Bethoux, G. Ouillon and M. Nicolas
underneath the Alpine range (see its location on the structural
map in Fig. 8(b). In this area we find coherent volumes of
seismicity between 0 and 5 km depth. Another wide coherent
structure is visible for 20–25 km depth. This result is consistent with a study by Deichmann (1987), who observed a
lack of seismicity in the depth range 5–20 km along a profile in northern Switzerland and concluded that the main
reason for this behaviour was stress release through non-brittle
mechanisms such as creep failure combined with shear melting.
4.2.4. T he L igurian Sea, northeastern part of the western
Mediterranean Sea
Figure 6. (Continued.)
Now let us focus on the two regions corresponding to the
two highest levels of seismic energy as revealed in Fig. 3.
4.2.3
Valais, southwestern Switzerland
The wavelet transform has been calculated for events that
occurred in an area covering 7° to 9°E and 46° to 47°N. Fig. 8
shows that the biggest coherent structures correspond to
seismicity ranging from 0 to 10 km depth. One main direction
(140°N) appears in the shape of these structures, trending
perpendicular to the direction of Alpine structures in the area
(Fig. 8c). In the following, we will only deal with the study of
seismic structures ranging between 7°E and 8°20∞E, and 45°50∞
and 46°40∞N (see also Fig. 7).
The coherency of seismicity disappears below 10 km except
in the northwest, corresponding to the Molasse Basin, a tertiary
foredeep of the Alps, due to the plunge of the European crust
The region under study corresponds to the southern end
of the Argentera massif, the Riviera coast, and offshore to
the northern continental margin and basin (Fig. 9c). In the
northwest the structure is shallow, trending along the coast
and the continental margin (Fig. 9a). Offshore, a coherent
structure is shown, located in the range 42°50∞ to 43°40∞N,
7°35∞ to 8°30∞E, corresponding to the sections at 10 and 15 km.
The main directions of this structure may be linked to the
structural framework of the basin with the rifting axis trending
N30°–N40°E and the transform fault trending N110°–N130°E
(Fig. 9c). Note that the earthquake of 1963 with magnitude
5.9, not belonging to the data set, which is limited to the
period 1980–1995, is located in the southern part of the volume
defined (8.15°E, 43.44°N).
In conclusion, the 3-D wavelet analysis acts as a filter which
enhances the spatial shape of the seismogenic volumes. The
comparison between the representation of the hypocentres as
a function of depth shows the advantage of the statistical
filter, i.e. the wavelet transform. One of the results is that the
seismogenic contours are defined more clearly for each area
studied, and, in the case of the Alpine region, evidence is
provided of the separation of the earthquakes into distinct
seismogenic volumes: the biggest ones corresponding to shallow
events in restricted areas, and other small volumes located
deeper than 20 km. In the following regional analysis we will
use only the main shallow volumes determined by regional
analysis.
5
RE GI O NA L AN A LY S IS
5.1 Frequency–magnitude distribution
A fundamental earthquake scaling relationship is expressed in
the Gutenberg–Richter (1949) frequency–magnitude distribution: log N(m)=a−bm, where N(m) is the number of earthquakes with magnitude >m during a specified time interval in
a given region, a is a constant describing the level of seismicity,
and b is a constant describing the relation between the numbers
of large and small events. The variation of b could have a geophysical meaning reflecting different properties of the seismic
regime.
The Gutenberg–Richter relation is computed for some of
the seismogenic volumes defined above, first for a period of 30
years (Fig. 10). The b values, deduced from least-squares computation, vary from one area to the next, falling approximately
into two classes:
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Instrumental seismicity of the western Alps
187
Figure 7. Northern part of the region. (a) Sections at depth z (0, 5, 10, 15, 20, 25, 30, 35) in steps of 5 km of the volumes computed by 3-D wavelet
analysis, with a=5 km. (b) Corresponding distribution of seismicity in slices 2.2 a thick (here a=5 km) centred on z in steps of 5 km. The crystalline
massifs are superimposed. (c) The crystalline massifs: B, Belledonne; Aa, Aar; MB, Mont Blanc; DB, Dent Blanche; GP, Grand Paradis; AR, Aiguilles
Rouges; MR, Mont Rose. The location of the ECORS seismic profile and of the Vuache fault (VF) is displayed. (d) Seismicity projected on the
interpretated seismic profile ECORS-CROP (Truffert et al. 1990) E: cluster of seismicity recognized on the structure obtained by wavelet analysis.
© 1998 RAS, GJI 135, 177–194
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N. Bethoux, G. Ouillon and M. Nicolas
(d)
Figure 7. (Continued.)
(1) b close to 1, for the most active regions;
(2) b larger than 1.2, for regions with a low rate of energy
release, comparable to results corresponding to other areas of
western Europe (Panza, Prozorov & Suhadolc 1990).
In order to verify the Poissonian character of these distributions, we first check the stability of the results for a period
of 30 years. As we have a catalogue of 34 years available, from
1962 to 1995, we computed the regression for various windows
of 30 years and verified that the results are included in the 96
per cent confidence levels for the determination of a and b.
Next we computed the regression relation for 20 years
(1962–1981) and (1974–1993). The b value remains stable
except for the Ligurian Sea (b varying from 0.908 to 1.06),
owing to the influence of the 1963 event (M =5.9).
L
5.2
Evaluation of the seismic deformation
According to the formula of Kostrov (1974), the tensor strain
components can be linked to the moment tensor components:
1
e =
i,j 2mV T
∑ M (k) ,
(1)
i,j
1<k<n
where n is the number of events that occurred in the period T
in a volume V , and m is the shear modulus (in the following
we take m=3×1011 dyne cm−2). Jackson & McKenzie (1988)
performed a complete study of the relationship between active
deformation and seismic activity and showed the limits of
the applicability of this formula. In particular these authors
stressed the necessity of splitting a deforming region into zones
of relatively homogeneous deformation before examining the
summed moment tensors.
We can now attempt at least a coarse evaluation of the
present seismic deformation of some of the seismogenic volumes
defined above, where the determination of focal mechanisms
shows that the style of deformation is fairly homogeneous. For
the regions studied, the most characteristic focal mechanisms
are displayed in Fig. 11. Using eq. (1), the components of the
moment tensor are deduced from them (Aki & Richards 1980),
and displayed in Table 1. Thus
1
e =m
i,j
i,j 2mV T
∑ M (k) .
0
1<k<n
So far, no seismic moment catalogue has been published for
the western Alpine domain. Consequently we approximate the
modulus of the seismic moments with the values of magnitudes:
m=2/3 log M −10.7 (M is in dyne cm) ,
0
0
following the relation defined by Hanks & Kanamori
(1979).
© 1998 RAS, GJI 135, 177–194
Instrumental seismicity of the western Alps
189
Figure 8. (a) Sections at depth z (0, 5, 10, 15, 20, 25, 30, 35) in steps of 5 km of the volumes computed by 3-D wavelet analysis for the Valais region.
( b) Global distribution of seismicity in this area.
5.2.1
T he Valais region
Seismicity studies effectively confirm the large-scale regularities
in the pattern of the crustal stress and strain field in Switzerland
(Pavoni & Roth 1990). We limit the summation of seismic
moments to the seismogenic volume defined by the wavelet
© 1998 RAS, GJI 135, 177–194
analysis, for which several very coherent focal mechanisms
have been published (Pavoni 1980; Nicolas, Santoire &
Delpech 1990; Pavoni & Roth 1990); that is to say, N–S strikeslip faults with a P-axis trending NW–SE (displayed in Fig. 11,
with the corresponding seismic moment tensor displayed in
Table 1).
190
N. Bethoux, G. Ouillon and M. Nicolas
45°N
N
44°N
N
43°N
N
42°N
N
6°E
E
7°E
E
8°E
E
9°E
E
10°E
E
Figure 9. (a) Sections at depth z (0, 5, 10, 15, 20, 25, 30, 35) in steps of 5 km of the volumes computed by 3-D wavelet analysis for the Ligurian
Sea. (b) Global distribution of seismicity in this area. (c) Structural map after Rehault et al. (1984).
For this region, the modulus of deformation,
1
2mV T
∑ M (k) ,
0
1<k<n
is evaluated to be 5.8×10−10 yr−1 (with
∑ M (k)=6.6×1023 dyne cm
0
1<k<n
and a seismogenic volume of 59×1018 cm3).
5.2.2 Northeast of the Western Mediterranean Sea, the
L igurian basin
This region also seems to be a deformed fairly uniformly
(Bethoux et al. 1992); compressive focal solutions prevail and
are similar to the focal mechanism of the 5.9 event of 1963,
with a N40° fault dipping 40°W, and N119°E P-axis (displayed
in Fig. 11, with corresponding moment tensor in Table 1).
Owing to the occurrence of an event of magnitude 5.9 in this
area,
1
2mV T
∑ M (k)
0
1<k<n
is evaluated here to be 2.5×10−8 yr−1 (with
∑ M (k)=9.95×1024 dyne cm ,
0
1<k<n
and the seismogenic volume defined by the wavelet filter being
1.9×1019 cm3).
5.2.3 T he Durance fault and the Vuache fault
Among the seismogenic areas defined in the external parts of
the western Alpine regions, two are rather simple systems
characterized by seismicity located around strike-slip faults:
the Durance fault and the Vuache fault (DF and VF in Figs 1
© 1998 RAS, GJI 135, 177–194
Instrumental seismicity of the western Alps
Ligurian Sea
3.0
3.0
2.5
2.5
2.0
2.0
log (N )
log (N )
Valais
191
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
magnitude
magnitude
log(N )=(5.3+/–0.2)–(1.04+/–0.06)M
log(N )=(4.4+/–0.1)–(0.85+/–0.03)M
Internal area
7
Durance fault
3.0
3.5
2.5
3.0
2.0
log (N )
log (N )
2.5
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
magnitude
magnitude
log(N )=(5.3+/–0.3)–(1.32+/–0.09)M
log(N )=(5.99+/–0.5)–(1.51+/–0.2)M
7
Figure 10. Curve of the frequency–magnitude distribution (Gutenberg–Richter law) computed for some of the seismogenic volumes defined previously.
and 11). Note that the last event of Annecy in July 1996
(M =5.3) confirms our knowledge of the local deformation of
l
the Vuache fault. The sinistral strike-slip mechanism computed
for this event (Thouvenot et al. 1998) is very close to solutions
established by Sambeth & Pavoni (1988) for older events and
is coherent with observed local deformation. For this fault, we
include the recent seismic activity, up to July 1996. The
seismicity and microtectonics of the Durance fault have been
thoroughly studied (Combes 1984; Grellet et al. 1992). This
fault is clearly defined as a sinistral strike-slip fault (Fig. 11).
At present, this region is characterized by very low seismic
activity.
For strike-slip movement along a fault, Jackson &
McKenzie (1988) have shown that eq. (1) is compatible with
the computation of seismic slip rate (Brune 1968):
u̇=
1
2mAT
∑ M (k) ,
0
1<k<n
© 1998 RAS, GJI 135, 177–194
where A is the surface of the fault, m the shear modulus and
T the period studied. The seismic moment is again estimated
from the magnitudes.
The computation of cumulative slip, converted to mm yr−1,
allows at least an order-of-magnitude estimate of these
movements. We find
(1) for the Durance fault,
S M (k)=8.44×1022 dyne cm, for
0
(2) for the Vuache fault,
S M (k)=1.66×1024 dyne cm, for
0
u̇=0.011 mm yr−1,
32 years;
u̇=0.192 mm yr−1
35 years.
with
with
5.2.4 Estimation of errors in deformation rate
The seismogenic depth, necessary to evaluate the surface of
faults or seismogenic volumes, has been deduced from our
wavelet filter analysis with an uncertainty of 5.5 km, corresponding to the parameter a=5 km, which is linked to the
N. Bethoux, G. Ouillon and M. Nicolas
192
mation is kept and may be logically compared with levelling
and horizontal movement measurements.
5.2.5 Comparison with geodetic results
Horizontal movements evaluated along the Durance fault
provide low values of around 1 mm yr−1 (Ferhat et al. 1998),
which is still bigger than the values corresponding to the
seismic activity of recent years (10−2 mm yr−1). Since this
region is in an area of regular historical seismicity, this strongly
indicates a gap in the seismic activity.
The horizontal movements evaluated around the Vuache
fault by Jouanne et al. (1994) range between 1 and 5 mm yr−1
(this last value is probably due to local movements, linked to
nappe driving, according to the authors), whereas the order of
magnitude of recent seismic deformation is 0.2 mm yr−1. Here
also it is suspected that there is a gap in the seismicity.
In the Valais region, geodetic measurements give uplift rates
of up to 1.5 mm yr−1 (Geiger, Kahle & Gubler 1986) and
horizontal deformations of 0.10 mrad yr−1 (Reilly & Gubler
1990). The engineering shear strain rate ċ can be compared
with the components of the strain tensor (Prescott 1981).
Because these components have already been computed, a more
straightforward method is to deduce a ‘seismic’ engineering
shear strain from e , e , e :
xx yy xy
ċ2=5×10−10 rad yr−1 ,
ċ1=5.8×10−11 rad yr−1 ;
Figure 11. Map of the representative focal mechanisms corresponding
to the four areas where the seismic deformation is evaluated. VF: Vuache
fault, DF, Durance fault.
Table 1. (a) Seismic moment tensor as derived from the focal mechanism chosen as the most characteristic of the seismic deformation in
Valais (southern Switzerland).
m =
i,j
A
−0.29 0.88 0.01
0.88
0.19
0.39
0.01
0.39
0.10
B
where M =6.6×1023 dyne cm.
0
( b) Seismic moment tensor as derived from the focal mechanism
chosen as the most characteristic of the seismic deformation in the
Ligurian Sea (north of the western Mediterranean basin).
A
0.05
0.34
m = 0.34 −0.88
i,j
0.31 0.23
0.31
0.23
0.83
B
where M =9.95×1023 dyne cm.
0
concept of the scale of coherency between the distributions of
the foci. Therefore, the choice of the seismogenic thickness can
involve an error of 100 per cent, as for the Durance fault,
where the previous estimate of this parameter was 5 km. The
relative errors on the other parameters (relative error on
superficial extension of the seismogenic zone and error on the
sum of seismic moments) are less important. As a whole, we
can assume an error of 200 per cent on previous evaluations.
However, the order of magnitude of the recent seismic defor-
therefore ċ=5×10−4 mrad yr−1, that is to say 0.5 per cent of
the geodetic deformation. If we carry on the computation,
including the 1946 Valais earthquake (M =5.7) it becomes
l
1 per cent.
Laser observations between the astrophysical observatory
of Caussols (Smith et al. 1994) near the Provencal coast and
Sardinia yield a southeastern shortening of 5 mm yr−1, which
is a rather approximate value and close to the estimated error
of the measurements. In the Ligurian basin, the shortening
rate in the SE–NW direction, deduced from seismological data,
is given by e −e and the value obtained is 1.3×10−8 yr−1
xx
yy
over a distance of about 80 km. This implies shortening in a
southeasterly direction of 1.1 mm yr−1. It is interesting to note
that the discrepancy between the two evaluations is much
smaller than observed for the Durance and Vuache faults.
At the opposite end of the scale to this rather good agreement
between geodetic and seismicity results, Jouanne et al. (1994,
1995) deduced, from the data of two high-precision levelling
networks, an uplift of the internal Jura of 2 mm yr−1 and
horizontal displacement rates of 4 mm yr−1 at the internal
Jura ramp, despite the fact that the recent seismic activity is
very low (S M (k)=1021 dyne cm for the southern Jura). Either
0
this crustal shortening along a major thrust fault involving
basement is a quasi-aseismic deformation, or some sparse
major shocks provide the strain release. The Basel event of
1356, estimated to have a maximum intensity of IX in the
epicentral area, was located too far north (Meyer et al. 1994)
of this area, whereas the macroseismic shocks known in
southern Jura are sparse and of rather low intensity, not higher
than V (Levret et al. 1994).
Even if accurate geodetic results are not yet available for
the whole western Alps, and if a systematic comparison between
seismic activity and shallow deformation is not yet possible,
seismic deformation seems to be clearly inferior to the observed
movements. Nevertheless, the rate in some regions is more
© 1998 RAS, GJI 135, 177–194
Instrumental seismicity of the western Alps
balanced than in others, enhancing the spatial heterogeneity
of deformation in the western Alps.
6
CO N CLU SI O NS
In the context of moderate and diffuse seismicity, it is
particularly difficult to define with accuracy the different
seismogenic areas, and therefore to search for 3-D structures
in the seismicity. In order to smooth the errors of hypocentral
determination we present here a new methodology using
wavelet filters. Mapping the areas where the wavelet coefficient
is positive highlights the characteristics of the foci distribution
better than the seismicity map. Clear examples are the N–S
elongated swarm along the Dora–Maira massif (Fig. 7) and
the discontinuity in depth observed for the Belledone thrust
(Fig. 7). The influence of the Ivrea slices is highlighted (Fig. 6).
The direction of structural accidents is more apparent in
Switzerland (Valais region, Fig. 8) and in the Mediterraean
Sea (Ligurian basin, Fig. 9). Consequently, the coherence
between the statistical analysis presented above and tectonic
features allows us to conclude that the wavelet method provides
a realistic 3-D picture of the seismicity pattern: the western
Alpine seismicity is characterized by discontinuities in horizontal
as well vertical directions. This seismic behaviour is linked
both to the complex structure of the range (the main influence
of the overthrusting ramps is shown) and to rheological features
(Deichmann 1987).
From the temporal analysis, only two regions (Valais and
Ligurian Sea) reveal noticeable short cycles of activity, and
sophisticated methods such as these proposed by Sornette &
Sammis (1995) or Zschau (1995) may only be attempted in
the western Alps for these two areas. In the other regions, microseismicity is either a ‘permanent’ characteristic or a quiescent
period between two important shocks, as we postulate for the
Durance fault. Consequently, the seismic hazard would be
underestimated by using the b values of recent seismicity.
The temporal evolution of this seismicity in the future may
allow one to solve this problem. Our spatial analysis should
be used in more complete temporal analyses.
The discrepancy observed between the high local rate of
deformation, low seismic activity and moderate average velocity
between Europe and the Apulian plate needs to be explained
in the light of a better understanding of the recent tectonics of
the western Alps.
A CK NO W L ED GM EN TS
We thank the anonymous reviewers for their constructive
remarks. We are grateful to E. Calais, G. Nolet and A. Ribodetti
for their help. This work was supported by LDG/CEA and by
INSU-CNRS through project ‘PNRN’. It is contribution
No. 192 of UMR Geosciences Azur.
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