Variations of stress directions in the western Alpine arc

Abstract

The western Alpine arc originated during the Cretaceous orogenesis as a consequence of the continental collision between the European and Adriatic plates. The distribution of forces acting in this sector of the Alps is still somewhat uncertain. In the past, some efforts have been made to map the distribution of P and T axes but it is known that these can be substantially different from the principal stress directions.

In recent work, we presented a first attempt to determine the directions of σ₁ and σ₃, which we could compute only for a ‘local’ regime at the level of the magnitude of the larger events that occurred in the area. To obtain the stress orientation, we applied the technique developed by Gephart and Forsyth to invert fault plane solutions.

In this work we present the results of a detailed analysis performed on a larger area, applying the same methodology. A total of 86 earthquakes with magnitudes ranging from 2.5 to 5.3 has been used for inversion. The results confirm the impossibility of defining, within the available data, a regional stress field. In fact, different local behaviours have been demonstrated in four subregions. For the first subregion, namely the northern part of the western Alps, the inversion of 28 earthquakes, resulting in a misfit of 5.9°, revealed a distensive regime orientated N-S. For the second subregion, the outer part of the western Alps, the inversion of 16 earthquakes led to a misfit of 5.3° for a distensive E-W orientated regime. In the inner part of the chain, an opposite result was obtained by the inversion of 14 earthquakes, confirmed by a misfit of 4.7°. Finally, the region of the Ligurian Sea revealed an almost horizontal NW-SE orientated σ₁, whereas σ₃ is NE-SW orientated with a dip of around 30°–40°. The inversion for this subarea was carried out on a data set of 28 earthquakes and characterized by a misfit of 7.1°. The uncertainty of the stress axis orientation (90 per cent confidence limits) is, on average for all inversions, around 40°.

fault plane solutions (FPS), seismotectonics, stress distribution

Introduction

Since the early 1980s, the western Alpine arc has undergone a thorough seismic monitoring. The aim was to improve the understanding of this sector of the Alps, which originated during the Cretaceous orogenesis as a consequence of the continental collision between the European and Adriatic plates.

The development in the last decade of a large number of recording instruments and the increased accuracy of earthquake locations have evidenced the main trend of seismicity for this area (Fig. 1) (Eva et al. 1990).

Figure 1

Seismicity from 1983 to 1996 in the western Alpine arc. Events have magnitude >2.5; Erh, Erz <5 km. The distribution of earthquakes reflects well the tectonic structure of the area (Eva et al. 1997).

In the Swiss sector of the studied area, seismicity is mainly located in the Valais region, where very strong earthquakes have occurred in the past (Mayer-Rosa & Mueller 1979). In the western Alps, seismic activity, consistent and of low magnitude, is mainly concentrated around the border between France and Italy. In this area, seismicity seems to be organized into two branches that clearly reflect the tectonic sketch, being almost coincident, within the location errors, with the Penninic front and the border of the Penninic unit and the Po plain. The external crystalline massifs appear as aseismic units and the seismic activity is concentrated along their margin. In the Ligurian Sea, seismicity is mainly located at the western side at the foot of the continental margin, although a seismic-swarm-like activity affects the inland region.

The recognition of these seismic behaviours is very important for the definition of subareas of homogeneous characteristics, as emphasized in the following.

Although the tectonic aspects of the formation and evolution of the orogen and the associated seismicity are now fairly well known, the distribution of forces currently acting and, as a consequence, the distribution of the P and T axes of the focal mechanisms are still somewhat confused. Previous studies evidenced a great variability of the P and T axes: a progressive rotation of the P axis roughly perpendicular to the chain was proposed by Fréchet (1978) and Ménard (1988), while the priority of transcurrent and transpressive solutions was the main feature of the western Alps according to Pavoni (1986).

The knowledge that the distribution of P and T axes can differ greatly from that of the principal stress directions leads us to realize that even if we were able to clear up any doubt about the behaviour of the P and T axes, this could not be considered as providing a conclusive account of the distribution of stresses affecting this sector of the Alps.

In recent work (Eva et al. 1997) we presented our first attempt at computing the stress tensor orientation by the inversion of fault plane solutions for the southwestern Alpine sector. In that study we came to the conclusion that, as the scale of geodynamic processes under investigation is controlled by the range of magnitudes of the events used (Rebai, Philip & Taboada 1992), we could not compute a ‘regional’ stress behaviour but only a local regime. We add here that, because the magnitudes of events do not exceed 5.3 (except for two events in the Ligurian Sea, estimated to be 6.0), we can only determine local regimes for the different subareas and subsets into which the western sector of the Alps and the Ligurian Sea can be divided.

This work represents a more detailed evaluation of the various stress regimes acting in a wider area of the western Alps. Through the results we can confirm, as stated by Rebai et al. (1992), that variations of stress directions are present in the western Alpine arc and that we have defined exactly their orientations. Determination of the changes of the stress tensor over this area and their comparison with the available information on local tectonics are the main goals of our investigation.

Data Collection

The development in the last two decades of several seismic networks [in France, Renass (Strasbourg), Sismalp (Grenoble) and LDG (Paris); in Switzerland, ETH (Zürich); and in Italy, IGG (Genoa) and ING (Rome)] over the whole area under study allowed us to compute high-quality focal mechanisms down to a magnitude of 2.5 for the principal events.

The fault plane solutions were compiled into a database made from directly computed focal solutions and focal solutions taken from the literature. Both groups of solutions include focal mechanisms computed using the first-motion technique. In particular, computed focal solutions were obtained by means of the fpfit code (Reasenberg & Oppenheimer 1985), which searches for the double-couple fault plane solution that best fits a given set of observed first-motion polarities for an earthquake.

The choice of including in our database focal solutions taken from the literature is useful to complete the data set, although some problems may arise from this option. In fact, it is not directly possible to estimate a quality factor for these events, and thus a selection among the available published mechanisms is necessary as a prerequisite for their usage. This selection and weighting of solutions was performed by evaluating all available information: the polarity distribution on the focal sphere, estimates of quality parameters, and the network configuration used for hypocentre and focal-mechanism computations.

Out of the 86 solutions used, with a local magnitude ranging between 2.5 and 5.3, 44 were taken from the literature (grey-shaded) (Fréchet & Pavoni 1979; Béthoux et al. 1988; Deverchere et al. 1991; Madeddu, Béthoux & Stephan 1996; Maurer 1997; Menard 1988; Nicolas, Santoire & Delpech 1990). The uncertainties of the fault parameters for these events were evaluated and found not to exceed, in general, about 20°.

The remaining 42 focal mechanisms were taken from those computed at DISTER (Dipartimento di Scienze della Terra, University of Genoa) for events occurring in the period 1980–1997, except for a few cases of older suitable events. They were selected on the basis of the restrictive criteria of a magnitude >2.5, a minimum of 20 polarities and a reasonable azimuthal coverage of stations (gap <70°). The DISTER solutions selected for stress inversion show fault parameter uncertainties not greater than 15–20°.

Method and Analysis

To compute the stress inversion from the focal solutions, we applied the method of Gephart & Forsyth (Gephart & Forsyth 1984; Gephart 1990a, b). This methodology is well known and a complete description is beyond the scope of this work. Briefly, under the basic assumption that the deviatoric stress tensor is uniform over a given rock volume and time interval, this method inverts the parameters of the focal mechanisms of earthquakes to compute the orientations of the main stress axes σ₁, σ₂ and σ₃, which are estimated together with the value of the R parameter [=(σ₂−σ₁)/(σ₃−σ₁)]. The program finds the solution corresponding to a minimum average misfit (F), regarded as the discrepancy between the stress tensor and the observations (fault plane solutions). The misfit of a single focal mechanism is defined as the minimum rotation about any arbitrary axis that brings one of the nodal planes and its slip vector into an orientation that is consistent with the stress model.

The value of the minimum average misfit, together with the confidence limits of the solution, computed by a statistical procedure described by Parker & McNutt (1980) and Gephart & Forsyth (1984), gives an a posteriori estimation of the quality of the results and provides a guide to decide whether the area considered is in a homogeneous stress field. In fact, the confidence limits of the solution generally tend to become larger for increasing stress heterogeneity and can also be an important a posteriori indicator of the suitability for stress inversion of the FPS data set.

According to Wyss et al. (1992) and Lu, Wyss & Pulpan (1997), F-values not larger than 3°, 6° and 8° are related to errors of 5°, 10° and 15°, respectively, in the focal-mechanism parameters. The errors in the focal-mechanism parameters in our FPS data set are estimated to be of the order of 15–20°, so F-values not exceeding 8° are assumed as a condition of a homogeneous stress tensor in the present study.

As the scale of the geodynamic processes under investigation is controlled by the magnitude range of the events used, it is very important to consider areas where the stress field is homogeneous. Definingsubsectors where the stress is hypothesized to be homogeneous is a sort of ‘trial and error’ technique based on severala priori and a posteriori criteria. Although there is no real rule, some important parameters can influence the initial choice, but can be disclaimed or confirmed after an inversion run. Among the a priori parameters there are the structural pattern and the seismicity and focal-solution distributions; the a posteriori parameters are linked to the results of computation and depend on the value of F (averaged minimum misfit) and of the confidence limits.

In a first attempt, we divided the studied area into three subsectors (Zone A: south Valais and northwestern Italy; Zone B: southwestern Alps; Zone C: western Ligurian Sea) (Figs 2–4). In the following, we describe results obtained from the inversion of fault plane solutions for the various subdivisions.

Results of Inversion

Zone A

For zone A (Fig. 2) we used 28 focal solutions, of which 14 were taken from the literature (Nicolas et al. 1990; Maurer 1997) and 14 were computed at DISTER (Table 1). The quality of the focal solutions is fair and we estimate the uncertainty of the positions of the nodal planes as 15°–20°. The stress inversion gave meaningful results for the analysed area. The F-value (5.92°), taking into account the results of Wyss et al. (1992) and Lu et al. (1997), indicates that the stress can be considered uniform and the 90 per cent and 50 per cent confidence limits of the solutions indicate very constrained solutions. Fig. 5 evidences an almost vertical σ₁ and a nearly horizontal NNW-SSE σ₃. The R-value (0.3) indicates that in both volumes the amplitude of σ₂ lies in the middle of the range defined by the amplitudes of σ₁ and σ₃.

Figure 2

Focal solutions for zone A (28 events): black, computed; grey, collected from literature.

Table 1

Locations and focal-mechanism parameters for the 28 events in zone A.

Figure 5

Summary of 90 per cent confidence limits computed for results of inversion runs.

Zone B

For zone B (Fig. 3), in the first attempt, the entire set of fault plane solutions, composed of 16 focal mechanisms taken from the literature and 14 computed at DISTER (Table 2), was inverted for stress. The fairly large value of misfit (F=13.4°) showed that no uniform stress distribution could explain the whole set of data. The data set was therefore subdivided into two parts, one consisting of the earthquakes of the external (west) side of the southwestern Alpine chain, and the other consisting of the earthquakes of the inner (east) side (Eva et al. 1997). In these two sectors, the focal mechanisms indicate different deformation styles. Reverse mechanisms prevail in the eastern part (labelled E in Fig. 3), in contrast to normal faulting to the west (labelled W in the same figure). The stress inversion gave meaningful results for both the western and the eastern zone. Fig. 5 shows the orientations of the maximum and minimum compressive stress (σ₁ and σ₃) for the two areas and also displays the 90 per cent confidence limits of the solutions. The F-values (7.5° and 5.4° for the western and eastern zones, respectively) indicate that the stress can be assumed to be uniform in the corresponding volumes. Fig. 5 shows a high-dip σ₃ and a nearly horizontal E-W σ₁ in the east, and reveals that σ₁ is almost vertical in the west, where σ₃ is E-W orientated with a dip of approximately 0°–20°.

Figure 3

Focal solutions for zone B (30 events). After a first attempt, this sector was subdivided into two subzones, east (E) and west (W) [see text or Eva et al. (1997) for details].

Table 2

Locations and focal-mechanism parameters for the 28 events in zone B.

Zone C

The last sector (Fig. 4) is the area of the western Ligurian region and the western Ligurian Sea. For this area we took into account 28 focal mechanisms, of which half were taken from the literature (Table 3). The inversion results give an F-value of 7.1°, which represents a homogeneous stress in the area, and the 90 per cent and 50 per cent confidence limits (Fig. 5) show solutions that are not scattered, with the principal axes of σ₁ and σ₃ orientated NW-SE almost horizontally, and NE-SW with a dip of around 30°–40°, respectively.

Figure 4

Focal solutions for zone C (28 events).

Table 3

Locations and focal-mechanism parameters for the 28 events in zone C.

Discussion

The stress inversion results, reported in summary in Fig. 6, appear to be in agreement with the geodynamic information available for the study area. The structural pattern of the northwestern Alps is supposed to be the product of the interaction between Adria and Europe (see for example Steck & Hunziker 1994). The anti-clockwise rotation of the Adriatic indenter relative to Europe produces a force system trending E-W in the Po plain and N-S in the northern part of the western Alps. This force system causes crustal shortening, thrusting, an accretionary wedge of soft crust in the front of the northwestern Alpine belt and strong uplift along the crest of the chain (Bernoulli, Heitzmann & Zingg 1990; Doglioni 1992, 1993). In the areas A and B the uplift is high.

Figure 6

Distribution of stress orientations in western Alpine arc for subzones A, B and C as derived from the present work. All earthquakes 1983–1996 are shown.

The earthquakes used for stress inversion were located in the depth range 0–10 km for zone A. The fairly low misfit value obtained (F=5.92°) indicates stress homogeneity. The 90 per cent confidence limit of the solution is fairly small and shows, in particular, a satisfactory level of constraint on the orientations of the principal axes of stress: a high-dip σ₁ is found. The R-values (0.3) indicate that the σ₂ amplitude is nearly equidistant from the σ₁ and σ₃ values.

The stress inversion results, together with the hypocentre distribution, give further support to local geodynamic models that assume a regional compression in the area under study, deriving from the Adria-Europe interaction, and producing secondary tensional effects at very shallow depths. According to Molnar & Lyon-Caen (1988), one of the forces that opposes the push of two plates is gravity. Potential energy is thus stored in each column of rock, while the elevation of the chain increases to a mean value related to the force at which the plates are pushed together. When the maximum elevation is reached, convergence continues but the crest of the chain can locally undergo crustal extension.

These effects are confirmed also by the results obtained for zone B, where the R-values (0.5 and 0.6 for the western and eastern parts, respectively) (Table 4) indicate that in both volumes the σ₂ amplitude lies in the middle of the range defined by the σ₁ and σ₃ amplitudes. Thus, in the west the stress in the E-W direction (minimum compressive stress) is significantly smaller than in the N-S direction (an intermediate stress), in agreement with the preferentially N-S trend of the normal fault systems present in this specific volume (Labaume, Ritz & Philip 1989). Similarly, in the east, the stress in the vertical direction (minimum) is smaller than in the N-S direction (intermediate), in agreement with the E-W thrusting assumed for the same volume by local geodynamic models (Bernoulli et al. 1990; Doglioni 1992, 1993).

Table 4

Summary of results of inversion runs. For the meaning of B/East and B/West, see text. N is the number of focal solutions used for inversion, F is the misfit and R=(σ₂–σ₁)/(σ₃–σ₁).

The stress inversion results reported in Fig. 6 and Table 4 appear to be in agreement with the geodynamic uplift associated with the regional-scale thrusting process, which has reactivated, as normal faults, pre-existing shallow structures (Labaume et al. 1989). For the Ligurian Sea subzone, the results of inversion show a rotation of the principal stress axes with respect to the western Alps and correspond to an area with a NW-SE compressive trend. This compressive regime can be associated with the closing direction of the Ligurian Sea (Réhault & Béthoux 1984).

Conclusions

Stress inversion from 86 earthquake fault plane solutions of the western Alps (depth <25 km) shows different orientations of the principal stress axes (σ₁ and σ₃) for the various subzones into which we divided the area. These orientations are characterized by slight to significant deviations from the expected compressional force due to the collision between the Adriatic and European plates. Several local stress fields are superimposed on, or partly derived from, this more regional compressive force.

In both the northern and the southern sectors of the western Alpine arc (zones A and B), the gravitational collapse occurring during the orogenesis (Molnar & Lyon-Caen 1988) is responsible for a local distensive stress regime accompanied by shallow earthquakes. In the northern part (zone A), the stress orientation is rotated by almost 90° with respect to the southern sector as a consequence of the bending of the Alpine chain.

For the southern zone (zone B), the availability of a greater number of events allowed us to perform two inversions, one using shallow events, whose result is a distensive local stress regime, and one performed with deeper events, showing a compressive E-W-orientated stress field.

In the case of the Ligurian Sea, the stress regime can be considered as the consequence of the collision between the African and European plates along a N-S direction, and has the same properties of that of western Europe (Mueller et al. 1992). In this sense, the general behaviour of the Ligurian Sea should be considered independently from the Alpine chain. Compression in the Ligurian Sea could also be responsible for the triggering of the reactivation of the complex system of faults in the Nice arc and for the seismicity of the northern margin of the Ligurian Sea.

Acknowledgements

We are indebted to Hervé Philip and two anonymous reviewers, who improved the manuscript with their valuable suggestions.