This study is devoted to a systematic analysis of the state of stress of the central European Alps and northern Alpine foreland in Switzerland based on focal mechanisms of 138 earthquakes with magnitudes between 1 and 5. The most robust feature of the results is that the azimuth of the minimum compressive stress, S3, is generally well constrained for all data subsets and always lies in the NE quadrant. However, within this quadrant, the orientation of S3 changes systematically both along the structural strike of the Alpine chain and across it. The variation in stress along the mountain belt from NE to SW involves a progressive, counterclockwise rotation of S3 and is most clear in the foreland, where it amounts to 45°–50°. This pattern of rotation is compatible with the disturbance to the stress field expected from the indentation of the Adriatic Block into the central European Plate, possibly together with buoyancy forces arising from the strongly arcuate structure of the Moho to the immediate west of our study area. Across the Alps, the variation in azimuth of S3 is defined by a progressive, counterclockwise rotation of about 45° from the foreland in the north across the Helvetic domain to the Penninic nappes in the south and is accompanied by a change from a slight predominance of strike-slip mechanisms in the foreland to a strong predominance of normal faulting in the high parts of the Alps. The observed rotation can be explained by the perturbation of the large-scale regional stress by a local uniaxial deviatoric tension with a magnitude similar to that of the regional differential stress and with an orientation perpendicular to the strike of the Alpine belt. The tensile nature and orientation of this stress is consistent with the “spreading” stress expected from lateral density changes due to a crustal root beneath the Alps.
 The Alps are the most prominent young tectonic structure in Europe: they represent the western European segment of the Tertiary collision zone between the African and the Eurasian continents (Figure 1a). Present convergence rates of up to 9 mm/yr have been estimated for the relative motion between Africa and Europe [DeMets et al., 1994]. In this study we address the question of whether compression related to the collision is still the dominant force acting in the Alps and Alpine foreland or whether the present stress field reflects local perturbations due to other causes. Answers to this question are not only of interest for our understanding of the tectonic processes and evolution of the Alps but are also pertinent to the problem of seismic source zonation for earthquake hazard assessment.
 Earthquake focal mechanisms are among the most valuable sources of information for assessing the state of stress of the Earth's crust. Pavoni [1975, 1977] used the direction of the deformational axes, P (compression) and T (extension), obtained from fault plane solutions in a first attempt to estimate the state of stress in Switzerland. His results indicate a fan-like spreading of the compressional axes perpendicular to the mountain belt. Since these early studies, the number and quality of available focal mechanisms has increased steadily and new methods of in situ stress measurement have been implemented. The data available until about 1990 have been compiled in the World Stress Map project to produce a map of stress directions and relative magnitudes for western Europe [Müller et al., 1992, 1997; Zoback, 1992]. On a regional scale these studies largely confirm Pavoni's [1975, 1977] observation of a fan-like rotation of horizontal stresses north of the Alpine front that can be related to the ongoing convergence of Africa and Europe. However, recent more detailed studies suggest that there exist significant local deviations from this regional stress field.
 In the Jura Mountains and the northern part of the Molasse Basin, numerous in situ stress measurements have been carried out at depths of a few meters [e.g., Greiner and Illies, 1977; Becker et al., 1987; Becker, 1999], and stress-induced borehole breakouts have been observed in deep wells [Blümling et al., 1992]. Analyses of the orientation of P and T axes as well as stress inversions have been performed on earthquake fault plane solutions for several areas, which include the southern Rhine Graben, parts of northern Switzerland, the Wallis, the western Alps, and the western part of the Po Plain [Roth et al., 1992; Plenefisch and Bonjer, 1997; Maurer et al., 1997; Eva et al., 1997; Eva and Solarino, 1998; Evans and Roth, 1998; Sue et al., 1999; Deichmann et al., 2000b]. To date, however, no comprehensive stress analysis has been performed for the whole northern Alpine foreland and central Alps. This is the objective of the present paper. We have compiled a data set of 138 high-quality earthquake focal mechnisms and applied Gephart and Forsyth's  as well as Michael's  stress inversion methods to different subsets of these data to investigate spatial variations in stress orientation and relative magnitudes. As there is some controversy regarding the reliability of the uncertainty estimates of the different inversion methods [e.g., Hardebeck and Hauksson, 2001], the comparison of the results of the two methods allows us to assess the significance of possible spatial stress variations with more confidence. Our results confirm earlier observations of a fan-like rotation of the axis of maximum compression in the northern foreland. In addition, they present evidence for a systematic rotation of the least compressive stress and for a change in style of faulting between the foreland and the highest parts of the Alps in Switzerland. We interpret this in terms of the superposition of a local uniaxial tensional stress, related to spreading effects within the orogen, upon the regional compressive stress, associated with the large-scale continental convergence.
2. Tectonic Setting
 The European Alps are the most significant young tectonic structure in central Europe. They stretch in an arc around northern Italy, striking more or less N-S in the west and bending to an ENE-WSW strike at the latitude of Switzerland (Figure 1a). Throughout this paper we refer to the westernmost portion of the Alps between France and Italy as the western Alps, the easternmost part in Austria as the eastern Alps, and the Swiss part in between as the central Alps. (Note that ‘western’ and ‘eastern’ are adjectives (hence the first letter is lower case), and that the “western Alps' must not be confused with the ‘Western Alps’ mountain range which comprises our western Alps as well as the Alps in western Switzerland (Wallis). Similarly, the conventional ‘Eastern Alps’ include the Alps in eastern Switzerland and beyond. There is no Central Alps mountain range.) The tectonics of Switzerland are deeply influenced by the Alpine orogeny because the country lies within the Tertiary collision zone between the African and the Eurasian plates. N-S convergence between the African and the Eurasian plates began approximately 120 Myr ago and was related to a counterclockwise rotation of the African plate. After the Alpine Tethys ocean, which lay in between Eurasia and the African microplate Adria, had been subducted to the south, the two continents collided in the area of the eastern Alps at about 65 Ma. [e.g., Schmid et al., 1996, 1997]. As convergence continued, the upper crustal parts of the Adriatic continental microplate were thrust over the oceanic and European crust while the lower Adriatic crust and upper mantle intruded into Eurasia, splitting the Eurasian crust horizontally [Pfiffner et al., 1997]. During the early Miocene (about 23 Ma), the continuing indentation of the Adriatic plate caused the uplift of the Alps, while the debris of the rising mountains were deposited in the foreland basin to the north to form the Molasse Basin. Continuous crustal shortening resulted in the most recent tectonic movements north of the Alps which affected the foreland basin. This deformation started less than 12 Myr with the overthrust of the most southern parts of the Molasse (Subalpine Molasse) and produced a slight folding of the entire Molasse section. Finally, detachment along Triassic evaporites in northwestern Switzerland and eastern France and continued compressional deformation formed the Jura Mountains around 3–5 Ma. Whether the foreland is still active as a fold and thrust belt [e.g., Meyer et al., 1994; Calais, 1999] or whether this deformation has ceased or changed is subject to debate [e.g., Becker, 1999].
 The major tectonic units in the area of Switzerland are shown in Figure 1a. They are the Molasse Basin, the Jura Mountains and the Alps proper. A further subdivision can be made within the Alps by distinguishing between members of the series of stacked nappes. Generally, the higher the relative position of a nappe, the further south its origin. The three major nappes from top to bottom are the Eastern Alpine nappes which originated from the Adriatic plate, the Penninic nappes, which were located in the region of the Alpine Tethys, and the Helvetic nappes which derive from the margin of the Eurasian continent [see Schmid and Kissling, 2000, Figure 1]. The Penninic nappes are separated from the Helvetic nappes by the Basal Penninic Thrust. Further north, the Helvetic nappes are separated from the foreland by the Helvetic front.
3. Seismicity and Focal Mechanism Data
 Seismicity in Switzerland has been monitored since the mid 1970s by a dense short period telemetered network operated by the Swiss Seismological Service [Baer, 1990]. All waveforms have been available in digital form since the end of 1983. The permanent national network has been augmented from time to time by several temporary local networks [Roth, 1990; Maurer, 1993; Baer, 1990]. Stations in neighboring countries are also utilized for constraining the location and the fault plane solutions of earthquakes situated on the periphery or outside the Swiss network (see acknowledgments for list of institutions that supplied data for this study).
 The collision between the African and the Eurasian Plate is currently most active in southeastern Europe along the Adriatic and the Mediterranean Sea. In comparison, in Switzerland, where the Tertiary collision zone was located, seismicity is only low to moderate. Relatively high levels of seismicity are found in the southern Rhine Graben area, the Rhine Valley of St. Gallen, in Graubünden, and in the Wallis (Figure 1a).
 The fault plane solutions of 138 earthquakes recorded between 1961 and 1998, with magnitudes of between ML = 1.1 and 5.2, have been compiled for the present study (Figures 1b and 2 and listed in Table 1). FPSs with a magnitude of less than ML ≤ 2.0 in northern Switzerland and in the Wallis are based on data recorded by local temporary networks [Maurer, 1993; Bonjer, 1997; Deichmann et al., 2000b]. As a consequence, despite their small magnitude, these FPSs are well constrained. The question remains whether focal mechanisms of such small events are representative of the regional stress field. In fact, focal mechanisms of small aftershocks often exhibit a large scatter due to stress perturbations caused by the main shock. However, the small earthquakes included in our study are mostly independent events and the fact that their focal mechanisms do not increase the scatter of observed P and T axis orientations confirms that these mechanisms can be regarded as representative and provide robust estimates of the stress field. New fault plane solutions as well as those published in sources that are not readily accessible are displayed in Figure 3. All events taken from the literature were checked for consistency regarding orientation and orthogonality of the nodal planes. This mainly concerns events recorded prior to 1984. All subsequent events have been studied in detail by various authors (see references in Table 1). Takeoff angles and focal depths were reevaluated by two-dimensional (2-D) ray tracing using the program MODD of Gebrande  where it was necessary to account for a laterally heterogeneous crust [e.g., Eva et al., 1998]. The hypocenters of most earthquakes are estimated to be accurate to ±2 km laterally and ±3 km vertically. It was possible to apply cross correlation and precise relative location methods to determine which of the two nodal planes was the fault plane in 20 out of the 138 events [e.g., Deichmann and Garcia-Fernandez, 1992; Roth et al., 1992; Maurer and Deichmann, 1995]. These planes are marked by the bold line on 20 of the fault plane solutions (FPSs) shown in Figure 2. These 20 events are also identified in Table 1.
Table 1. List of All Events in Switzerland and Adjacent Areas for Which Fault Plane Solutions (FPS) Have Been Determined
 The distribution of earthquakes for which a fault plane solution is available is not uniform throughout Switzerland (Figures 1a and 1b). This distribution primarily reflects regional variations in seismic energy release over the period monitored. The scarcity of data is particularly problematic for the stress analysis in the western region of the area studied. Here, besides the low number of events recorded, the uncertainty in the location and fault plane solutions of some of these events is relatively large, since they occurred prior to 1976 when the network was less dense (events 139–142 in Figure 2). For example, the locations of events 141 and 142 are only known to within several tens of km [Fréchet, 1978; Dorel at al., 1983]. Thus the FPS of the three events in the western Jura (139, 140, and 142) should be interpreted with caution. Several other events elsewhere also have poor depth constraints, but their fault plane solutions are nonetheless well constrained (39 and 101). The only two events listed in Table 1 which were excluded from the stress inversion owing to a poorly constrained focal mechanism were the 1964 Sarnen event (94) and the earthquake close to St. Blaise in 1979 (146). The overall uncertainty of the focal mechanism parameters is considered to be on average 5°–10°.
 Simple inspection of the focal mechanism plots for Switzerland indicates a contrast in deformational style between the foreland in the north and the high Alps to the south (Figures 1b and 2). Whereas most earthquakes in the foreland show a predominantly strike-slip mechanism and some normal faulting, the proportion of normal faulting events increases significantly in the highest and formerly compressional parts of the Alps to the south. Thrust faulting events are occasionally seen in some localities, but are rare. Stereographic plots of the P and T axes of the events, grouped into the local data subsets we will later use in our stress inversions (Figure 4a), are shown in Figure 4b. They show a progressive counterclockwise rotation of the horizontal component of deformation from east to west in the Alpine foreland and from north to south across the Alps. Thus it is clear that present-day strain is not uniform throughout Switzerland, and it is of interest to determine how these variations are expressed in terms of stress.
4. Stress Inversion Methods
 Subsets of the 138 fault plane solutions were inverted to estimate the regional deviatoric stress tensors in Switzerland using the two most commonly used methods developed by Gephart and Forsyth  (hereinafter referred to as GF), Gephart , and by Michael [1984, 1987]. Both methods search for the stress tensor which brings the shear tractions resolved on the fault planes into alignment with the corresponding slip directions (i.e., rake) of the fault plane solutions. The parameters solved for in the inversions are the orientation of the principal stress axes, S1, S2, and S3 (with S1 > S2 > S3 under the compression-positive stress convention) and the value of the stress deviator, R = (S2 − S1)/(S3 − S1), [e.g., Etchecopar et al., 1981]. Thus the inversion constrains the shape and orientation of the stress ellipsoid but yields no information about the absolute magnitude of the stresses.
 We applied both methods because they are based on slightly different assumptions and use different inversion strategies [Gephart, 1990; Michael, 1984, 1987] (for comparison, see Kastrup ). Runs with GF's program were initially performed using a 10° grid and a range of 90° (search of the whole grid). Those data sets, which yielded results indicating a uniform stress state, were reevaluated with a 5° grid, which usually tightened the confidence limits. R was searched over the range from 0 to 1 in steps of 0.05. Two runs were made for each data set with the 10° grid: the first with no plane specified as the active fault plane, and the second with the active plane specified for all events in the data set for which it was known. Additional remarks to GF's method are made by Kastrup . In this paper we report only results obtained using the 5° grid with the known fault planes specified. For the inversions with Michael's program, three different approaches were tried. These approaches differ primarily in the implementation of the bootstrapping method to compute confidence limits. A detailed comparison of the results is given in Kastrup . Here we present only the results obtained with the method referred to by Kastrup  as Bootstrap variant 2. In this method, which is closest to that proposed by Michael , the bootstrap process repeatedly selects a subset of planes at random from a data set that contains all active fault planes from events where they are known and all nodal planes from events where the fault planes are not known. All planes in the data set are assigned the same probability of being selected, perhaps more than once. The computation of confidence limits in the bootstrapping method requires that a best fit solution be defined in order to serve as a reference vector from which distances (in a vector space sense) of solutions can be computed. The best fit solution that we use is obtained by inverting the set of planes identified by GF's method as the set that yields the lowest misfit (one plane for each event). The use of GF's method to identify the collection of planes most likely to have failed in the earthquakes is a rational approach in situations where a choice cannot be made on the basis of relative hypocentral locations or of structural information [Kastrup, 2002]. In this way, both best fit inversions use the same set of planes as input, and thus the effect of the different assumptions and procedures inherent in the methods can be judged by simply comparing solutions.
 Comparison of the results presented in Table 2 and Figure 5 shows that whereas both methods yield similar estimates for the best fitting stress tensors, they differ radically in the estimated confidence limits. Confidence limits derived from Gephart and Forsyth's  method are generally larger than those obtained from Michael's [1984, 1987] method. Hardebeck and Hauksson , in their comparative study based on synthetic focal mechanism data with random errors, found that Michael's confidence regions are usually correct while GF's are too large. The discrepancy in the size of the confidence regions was sometimes important in deciding whether changes in stress between neighboring regions were resolved in Switzerland. Thus the matter is discussed at some length by Kastrup . Following Hardebeck and Hauksson's  results, our interpretations rely on the confidence limits obtained from Michael's method. However, recognizing that the reasons for the discrepancy are not understood, we present the results from both methods.
Regional data set (see Figure 4a) (numbers connected by a plus refer to combined data sets); (M) refers to the inversion results run with Michael's inversion scheme; amount of inverted focal mechanisms (first number) and the amount of focal mechanisms thereof for which the active fault plane is known; misfit of the best stress tensor; plunge and azimuth of S1 (best stress tensor); plunge and azimuth of S2 (best stress tensor); plunge and azimuth of S3 (best stress tensor); PHI value (following GF's definition) of the best stress tensor (angle between S1 and the vertical axis in the plane perpendicular to S3; R value (S2 − S1/S3 − S1) of the best stress tensor.
F2 + F3
Different depth ranges (Foreland only)
10 < F4 < 15
10 < F4 < 15 (M)
F3 < 15
F3 < 15 (M)
F5 < 15
F5 < 15 (M)
F3 > 15
F3 > 15 (M)
F5 > 15
F5 > 15 (M)
15 < F4 < 20
15 < F4 < 20 (M)
F2 + F3 < 20
(M) F2 + F3 < 20
F3 < 20
F3 < 20 (M)
F5 < 20
F5 < 20 (M)
F3 > 20
F3 > 20 (M)
F5 > 20
F5 > 20 (M)
Foreland and Helvetic nappes
F1 + H1
F1 + H1 (M)
 The resolution of the R value is poor in comparison to the orientation of the principal stress axes. Hardebeck and Hauksson  also found that GF's estimates for R are unreliable for the case in which the stress state is actually axisymmetric (i.e., R = 0 or 1). In such situations, the best fit solution tends to a value of 0.5, and the confidence limits are too small, in contrast to the more general nonaxisymmetric situation, where the confidence limits tend to be too large. This also turned out to be a problem in this study. Nonetheless, in most cases the R value is sufficiently well resolved to determine whether R is greater than or less than 0.5 (i.e., whether the magnitude of S2 is closer to S1 or S3).
 Numerous inversions were run with varying subsets of the whole data set to evaluate whether the stress field in any two neighboring regions is significantly different. The average misfit of the best fit solution obtained from GF's method was used as a discriminator: following Wyss et al. , data sets which yield an average misfit of >6°fs were rejected as containing too great a mean error in the FPSs, or as stemming from a data volume in which stress is not homogeneous [Kastrup, 2002]. If possible, we tried to reduce the average misfit to <4°. If the GF misfits and stress tensors obtained from the inversion of subsets of a data set yield the same result as the combined data set, the stress field is considered to be homogeneous. The stress states of two adjacent regions are considered different if the 95% confidence regions obtained from Michael's [1984, 1987] method around any one of the principal stress axis orientations or around the R value do not overlap.
 The 138 fault plane solutions were divided into the nine regionally distinct data sets shown in Figure 4a. There are five data sets in the foreland, two in the Helvetic nappes, and two in the Penninic nappes. The choice of subdivisions within these three principal structural units was unavoidably influenced by the natural clustering of the events. Nonetheless, the coverage is sufficient to determine whether systematic changes in stress occur, and whether they correlate with such variables as topography and crustal thickness.
 Comparison of best fit solutions from the GF and Michael methods in Table 2 shows that the orientations of the stress axes are generally in accord, indicating that the different assumptions and methodologies inherent in the two methods do not have a significant effect on the solutions. The 95% confidence limit contours obtained from the Michael (variant 2) method usually matches the 68% contours obtained from the GF method closely. Michael's method is preferred in situations where GF's method of selecting the fault plane is prone to error. This is the case when the magnitude of two of the principal stresses is similar (axisymmetric stress state), and when the difference between the two misfit angles of the individual nodal planes of an event for the best fit solution is small.
 The results confirm the expectation that the stress regime in Switzerland is characterized by a strike-slip to normal faulting regime with S3 subhorizontal. Thus for most data sets, S3 represents the minimum horizontal stress, Sh (Figures 4c and 5 and Table 2). More importantly, the orientation of S3 is usually much better constrained and more stable than the orientation of either S1 or S2. Indeed, the best fit solutions for S1 and S2 vary greatly between neighboring data sets, and their 95% confidence limits from both methods commonly overlap, forming a band across the stereonet in the plane perpendicular to S3. Exceptions to this behavior are the inversion results for the data sets in the southwest (F1 + H1) and in central Switzerland (H3), where a few thrust mechanisms cause an overlap of the orientations of S2 and S3 (Figure 5).
 Two distinct trends in stress are evident: one trending north-south and the other northeast-southwest, or approximately normal and parallel to the Alpine mountain belt. (Figure 4c).
5.1. Variation of Stress Along the Strike of the Alpine Chain
 Here we examine the variation of stress along the Alpine chain within each of the three main structural units (foreland, Helvetic nappes, and Penninic nappes). In the foreland, north of the Helvetic front, the pattern of stress variations from east to west is best seen in the results of Michael's [1984, 1987] method applied to data sets F1+H1, F3 and F5 (Figure 5 and Table 3). The GF misfit of the best fit solution for each of these data sets is less than 6°, and thus they are considered to define zones within which the stress is acceptably uniform. Smaller misfits were obtained for local subsets of the F5 data set (e.g., F5-2 in Figure 6), which might indicate some degree of stress heterogeneity within the F5 data region (see section 4 and Kastrup ). However, the corresponding stress descriptions were largely the same, and hence, for simplicity, we work with the lumped data set (F5). The results from both methods show that the F3 and F5 regions are characterized by a strike-slip/normal fault stress regime with S3 subhorizontal, and S1 and S2 orientations unconstrained within a band normal to S3. This suggests that S1 and S2 are approximately equal in magnitude. Both methods also indicate a counterclockwise rotation in S3 orientation from east (F5) to west (F3). This rotation of some 25° is just resolved at Michael's 95% confidence limits, but not at GF's 68% limits. However, if the extreme southwest foreland region F1 + H1 (which lies entirely in France and includes seven foreland earthquakes augmented by two events in the Helvetic realm) is included, the net Sh rotation across the arc of the foreland, from F5 to F1 + H1, increases to 40°–50°, and is resolved by both methods. The increase in the rotation of Sh direction around the arc is progressive. This is seen most clearly in the P and T axes plot of Figure 4b, which includes the data from region F2 where there are too few data with different mechanisms to perform a formal stress inversion. The strong rotation in Sh orientation that occurs between regions F3 and F1 + H1 is accompanied by a change in the stress regime from strike-slip/normal (F3) to strike-slip/thrust (F1 + H1). This is indicated most clearly by the results of Michael's method for F1+H1 where the 95% confidence limits for S2 and S3 are unconstrained within a band normal to S1, indicating the magnitudes of S2 and S3 are similar (for F3, the band extends between S1 and S2). It is also indicated by the contrast in R values obtained from Michael's method, which tend to be significantly larger for F1 + H1 than F3 or F5 (Figure 5).
Table 3. Stress Inversion Results Using Michael's and Gephart and Forsyth's Method for Foreland Data Sets Along the Strike of the Alpine Arc
S1 Axis Dip/Azimuth
S3 Axis Dip/Azimuth
Gephart and Forsyth
Gephart and Forsyth
Gephart and Forsyth
F1 + H1
 The results for the southern Rhine Graben data set (F4) are consistent with those obtained by Plenefisch and Bonjer  for the same region and will thus not be discussed here (for details, see Kastrup ).
 The variation in stress along the structural strike within the Helvetic nappes is given by the results from regions H2 and H3 shown in Figure 5. In the southwest (H2), both methods indicate that S3 is oriented NE-SW, and is well constrained and subhorizontal. S1 and S2 are largely unconstrained within the plane normal to S3, implying a predominantly strike-slip regime with a normal faulting component. In the northeast (H3), the orientation of S3 is also NE-SW, with no rotation relative to its orientation in H2 resolved at Michael's 95% confidence level. However, in H3, S3 is unconstrained within a vertical band formed with S2, indicating a strike slip to thrust faulting regime (only resolved with Michael's method). This change in the stress regime along the arc, even though not resolved at the 95% confidence limits is also reflected in the R values obtained from Michael's method. Specifically, although no difference in R value is resolved at the 95% confidence limit, the R values tend to be larger than 0.5 in the northeast and less than 0.5 in the southwest, indicating a bias toward thrust faulting (S2 = Sv closer to S3) in the northeast and normal faulting in the southwest (S2 = Sv closer to S1). Examination of the fault plane solutions supports this contention: many events in the northeast display a significant thrust component (e.g., FPS 95, 98, 100, 103, 108 in Figure 2), whereas those in the southwest tend to display a larger normal faulting component.
 The variation in the state of stress along the strike of the Penninic nappes is obscured by the poor resolution of the stress axes obtained for the Graubünden (P2) data set in the east. This is due to a lack of diversity in the focal mechanism solutions available for that region. Nevertheless, the fault plane solutions themselves indicate that the style of ongoing deformation in the eastern Penninic nappes is similar to that in the western Penninic nappes in southern Wallis (data set P1), except for an apparent counterclockwise rotation of some 25°. This can be seen from the plots of P and T axes of events from the P1 and P2 regions shown in Figure 4b, suggesting that the orientation of Sh is similarly rotated. In any case, we conclude that the ongoing deformation, and possibly the stresses, in Graubünden appears to involve extension toward ∼30°N and thus strikes obliquely at ∼45° to the local trend of the Alps (75°N).
 Variations of stress with depth were examined in the northern foreland by analyzing the data for focal depths less than and greater than 15 km separately. The rotation along strike of the Alps seems to be less pronounced for the deeper events than for the shallower events. However, as the 95% confidence limits overlap and there are no lower crustal events in the southwest, a significant variation of the stress field with depth in the northern foreland is not sufficiently well constrained by the available data [Kastrup, 2002].
5.2. Variation of Stress Across the Strike of the Alpine Chain
 Here we examine the variation in stress along profiles normal to the Alpine chain in eastern and western Switzerland. The available data in eastern Switzerland is limited to the results obtained by Michael's method and concerns only the foreland and the Helvetic nappes, owing to the poor resolution of stress in the eastern Penninic nappes (P2). Stress in the eastern foreland is characterized by the results from data set F5, while the relevant data set in the Helvetic nappes is H3. North of the Helvetic front, S3 is oriented approximately ENE-WSW, whereas to the south (H3) it is more NE-SW oriented (Figure 5), implying a counterclockwise rotation of up to 30° resolved at Michael's 95% confidence limits. This is accompanied by a change in R value across the Alpine front with values tending to be less than 0.5 in the north and greater than 0.5 in the south (according to estimates from Michael's method). Even though the 95% confidence limits overlap, this change can also be traced with the best fit R values. This implies a change in stress regime from strike-slip/normal faulting in the eastern foreland to strike-slip/thrust faulting in the eastern Helvetic nappes. As noted earlier, the significant component of thrust faulting in the latter region is also evident in the fault plane solutions in Figure 2.
 For the eastern Penninic nappes, we can only refer to the mean axis of deformation (Figure 4b) to evaluate differences with respect to the Helvetic nappes. Also here, a 20° counterclockwise rotation in Sh orientation from north to south is suggested, accompanied by a change in deformation style from thrust/strike slip faulting in the Helvetic nappes to normal faulting in the Penninic nappes.
 The data in western Switzerland provide a complete NNW-SSE profile of the state of stress across the three main structural units. The relevant data sets from north to south are F3, H2, and P1. The stress inversion results for these regions are listed in Table 4. Comparison of the results from Michael's method in Figure 5 shows that a well-resolved 20°–25° counterclockwise rotation in S3 orientation occurs between each of these three units from north to south. The results from GF's method confirm the S3 rotation between the Helvetic and Penninic nappes, but the rotation between the Helvetic nappes and the foreland is not strictly resolved. However, comparison of the F3 and H2 stereonets in Figure 5 shows that the GF 68% confidence regions appear rotated by about 20° with respect to each other. This further supports our interpretation, based on the results obtained with Michael's algorithm, that the rotation is real. The horizontal stress rotation between the Helvetic and Penninic nappes is also accompanied by a change from strike-slip/normal faulting in the north (S1 horizontal or vertical) to predominantly normal faulting in the Penninic nappes (S1 predominantly vertical). No change in faulting regime is evident in the west between the Helvetic nappes and the foreland.
Table 4. Stress Inversion Results Using Michael's and Gephart and Forsyth's Method for Data Sets That Define the Western Profile Across the Alpine Belt
S1 Axis Dip/Azimuth
S3 Axis Dip/Azimuth
Gephart and Forsyth
Gephart and Forsyth
Gephart and Forsyth
 Thus both in western and in eastern Switzerland we observe a counterclockwise horizontal rotation of the stress axes of 40°–45° from the Alpine foreland to the Penninic nappes, with largely strike-slip deformation in the north giving way to extensional deformation in the Penninic nappes.
5.3. Ambiguity in S1 Inclination: Similarity in the Magnitude of S1 and S2?
 Most of the results in the foreland indicate that the inclinations of S1 and S2 are poorly constrained: the 95% confidence limits from both methods extend across the stereonet as a band in the plane normal to S3. Plenefisch and Bonjer  and Evans and Roth  also inverted data sets from the central foreland using GF's method and obtained similar results. There are two possible explanations for the ambiguity in S1 inclination that we mention.
 One explanation is that the ambiguity in S1 inclination reflects stress heterogeneity within the data volumes. While we cannot wholly discount this owing to the difficulty in estimating heterogeneity, we note that the same ambiguity is seen in the results of inversions of subsets of the data, when very small GF misfits are obtained. An example is presented in Figure 6 where we show the results of inverting a local subset of data from region F5 (referred to as F5-2 and indicated on Figure 4a). The GF misfit angle for the best fit solution is only 2.8°. Thus we consider stress heterogeneity to be an unlikely explanation.
 The second and simpler explanation is that the magnitudes of S1 and S2 are similar. This necessarily implies that the R value must be close to zero. Plenefisch and Bonjer  and Evans and Roth  both found R values close to 0.5 and the latter remarked that this was inconsistent with S1 = S2. Examination of the R values from our inversions of the northwestern and northeastern foreland data sets (Figures 5 and 6 and Tables 2 and 5) shows that the 95% confidence regions for R obtained from Michael's method (or 68% for GF's) are mostly in the 0–0.5 range, with best fit values from Michael's method tending to the lower end of this range and those from GF's method to the higher. Hardebeck and Hauksson  suggest that the R value estimates from GF's method are unreliable when the stress state is close to axisymmetric (e.g., S1 = S2). Nonetheless, to better understand the resolution of R value, we examined whether the R-value confidence estimates vary with S1 orientation (i.e., whether the distributions of acceptable values for S1 and R are correlated). Therefore we plotted the 68% and 95% confidence regions (contours of equal misfit) of S1 and R for all GF solutions of data set F5-2 that lie in the plane normal to the best fit value of S3 (Figure 7). The distribution of R-values is essentially independent of the orientation of S1, demonstrating that the two are not correlated. Thus we conclude that the ambiguity in S1 orientation that characterizes the northeastern and northwestern foreland probably reflects a similarity in the magnitude of S1 and S2.
Table 5. Comparison of Misfits and R Values for the Results Obtained With Gephart and Forsyth's Method and Michael's Bootstrap Variant 2 Method
Regional Data Set
Misfit Associated With the Best Fit Solution
Best Fit R Value
Limits of R Values
Michael Variant 2
Michael Variant 2
F1 + H1
possibly axisymmetric (S2 = S3)
possibly axisymmetric (S1 = S2)
possibly axisymmetric (S1 = S2)
0.01 – 0.37
axisymmetric (S1 = S2)
possibly axisymmetric (S1 = S2)
possibly axisymmetric (S2 = S3)
6. Possible Explanations for Stress Field Variations
 In this section we examine the correlation between the resolved variations in stress regime and potential causes such as topography, Moho depth, major tectonic structures, indentation of the Adriatic microplate, and crustal thickness. To this end, we place our results in a larger regional context that also includes stress field estimates from other studies (Figure 8).
6.1. Changes in the State of Stress Along the Strike of the Alpine Chain
 The rotation in the horizontal stresses of 40°–50° around the foreland of Alpine chain described above is also seen in paleostress data from the Jura Mountains (3–5 Ma) and the Molasse Basin (11–26 Ma) [e.g., Laubscher, 1972; Becker, 2000, and references therein] and in the pattern of P and T axes [Pavoni, 1980, 1987, 1992] (Figure 4b). It is not evident in near-surface stress measurement data from the northern Alpine foreland which indicate large local variations in minimum principal horizontal stress orientation [e.g., Becker et al., 1987; Becker 1999, 2000; Evans and Roth, 1998, and references therein]. However, this variability probably reflects the structural complexity of the upper 2–5 km. The low misfits of our results suggest that the degree of stress heterogeneity in the deeper basement where the earthquakes occur is less pronounced, even for the region at intersection of the foreland with the Rhine Graben (data set F3) where a major structural disturbance to the basement is found [Mayer et al., 1997].
 The most relevant observation in our view is that the rotation follows the curvature of the Alpine arc, and that it is only observed in the vicinity of the Alps (Figure 8). At greater distance, basically beyond the foreland, it melts away into the rather uniform NW-SE compressional stress field of Western Europe that is probably related to the push from the North Atlantic Ridge and to the convergence between Africa and Europe [Müller et al., 1992]. Thus this rotation reflects a stress perturbation, remnant or active, arising from the processes of Alpine collision, and which is defined at the scale of the Alpine arc. It follows that its cause must also be coherent on the scale of the Alpine arc. There are two candidate mechanisms that act at this scale: rigid indentation by a plate, and large-scale perturbation of crustal and lithospheric thickness.
Pavoni  first proposed that the rotation reflected stresses arising from the indentation of a rigid body into a viscoelastic material. Grünthal and Stromeyer  and Regenauer-Lieb and Petit  used conceptually similar models to show that the observations are consistent with the expected rotation of the stresses around the corner of the indenting Adriatic plate. On the basis of their results, Regenauer-Lieb and Petit  proposed that at present, the entire Central European plate gives way to the penetrating Italy/Adria Block by a NE-SW extension mechanism and a volume flux into the Mediterranean to the west of the Alps, a hypothesis that can explain why the NE-SW orientation of S3 is the most stable facet of the stress field throughout the foreland.
 An alternative explanation is that the along-strike stress rotation reflects the effect of buoyancy forces arising from the 3-D structure of the Moho (Figure 8) and perhaps an underlying lithospheric root. This mechanism is described in detail in section 6.2.1, where it is invoked to explain the across-strike variations in horizontal principal stress orientation. At first sight it seems improbable that the along-strike stress rotation can be due to variations in Moho depth or surface topography since both are more or less uniform along the foreland in Switzerland. However, as Figure 8 shows, the deviation for 2-D uniformity of Moho depth into the strongly 3-D, arcuate form in the western Alps has already occurred in the region of our westernmost data set F1 + H1, where the rotation was most clearly manifest. However, significant rotation is also seen eastward of this point around the arc where the Moho is more 2-D (Figures 4b and 4c). It remains for future geodynamical modeling to evaluate whether the 3-D structure of the Moho in the west can account for the observed along-strike rotation in stresses in the east.
6.2. Changes in the State of Stress Across the Alpine Chain
 Deformation in the Penninic domain differs from that in the rest of Switzerland by displaying a larger component of normal faulting accompanied by the counterclockwise rotation of the horizontal stresses by about 20°–25° with respect to the Helvetic nappes, and 40°–50° with respect to the foreland regions. Roth  and Maurer et al.  both proposed that different stress regimes exist in the northern and southern Wallis. Our results confirm their assertion, and further suggest that the Helvetic nappes represent a transition zone between the contrasting stress regimes in the Penninic nappes and the foreland. The vertical orientation of S1 in Southern Wallis is an important result as it implies that deformation in the highest parts of the Alps is no longer governed by compression. It is not unusual to observe ongoing extensional deformation in convergent mountain belts. Examples of mountain belts where crustal shortening is observed along the flanks and normal faulting in the upper parts include the Andes [e.g., Dalmayrac, 1974; Dorbath et al., 1991; Deverchère et al., 1989; Lindo, 1993], and the Himalayas [e.g., Molnar and Tapponier, 1975, 1978; Mercier et al., 1987; England, 1983]. In contrast to the aforementioned mountain belts, however, extension occurs obliquely to the strike of the belt in the central Alps and perpendicular in the western Alps.
 1. Both crustal thickness and topography increase from the foreland to the Alps proper. For example, across the foreland up to the Helvetic front, the European Moho lies at a depth of 28–30 km, whereas it is found at a depth of 50–58 km beneath the Insubric Line in the south (Figures 5 and 8) [Waldhauser et al., 1998]. The increasing crustal thickness is accompanied by pronounced negative isostatic gravity -anomalies [Klingelé and Kissling, 1982]. The topography also increases from a moderate average elevation of 585 m in the foreland to an average elevation of 1880 m in the central Alps of Switzerland.
 2. Deformation is ongoing: geodetic measurements show that highest rates of ongoing vertical uplift in the Alps of 1.5 mm/yr occur in the Wallis and in Graubünden [Schlatter et al., 1999].
 In section 6.2.1. we examine the consequences of the increase in crustal thickness along our cross-strike profiles with a view to explaining the observed stress changes.
6.2.1. Gravitational Potential Energy
 We will investigate whether a local or “second-order” uniaxial extensional stress [Zoback, 1992] that might correspond to a positive gravitational potential energy stored in the thickened crust (negative density anomaly) can explain the observed extension and rotation of the horizontal stresses in the high Alps [Artyushkov, 1973; Fleitout and Froidevaux, 1982, 1983; Molnar and Lyon-Caen, 1988; Coblentz at al., 1994]. The stress on which this local stress is superimposed will be referred to as regional or “first-order” stress, and the sum of both stresses, which is the stress actually observed, will be called the resultant stress.
 The orientation of the resultant stress will depend on the relative magnitudes and orientations of the regional and the local stress components which are known from our study. The strike of the crustal root is fairly well known so that the direction of the local stress, which is perpendicular to it, can be easily determined (Figure 8). However, the depth of the lithosphere is not well constrained [Kissling, 1993]. Available evidence suggests that beneath the central Alps the lithospheric mantle does not thicken. In the Wallis and the western Alps the lithospheric root could either dip very steeply or be absent altogether (slab break off) [Kissling, 1993; Lippitsch, 2002]. Because of this uncertainty, the influence of the mantle lid on the potential energy cannot be assessed quantitatively and the implied stress perturbation calculated. Therefore our analysis is essentially concerned only with geometric aspects of the problem.
6.2.2. Decomposition of Resultant Stress Into Regional and Local Components
Sonder  and Zoback  describe a scheme for assessing whether an observed local stress perturbation can be explained as due to the superposition of a local uniaxial stress on the regional stress. The calculation is based on simple tensor addition in the horizontal plane and is illustrated in Figure 9 [Jaeger and Cook, 1979; Sonder, 1990]. The angle γ represents the observed rotation of the perturbed Sh from the regional orientation, and the uniaxial perturbing stress is described by its magnitude, SL and its orientation, θ, measured with respect to the regional Sh. If the regional stress magnitudes are described by SH and Sh, then the variables are related through
 Using equation (1), we can plot contours of the predicted perturbation in stress orientation, γ, as a function of the uniaxial local stress orientation, θ, for specific values of (SH − Sh)reg/SL, the regional differential stress normalized by the uniaxial stress magnitude (Figure 10a). Since in the analysis both γ and θ are constrained by observations, we can obtain estimates for the normalized uniaxial local stress magnitude (in units of regional differential stress) from the contour values at the intersection of the constrained range of γ-θ values.
 The stress data indicate that the regional stress of western Europe, which most likely results from the ridge push in the North Atlantic and the convergence between the African and Eurasian plates, is locally disturbed in the vicinity of the Alps and shows a fanlike pattern along the arc (Figure 8). The horizontal stress directions in the Alps themselves do not align with this pattern but rather show a seemingly progressive, systematic rotation with respect to the stresses in the foreland (Figure 4c). Within the context of our proposed model, we will consider the rotation in stress across the Alpine chain to be the result of the superposition of a local and a regional stress. The choice of the regional stress requires some consideration owing to the tendency for observed horizontal stress directions in the foreland to rotate with position around the Alpine arc. In the analysis that follows, we consider variations in horizontal stress orientation along a profile that is normal to the local structural strike: that is, in the direction of local Moho dip (we are making here a 2-D approximation of a 3-D structure). Thus it is natural to take the regional stress as that which prevails in the foreland section of the profile in question, where the Moho depth becomes relatively stable.
6.2.3. Results of Stress Decomposition for the Central Alps (Switzerland)
 The crustal root in the Wallis strikes ∼N45°E (Table 6). Hence the horizontal uniaxial stress caused by the thickened crust strikes N135°E, thereby forming an angle θ = −82° with the regional Sh which is oriented N53°E (F3) (Figure 10b). This constraint on θ is shown in Figure 10a by the gray bar with black stripes. The second constraint is that the observed (i.e., resultant) stress in the southern Wallis is rotated 45° from the regional Sh, so that γ = 45°. This constraint on γ is shown in Figure 10a by the horizontal white bar with black stripes. At the intersection of the two lines in the γ-θ solution space, the contour of the stress ratio (SH − Sh)/SL takes the value −0.98. Thus the normalized horizontal uniaxial stress SL/(SH − Sh) = −1.02, where the negative sign indicates that it is tensional.
Table 6. Data for Evaluating Whether a Uniaxial Local Extensional Stress Perpendicular to the Crustal Root Can Be Responsible for the Observed Extension and the Rotation of the Horizontal Stresses in the Alpsa
Strike of Structure Causing Extension
Azimuth of Local Uniaxial Stress
Applied to scheme on Figure 10; for details, see text. Azimuth of local uniaxial stress is perpendicular to the structure; γ is angle between regional and resultant Sh; and θ is angle between local uniaxial stress and regional Sh.
 The data for the profile extending across eastern Switzerland into Graubünden are also listed in Table 6 and yield similar results to the Wallis profile. Here the strike of the crustal root is N70°E. If we accept the mean orientation of the T axis of N30°E as indicating the direction of the observed Sh, and take the regional Sh as oriented N79°E (F5), then we have γ = 49° and θ = −81°, values which are similar to those for the Wallis. From Figure 10a, the value of the stress ratio, (SH − Sh)/SL, at the intersection of these two values is −0.9, implying the normalized uniaxial stress, SL/(SH − Sh) = −1.1.
 Thus the observed rotation of Sh across the Alpine chain in western Switzerland can be explained by the local perturbation of the large-scale regional stress by a local uniaxial tension of magnitude similar to the regional differential stress and orientated perpendicular to the strike of the Alpine belt. We interpret this local stress to be a “spreading” stress that results from lateral density changes due to the presence of a crustal root [Artyushkov, 1973]. This interpretation is further supported by the observation that the rotation appears to occur gradually along the western profile, the S3 azimuth observed in the Helvetic nappes being intermediate between those in the foreland and Penninic nappes. The superposition of this local tension with the regional stress explains why the Penninic nappes should be currently extensional. A simple consideration shows that this is the only possibility. One characteristic of the regional stress regime in the northern foreland is that S1 and S2 are similar in magnitude with S3 horizontal. This means that S1 can be horizontal or vertical, and the stress regime favors equally normal and strike-slip faulting. If we now superimpose a horizontal uniaxial tensional stress, the effect will be to reduce the net horizontal compression in all directions (except in the orthogonal direction to the uniaxial stress which will remain unchanged). Thus regardless of the relative orientation of the horizontal components of the two stresses, the superposition will always serve to reduce horizontal compression and thus move the stress state toward normal faulting.
 The tendency toward a slightly compressional regime in the eastern Helvetic nappes as well as in the westernmost foreland could be related to the extension in the high Alps. In a simplified consideration, the thrust-faulting component can be understood as a paired compensational deformation to the extension occurring in the adjacent higher Alps [e.g., Molnar and Lyon-Caen, 1988].
 The pervasive west European “first-order” stress field with SH oriented NW-SE, which is believed to result from the ridge push in the North Atlantic and convergence between the African and Eurasian plate, is perturbed in the vicinity of the European Alps. Regional groups of fault plane solutions from earthquakes in the Swiss Alps have been inverted to determine the spatial variation of the stresses driving present-day deformation in the Swiss Alps and the northern Alpine foreland. A general feature of the stress inversion results is that the azimuth of S3 is generally well constrained for each data set and always lies in the NE quadrant. However, the azimuth of S3 changes systematically both along the NE structural strike of the Alpine chain and also across it. These trends are accompanied by changes in the predominant style of deformation, and are interpreted as reflecting the effects of two different “second-order” stress-generating mechanisms.
 The variation in stress along the chain involves a progressive, counterclockwise rotation of the orientation of Sh from east to west. It is most strongly defined in the foreland of our study area where it amounts to 45°–50°, and continues westward into the foreland of the western Alps [Sue et al., 1999]. A rotation in the same sense is also seen in the Penninic nappes, but no such rotation can be resolved in the Helvetic nappes. The pattern of rotation in the foreland is similar to the disturbance to the stress field expected from the indentation of the Adriatic Block into the Central European Plate [Pavoni, 1961; Regenauer-Lieb and Petit, 1997]. The indentation mechanism can also explain why the NE-SW azimuth of S3 is the most stable facet of the stress throughout the foreland and is consistent with the view that the entire central European plate gives way to the penetrating Italy/Adria Block by a NE-SW extension mechanism [Regenauer-Lieb and Petit, 1997]. However, buoyancy forces arising from the strongly arcuate structure of the Moho to the immediate west of our study area might also contribute.
 The variation in stress across the Alps is defined by a progressive, counterclockwise rotation in S3 azimuth along two profiles in east and west Switzerland that extend from the foreland in the north across the Helvetic nappes to the Penninic nappes in the south. The net rotation along both profiles between the foreland and the Penninic nappes amounts to 40°–50°, and is accompanied by a trend toward increasing dominance of normal faulting in the south. The contrast in stress states at either end of the profiles can be explained by the superposition of a local uniaxial tension in the south whose magnitude is similar to the regional differential stress in the north and whose orientation is perpendicular to the strike of the Alpine belt. The tensile nature and orientation of this stress is consistent with the characteristics of the stress expected to result from lateral density changes due to the crustal root. This is further supported by the observation of a gradual change in the direction of S3 as we go from the foreland to the high parts of the Alps.
 We would like to thank the Associate Editor Doug Schmitt, John Townend, Thomas Plenefisch, and an anonymous reviewer for their very thorough reviews. We are also thankful to Klaus Regenauer-Lieb for many interesting discussions and John Gephart for providing us with his stress inversion program and for being helpful whenever problems occurred. We also appreciated that Barbara Romanovicz hosted one of the authors (U. Kastrup) for 7 months at the Seismological Laboratory at University of California, Berkeley.