Mantle flow under the Central Alps: Constraints from non-vertical SKS shear-wave splitting

The association of seismic anisotropy and deformation, as e.g. exploited by shear-wave splitting measurements, provides a unique opportunity to map the orientation of geodynamic processes in the upper mantle and to constraint their nature. However, due to the limited depth-resolution of steeply arriving core-phases, used for shear-wave splitting investigations, it appears difficult to differentiate between asthenospheric and lithospheric origins of observed seismic anisotropy. To change that, we take advantage of the different backazimuthal variations of fast orientation φ and delay time ∆t, when considering 5 the non-vertical incidence of phases passing through an olivine block with vertical b-axis as opposed to one with vertical c-axis. Both these alignments can occur depending on the type of deformation, e.g. a sub-horizontal foliation orientation in the case of a simple asthenospheric flow and a sub-vertical foliation when considering vertically-coherent deformation in the lithosphere. In this study we investigate the cause of seismic anisotropy in the Central Alps. Combining high-quality shear-wave splitting measurements of three datasets leads to a dense station coverage. Fast orientations φ show a spatially coherent and 10 relatively simple mountain-chain-parallel pattern, likely related to a single-layer case of upper mantle anisotropy. Considering the measurements of the whole study area together, our non-vertical-ray shear-wave splitting procedure points towards a b-up olivine situation and thus favors an asthenospheric anisotropy source, with a horizontal flow plane of deformation. We also test the influence of position relative to the European slab, distinguishing a northern and southern subarea based on verticallyintegrated travel times through a tomographic model. Differences in the statistical distribution of splitting parameters φ and 15 ∆t, and in the backazimuthal variation of δφ and δ∆t, become apparent. While the observed seismic anisotropy in the northern subarea shows indications of asthenospheric flow, likely a depth-dependent plane Couette-Poiseuille flow around the Alps, the origin in the southern subarea remains more difficult to determine and may also contain effects from the slab itself. 1 https://doi.org/10.5194/se-2020-5 Preprint. Discussion started: 24 February 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction
The propagation of seismic waves is affected by the properties of each layer they pass, providing the opportunity to deduce information about interior structures and dynamics of Earth. The observation of directionally-dependent phase velocities, called seismic anisotropy, is such a property, which can be related to e.g. crystal alignment in upper mantle minerals, referred to as lattice-preferred orientation (LPO) (see e.g. Mainprice, 2015). Olivine is known to be the most common anisotropic mineral 5 in this depth domain (see e.g. McDonough and Rudnick, 1998) and the fabric that it controls can have several types, depending on water content, temperature, and pressure conditions (Karato, 2008). Additionally, other minerals like orthopyroxene, clinopyroxene, and garnet also show anisotropy, and they effect the observations (Nicolas and Christensen, 1987;Babuska and Cara, 1991;Karato, 2008;Mainprice, 2015, and references therein). 10 Following Vinnik et al. (1984) and Silver and Chan (1988) the occurrence of shear-wave splitting (SWS) is one of the observations that reveal seismic anisotropy. Shear-wave splitting is comparable to the phenomenon of optical birefringence and it describes that an S-wave splits into two waves, when it passes through an anisotropic layer -forming waves with a slow and a fast polarization orientation φ. The polarization of both quasi-S-waves (qS) is perpendicular to each other. The delay δt between the qS-waves accumulates depending on the strength of anisotropy (based on the variation of phase velocities) and the 15 length of the path through the medium.
The presence of receiver-side anisotropy shows up as elliptical particle motion when observing core phases, like SKS and SKKS, of stronger earthquakes (M > 5.5) in a certain distance (∼ 80 • -120 • ). Other than in the case of an isotropic Earth, not only the radial-, but also transverse component shows a signal. Using e.g. the minimum-energy technique of Silver and Chan 20 (1991), the SWS parameters φ and ∆t can be determined (see also Vinnik et al., 1989) applying a grid search to linearize the observed particle motion and thus removing the effect of anisotropy (see e.g. Wüstefeld et al., 2008).
Since the observed φ-∆t pattern reflects LPO anisotropy, SWS measurements hold the potential to relate mineral alignment, subsurface deformation, and geodynamic settings across scales, but due to the near-vertical arrival of core phases, the method 25 has only weak depth resolution. So the orientation of the rock foliation could not been derived for a long time, what was particularly unfortunate as it would suggest a flow-plane orientation (Bokelmann, 2002a(Bokelmann, , 2002b and references therein) and thus further restrict the cause of anisotropy. Whether the observed SWS pattern represents more recent flow activity in the asthenosphere (Vinnik et al., 1989;Savage and Silver, 1993) or is likely related to ancient deformation frozen-in lithosphere (Silver andChan, 1988, 1991), has thus been under debate. In Löberich and Bokelmann (2020) we have developed a procedure 30 to relate differences in the small-scale azimuthal variations in φ and ∆t to foliation orientation and subsurface deformation, taking advantage of the non-vertical arrival of SKS phases, assuming a dominant single-layer case of seismic anisotropy. Investigating a big dataset of automatically determined SWS measurements (Liu et al., 2014), we were able to determine the source of seismic anisotropy beneath Western/Central US as a mainly subhorizontally-oriented flow plane of deformation.
Such a density and amount of stations and measurements are indeed unique for SWS studies, but using a reasonable number of SWS measurements of higher precision, as available e.g. in the Central Alps, yields another opportunity to test our approach.
In this study we demonstrate how the analysis of non-vertical SWS can help to constrain the cause of seismic anisotropy below the Central Alps, improving our knowledge on deformation mainly in the European upper mantle. Combining previous 5 SWS measurements in the Alps (Barruol et al., 2011;Qorbani et al., 2015;Salimbeni et al., 2018), the fast orientations φ reveal a spatially consistent pattern, usually described as being parallel to the mountain-chain (see e.g. Bokelmann et al., 2013), and related to a single-layer case of seismic anisotropy in the Western and Central Alps. However, the Eastern Alps show evidence for a double-layer case possibly related to the presence of a slab detachment (Qorbani et al., 2015). Even if the Western and Central Alpine region seems to be less complex in terms of SWS, our understanding of tectonic settings and related geody- 10 namic processes is still incomplete or even contradicting (see e.g. Kästle et al., 2019).
Subsequently we investigate the backazimuthal variations of SWS parameters in the whole Central Alps study area simultaneously and in a northern and southern subarea separately, to examine whether their distributions can be related to a Simple Asthenospheric Flow (SAF) or Vertically-Coherent Deformation (VCD). In this context we also compare the SWS pattern 15 with the dV p model of Koulakov et al. (2009) to determine whether the behavior of SWS measurements, in relation with the different dV p polarities in upper mantle depths, favor different causes of seismic anisotropy in the two subareas.

Tectonic Setting
The history of Alpine orogeny, leading to the arc-like mountain-chain ( Fig. 1) known today, was controlled by the convergence of Eurasia and Africa, two major continental plates; it was further defined by related opening and closing processes of oceanic domains (see e.g. Coward and Dietrich, 1989). Following Handy et al. (2010), Neotethys with its subbranches (Ionian Sea and Meliata-Maliac-Varder) opened during the late Paleozoic-Mesozoic, while Pangea broke apart. However, in the 5 Jurassic-Cretaceous both branches have been reworked during subduction and obduction processes (Handy et al., 2010, based on Stampfli et al., 1998Schmid et al., 2008;Faupl and Wagreich, 2000), while the Alpine Tethys (Handy et al., 2010, based on the naming in Stampfli and Borel, 2002) and Atlantic Ocean opened jointly. Eventually, the Alpine Tethys formed upon two ocean basins, namely Piemont-Ligurian and Valais, separated by the Briançonnais terrain (for further details see e.g. Stampfli, 1994, based on Stampfli, 1993. When the European Plate underwent subduction below Adria, a microplate assumed to be an 10 African promontory (Handy et al., 2010, based on Argand, 1924Channell and Horváth, 1976;Channell et al., 1979), these entrapped basins closed successively, starting with Ligurian segments (131-118 Ma), followed by Piemont, and further Western . This process was completed by the incipient Alpine collision 35 Ma ago (see e.g. Handy et al., 2010). Following e.g. Schlunegger and Kissling (2015) (based on Schmid et al., 1996) the change from the initially subducted southern oceanic rim to continental lithosphere of the European plate, caused differential forces in the subduction 15 system  what finally led to a slab break-off of the oceanic section (Dal Piaz and Gosso, 1994;Von Blanckenburg and Davies, 1995) and further an asthenospheric upwelling. As consequence, exhumation took place till 20 Ma (Schlunegger andKissling, 2015, based on Pfiffner, 1986;Schlunegger et al., 1997;Kempf et al., 1999), followed by a northward movement of the Apenninic slab (Salimbeni et al., 2018, based on Malusà et al., 2015Malusà et al., 2016).
However, the slab break-off occurrence time and subsequent movement in each Alpine section are still under debate (Handy 20 et al., 2010, and references therein).
Nowadays we assume the Alpine mountain range to be built upon a two-lithosphere root system, namely the slabs situated under the Western/Central Alps and Eastern Alps (see e.g. Qorbani et al., 2015, based on tomographic models of Lippitsch et al.,2003;Koulakov et al., 2009;Mitterbauer et al., 2011). This geodynamic situation is already complex, but the appearance 25 of the surrounding Appeninnic, Carpathian, and Dinaridic slabs, dipping southwest-, east-, and northeastwards (see e.g. Handy et al., 2010or Salimbeni et al., 2018, based on Lucente et al., 1999Piromallo and Morelli, 2003;Giacomuzzi et al., 2011;Zhao et al., 2016;Hua et al., 2017), shows the overall tectonic diversity and related activity, e.g. the ongoing consumption of Adria, in the Mediterranean region (Handy et al., 2010). The variety of subsystems of the Central Mediterranean tectonics makes it difficult to derive a unique model from geophysical measurements capable to explain and relate all geodynamic im- Beside the velocity structures obtained from different inversion methods of various wave types and phases investigated at a certain time, seismic anisotropy and particularly SWS measurements hold the potential to complete our basic (model-like) understanding of upper mantle processes, e.g. by taking advantage of the relation between the direction of accumulated deformation and observed fast orientation φ. Barruol et al. (2011) stated that the gradual clockwise rotation of φ along the Alpine belt indicates a curvature of the geometry of internal deformation. Further, the delay time ∆t provides quantitative information about the thickness and strength of an anisotropic layer. However, internal Alpine regions surprisingly unveil relatively weak 5 anisotropy, although this area probably underwent higher rates of deformation than external regions, which show stronger anisotropy. This previous work already indicated that the Western Alps SWS pattern could be caused by an asthenospheric source, discussing a passive flow, shaped by a European slab keel, following the absolute plate motion of Eurasia. Other possibilities are described by an active flow, e.g. generated by a European slab detachment (see e.g. Lippitsch et al., 2003) or due to the influence of the European and Appeninic slab rollbacks upon the flow system (Barruol et al., 2011, based on Funiciello 10 et al., 2006Piromallo et al., 2006;Vignaroli et al., 2008).
Recently Salimbeni et al. (2018) provided additional SWS measurements in Western Alps and Apennines, spatially densifying the general mountain-chain-parallel pattern of φ. Contrary to Barruol et al. (2011), this study excluded the approach of an active flow, driven by a discontinuous European slab, based on the recent tomography findings of Zhao et al. (2016). It 15 disagreed with the possibility of a European slab rollback (Salimbeni et al., 2018, based on Handy et al., 2010Malusà et al., 2015) and further reinterpreted the influence of the Apenninic slab rollback as follows. Based on the model of Zhao et al. (2016), the European and Apenninic slabs seem to be connected. Hence a toroidal flow, as would have been generated by the Apenninic slab rollback, could not form. This led to a mass deficit west of the Apenninic slab. To overcome this imbalance, it is assumed that asthenospheric material was pulled behind from western and northern areas, generating a counterflow, shaped 20 according to the European slab appearance. This may include small-scale upwelling (Salimbeni et al., 2018, based on Long andBecker, 2010;Díaz et al., 2013), which would evoke an upper-mantle temperature anomaly and might facilitate topographic uplift (see e.g. Salimbeni et al., 2018, based on Chéry et al., 2016Nocquet et al., 2016 or Sternai et al., 2019, andreferences therein) in agreement with the highest mountains being generally situated in the Western Alps. 25 Beside the asthenospheric cause of SWS, Salimbeni et al. (2018) (and references therein) also pointed out the potential of additional lithospheric (slab-related) anisotropy, so called fossil fabric, based on frozen-in deformation from Tethyan rifting.
Such an additional lithospheric source of anisotropy has been found in the Eastern Alps. While the gradual clockwise rotation characteristic of φ remains preserved (see e.g. Bokelmann et al., 2013), Qorbani et al. (2015) observed a π/2-periodicity in the Eastern Alps, consistent with a double-layer anisotropy case. Here the upper layer is characterized by a NW-SE fast orientation, 30 possibly linked to asthenospheric flow activity, contrary to the deeper layer, which unveils a generally NE-SW pattern associable with a European slab detachment. Whether the observed pattern of SWS shows a dominant asthenospheric or lithospheric origin is often difficult to distinguish, but following the non-vertical SWS procedure we are now able to further constrain the cause of seismic anisotropy.
As introduced in detail in Löberich and Bokelmann (2020) our approach is based on a Taylor-series expansion, derived by Davis (2003) for a horizontally-oriented single-layer case of (orthorhombic) seismic anisotropy, which describes the azimuthal behavior of both SWS parameters in the case of non-vertical SKS phase arrival (incidence: θ ≤ 30 • ). Eq. 1-2 show the related solution of the fast orientation φ as sum of the vertical incidence case φ 0 and an additional term of small-amplitude oscillation 5 δφ: This variation introduces angular dependencies, namely a 180 • -periodicity on azimuth z with amplitudes being controlled by the incidence θ. The effect of the medium and its orientation, as represented by the stiffness tensor C, is expressed by d 1 as: with Since d 1 specifies the phase polarity we subsequently refer it as "oscillation parameter". A similar expression can be derived 15 for the delay time ∆t in the case of non-vertical incidence, where: with δ∆t = e 2 cos(2z)θ 2 .
Then 20 with ρ being the density, D specifying the path length, and c = C 1313 C 2323 .
In Löberich and Bokelmann (2020) we have shown that d 1 and e 2 vary for different orientations of olivine. Assuming a horizontal a-axis (Nicolas and Christensen, 1987) together with a vertically-oriented b-axis (b-up) or c-axis (c-up) changes the amplitude of δ∆t due to e 2 alteration and shifts the phase in δφ, meaning opposite polarities of d 1 (Fig. 2). While a b-up orientation leads to a negative d 1 value, a c-up alignment causes a positive d 1 . Hence, assuming a broad backazimuthal distribution of high-quality individuals SWS measurements, both cases are indeed distinguishable especially due to the difference in the os-5 cillation parameter. This is particularly interesting as these orientations can be related to a SAF and VCD scenario, mentioned before. Silver (1996), and references therein, summarized that anisotropy, caused by the asthenosphere, is associated with a b-up olivine orientation, assuming a horizontal flow plane of deformation and foliation orientation, and lithospheric anisotropy, related to frozen-in deformation and vertical foliation, might lead to a c-up olivine alignment.

10
To distinguish both cases, we investigate only good quality individual SWS measurements of SK(K)S phases determined using the minimum energy technique (Silver and Chan, 1991)  The variations δφ and δ∆t of the observed SWS parameters provide a possibility to constrain d 1 and e 2 , as shown in Eqs. 2 and 6. To derive δφ and δ∆t, we follow the workflow described in Löberich and Bokelmann (2020). do not occur at every azimuth the distribution itself is biased, missing information e.g. from north and southeast direction.
Furthermore, SWS parameters cannot be obtained for backazimuths parallel or perpendicular to φ and lead to so called Null measurements. For the subsequent investigation we only consider stations with more than five measurements to ensure that the means per station, φ and ∆t, are determined stably. The backazimuthal distribution of the SWS parameters is then corrected for the corresponding φ and ∆t, which should align the measurements as if they would have been recorded at a single   rence of the European slab, respectively. The SWS pattern, usually described as mountain-chain-parallel, can apparently be separated, into the low-and the high-velocity anomaly. For each of the two anomalies the fast orientation seems to follow the shape of the anomaly. To understand this behavior we investigate three dV p depth profiles through the wider area.
Profile A (second row, left) slices the region diagonally from northwest to southeast, crossing the low-and high-velocity anomalies mentioned before. Considering the main part of both regions, they show a comparable depth extent. While the lowvelocity anomaly is situated at depths of ∼ 80 -260 km and thus extends 180 km vertically, the high-velocity anomaly has a slightly smaller vertical extent (150 km); it is between ∼ 90 -240 km depth. Both are separated by a sharp nearly-vertical transition (see e.g. Koulakov et al., 2009) at a profile distance of ∼ 290 km. However, between ∼ 240 -290 km the slab thins 5 massively and starting at ∼ 250 km gets overlain by a strong low-dV p Po plain anomaly (see e.g. Lippitsch et al., 2003, based on Spakman et al., 1993Solarino et al., 1996;Bijwaard andSpakman, 2000 or Koulakov et al., 2009), which has been argued to reveal a hydrated Adriatic mantle wedge (see e.g. Giacomuzzi et al., 2011, and for further reading Hearn, 1999). Similarly as in the tomographic image also φ (third row, left) shows a transition from NE to ENE along profile A between 260 -310 km, while ∆t values (bottom, left) are typically between ∼ 1 -2 s without showing a clear change when crossing both structures.
If we assume that the strength of LPO anisotropy is comparable throughout the study region, the path length D through the structures causing SWS should be also similar. This points at a different origin of the anisotropy in the north and the south. If the low-velocity block in the north is giving rise to the (flow-related) anisotropy there, as seen in the non-vertical SWS analysis, then it should be the fast-velocity anomaly in the south, giving rise to lithospheric anisotropy (see below).    Taking advantage of the spatial subdivision of high-quality SWS measurements, we follow the procedure as explained for the whole study area to investigate the backazimuthal variation of δφ and δ∆t for the northern and southern subarea separately ( Fig. 8 and 9). Both subsets show comparable parameter distributions (top row), however the northern subarea is better constrained due to the higher number of measurements. Applying the same criteria for thresholds and intervals (second row) as before, reveals a similar behavior for δφ and δ∆t (third row) in the northern subarea as seen for the whole study region.
reduced amount of datapoints, e.g. at 135 • , the uniqueness of the distinction gets lost (2σ error) and the significance is reduced.
In the southern subarea the significance of most intervals is lower due to the reduced coverage in the selected, φ-compensated backazimuthal distribution (third row). A stable differentiation between different olivine orientation (bottom row), based on the non-vertical SWS approach, is thus difficult with the amount of currently available high-quality SWS measurements in the 5 subarea.
The analysis of high-quality SKS splitting measurements in the Central Alps suggests that the SKS splitting indeed shows small but systematic variations with backazimuth. The angular dependence revealed is consistent with that expected from the dominant foliation orientation of anisotropic minerals in the upper mantle; it thus holds direct constraints on subsurface deformation and the nature of the seismic anisotropy, which was ambiguous previously due to the weak depth resolution of SWS.

5
Considering measurements in the entire study area at once, the variations agree with a simple model of olivine with a horizontal foliation and vertical b-axis (b-up olivine), just as the one indicated in Fig. 2. This kind of anisotropy is expected, if the LPO is generated by an asthenospheric flow around the Alps.
As the observed backazimuthal variation of splitting parameters is not large and requires a broader azimuthal distribution 10 to become more apparent, it has not been studied before. In any case, the importance of an observation is not necessarily related to its size; if one had not considered small effects there would be no quantum mechanics, no gravitational waves etc.
All that matters is whether the effect is significant, and this is the case, judging from the error bars in Fig. 4. Even a moderate number of "good" quality splitting measurements is apparently enough to constrain the effect, which suggests that such studies can also be performed at regional scale. 15 Our analysis has assumed that the anisotropy is well-characterized by a single horizontal layer of anisotropy. Indeed, the Central Alps have been well-characterized by single-layer anisotropy before, and there are no signs of two-layer cases (90 • periodicity) or a dipping layer (360 • periodicity) in the area. In the latter case of dipping layer anisotropy the equations used here could be further adjusted following Davis (2003). If there were more anisotropic layers, but only one would be dominant, 20 this would not necessarily rule out our approach, but it would require more data and a wider range of backazimuths to stabilize the procedure (see Löberich and Bokelmann, 2020). Since the area of study is already quite well-covered with permanent broadband instruments, the presence of AlpArray does not provide many additional stations, but as the dataset so far only covers a relatively limited time duration it can in principle be extended for a longer time period. 25 As much as one might wish to be able to use a larger range of backazimuths, we must admit that near the Null directions, parallel or perpendicular to the fast orientation, the observations become less stable. Hence, we need to average over a backazimuthal window, which is set to ±33.25 • width around maxima and minima of δφ to distinguish SAF and VCD. This stabilizes the effect in δφ, but it has the adverse effect of rendering the constraint in δ∆t less useful. However, the two endmember models can hardly be distinguished by the splitting delay variation anyway. 30 Considering the models themselves, it is remarkable that the SWS observations were fit by our simplistic starting configuration without adapting it. Since the actual amount of aligned olivine is not known, we assumed the approximately 70 % olivine of the upper mantle (see e.g. McDonough andRudnick, 1998 or Faccenda andCapitanio, 2013) to be perfectly-aligned, while 30 % remain randomly-oriented. However, we have shown in Löberich and Bokelmann (2020) that reasonable changes of this ratio do not significantly affect the d 1 parameter. To approximate the observations, it was also not necessary to consider other minerals like orthopyroxene (Nicolas and Christensen, 1987;Babuska and Cara, 1991;Karato, 2008;Mainprice, 2015, and references therein) or to involve the effect of e.g. pressure (depth) to make the model more realistic. So we used the Voigt-Reuss-Hill average, as in our previous study in the Western and Central US, to model the behavior of seismic anisotropy, and it is striking, but probably not fortuitous, that the same b-up configuration can also explain the Central Alps data.
An intriguing consequence of the observations is that a girdle configuration of olivine grains, as would be implied by several deformation mechanisms (see e.g. Nicolas and Christensen, 1987), is clearly ruled out by the data, which rather favors a "high-temperature mechanism". Otherwise we would obtain d 1 values in the vicinity of zero (Löberich and Bokelmann, 10 2020). We regard this as an important conclusion, since petrologists often assume such girdle configurations, based on findings of individual xenoliths (see e.g. Soustelle et al., 2010). However, the latter give rather localized information and may not be representative of larger regions of the upper mantle.
Considering smaller regions, we found indications that the backazimuthal variations in the northern subarea are also con-15 sistent with the predictions for a horizontal alignment of foliation planes, as expected from the SAF model. However, the reduced amount of measurements makes it more complicated to constrain the b-up situation here.
Assuming the source of anisotropy to be related to the presence of the horizontal upper mantle flow, seen along profile B around the Alps (Fig. 10 left), we subsequently consider further inferences about the flow type. The SAF model used here is a 20 first approximation to understand the flow field to some extent, but as seen in Fig. 6, shallower depth already indicated the possibility of a more complex, depth-dependent system. In general, there are two simple flow types that are relevant at this spatial scale, planar Poiseuille flow (Fig. 10 center) and Couette flow (Fig. 10 right). Following Richardson (2011a, 2011b) these concepts consider a Newtonian fluid, which is incompressible and bounded by parallel plates. While one of them can move relative to the stable other in Couette flow ("drag-induced flow"), they are fixed during Poiseuille flow (Brennen, 2006;Richardson, 25 2011a, 2011b; Natarov and Conrad, 2012, based on Couette, 1890). Since the latter case requires a changing pressure field it is classified as "pressure-induced flow" or "channel flow" (Richardson, 2011b;Natarov and Conrad, 2012, based on Poiseuille, 1840a, 1840b, 1840c). The resulting laminar flow in each case can be considered fully developed. However, the velocity-depth distributions follow a linear slope in Couette flow, and a parabolic curve for Poiseuille flow (Brennen, 2006;Richardson, 2011aRichardson, , 2011b. Each of them is associated with simple-shear deformation (see e.g. Brennen, 2006), but the velocity distribution differs Following Natarov and Conrad (2012), the SAF model we used here in fact illustrates Couette flow, deforming the asthenosphere due to the relative movement of lithosphere and mantle convection, generating LPO (based on McKenzie, 1979;Ribe, 1989;Karato and Wu, 1993;Richards et al., 2001). However, Couette flow may be expected to control intraplate domains,  Now we return to the Alps and to the question whether a pure Couette flow, as assumed in the SAF model, can explain the azimuthal distribution of φ in the Central Alps. Figure 11 compares φ with surface motions derived from GNSS measurements by Sánchez et al. (2018), to see whether mantle and surface deformation can be related to each other. At first site geodetic motions and fast orientations seem to have little relation to each other. The reference system in that study was stable Eurasia, and the question is whether another reference model can be found that renders geodetic motions and fast orientation similar.
Poiseuille flow is therefore the more likely deformation model for the area. Such a flow would be consistent with the vertical alignment of olivine b-axes found in our study. Since we assume the flow in the north to be related to the pulling force of the Apenninic slab rollback, a change in the pressure field can be expected. From a geodynamic point of view, a Poiseuille contribution does not require involvement of the transition zone, which in principle could be investigated by inspecting temper-10 atures in the transition zone, e.g. from receiver functions. However, the flow around the Alps, is perhaps too spatially confined to be resolved by the necessarily long-period receiver functions.

Natarov and Conrad
The interpretation in the southern part, where we have observed a considerably weaker fit with each of the anisotropic models and weaker splitting, is more difficult as the region is affected by different processes. On one hand, a similar flow as for the northern part could affect the SWS, but whether the splitting occurs in the deep low-velocity region beneath the European slab 25 detachment in profile A remains an open question considering the presence of a strong low-dVp Po plain anomaly (Lippitsch et al., 2003, based on Spakman et al., 1993Solarino et al., 1996;Bijwaard andSpakman, 2000 or Koulakov et al., 2009) on top of the slab. If this area can be understood as hydrated (see e.g. Giacomuzzi et al., 2011, andfor further reading Hearn, 1999), serpentine, known to react highly anisotropic (see e.g. Katayama et al., 2009or Salimbeni et al., 2018, based on Bezacier et al., 2010, must be further considered. However, assuming A-type olivine a flow crossing the slab can be ruled out as origin of An indication for this is provided by a zone of weaker positive vertically-integrated travel times at 11 • longitude. This area has been suggested before to represent a discontinuity, potentially separating the Western/Central and Eastern European slabs (see e.g. Kästle et al., 2019, based on Lippitsch et al., 2003Koulakov et al., 2009, Mitterbauer et al., 2011Zhao et al., 2016;Hua et al., 2017). Here also the splitting decreases along profile C, suggesting that indeed slab anisotropy plays a more important role in the southern part. In this study we have applied the non-vertical-ray shear-wave splitting approach to high-quality shear-wave splitting measurements of previous studies in the Central Alps to further constrain the cause of seismic anisotropy in a single-layer case. We have compared modeled and derived angular shear-wave splitting variations δφ and δ∆t and took advantage of the polarity difference of the oscillation parameter d 1 for olivine in a b-up or c-up configuration to distinguish between more recent flow is more likely. In the southern subarea the behavior of δφ and δ∆t is not uniquely explainable by one of the investigated endmember models so far. Besides a possible flow contribution as in the northern subarea below the European slab detachment, effects from serpentinization above the slab might possibly occur. The spatial correlation between shear-wave splitting and vertically-integrated travel times depth renders a contribution of the lithospheric slab likely. Finally, our study showed, that even an initially simple-looking shear-wave splitting pattern might reveal unexpected complexity and lead to crucial insights.
To test our separation into subareas based on the tomography model of Koulakov et al. (2009), we further calculate the vertically-integrated travel times also for the model of Hua et al. (2017) (reference model: iasp91 by Kennett and Engdahl, 1991; EuCRUST-07 by Tesauro et al., 2008). Similar as in Fig. 6, the dV p depth slices in Fig. A1 are strongly influenced by the occurrence of high-dV p anomalies, related to the Western/Central European slab and the western end of the Eastern 5 European slab, surrounded by a flow system (low-dV p anomalies). However, different from the tomography of Koulakov et al. (2009), this pattern is less obvious at 90 km, but with increasing depth the complexity develops. In comparison to the low-dV p zone in Fig. 6, associated with the counterflow mentioned before (Salimbeni et al., 2018), the anomaly is laterally more focussed here and connected to an even stronger low-dV p Po plain anomaly (Lippitsch et al., 2003, based on Spakman et al., 1993Solarino et al., 1996;Bijwaard andSpakman, 2000 or Koulakov et al., 2009), possibly explainable by a hydrated Adriatic 10 mantle wedge (see e.g. Giacomuzzi et al., 2011, and for further reading Hearn, 1999). The slabs are thus separated more clearly, but a mountain-chain-perpendicular flow in between is not indicated by the fast orientations. Overall, the SWS pattern seems to correlate more with the spatial distribution of dV p anomalies in the model of Koulakov et al. (2009), but as individual depth slices might not be indicative enough, we also determine the vertically-integrated travel times subsequently (Fig. A2). The slower regions also appear around the faster areas; yet their appearance is somewhat different: the depth range differs slightly following Hua et al. (2017), and more complex. For this reason we decided to use the tomography of Koulakov et al. (2009) for the separation. Here we give some details on the two deformation models presented in Fig. 10, the planar Poiseuille model as well as the Couette model (after Brennen, 2006). Both describe steady laminar flow between two infinitely long parallel plates. The difference is that in Couette flow one of the plates has a velocity U relative to the other, which is assumed to be at rest, for the sake of the argument. There is no pressure gradient in the fluid. In contrast, the Poiseuille model presents the case, where both plates are 5 at rest, and the flow is caused by a lateral pressure gradient, parallel to the plates.
Assuming that the only non-zero component of the flow is U x , and that velocity and pressure are independent of time, the continuity equation for an incompressible fluid is ∂U x ∂x = 0 (B1) 10 and U x (z) is a function of z only. For an incompressible fluid with constant viscosity η, the flow equations become and ∂p ∂z = 0 .
The pressure p is a function of x only, and the flow velocity becomes 15 U x = 1 η dp dx with the integration constants C 1 and C 2 .
For Couette flow we have dp/dx = 0, and no-slip conditions at the upper and lower boundaries provide with maximum velocity U max and channel thickness h. The velocity gradient within the channel is Poiseuille flow with no-slip conditions yields Assuming a constant lateral pressure gradient −dp/dx = A, the velocity gradient is which attains its maximum value Ah 2η at the top of the channel. For convenience, we introduce a scaled flow velocity relative to the maximum velocity U max . For Poiseuille flow, the maximum velocity occurs in the center of the channel and it is The scaled velocity gradients are therefore The absolute level of strain rate (or velocity gradient) |∂U x /∂z| determines the increase in seismic anisotropy at a given depth 10 and time. For long periods (Montagner et al., 2000;Wüstefeld et al., 2009), SKS splitting can be related to its vertical integral This assumes that no saturation effects occur in the deformation-anisotropy relation (see e.g. Ben Ismaïl and Mainprice, 1998).
It follows that Poiseuille flow is twice as efficient in generating strain (and SKS splitting) compared with Couette flow, for a given maximum velocity (which can be constrained from geodynamics/tectonics). Author contributions. The work presented here was carried out and written down by the first author. Appendix B was accomplished by the 5 co-author, who also controlled texts and figures. Related suggestions were included by the first author.
Competing interests. We declare that no competing interests are present.
Acknowledgements. We thank Irene Bianchi for her comments and suggestions, which helped to improve the section on tectonic settings in the Alps. Further we want to acknowledge all data suppliers mentioned above, and the operators of the Swiss Digital Seismic Network/Switzerland Seismological Network ( Ferranti and Hormann, 2014). Line lengths give splitting delay ∆t, orientation the fast orientation φ. The dashed rectangle surrounds the study area as in Fig. 1