## Abstract

The contribution of vertical ductile thinning to the exhumation of high-pressure rocks is evaluated by estimating finite strain in 75 exhumed high-pressure rocks of the Cycladic blueschist unit in the Aegean Sea, Greece, and western Turkey. Strain data indicate heterogeneous deformation; principal stretches are 1.24–5.03 for *S*_{X}, 0.63–2.53 for *S*_{Y} and 0.10–0.81 for *S*_{Z}, with a tensor average of *S*_{X}:*S*_{Y}:*S*_{Z}=1.52:1.28:0.51. A 1D numerical model, which integrates velocity gradients along a vertical flow path with a steady-state orogen, is used to estimate the contribution of ductile thinning of the overburden of the high-pressure rocks to exhumation. Using a strain-rate law that is proportional to depth, averaged results show that ductile flow contributed *c*. 20% to exhumation. A major implication is that the vertical strain in the exhumed rocks is an overestimate of the contribution that ductile flow makes to the total exhumation. A proportional strain-rate law that scales linearly with depth implies that material points rising towards the surface move quickly out of the more rapidly deforming part of the orogen. Therefore, very large vertical strains >90% in deeply exhumed rocks are needed for vertical ductile thinning to be a major exhumation process.

Metamorphic rocks of deep-seated origin are commonly found in the interiors of orogens. The exhumation of these rocks occurs by vertical ductile thinning, normal faulting and erosion (Ring *et al*. 1999*a*) (Fig. 1). A number of studies have shown that normal faulting and erosion can be fast and significant exhumation processes (Platt 1986; Kamp *et al*. 1989; Brandon *et al*. 1998; Thomson *et al*. 1998*a*; Ring *et al*. 2001*a*; Brichau *et al*. 2006). The third exhumation process, vertical ductile thinning, has hardly been addressed at all quantitatively and therefore the role that vertical ductile thinning plays in the exhumation of deeply buried rocks remains more obscure. Vertical ductile thinning is defined as the change in the thickness of the overburden above a material point as a result of ductile flow within that overburden (Feehan & Brandon 1999). The presence of a subhorizontal foliation is commonly diagnostic of vertical ductile thinning (Selverstone 1985; Wallis 1992; Kassem & Ring 2004). Wallis (1992) argued that vertical ductile thinning might account for up to 40% of the total exhumation of high-pressure rocks from the Sanbagawa belt of Japan. Kumerics *et al*. (2005) showed that on Ikaria in the Aegean Sea vertical ductile thinning accommodated 20% of the exhumation of mid-crustal rocks whereas normal faulting was the major agent of exhumation.

Platt *et al*. (1998) assumed that homogeneous stretching of the entire lithosphere, expressed by vertical ductile thinning of 75%, is mainly responsible for exhuming high-grade rocks in the western Mediterranean. By making this assumption they successfully modelled a *P*–*T* path from rocks drilled at Ocean Drilling Program Site 976 in the Alboran Sea. The *P*–*T* path shows that decompression from *c*. 40 km to *c*. 13 km is associated with an increase in temperature from *c*. 550 °C to *c*. 675 °C (Soto & Platt 1999). Platt *et al*. (1998) considered several variables in their modelling exercise and concluded that the only combination that explains the observed characteristics of the *P*–*T* path includes high radiogenic heat production combined with extension by a factor of three in 6 Ma. They assumed that homogeneous stretching of the lithosphere accomplished large-scale horizontal extension; that is, that vertical ductile thinning at a rate of 4.5 km Ma^{−1} was the primary process that exhumed the high-grade rocks in the Alboran Sea. This proposition is in contrast to the argument of Ring *et al*. (1999*a*) that exhumation by ductile thinning is generally operating at significantly slower rates.

The purpose of this paper is to quantitatively evaluate the significance of vertical ductile thinning for the exhumation of deep-seated rocks through a finite-strain study in exhumed high-pressure rocks of the Cycladic blueschist unit in the Aegean Sea, Greece, and western Turkey. This has implications for the role that ductile thinning plays in the exhumation of metamorphic rocks and for modelling their exhumation.

## Vertical ductile thinning and exhumation of metamorphic rocks

In the simplest case, where ductile deformation is entirely exhuming rocks of deep-seated origin, vertical ductile thinning is given by the average vertical stretch, *S*_{vert}, because *S*_{vert} represents how much the vertical has changed in thickness (Feehan & Brandon 1999). For complete exhumation of deep-seated rocks *S*_{vert} must be zero. Therefore, ductile thinning by itself cannot fully exhume rocks and additional shallow exhumation processes, such as normal faulting or erosion, are required to bring the rocks back to the Earth's surface (Fig. 1) (Platt *et al*. 1998; Feehan & Brandon 1999; Ring & Brandon 1999).

If shallow exhumation processes are also active, the overburden thins at a faster rate than would occur if ductile thinning was the only exhumation process. In this case, the contribution of ductile thinning to the overall exhumation is more difficult to quantify and the rate of thinning of the remaining overburden at each step of the exhumation path has to be considered. The increment of vertical strain is then distributed over a thinner section of the overburden and so the increment of ductile thinning is smaller than in the case where ductile thinning is entirely exhuming the rocks. To quantitatively address this problem, Feehan & Brandon (1999) introduced a 1D numerical model, which tracks the vertical rate at which a rock moves through its overburden. This model considers both the vertical rate at which the rocks move through the orogenic overburden and the rate of thinning of the remaining overburden at each step along the exhumation path. As the rate of ductile thinning depends on depth, vertical ductile thinning is defined as the change of thickness of the overburden above a particle caused by ductile deformation within that overburden. The deformation rate along the exhumation path is represented by the velocity-gradient tensor, L(*z*), which changes with depth. Using a depth-proportional strain-rate law, L(*z*) increases linearly with depth (Feehan & Brandon 1999) (Fig. 1). For such a strain-rate law the amount of vertical ductile thinning would decrease exponentially towards the Earth's surface when L(*z*) was integrated along a vertical flow path within a steady-state orogen. The exponential decrease of ductile thinning results from the coeval decrease of the overburden by other exhumation processes.

A major implication of applying this 1D model to exhumed metamorphic rocks is that the vertical strain in the exhumed rocks is a significant overestimate of the contribution that ductile flow makes to the total exhumation (Feehan & Brandon 1999; Ring & Brandon 1999). If these results were taken into consideration, the finite vertical strain in the exhumed high-grade rocks in the Alboran Sea would need to be extremely great to account for 75% of vertical ductile thinning of their overburden.

The Alboran Sea and the Aegean Sea are Miocene to Recent extensional basins at opposite ends of the Mediterranean but the two settings have a number of similarities. Convergence between the African and European plates from the Late Cretaceous to the Tertiary produced the Rif–Betic Cordillera in the western and the Hellenide–Anatolide orogen in the eastern Mediterranean. In the course of continued convergence, the dense incoming lithosphere caused subduction-zone retreat, extension and the formation of Miocene to Recent intra- or back-arc basins in the overriding plate (Royden 1993; Lonergan & White 1997; Fadil *et al*. 2006).

## Regional setting

The Hellenide–Anatolide orogen in the eastern Mediterranean forms an arcuate orogen to the north of the present-day active margin (Fig. 2), which marks the site of northward subduction of the African plate beneath the Apulian and Anatolian plates. The Hellenides can be subdivided from top (north) to bottom (south) into: (1) the Internal zone; (2) the Vardar–I2zmir–Ankara zone; (3) the Lycian nappes; (4) the Cycladic zone; (5) the External Hellenides. In the Anatolides of western Turkey the Menderes nappes as part of Anatolia form the lowermost tectonic unit, instead of the External Hellenides (Godfriaux 1968; Dürr *et al*. 1978; Robertson *et al*. 1996; Shaked *et al*. 2000). The Internal zone consists of continental fragments of the Eurasian plate, underneath which oceanic crust of the Neotethys was subducted during Cretaceous convergence (Robertson *et al*. 1996). The related suture is the ophiolitic Vardar–I2zmir–Ankara zone, which in part was metamorphosed under blueschist-facies conditions in the Late Cretaceous (Sherlock *et al*. 1999). The underlying Lycian nappes are a thin-skinned thrust belt, which is assumed to root in the Vardar–I2zmir–Ankara zone (Collins & Robertson 1998) and was metamorphosed under incipient high-pressure conditions (Franz & Okrusch 1992) in the Late Cretaceous (Ring & Layer 2003). The Cycladic zone consists of continental fragments of the Adriatic plate and can be subdivided into three tectonic units; these are from top to bottom: (1) the non- to weakly metamorphosed ophiolitic Upper unit; (2) the high-pressure rocks of the Cycladic blueschist unit, which is subdivided into three separate members ((a) an ophiolitic mélange; (b) a Permo-Carboniferous to latest Cretaceous passive-margin sequence; (c) a Carboniferous basement nappe, which also occurs as slices in the passive-margin sequence); (3) the Basal unit as part of the External Hellenides, which consists of Mesozoic and Early Cenozoic platform carbonates found in several tectonic windows in the Cyclades (Avigad & Garfunkel 1989).

In western Turkey, the Menderes nappes underlie the Cycladic blueschist unit. In contrast to parts of the External Hellenides, the Menderes Nappes do not show Alpine high-pressure metamorphism (Ring *et al*. 2001*b*; Whitney & Bozkurt 2002; Régnier *et al*. 2003). Another difference is that the basement of the Menderes nappes is of Neoproterozoic to Cambrian age (Loos & Reischmann 1999; Gessner *et al*. 2001*a*, 2004). The absence of Alpine high-pressure metamorphism in the Menderes nappes and the lack of a well-defined subduction zone to the south of western Turkey suggest that subduction ceased after the collision of the exotic Anatolide microcontinent in the Eocene (Gessner *et al*. 2001*b*).

To address the role of ductile flow in the Cycladic blueschist unit its residence time in the ductile crust is an important parameter. The high-pressure event in the Cycladic blueschist unit (15–20 kbar and 450–550 °C) occurred at c. 55 Ma and was followed by one or more greenschist- to amphibolite-facies overprints (Altherr *et al*. 1982; Wijbrans *et al*. 1990; Will *et al*. 1998; Schmädicke & Will 2003; Tomaschek *et al*. 2003). In the Middle to Late Miocene, the Cyclades became part of the magmatic arc of the southward retreating Hellenic subduction zone, as indicated by arc-related volcanic rocks with ages ranging from 5 to 12 Ma (Fytikas *et al*. 1984; Weidmann *et al*. 1984) and granites spanning an age range from 10 to 15 Ma (Keay 1998). The granites are synkinematic to major extensional detachments. These Miocene detachments caused the final exhumation of the Cycladic blueschist units across the brittle–ductile transition. Numerous fission-track and (U–Th)/He ages constrain the arrival of the Cycladic blueschist unit in the brittle crust to *c*. 10 Ma (Altherr *et al*. 1982; Thomson *et al*. 1998*a*, 1999; Hejl *et al*. 2002; Ring *et al*. 2003; Kumerics *et al*. 2005; Brichau *et al*. 2006, 2007, 2008).

## Strain analysis

To describe finite strain in a rock six independent variables are required. Three variables describe the orientation of the principal stretching directions *X*, *Y* and *Z*, where *X* represents the maximum stretching direction, *Y* the intermediate stretching direction, and *Z* the maximum shortening direction. The remaining three variables describe the magnitude of the principal strain along these directions, which are represented by the absolute principal stretches *S*_{X}, *S*_{Y} and *S*_{Z} (*S*_{X} ≥ *S*_{Y} ≥ *S*_{Z}). The stretches are defined by *l*_{f}/*l*_{i}, where *l*_{i} and *l*_{f} are the initial and final lengths of a material line. For practical purposes usually the principal axial ratios *R*_{XY}, *R*_{XZ} and *R*_{YZ} are used to describe strain, where *R*_{XY}=*S*_{X}/*S*_{Y}, *R*_{XZ}=*S*_{X}/*S*_{Z} and *R*_{YZ}=*S*_{Y}/*S*_{Z}. The volume strain *S*_{V} is defined as *S*_{V}=*V*_{f}/*V*_{i}, where *V*_{f} is the final and *V*_{i} the initial volume of an elementary volume.

To investigate the possibility of deformation-related volume change, major oxide and trace element concentration were plotted on isocon diagrams (Grant 1986). These diagrams compare element concentrations in the altered rock (mylonite) with concentrations in the original rock (protolith). The basic argument is that some components are likely to have been immobile in the alteration process and, for example, should be relatively enriched (or depleted) in mylonite that underwent volume loss (or gain) (O'Hara & Blackburn 1989). If these elements can be identified, volume change can be calculated assuming that the volume change is a factor common to the behaviour of all components. During regional deformation, Al, Ti and Zr are usually immobile.

We collected 75 samples from the Cycladic blueschist unit and the directly underlying Basal unit on several Aegean islands and in southwestern Turkey (Fig. 3). Finite strain data are available online at http://www.geolsoc.org.uk/SUP18309. Some of the samples are ultramylonites whereas others are moderately deformed metamorphic rocks. It was our major goal to obtain a reliable average of the strain that accumulated in the high-pressure rocks during their exhumation, and therefore sampling was carried out as randomly as possible. However, suitable rock types for strain analysis imposed limits on the random sampling philosophy.

To quantify finite strain, the Rf/phi technique (Ramsay 1967; Dunnet 1969; Ramsay & Huber 1983) was applied. The Rf/phi technique calculates the strain ellipse by comparing the initial form and orientation of an elliptical object with its final form and orientation. Most of the analysed samples are metamorphosed conglomerates (Fig. 4). The conglomerates are made up by marble pebbles in a marble matrix, marble and schist pebbles in a schist matrix, or quartzite pebbles in a quartzitic matrix. There is no foliation refraction between the pebbles and the matrix, suggesting homogeneous deformation between the objects and their matrix (Ramsay & Lisle 2000). On Paros and Naxos we also measured feldspar grains from augen gneiss that was deformed at temperatures well above 500 °C ensuring largely homogeneous deformation of the feldspar augen and matrix.

To prove that strain analysis by the Rf/phi method yields meaningful results, we also analysed 15 samples by the Fry method to check the Rf/phi estimates. The Fry method (Fry 1979) provides a graphic solution to the centre-to-centre method. The basic principle of the latter is that the distances between the centres of objects are systematically related to the orientation of the finite-strain ellipsoid. The Fry strains are thought to correspond to bulk-rock strains because both the grain and matrix strains contribute to the change of centre-to-centre distances. The Rf/phi strains, on the other hand, describe the fabric ellipsoid or clast strain (Hossack 1968; Ramsay & Huber 1983; Kassem & Ring 2004). Fry analysis was especially applied to the deformed augen gneiss to see whether or not the feldspar augen deformed homogeneously with their matrix. The Fry strains are not fundamentally different from the Rf/phi strains (see the Supplementary Publication). In most cases, the Rf/phi strains are slightly greater than the Fry strains, but in other cases the opposite is the case (Fig. 5). Therefore, we conclude that there was no significant competence contrast between the matrix and the feldspar porphyroclasts and pebbles during the accumulation of finite strain. Hence, Rf/phi strains are thought to be representative for regional strain.

Two-dimensional strain measurements were made on *XY*, *XZ* and *YZ* sections to estimate the 3D strain geometry. A least-squares best-fit ellipse was calculated for each marker outline as well as its relative position and orientation. For Rf/phi analysis, the long and short axes of up to 55 pebbles or grains per section were measured. Tectonic strains were determined from the χ^{2} minima of the Rf/phi analyses (Peach & Lisle 1979). For Fry analysis, the central points of more than 100 pebbles and/or feldspar grains per section were used to calculate strain. The strain estimates were used to calculate the finite-strain ellipsoid according to the modified least-squares technique of Owens (1984). Assuming no volume change, the principal stretches *S*_{X}, *S*_{Y} and *S*_{Z} were calculated from the axial ratios by $$mathtex$$\[S_{Y}=\sqrt{3\ \frac{R_{XZ}}{\ R{_{\ XY}^{2}}}}\]$$mathtex$$ $$mathtex$$\[S_{X}=R_{XY}{\times}S_{Y}\]$$mathtex$$ $$mathtex$$\[S_{Z}=\frac{1}{\ S_{X}{\times}S_{Y}}.\]$$mathtex$$ The principal axes of samples Tü1–Tü7 from southwestern Turkey were restored around a vertical axis. A detailed field study by Régnier *et al*. (2003) showed that the Cycladic blueschist unit was passively rotated by *c*. 90° after ductile strain accumulated. To undo this late rigid-body rotation, the samples from the Cycladic blueschist unit in western Turkey were rotated until the *X*, *Y* and *Z* axes acquired their original positions with the stretching lineation showing the regional NNE–SSW trend.

## Volume strain

In the isocon diagrams in Figure 6, the chemical compositions of the matrices of highly deformed marble and quartzite conglomerate as well as orthogneiss samples have been plotted against the concentration of the least-deformed samples of the same rock type. We realize that least-deformed samples do not represent a real protolith of the deformed samples. However, our aim is to investigate in a semi-quantitative fashion whether pronounced deformation in the highly deformed samples was accompanied by significant volume change. We argue that the isocon diagrams in Figure 6 illustrate the depletion or augmentation of the analysed elements during progressive deformation.

It is evident that no single isocon can be fitted to the data points in most diagrams, which suggests differential element behaviour. None the less, Al_{2}O_{3}, Zr and Ti plot on reasonably defined isocons in the diagrams. There is no systematic increase in the amount of volume loss or gain with increasing deformation intensity. The data suggest overall constant-volume or isochoric deformation.

## Finite-strain data

The finite-strain data are summarized in the Supplementary Publication, the finite-strain axes are plotted in stereograms (Fig. 7), the *X* axes on a map (Fig. 3) and in a Flinn diagram (Flinn 1962) (Fig. 5), and data from four areas are also shown as a function of distance below the major extensional detachment in that area (Fig. 8).

All three principal stretches depict some variation in magnitude and orientation. The maximum stretch, *S*_{X}, ranges from 1.24 to 5.03. The minimum stretch, *S*_{Z}, ranges from 0.10 to 0.81, indicating a huge variation in vertical shortening from 90% to 19%. *S*_{Y} ranges from 0.63 to 2.53. The maximum axial ratio of the strain ellipse in sections parallel to the tectonic transport direction and perpendicular to the foliation, *R*_{XZ}, ranges from 1.70 to 40.81, again illustrating extreme strain heterogeneity.

The pronounced variations in strain magnitude are also evident in the Flinn diagram (Fig. 5) and in the strain–distance diagrams (Fig. 8). Most strain ellipsoids have flattening strain type (47 samples), but constrictional strains are also common (27 samples); one sample plots directly on the plane-strain line. The most extremely deformed samples usually have strong flattening strain with extension in the *Y* direction of more than 100% (samples Tü17, Sa20, Sa21, Pa41, Pa42).

The strain–distance diagrams illustrate the spatial variation of *R*_{XZ} in vertical sections as a function of distance below the major extensional detachment in a specific study area. The graphs again display the very heterogeneous nature of strain and also show that there is no systematic strain gradient with distance from detachment or with position in tectonic pile depth.

The orientational data show that the shortening axes have a very strong vertical maximum (Fig. 7a). The *X* and *Y* axes both have a subhorizontal trend and show some scatter in direction. The contoured maxima agree well with the axes of the tensor average. The north–south maximum for the *X* axes is statistically significant and in agreement with measured stretching lineations in the field (Avigad & Garfunkel 1989; Buick 1991; Avigad 1993; Vandenberg & Lister 1996).

The variability in strain magnitude and orientation can be attributed to local variations in the deformation field and possibly also random errors in our measurements. To address questions of regional importance it is therefore useful to obtain an average of the various strain determinations referred to a geographical coordinate system. The calculated average would correspond to the single strain tensor that most closely represents the deformation of a material surface that bounds the sampled region (see Cobbold & Percevault 1983). The entire strain tensor must be averaged to ensure that the orthogonality of the axes is preserved and that the magnitudes and directions of the principal stretches are correctly associated. In this study, the tensor averaging method of Brandon (1995) is used. The average internal rotation was determined by first converting all internal rotations to vectors with magnitudes corresponding to the magnitude of the rotation angle and then finding the vector mean for this vector distribution. The direction of each vector is consistent with the sense of rotation and the convention of the right-hand rule. The method will produce accurate estimates of the average deformation as long as the magnitude of the rotation is relatively small (less than *c*. 10°) and the deformation in all samples occurred simultaneously. The average extension parallel to the north–south-trending *X* direction of the tensor average is 52% (*S*_{X}=1.52). The average *Y* axis shows an extension of 28% (*S*_{Y}=1.28), reflecting that the most highly deformed samples have flattening strain type. The *Z* axis of the tensor average shows a shortening of 49% (*S*_{Z}=0.51). The directions of the average strain axes correspond well to the contoured maxima for those axes and also to field measurements of foliations and stretching lineations.

## Vertical ductile thinning

### Cycladic blueschist unit

On average our strain data indicate ductile shortening of 49% perpendicular to the pervasive subhorizontal foliation. To address the question of how much total thinning occurred above the Cycladic blueschist unit, we have to consider the total amount of vertical thinning of the entire crustal section above the Cycladic blueschist unit. The problem is that we have no finite-strain data from the units that used to overlie the Cycladic blueschist unit. To circumvent this shortcoming we have to assume a steady-state Hellenide–Anatolide orogen in the Tertiary. The steady-state assumption demands that all rocks in the overburden underwent the same deformation as the examined rocks from the Cycladic blueschist unit. We further assume that the rate of ductile deformation scales linearly with depth (Fig. 1). By making the steady-state assumption and by defining a strain-rate law we can use the average of our 75 finite-strain measurements as being representative for orogenic strain of the Hellenide–Anatolide orogen in the Tertiary.

To model vertical ductile thinning, we need to know the directions and magnitudes of the principal stretches, the depth from which the rocks were exhumed, the residence time of the exhuming rocks in the ductile crust and the azimuth of the transport direction during the accumulation of ductile strain. We use the principal stretches of the tensor average of *S*_{X} :*S*_{Y} :*S*_{Z}=1.52 :1.28 :0.51 and the average *X* direction to represent the tectonic transport direction (see the Supplementary Publication). *P*–*T* data and timing information summarized above show that the exhumation depth is *c*. 60 km and that rocks resided in the ductile crust for *c*. 45 Ma.

The amount of internal rotation is also critical. Horizontal simple shear (kinematic vorticity number (Wk)=1) would not cause any vertical ductile thinning and a pure shear deformation (Wk=0) with a vertical shortening axis would produce the largest possible amount of vertical ductile thinning. We do not have any quantitative data constraining the rotational component of deformation. The observation that the most extremely deformed samples usually have strongly flattening strain type indicates pronounced deviations from simple shear deformation. Vandenberg & Lister (1996), Ring *et al*. (1999*b*) and Rosenbaum *et al*. (2002) suggested largely coaxial deformation during the early high-pressure stage. During Miocene extension, deformation was largely localized along the detachments. Kumerics *et al*. (2005) quantified the degree of rotation in the footwall of the Messaria detachment on Ikaria and concluded that deformation was moderately noncoaxial with Wk ranging from 0.13 to 0.80. Strain data from the high-temperature ductile extensional shear zone on Naxos (U. Ring, unpubl. data) also show pronounced deviations from simple shear and suggest that strongly noncoaxial deformation was localized in thin zones whereas intervening areas underwent coaxial flattening. Based on this brief summary we believe that the overall Eocene to Miocene deformation deviated considerably from simple shear and involved a large degree of pure shear. For our calculations we therefore use kinematic vorticity numbers of 0.75, 0.50, 0.25 and zero. It should be noted that pure and simple shear components have a non-linear relationship and make equal contributions to the overall deformation at Wk=0.71 (Law *et al*. 2004).

The results of our calculations are listed in Table 1 and shown in Figure 9. For pure shear deformation the percentage of total exhumation caused by ductile flow is 21%, or 12.6 km. The asymptotic convergence of *S*_{Z} to its final value of 0.49 illustrates that ductile deformation is most effective at the base of the orogenic wedge and becomes less effective while rocks move towards higher crustal levels. This is a direct consequence of using a proportional strain-rate law. Increasing Wk does not change the contribution of vertical ductile thinning to exhumation in any significant way (Table 1). We can also derive strain rates from the model calculations. The maximum vertical strain rate we calculated is 1.2 × 10^{−15} s^{−1} and maximum horizontal strain rate is 4.4 × 10^{−16} s^{−1}.

Our calculations illustrate that the contribution of ductile thinning to exhumation depends on interactions with other exhumation processes, and also depends on how ductile deformation is distributed with depth. Ductile thinning makes the smallest contribution when that deformation is depth dependent. The reason is that as a material point rises toward the surface of the wedge, it moves out of the more rapidly deforming part of the orogen. Thus, the thinning rate for the remaining overburden is less than that for a case in which deformation is not depth dependent. However, we regard such a case to be unrealistic. This line of reasoning suggests that a dislocation-controlled rheology, which should be strongly nonlinear with depth, would further reduce the contribution of ductile thinning to exhumation.

A major implication of applying the 1D model of Feehan & Brandon (1999) to exhumed metamorphic rocks is that the vertical strain in the exhumed rocks itself will always significantly overestimate the contribution that ductile flow makes to the total exhumation. As mentioned above, this also means that the finite vertical strain in the exhumed high-grade rocks in the Alboran Sea must be very great to account for 75% of vertical ductile thinning of its overburden. We explore this aspect in the next section.

### Backcalculation of finite-strain data for high-grade rocks of the Alboran basin

In their model exercise of the exhumation of the high-grade rocks in the Alboran Sea, Platt *et al*. (1998) assumed that a vertical stretch of 0.25 exhumed the rocks in 6 Ma with a rate of vertical thinning of 4.5 km Ma^{−1}. Using the numerical model of Feehan & Brandon (1999), we can backcalculate *S*_{vert} for the high-grade rocks from the Alboran Sea. Assuming plane strain constant-volume deformation and a strain-rate law that increases proportionally with depth, we estimate that the high-grade rocks must have *S*_{vert}=0.03 to account for the envisaged exhumation by vertical thinning of their overburden. Given the constant-volume plane-strain assumption, the maximum stretch, *S*_{X}, must be at least 30; that is, the aspect ratios in the *XZ* section of the high-grade rocks from the Alboran Sea on average have to be of the order of 1000. We regard such values as unrealistic. Even if our plane-strain isochoric deformation assumption was incorrect, huge strains would still be needed.

## Discussion

### Exhumation of the Cycladic blueschist unit

The overall conclusion from the results of our model calculations is that vertical ductile thinning was not a major factor in the exhumation of the Cycladic blueschists and did not cause more than *c*. 12 km of exhumation. In other words, most of the *c*. 60 km of blueschist exhumation must have been accommodated by other processes such as normal faulting or erosion. We have no control on erosion. Topography above a retreating subduction zone is generally considered to be subdued (Royden 1993) and therefore erosion rates were probably small, as shown by Thomson *et al*. (1998*b*) for Miocene times on the island of Crete. Assumed erosion rates of 0.2–0.4 km Ma^{−1} yield a total erosion of 9–18 km. It follows that *c*. 30–40 km of the exhumation must have been caused by normal faulting.

Numerous workers have shown that detachment faulting during large-scale Miocene extension of the Aegean was also not important for the exhumation of the Cycladic blueschist unit (Avigad *et al*. 1997). The amount of detachment-related exhumation was *c*. 12 km for the Messaria detachment on Ikaria (Kumerics *et al*. 2005), <6 km for the Livadi detachment on Tinos (Brichau *et al*. 2007), 6–9 km for Vari detachment on Syros and Tinos (Ring *et al*. 2003), and *c*. 12 km for the Mykonos detachment (Brichau *et al*. 2008). However, for the Miocene extensional system on Naxos and Paros the amount of exhumation was distinctly greater. Brichau *et al*. (2006) showed that the cumulative displacement on the Naxos–Paros extensional system was >50 km and caused *c*. 25 km of exhumation.

Ring *et al*. (2007*a*, *b*) stressed the importance of extrusion wedges, defined by the simultaneous movement on a basal thrust and a normal fault at the top, for the early exhumation of the Cycladic blueschist unit in the Eocene and Oligocene. For Evia in the western Aegean and Samos and adjacent Turkey in the eastern Aegean, Ring *et al*. (2007*a*, *b*) showed that displacement on the normal fault at the top of the extrusion wedges can account for up to 30–40 km of exhumation. The basal thrust indicates that extrusion wedges form during overall shortening and the normal fault at the top of the extrusion wedge is a geometric effect only.

Overall, the available data suggest that normal faulting, especially normal faulting above extrusion wedges, appears to be the dominant factor in exhuming the Cycladic blueschist unit. Vertical ductile thinning can account for only *c*. 20% of exhumation and is thus a minor exhumation process in the Aegean.

### Ductile flow and the exhumation of deep-seated rocks

Our calculations show that the contribution of ductile thinning to exhumation is considerably less than the value indicated by the estimated finite vertical shortening, *S*_{vert}, in the studied high-pressure rocks. It follows that significant vertical shortening and a very high value for *S*_{vert} will be needed if vertical ductile thinning is envisaged to make a significant contribution to the exhumation of high-grade rocks. In the Cycladic blueschist unit, seven of the analysed samples are ultramylonites with vertical shortening of *c*. 80–90%. Nevertheless, other samples from the Cycladic blueschist unit are almost undeformed. Strongly heterogeneous deformation seems to be the rule for exhumed metamorphic terranes and therefore it is essential not to focus on mylonitically deformed rocks only, and to calculate an average of the data. The tensor average for the Cycladic blueschist unit indicates that *S*_{vert} accounts for *c*. 50% shortening in the exhumed high-pressure rocks. However, the shallow orogenic overburden of the Cycladic blueschist unit was thinned by ductile flow less than the blueschists itself and therefore the strain recorded in the Cycladic blueschist unit strongly overestimates the total vertical ductile thinning of the entire orogenic overburden. We have estimated that for the case considered by Platt *et al*. (1998) average aspect ratios in *XZ* sections of almost 1000 are needed to fulfil the assumptions made for numerical modelling. These values are considered unrealistic for regional deformation in deep-seated rocks. Therefore, we suggest that in general vertical ductile thinning is not an important process in common orogenic settings.

### Ductile flow and orogenic deformation

Although we have suggested that ductile flow is not important for exhuming rocks of deep-seated origin, we do not imply that ductile flow does not play a significant role in orogenic deformation. Norris (2004) showed that ductile deformation in the Alpine Fault accommodates *c*. 60–70% of the entire plate convergence between the Australian and Pacific plates in the South Island of New Zealand. Shear strain estimates in the mylonites reach 200–300 in the most highly strained rocks, and provide an integrated displacement across the zone of 60–120 km, which is consistent with the amount of displacement during the last 5 Ma and suggests that displacement on the Alpine Fault is localized within a 1–2 km wide ductile shear zone to depths of *c*. 30 km.

Kassem & Ring (2004) and Ring & Kassem (2007) stressed the importance of ductile flow by showing that vertical ductile thinning associated with a subhorizontal foliation can quantitatively explain the occurrence of higher-grade metamorphic rocks above lower-grade ones in the Western Alps. Their work showed that ductile flow is capable of accounting for *c*. 12 km of the exhumation of deep-seated nappes during overall crustal shortening. Heterogeneous vertical ductile thinning produced a subhorizontal foliation typical of the internides of many orogens. The findings of Kassem & Ring (2004) and Ring & Kassem (2007) are interesting regarding the role of vertical ductile thinning in the exhumation of deep-seated rocks. They showed that if deformation occurs by subhorizontal general shear it does not make much difference whether this shear is a result of nappe stacking or horizontal extension. The amount of vertical thinning and thus exhumation is not significantly different whether displacement on a 10–30°-dipping general shear zone was up- or down-dip.

## Conclusions

Our finite-strain data along with the modelling calculations show that vertical ductile thinning contributes only a small portion of the total exhumation of the high-pressure metamorphosed rocks of the Cycladic blueschist unit in the Aegean. This is despite the fact that some of the rocks we analysed show subvertical shortening of up to 90%. Finite strain is very heterogeneously distributed within the Cycladic blueschist unit and the average vertical shortening as calculated from 75 samples is *c*. 50%. A major implication of this study is that the vertical strain in deeply exhumed rocks is a significant overestimate of the contribution that ductile flow makes to the total exhumation because it depends on how ductile deformation is distributed with depth. The use of a proportional strain-rate law forecasts that rocks rising towards the surface move quickly out of the more rapidly deforming part of the orogen. This effect would be much more pronounced if a power-law dislocation-controlled rheology was considered. As a consequence, very large vertical strains >90% would be needed for vertical ductile thinning to be a major exhumation process. For the Cycladic blueschist unit we conclude that normal faulting was the primary process that exhumed the Cycladic blueschist unit.

## Acknowledgements

This study was funded through various grants from the Deutsche Forschungsgemeinschaft (Ri 538/16, /18 and /23) and the Brian Mason scientific and technical trust (project E5345) of New Zealand. We thank R. Lisle for a thorough and constructive review. A plethora of anonymous *Tectonics* referees also commented on the paper.

- © 2008 The Geological Society of London