We have modeled linear viscoelastic relaxation of a uniform-viscosity asthenosphere following large earthquakes in the Aegean-Anatolian region during the 20th century to evaluate whether this process contributes significantly to the regional velocity field. We address in particular whether southward motion of the Aegean Sea region relative to central Anatolia (and thus extension of western Turkey) can be attributed to a postseismic strain pulse. Our models show that postseismic relaxation of a thick (250 km) viscoelastic substrate cannot generate the observed extension in western Turkey, regardless of the choice of viscosity. We also find that the asthenosphere viscosity must exceed about 5 × 1020 Pa s, at least north of the North Anatolian Fault Zone (NAFZ), to be consistent with low GPS site velocities in the Black Sea region and highly localized strain around the fault.
 The eastern Mediterranean velocity field [McClusky et al., 2000; Straub et al., 1997] shows that significant north-south extension is occurring in western Turkey as the Aegean Sea region moves en masse southward relative to the Anatolian plate. Southward motion of the Aegean block cannot be explained simply by horizontal edge loading from adjacent plates. Several modeling studies attribute this motion to mantle tractions resulting from subduction of the African plate at the Hellenic Arc [e.g., Meijer and Wortel, 1997; Cianetti et al., 1997], possibly combined with gravitational collapse of western Turkey [Lundgren et al., 1998].
 Since the eastern Mediterranean region regularly experiences earthquakes large enough to trigger widespread viscoelastic relaxation of the crust and mantle [e.g., Nalbant et al., 1998; Barka, 1996; Stein et al., 1997], it makes sense to ask whether some features of the velocity field, including extension in western Turkey, could be the result of postseismic deformation. Postseismic relaxation of a viscoelastic substrate can cause a diffusive strain pulse to travel through the crust [Rice, 1980], leaving extension in its wake as it passes through a region. This has been suggested as a possible cause of extension in western Turkey [Mantovani et al., 2001]. If postseismic mantle relaxation were responsible for this extension, it might also cause errors in geodetic estimates of slip rate along the North Anatolian Fault Zone (NAFZ).
 We have modeled viscoelastic deformation triggered by large, 20th century earthquakes in the Anatolia-Aegean region to evaluate whether these events are still contributing significantly to regional surface deformation. We also calculate velocities relative to Eurasia at GPS sites near the NAFZ, and compare them to the measured (GPS) velocities to bracket admissible asthenosphere viscosities.
 We use the code VISCO1D [Pollitz, 1997] to model contributions to GPS site velocities from viscoelastic relaxation following 20th-century earthquakes. GPS site velocities relative to Eurasia prior to the 20th century (i.e. from all of the preceding earthquake cycles) are estimated using the analytical method of Savage . The sum of these velocities is the current site velocity relative to Eurasia.
 For the VISCO1D modeling, the crust and mantle are assumed to be Poisson solids with G = 35 and 70 GPa, respectively. Below the crust, a single layer spanning the lower crust (25–30 km) and uppermost mantle (30–275 km) is modeled as a Maxwell material with characteristic times of about 1 to 104 years (i.e., viscosity values of 1018 to 1022 Pa s). The mantle below this layer is modeled as an elastic solid.
Table 1 shows the 20th century, Mw > 7.0 earthquakes that are included in our model, as well as how these events are represented. We calculate the mean slip per event from the seismic moment, assuming that seismic slip extends to 15 km depth, though we model this slip down to 25 km. This provides a generous allowance for afterslip deeper in the crust than the coseismic rupture, like most of the aseismic slip following the 1999 Izmit earthquake [Reilinger et al., 2000].
Table 1. Earthquake Data
Mean Slip (m)
Information for the 1939 and 1940's earthquakes is from Stein et al. ; information for all other earthquakes is from Nalbant et al. . Slip was estimated from rupture dimensions assuming G = 35 GPa, the crustal shear modulus in our VISCO1D models. All events were right-lateral strike slip except the 1970 Gediz earthquake, which was a normal faulting event. Rupture widths were assume to be 15 km (30 km for the Gediz event) when converting moments to mean slip. The Mw = 6.9, 7.7, and 7.5 earthquakes of December 1942, November 1943, and February 1944 have been summed and modeled together because they occurred less than a year apart on contiguous segments of the NAFZ.
 The Savage  2D analytical solution yields surface velocities due to an infinite number of repeated earthquakes on a strike-slip fault in an elastic plate overlying a viscoelastic halfspace. For this solution, elastic parameters are assumed to be uniform throughout the modeled volume (we use G = 70 GPa). The thickness of the elastic layer and the substrate viscosity are the same as for the VISCO1D models. We assume a recurrence interval of 300 years and a long-term slip rate (Vo) of 14 or 24 mm/yr [Schindler, 1997; McClusky et al., 2000].
 To make sure that the Savage  solution (with its assumptions of 2D geometry and uniform elasticity) is appropriate for calculating the pre-20th century velocities at the GPS sites we have chosen (YOZG, KKIR, ANKR, HALI, SINO, and SAMS, Figure 1), we have adapted it to calculate postseismic velocities from a single earthquake, rather than an infinite sequence of earthquakes. This allowed us to estimate velocity perturbations caused by 20th century earthquakes and compare them with the VISCO1D results. Velocity perturbations calculated at all six GPS sites with both methods agree to within about 1 mm/yr, indicating that we may use the Savage  solution to estimate pre-20th century velocities at these locations.
3. Results and Discussion
Figure 1 compares modeled postseismic velocities due to large 20th century earthquakes, assuming an asthenosphere viscosity of 1019 Pa s, with GPS site velocities relative to Eurasia [McClusky et al., 2000]. This model predicts maximum westward velocities of about 5 mm/yr in central Turkey. In western Turkey, our modeled postseismic velocities are southwestward, and minor shortening is predicted. (Our models also predict little or no shortening across the Caucasus region.) North of the NAFZ, the maximum velocity change is lower than to the south (∼3–4 mm/yr), mainly because the arcuate distribution of the earthquake ruptures concentrates strain south of the NAFZ. However, GPS data from sites north of the NAFZ (HALI, SINO, and SAMS, Figure 1) show that the crust in this region is essentially stationary relative to Eurasia.
 The model velocities in Figure 1 include only the “postseismic” contributions from 20th century earthquakes. The observed velocities include the “secular” contributions from all pre-20th century earthquakes as well. We approximate the effects of the pre-20th century earthquakes using the Savage  viscoelastic solution, which assumes infinitely long faults. In calculating the postseismic effects of the more recent (20th century) earthquakes, we use the VISCO1D model in order to more accurately represent the rupture geometries for these events. North of the NAFZ, the two contributions are of opposite sign and tend to cancel. South of the NAFZ, where the 20th century postseismic and pre-20th century velocities are in the same direction, they may sum in a manner that leads to a block-like velocity profile, with highly localized strain across the fault. To evaluate the significance of viscoelastic contributions to the velocity field, we calculate velocities at SINO, SAMS, and HALI north of the NAFZ, and ANKR, KKIR, and YOZG south of the NAFZ. relative to Eurasia, and compare these velocities with GPS data.
Figures 2a and 2b show modeled postseismic velocity contributions at these sites from 20th-century NAFZ earthquakes, plotted against asthenosphere viscosity. Figures 2c and 2d show estimated site velocities just prior to the 20th-century earthquake sequence, again as a function of asthenosphere viscosity. The sum of these velocities (i.e. a plus c and b plus d) is our estimate of the current site velocity relative to Eurasia. Residuals (GPS velocities from McClusky et al.  minus modeled velocities) are plotted against viscosity on Figures 2e and 2f. For models consistent with the GPS data, these residuals should be close to zero.
Figure 2e illustrates that the low velocities of stations SINO, SAMS, and HALI relative to Eurasia require an asthenosphere viscosity of greater than 5 × 1020 Pa s, at least north of the NAFZ. This is consistent with the observation that the Black Sea region behaves as a “backstop” deflecting motion of the Anatolian plate [McClusky et al., 2000]. Though lower viscosities appear to be permissible to the south (Figure 2f), we note that GPS sites ANKR and YOZG are located between the plate boundary and the Anatolia-Eurasia Euler pole, which is just 900 km south of these sites [McClusky et al., 2000]. ANKR and YOZG move 2 to 3 mm/yr more slowly than they would if the Anatolian plate were not rotating relative to Eurasia. The effect of this rotation is to shift the curves on Figure 2f up by 2–3 mm/yr (to the positions shown), making them appear consistent with moderate asthenosphere viscosities. We cannot conclude that the asthenosphere south of the NAFZ is less viscous than to the north, though this would make sense given the low heat flow [Schindler, 1997, and references therein] and the presence of some oceanic lithosphere in the Black Sea region. (We also note that slip on the right-lateral Alaca fault south of KKIR may cause this site's westward velocity to be lower than expected relative to Eurasia. This may have shifted the KKIR velocity curve up on Figure 2f).
 In calculating the site velocities on Figures 2c and 2d , we have assumed a long-term NAFZ slip rate (Vo) of 24 mm/yr. However, the value of Vo is somewhat uncertain. Geologic estimates of the post-Pliocene NAFZ slip rate range from 14 to 22 mm/yr [Westaway, 1994; Armijo et al., 1999; Straub et al., 1997; Schindler, 1997], while geodetic estimates of the current slip rate are 22–24 mm/yr [McClusky et al., 2000; Straub et al., 1997; Wright et al., 2001]. Our modeling suggests that to reconcile Vo with highly localized strain around the NAFZ and the 21 mm/yr velocity of central Anatolia relative to sites along the south shore of the Black Sea, Vo must be of the order of 24 mm/yr. Because of the high asthenosphere viscosity and the short recurrence interval, surface velocities around the NAFZ in central Turkey do not vary much between earthquakes (once early afterslip is complete). The NAFZ slip rate estimated from GPS data should thus be comparable to the geologic rate.
 Extension across western Turkey, quantified as the velocity of the Aegean Sea block relative to central Anatolia, is about 8 mm/yr [McClusky et al., 2000]. We estimate this extension by subtracting the mean of velocities at ANKR and YOZG from the mean of velocities at CEIL and HIOS (Figure 1). These sites are about the same distance from the Anatolia-Eurasia Euler pole, so any lengthening between them must be due to deformation. Our models show that postseismic relaxation from 20th-century NAFZ earthquakes may produce minor SW-NE oriented extension or shortening (<1.5 mm/yr) across this region, depending on asthenosphere viscosity. Postseismic relaxation following 20th-century earthquakes cannot be responsible for extension in western Turkey.
 Our conclusions are sensitive to the geological slip estimates for 20th century earthquakes (Table 1). Given the recurrence interval of 300 years and mean slip values from Table 1, the long-term NAFZ slip rate should be less than 10 mm/yr. This is far less than both geodetic and geologic estimates (14–24 mm/yr). Either the 20th-century earthquakes were unusually small or the geological slip estimates for these events are low. We have implicitly assumed the former. If we model more slip for 20th-century earthquakes, somewhat lower minimum mantle viscosities may be admissible.
 Our conclusions differ from those of Mantovani et al. , who suggest that a postseismic stress pulse is responsible for current extension in western Turkey. In their 1D viscoelastic model, Mantovani et al.  represent 3 m of slip normal to a north-south oriented surface bounding the Anatolian plate to the east, and extending to a depth of 100 km. On the other hand, we model right-lateral strike-slip earthquakes along the NAFZ, which borders the Anatolian plate to the north, and we allow slip down to a depth of 25 km. Much of the difference in our results arises from our assuming completely different geometries. Our smaller postseismic velocities (and strains) result from modeling the problem in three dimensions, with finite dislocations.
 Postseismic viscoelastic relaxation of uniform-viscosity asthenosphere following large 20th-century earthquakes along the NAFZ cannot explain the current, high rate of north-south extension across western Turkey, regardless of the mantle viscosity. To explain the low velocities relative to Eurasia of GPS sites along the south shore of the Black Sea, the asthenosphere viscosity must exceed about 5 × 1020 Pa s north of the NAFZ. Viscosities below the Anatolian plate may be comparable or somewhat lower. Once early afterslip is complete, interseismic changes in the velocity field around the NAFZ are minor. This means that geodetic and geologic estimates of the current NAFZ slip rate in central Turkey should be comparable.
 This research was funded by NSF grants INT 00001143 and EAR 9909730. We thank Kurt Feigl and Bob King for their comments on early drafts of this manuscript. We also thank Fred Pollitz and an anonymous reviewer for their insightful comments.