We use GPS measurements in the first geodetic study of plate coupling on the Andreanof segment, Aleutian subduction zone. Convergence of 7.3 cm/yr at the subduction zone results in northwestward displacements greater than 1 cm/yr at stations located on the west end of the Andreanof region, but velocities at the east end are smaller in magnitude and oriented west-southwest. These velocity variations are caused by differences in plate coupling along the subduction zone, which correlate with the rupture zones of the 1986 and 1996 Mw8 earthquakes. We construct a dislocation model to estimate the velocity of the arc in the Andreanof region relative to North America, and fault plane coupling coefficients. Our best model shows a southwestward velocity of 7.8 mm/yr, a high degree of coupling in the main thrust zone at the west end of the subduction zone, and little to no coupling at the east end.
 We use surface velocity estimates from repeated GPS observations to study subduction zone deformation in the Andreanof Islands, Aleutian arc (Figure 1). Previous studies of velocities of GPS sites on Unimak and Sanak Islands and the Alaska Peninsula, ∼1000 km to the northeast, show velocities of ∼4 mm/yr to the southwest [Freymueller and Beavan, 1999; Mann and Freymueller, 2003]. They found little indication of strain associated with subduction, so they interpreted the velocities as a southwestward translation of those regions relative to stable North America. Ekstrom and Engdahl  determined an arc-parallel translation velocity of the of Andreanof region of 30 ± 10 mm/yr relative to North America based on slip vector azimuths for thrust earthquakes from the Aleutian arc. Displacements recorded on the Andreanof Islands can be broken into two parts, a part that is caused by coupling in the subduction zone and a part due to the steady translation of the arc relative to North America. We invert the Andreanof Islands velocities to calculate the coupling on the subduction zone interface using dislocation modeling techniques while also solving for the translation velocity of the Andreanof region relative to North America.
 This tectonically and seismically active region of the Aleutian arc has ruptured in three major earthquakes over the last 50 years. The 1957 (Mw 8.6) earthquake ruptured the Andreanof segment of the Aleutian arc and propagated east 600 km to the Unalaska region [Taber et al., 1991]. The 1986 Andreanof Islands earthquake (Mw 8.0) and the 1996 event (Mw 7.9) again ruptured the western one-third of the 1957 rupture area. The 1996 rupture area included the region west of the Andreanof Islands and overlapped the western one-third of the 1986 rupture area [Tanioka and Gonzalez, 1998] (Figure 1).
 The 1986 earthquake was extensively studied. Engdahl and Gubbins  combined data from local and teleseismic stations to simultaneously solve for earthquake locations and a subduction zone velocity structure in the central Aleutian Islands. Further studies by Engdahl et al.  and Ekstrom and Engdahl  established that the main thrust zone that ruptured could be represented by two planes. The first plane ranges from 57 to 92 km from the trench and extends from 15 to 28 km in depth; the second plane continues from a distance of 92 km to 128 km from the trench and has a depth of 28 to 47 km. Ekstrom and Engdahl  inferred there was little or no coupling between the subducting slab and the overriding crust in the forearc wedge, based on the lack of seismicity there.
2. GPS Data
 We measured GPS velocities of sites on four islands: Kanaga, Adak, Great Sitkin, and Atka. Kanaga and Great Sitkin are volcano-monitoring networks; our observations revealed that sites on Great Sitkin and one site on Kanaga could not be used in this study because a small volcanic signal was present in the data. Most sites were surveyed two to four times over a 6 to 7 year time span (auxiliary material Table S1).
 We used the GIPSY/OASIS II software version GOA4 to obtain daily coordinate and covariance estimates of our stations and regionally distributed stations in the ITRF2000 reference frame [e.g., Freymueller et al., 2000]. We estimated site velocities in ITRF2000, and then converted to velocities relative to the North America plate using the REVEL2000 model of Sella et al. . The velocities and uncertainties relative to stable North America are given in Table 1.
Table 1. Site Velocities Relative to Stable North Americaa
 Strain accumulation at a subduction boundary is modeled using elastic dislocation theory following the methods of Okada . The earth is represented by a uniform elastic half-space and the plate interface by one or more planar faults, and the strain accumulation rate is assumed to be constant through the interseismic period. The interseismic deformation rate is computed from the superposition of steady state subduction along the entire plate interface, and steady normal slip (back slip) in the main thrust zone at the plate convergence rate, resulting in a plate interface that has a locked main thrust zone and is slipping freely above and below this zone [Savage, 1983]. Appropriate strike-slip and dip-slip components are determined by the convergence direction of the subducting plate and the strike of the trench. Because the Aleutian arc is likely to be moving relative to North America, the convergence velocity is the Pacific plate velocity minus the North American plate velocity minus the velocity of the Aleutian Arc relative to stable North America.
 We extend the method of Savage  by allowing the main thrust zone to be either fully locked or partially creeping, with the slip deficit on the interface parameterized by a coupling coefficient. The coupling coefficient is one minus the slip between the two plates expressed in terms of a unit plate convergence rate. For example, if there is no slip the coupling coefficient is one, and if the slip between the two plates is equal to the rate of plate convergence, the coupling coefficient will be zero. The coupling coefficient can represent the percentage of the total interface that is locked.
 The subduction zone interface includes the 1986 and 1996 rupture zones. We use the fault plane locations specified by Ekstrom and Engdahl  to represent this area. The rupture area is bounded with a fault plane that connects the trench to the main thrust zone and a fourth plane that extents deeper beyond the specified main thrust zone (auxiliary material Figure S1). We refer to the faults from top to bottom as the “upper”, “middle”, “lower”, and “bottom” planes. We construct a second set of four fault planes for the Atka region, with the strike of the planes adjusted to agree with the change in strike of the trench. The east end of the Adak planes and the west end of the Atka planes meet approximately halfway between the two networks, except for the “middle” plane which meets another 95 km to the east based on the 1986 event's moment release patterns (see Discussion). The planes extended far enough laterally to avoid end effects.
 Because the convergence direction depends on the (unknown) arc velocity relative to North America, the inverse model is non-linear and we solve for the arc velocity and plate-coupling coefficients using a gridded search-inversion procedure. For each candidate arc velocity, we estimate the plate coupling coefficients that minimize the overall data misfit (total χ2). After a search over a wide range of candidate arc velocities, the model with the minimum misfit is the best overall model. We use both horizontal and vertical velocities in the inversion.
 Using the assumed fault plane geometry, we calculated the 3D surface displacements at each station assuming 100% coupling on all fault planes. This generates the unit Green's functions that map the coupling on each fault plane to the displacements measured on the surface. The coupling coefficients (m) are found using a MATLAB script “lsqlin”, which solves for m using linear least squares with inequality constraints. Before solving for m, the translation velocity of the arc (VArc) is subtracted from the measured velocities (d) to isolate the strain caused by the subducting Pacific plate, d* = d − VArc.
 This leaves d* as displacements caused by interseismic strain accumulation. The boundary condition 0 ≤ m ≤ 1 is applied to all fault planes except the bottom plane on the Adak side where m is allowed to range between −1 and 1. This condition allows for afterslip and/or viscous relaxation that could be present below the main thrust zone due to the 1986 or 1996 earthquakes.
 The best-fitting model has a reduced χ2 of 2.81 and the arc velocity is 4.1 mm/yr west and 6.7 mm/yr south (Figure 2a). This is equivalent to 4.9 mm/yr arc parallel (positive west) and 6.1 mm/yr arc normal (positive south), or a total velocity of 7.8 mm/yr at an azimuth of 210.3°.
 The coupling coefficients for the eight fault planes are shown in Figure 3. Our best model predicts little to no coupling in the Adak and Atka upper fault planes; this result is consistent with moment release distribution and seismicity patterns. A significant tradeoff can exist between model parameters, making the uncertainty of the coupling coefficients difficult to indicate clearly. Tradeoff between the Adak bottom and lower planes allows the coupling coefficient for the bottom plate to vary between −72% and 5% while remaining within the 95% confidence region, while the coupling on the lower plane must fall between 50% and 100% (auxiliary material Figure S1). There is not a significant tradeoff between the coupling on the middle and bottom planes, which make up the main thrust zone, the best model has both parameters near their upper limits of 100%. A tradeoff can also exist between the coupling and the arc translation velocity.
 The bottom plane of the Adak region best fits the data with a coupling of −28% of the plate convergence rate. This may be attributed to postseismic-deformation resulting from the 1986 and 1996 earthquakes, although viscoelastic relaxation may explain this deformation better than afterslip. The 95% confidence bound on this parameter includes zero (auxiliary material Figure S1).
 A strong along strike variation exists within the Andreanof segment of the Aleutian subduction zone. The thrust interface is nearly 100% locked in the western Andreanof region south of Adak from 60 to 130 km north of the trench axis, while the eastern region south of Atka is largely creeping. This variation is responsible for the along strike difference in strain determined using GPS and likely controls the extent of rupture area and moment release associated with major earthquakes.
 The estimated coupling coefficients show that the parts of the fault that are locked today (high slip deficit) correspond to the rupture areas of the 1986 and 1996 earthquakes. Houston and Engdahl  studied the spatio-temporal distribution of moment release for the 1986 Andreanof Island earthquake and found that 90% of the moment release occurred between 120 km west and 50 km east of the hypocenter. Boyd and Nabelek , who used long-period P and SH waves to invert for the source time-function and seismic moment of the earthquake also supported this finding. Engdahl et al.  showed that seismicity associated with the 1986 earthquake lies between 160 km west and 120 km east of the hypocenter in the middle plane and 0 to 120 km west of the hypocenter in the lower plane. We found the optimal boundary between the Adak high-coupled region and the Atka low-coupled region by testing models with the boundary in different places. We found that any along strike shift in this boundary away from that shown in Figure 1 resulted in a worse fit to the data (Figure 2b). If the boundary is shifted too far east, the data from the Atka are misfit significantly.
 From these findings, we believe our model accurately predicts a significant change in coupling behavior of the middle plane 80 km east of the 1986 hypocenter, while changes in coupling in the other planes occur near the 1986 hypocenter (Figure 3). Our recognition of an area of low coupling south of Atka suggests that the 1986 earthquake did not propagate further east because the creeping region had a low level of shear stress. However, the larger 1957 earthquake began in the western Andreanof region and was capable of propagating through the Atka low coupling region before rupturing areas further to the east. The 1957 earthquake may have reached the low coupling region with larger dynamic shear stresses, or if shear stress accumulates very slowly in the Atka region, the 1957 event may have ruptured this area and reduced that shear stress to a very low level. In this second scenario, by 1986 there was not enough shear stress built up to sustain rupture propagation through this region.
 We find an arc translation velocity of ∼7.8 mm/yr for the Aleutian arc in the Andreanof region (4.9 ± 2 mm/yr arc-parallel). This value is substantially slower than the estimate of Ekstrom and Engdahl  (30 ± 10 mm/yr arc-parallel relative to North America), which was based on slip vector azimuths for thrust earthquakes from the Aleutian arc. They used a simple model of slip partitioning in which the relative plate motion between the North American and the Pacific plates is accommodated by slip on the main thrust zone and strike-slip motion on a vertical plane coincident with the volcanic arc. Their analysis of slip vectors also suggested that extension of approximately 30 mm/yr occurs between 160°W and 177°W. McCaffrey  also analyzed slip vectors to calculate an arc parallel strain rate for the central Aleutians, and estimated a rate of extension even greater than that calculated by Ekstrom and Engdahl . These findings are in disagreement with our GPS observations, thus indicating either that this type of analysis is not applicable to the central Aleutians or that the structures responsible for slip partitioning are located offshore in the forearc. The velocity we determine for the arc in the Andreanof region is similar the velocity of Unalaska in the eastern Aleutians (4.7 mm/yr west and 2.7 mm/yr south) [Mann and Freymueller, 2003], indicating little extension currently exists between the central and eastern Aleutians.
 There are currently no identified features inboard of the arc that could be accommodating the motion of the Andreanof region relative to North America. We also note that the Andreanof translation velocity is similar to the velocity measured at St. Paul in the Pribilof Islands 600 km to the northeast. These velocities and other similar velocities in western Alaska and the eastern Aleutians may be related through the existence of clockwise rotating Bering plate as described by Mackey et al. .
 Using a fixed model geometry, we have simultaneously inverted for the interseismic coupling in the Andreanof segment of the Aleutian subduction zone and for the velocity of the Aleutian arc in the Andreanof region relative to North America. We find a strong variation in coupling between the west and east ends of this region in agreement with seismicity patterns and moment release for the 1986 Andreanof Islands earthquake. A translation velocity for the arc of 4.1 mm/yr west and 6.7 mm/yr south relative to North America is determined for the Andreanof region. This southwest motion maybe related to a clockwise rotating Bering plate.