Crustal deformation in the plate boundary regions in south Iceland is estimated from repeated Global Positioning System (GPS) geodetic measurements in the period 1986--1992. We compare coordinate solutions for the 1986 and 1989 surveys with the results from the most recent survey in 1992. Horizontal position uncertainty is about 2 cm for the 1986 and 1989 coordinates and about 4 mm for the 1992 coordinates. Little internal deformation is observed in the area west of the western volcanic zone (within the North American plate) and at the southern tip of the eastern volcanic zone (within the Eurasian plate). The observed relative velocity of these two areas is 2.1¿0.4 cm/yr in direction N117¿11¿E (1&sgr; uncertainties), compatible with the 1.94 cm/yr widening in direction N104¿E across south Iceland predicted from the NUVEL-1 global plate motion model. Left-lateral shear strain is developing across the intervening transform zone, the E-W trending south Iceland seismic zone (SISZ). Strain is concentrated within a 20- to 30-km-wide zone that correlates with seismic activity in the SISZ. About 85¿15% of the relative plate motion is accommodated by this zone in such a way that the area south of the SISZ is moving toward the east with the Eurasian plate and the area north of the SISZ is moving toward the west with the North American plate. Accordingly, north of the SISZ the western rift zone can accommodate a maximum of 15¿15% of the relative plate motion. Within the SISZ the shear strain results in an anticlockwise rotation of lineaments oriented north-south, at a rate of 0.5--1 μrad/yr.

The shear strain accumulation can be accommodated by ''bookshelf faulting'' on mapped recent north-south faults in the SISZ. If the deformation is accommodated by an array of N-S faults spaced 1--5 km apart, an average slip rate of about 0.5--5 mm/yr is required on each fault. The rate of geometric moment release due to earthquakes averaged over centuries, M˙o, expected from such an array is about the same as expected from a simple transform fault, 2&ngr;AD, where 2&ngr; is the relative plate motion, A is the total length of the seismic zone, and D is the thickness of the brittle crust. If 2&ngr;=(0.85¿0.15)¿1.94 cm/yr, D=10--15 km, and A=75--85 km, then M˙0=1.0--2.5¿107 m3/yr, comparable to the rate of geometric moment release in large historical earthquakes in the SISZ for the last several centuries. We conclude that historical seismicity in the SISZ can be attributed to left-lateral shear accumulation across the seismic zone at a similar rate throughout historical times as during the years 1986--1992. ¿ American Geophysical Union 1995