We use the finite element method to analyze stress variations
in and near a strongly coupled subduction zone during an earthquake cycle.
Deformation is assumed to be uniform along strike (plane strain on a cross
section normal to the trench axis), and periodic earthquake slip is imposed
consistent with the long term rate of plate convergence and degree of coupling.
Simulations of stress and displacement rate fields represent periodic fluctuations
in time superimposed on an average field. The oceanic plate, descending
slab and continental lithosphere are assumed here to respond elastically
to these fluctuations, and the remaining mantle under and between plates
to respond as Maxwell viscoelastic. In the first part of the analysis
we find that computed stress fluctuations in space and time are generally
consistent with observed earthquake mechanism variations with time since
a great thrust event. In particular, trench-normal extensional earthquakes
tend to occur early in the earthquake cycle towards the outer rise, but
occur more abundantly late in the cycle in the subducting slab down dip
of the main thrust zone. Compressional earthquakes, when they occur at
all, have the opposite pattern. Our results suggest also that the
actual timing of extensional outer rise events is controlled by the rheology
of the shallow aseismic portion of the thrust interface. The second
part of the analysis shows the effects of mantle relaxation on the rate
of ground surface deformation during the earthquake cycle. Models
without relaxation predict a strong overall compressional strain rate in
the continental plate above the main thrust zone, with the strain rate
constant between mainshocks. But with significant relaxation present,
a localized region of unusually low compressional, or even slightly extensional,
strain rate develops along the surface of the continental plate above and
somewhat inland from the down dip edge of the locked main thrust zone.
The low strain rate starts in the middle or late part of the cycle, depending
on position. This result suggests that the negligible or small contraction
measured on the Shumagin Islands, Alaska, during 1980 to 1991, may not
invalidate an interpretation of that region as being a moderately coupled
subduction zone. In contrast, mantle relaxation causes only modest
temporal nonuniformity of uplift rates in the over riding plate, and of
extensional stress rates in the subducting plate, even when the Maxwell
time is an order of magnitude less than the recurrence interval.