The geometry of Aleutian subduction: Three‐dimensional kinematic flow model

Abstract

We construct a steady state kinematic model of slab flow along the Aleutian Arc assuming the slab's geometry is known. The slab geometry is constrained by local network data where the slab is seismically active and by P wave residual‐sphere analysis of 11 earthquakes and one nuclear explosion where it is aseismic. The slab is approximated by a thin Newtonian sheet subducting in a less viscous and incompressible mantle. Particles enter the trench at known rates of relative plate motion and are required to subduct along the predefined slab geometry. For discrete, but small (0.1 m.y.) time steps, we determine the speed and direction of each slab particle that minimizes dissipation power as the spherical shell (oceanic lithosphere) deforms to obtain the observed slab shape. Because the dip of the slab in the central Aleutians is steep relative to the radius of curvature of the trench, the slab must stretch along arc to obtain its present configuration. Our kinematic model represents one internally consistent flow that results in the observed geometry. Furthermore, it provides a lower bound on the total amount of internal in‐plane deformation required by the shape and an estimate of stream lines and of the orientation and spatial distribution of the deformation rate. The predicted in‐plane strain rate field is dominated by along arc extension, reaching values as large as 10−15s−1 in the central Aleutians and decaying by an order of magnitude to the east and west. The slab accumulates an in‐plane strain of 10% by the time it reaches the depth of the seismicity cutoff. Along‐arc variations in both the magnitude and orientation of calculated strain rates are consistent with the spatial distribution of seismic moment release and source mechanism orientations of intermediate‐depth earthquakes, suggesting that in order to understand intermediate‐focus earthquakes one must consider along‐arc deformation. Three‐dimensional analyses of subduction in a spherical geometry, such as the present study, are required to model along‐arc effects. Relative plate motions along the trench vary from nearly normal in the eastern Aleutians to transform farther west. Coincident with this change, the maximum depth of seismicity within the descending slab decreases from 250 to 50 km and active andesitic volcanism ceases. The kinematic flow model predicts that the slab subducted obliquely along the central portion of the Aleutian Arc is transported laterally westward producing cold slab material to a depth of at least 300 km along the entire arc after only 15 m.y. of subduction. The lack of volcanic activity in the western Aleutians is apparently related to the lateral transport of the slab, perhaps indicating that the slab is dehydrated and incapable of producing the volatiles necessary for arc magmatism. The along‐arc variation in the maximum depth of seismicity can be explained thermally. We construct temperature estimates within the slab using a quasi three‐dimensional finite difference scheme, including entrained mantle flow, stream lines from the kinematic model and the time history of the age of the subducting lithosphere as a function of position along the trench. The theoretical temperature at the seismicity cutoff depth is remarkably close to a constant fraction of the depth‐dependent mantle solidus along the entire arc. This observation is consistent with the hypothesis that seismicity terminates because of the initiation of high‐temperature, steady state creep and provides an explanation for the lack of intermediate‐focus earthquakes in the western Aleutians even though slab material exists there.