3-D Numerical Simulation of Island Arc Deformation based on the Dislocation Model for Plate Subduction and its Insight into Topographic Evolution of Island Arcs

Elastic/viscoelastic dislocation theory is a fundamental tool in computing crustal deformation due to fault motion, not only for instantaneous coseismic deformation but also for gradual postseismic and interseismic deformation. Expressing the kinematic interaction between the subducting and overriding plates by dislocation along the plate interface, our group has developed a crustal deformation model due to plate subduction, named "dislocation model for plate subduction" (Matsu'ura & Sato 1989, GJI), which is a generalization of Savage's back slip model (Savage, 1983, JGR), including the effect of deformation due to steady plate subduction. Hashimoto et al. (2004, PAGEOPH) demonstrated that the pattern of uplift rates in and around Japan computed by this model shows excellent coincidence to the observed free-air gravity anomalies. Fukahata and Matsu‘ura (2016, GJI), using the 2D model, explained the physical mechanism of island-arc uplift, trench subsidence, and outer rise uplift by combining the effects of lithospheric rotation and gravity.

   In this study, we develop a 3D numerical model and compute vertical displacement rates in a subduction zone caused by steady slip along a plate interface, in which the trench axis has a bend convex toward the island arc. Computation results show that the island arc lithosphere significantly subsides around the bend, and that the subsidence is larger for a larger bend angle.

   This subsidence can be physically understood by mass deficit in the island arc lithosphere, as explained below. When a plate subducts along a trench with a bend convex toward the island arc, mass excess inevitably occurs in the subducting slab, which can be understood from an analogy of a tablecloth draped at a corner of a table. In the dislocation model, the motion of plate subduction is expressed by displacement discontinuity along the plate interface. The displacement discontinuity, which is equivalent to a force system of a double couple, requires two surfaces that sandwich a fault to move in exactly opposite directions each other, which results in mass deficit in the island arc, because mass excess occurs in the subducting slab.

   Along the main Japanese islands, we observe significant invasions of negative free-air gravity anomalies into the forearc around the Hidaka Trough, the Kanto Plain, and the Bungo Channel, which correspond to the junctions of the trench axes. In brief, these forearc negative free-air gravity anomalies can commonly be understood by the above mechanism. We also observe similar invasions of negative free-air gravity anomalies around the Arica bend, South America, and Cascadia, though the signals of negative gravity anomalies are smaller in these regions, reflecting gentler changes of the strikes of the trench axes.