 2006 Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or editing@geosociety.org. Geology; October 2006; v. 34; no. 10; p. 877–880; doi: 10.1130/G22462.1; 4 figures. 877 Curvature of oceanic arcs Gabriele Morra* Klaus Regenauer-Lieb † Domenico Giardini ETH Zu ¨ rich, Institute of Geophysics, 8093 Hoenggerberg, Switzerland ABSTRACT Oceanic arcs and deep-sea trenches are the surface expressions of oceanic plates sub- ducting into the Earth’s mantle. We use a new numerical technique for simulating the dynamical evolution of the lithosphere-mantle interaction in order to assess the causes of arc curvature. We group the possible causes into two classes, external feedback between the migrating lithosphere and the secondary induced mantle flow, and internal heteroge- neities within the lithosphere, e.g., owing to differences in cooling ages of the plate at the trench. We statistically assess that almost all arcs on the Earth can be described by these hypotheses. The method is also directly applied to the Tonga and Aleutian arcs, bringing new insights on the origin of their shapes. Keywords: island arcs, subduction, lithosphere, rheology. Figure 1. Main subduction zones superposed on ocean age map. Representative examples of their convex curved shape (convexity is defined from point of view of oceanic plate approaching trench): (1) Aleutian-Alaskan, (2) Kurils, (3) Marianas, (4) Java, (5) Banda, (6) New Hebrides–Fiji, (7) Tonga-Kermadec. Arrows indicate direction of subduction; magnitude is absolute plate velocity (in mm/yr). Background represents age of ocean floor. Dark gray indicates ei- ther very young (ridges) thermal age (<10 Ma) or very old (>90 Ma); light gray indicates intermediate age. Plate velocities come from Nuvel-1A poles model; plate boundaries are from PB2002 (Bird, 2003) model; oceanic age map is from database compiled by Mu ¨ ller et al. (1997). INTRODUCTION The key feature of plate tectonics is the subduction of cold oceanic lithospheric plates into a hot convective mantle. The gravitational pull associated with the negative buoyancy of cold subducting lithosphere has been identified as the main driver of plate tectonics. As they plunge into the mantle, slabs of cold lithosphere heat slowly, maintaining a cold core that controls their strength (Turcotte et al., 1978). The pres- ence of earthquakes in the slab down to 660 km indicates that a solid- like core of the slab persists and that elastic energy is stored and con- sequently seismically released (Giardini, 1988). The surrounding solid mantle flows slowly by different creep mechanisms; typical velocities are 1–10 cm/yr. Thus subduction can be described and modeled as the interaction between a solid-mechanical subducting lithosphere and a viscous flowing fluid-like mantle. A striking feature of oceanic trench systems is their alignment into a set of arc-shaped trenches and volcanic arcs (Fig. 1). Many trenches are intraoceanic (i.e., also the overriding plate is oceanic); they mostly retreat within the hotspot reference frame (Garfunkel et al., 1986) and assume convex arc shapes, as seen from the subducting plate (Fig. 1). Trench retreat is associated with the subduction of old, grav- itationally unstable oceanic lithosphere, and is often characterized by the opening of a backarc basin in the overriding plate (e.g., 3 and 7 in Fig. 1). The trench shape evolves at the equilibrium between active (slab pull) forces and mantle viscous resistance, and invariably results in a convex shape. When the overriding plate is a buoyant continental lithosphere, the shape of the continental margin also influences the shape of the trench. CAUSES FOR ARC CURVATURE A first quantitative analysis of trench curvature is in Figure 2, where the data set of Tovish and Schubert (1978) is plotted through the inverse arc radius r/AR (normalized by the Earth radius r = 6731 km) as a function of the normalized arc length (AL/r). Low values of r/AR (below the dotted line AR = AL; Fig. 2) indicate mild curvature, whereas high values of r/AR indicate strong curvature. Most of the arcs display substantial scale invariance (AR  AL). *E-mail: gabriele.morra@erdw.ethz.ch. † Current affiliation: School of Earth and Geographical Sciences, The Uni- versity of Western Australia and CSIRO Exploration & Mining, Perth, WA 6009, Australia. The curvature of arcs is commonly attributed to the Earth’s spher- icity (Frank, 1968). This hypothesis is an analogy between Earth and a ping-pong ball: the Earth’s surface would be cut by oceanic subduc- tion zones like the dent induced in a ping-pong ball. This hypothesis is based on the fact that an inextensible spherical shell that is bent