ALBERT

Description: Steady plate subduction elastically brings about permanent lithospheric deformation in island arcs, though this effect has been neglected in most studies based on elastic dislocation theory. We investigate the characteristics of the permanent lithospheric deformation using a kinematic model, in which steady slip motion is given along a plate interface in the elastic lithosphere overlying the viscoelastic asthenosphere under gravity. As a rule of thumb, long-term lithospheric deformation can be understood as a bending of an elastic plate floating on non-viscous fluid, because the asthenosphere behaves like water on the long term. The steady slip below the lithosphere–asthenosphere boundary does not contribute to long-term lithospheric deformation. Hence, the key parameters that control the lithospheric deformation are only the thickness of the lithosphere and the geometry of the plate interface. Slip on a plate interface generally causes substantial vertical displacement, and gravity always tries to retrieve the original gravitational equilibrium. For a curved plate interface gravity causes convex upward bending of the island-arc lithosphere, while for a planar plate interface gravity causes convex downward bending. Larger curvature and thicker lithosphere generally results in larger deformation. When the curvature changes along the plate interface, internal deformation is also involved intrinsically, which modifies the deformation field due to gravity. Because the plate interface generally has some curvature, at least near the trench, convex upward bending of the island-arc lithosphere, which involves uplift of island-arc and subsidence around the trench, is always realized. On the other hand, the deformation field of the island-arc lithosphere sensitively depends on lithospheric thickness and plate interface geometry. These characteristics obtained by the numerical simulation are consistent with observed topography and free-air gravity anomalies in subduction zones: a pair of topography and gravity anomalies, high in the arc and low around the trench, is observed without exceptions all over the world, while there are large variety in the amplitude and horizontal scale of the topography and gravity anomalies.

Description: Repeating earthquakes, the sequence of stress accumulation and release at isolated small asperities on a plate interface, can be regarded as a renewal process in statistics. From such a point of view, we modelled a sequence of repeating earthquakes and developed an objective Bayesian method to estimate the space–time distribution of interplate slip rates from the recurrence intervals of repeating earthquakes. The space–time distribution of slip rates is represented by the superposition of tri-cubic B-splines. The knots of B-splines in time are unequally allocated for representing co-seismic abrupt and post-seismic rapid changes in slip rates. In addition, to avoid overfitting, smoothness constraints are imposed and their optimal weights are determined by Akaike's Bayesian Information Criterion. We applied this method to the complete data set of repeating earthquakes in northeast Japan for about 18 yr before the 2011 Tohoku-oki earthquake, and revealed spatiotemporal variations of interplate slip rates off the Hokkaido-Tohoku region, where the 1994 Sanriku-oki (M7.6), 2003 Tokachi-oki (M8.0), 2004 Kushiro-oki (M7.1), and 2008 Ibaraki-oki (M7.0) earthquakes occurred. First, we confirmed the reciprocal correlation between the spatial distribution of average slip rates for a seismically calm period (1996–2000) and that of average slip-deficit rates, which has been estimated from GPS array data. Then, we examined the temporal variations of slip rates associated with the large interplate earthquakes in detail.