Figure 4

Models of the temperature and the thermal shear instability of the Tonga slab. (a) Schematic figure of the simulation of the subduction of the Tonga slab. The symbol σ _xx indicates the normal stress acting on the side boundaries. (b) Contour plot for the temperature model of the Tonga slab in the study area. Contour interval is 50°C. Model parameters used in the temperature calculation are as follows: C_p=1.046×10³ (J·kg⁻¹ K⁻¹), k=3.138 (J·m⁻¹ K⁻¹s⁻¹), and α=2×10⁻⁵ (K⁻¹), where C_p is specific heat at constant pressure, k is thermal conductivity, and α is thermal expansivity. The instability parameter is evaluated along the vertical line annotated with ‘A’ and ‘B’. The red circle shows the coldest point, therefore the representative deepest foci, along A-B. Blue and green circles are 30 and 44 km above the coldest point, respectively. (c) Properties associated with instability criterion across the stagnating part of the slab along A-B in (a). Horizontal axis is the distance across the slab from A to B. Top, middle, and bottom images show temperature (°C), stress (MPa), and logarithm of Θ (log10Θ), respectively. Red, blue, and green circles in the top image correspond to those in (a). Solid lines are for diffusion creep for the case of 1- μ m grain sizes when diffusion creep dominates over dislocation. Dashed lines are for dislocation creep for the grain size of 5 μ m when dislocation creep dominates over diffusion creep. The ratio between the dislocation glide length and climb length (l_g/l_c) is 200 (Shimojuku et al. [2009]). Other rheological parameters of ringwoodite are taken from Shimojuku et al. ([2009]).