Megathrust earthquakes of magnitude close to 9 are followed by large-scale (thousands of km) and long-lasting (decades), significant crustal and mantle deformation. This deformation can be observed at the surface and quantified with GPS measurements. Here we report on deformation observed during the 5 yr time span after the 2010 M w 8.8 Maule Megathrust Earthquake (2010 February 27) over the whole South American continent. With the first 2 yr of those data, we use finite element modelling (FEM) to relate this deformation to slip on the plate interface and relaxation in the mantle, using a realistic layered Earth model and Burgers rheologies. Slip alone on the interface, even up to large depths, is unable to provide a satisfactory fit simultaneously to horizontal and vertical displacements. The horizontal deformation pattern requires relaxation both in the asthenosphere and in a low-viscosity channel along the deepest part of the plate interface and no additional low-viscosity wedge is required by the data. The vertical velocity pattern (intense and quick uplift over the Cordillera) is well fitted only when the channel extends deeper than 100 km. Additionally, viscoelastic relaxation alone cannot explain the characteristics and amplitude of displacements over the first 200 km from the trench and aseismic slip on the fault plane is needed. This aseismic slip on the interface generates stresses, which induce additional relaxation in the mantle. In the final model, all three components (relaxation due to the coseismic slip, aseismic slip on the fault plane and relaxation due to aseismic slip) are taken into account. Our best-fit model uses slip at shallow depths on the subduction interface decreasing as function of time and includes (i) an asthenosphere extending down to 200 km, with a steady-state Maxwell viscosity of 4.75 × 10 18 Pa s; and (ii) a low-viscosity channel along the plate interface extending from depths of 55-135 km with viscosities below 10 18 Pa s.

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We present a detailed numerical study of the Gough & McIntyre model for the solar tachocline. This model explains the uniformity of the rotation profile observed in the bulk of the radiative zone by the presence of a large-scale primordial magnetic field, confined below the tachocline by flows originating from within the convection zone. We attribute the failure of previous numerical attempts at reproducing even qualitatively Gough & McIntyre's idea to the use of inappropriate boundary conditions at the radiative-convective interface. We emphasize the key role of flows downwelling from the convection zone in confining the assumed internal field. We carefully select the range of parameters used in the simulations to guarantee a faithful representation of the hierarchy of expected length-scales. We then present, for the first time, a fully non-linear and self-consistent numerical solution of the Gough & McIntyre model which qualitatively satisfies the following set of observational constraints: (i) the quenching of the large-scale differential rotation below the tachocline -including in the polar regions -as seen by helioseismology (ii) the confinement of the large-scale meridional flows to the uppermost layers of the radiative zone as required by observed light element abundances and suggested by helioseismic sound-speed data.Key words: MHD -Sun: interior -Sun: magnetic fields -Sun: rotation. I N T RO D U C T I O NThe presence of the tachocline, a thin shear layer located at the interface between the radiative and convective regions of the Sun, was established two decades ago (Christensen-Dalsgaard & Schou 1988;Kosovichev 1988;Brown et al. 1989;Dziembowski, Goode & Libbrecht 1989) but its modus operandi still remains mysterious.Anisotropic turbulent stresses associated with rotationally constrained eddies are thought to maintain the differential rotation profile cz (θ , r) observed within the convection zone:where for example at r = 0.75 R , eq /2π = 463 nHz, a 2 = 0.17 and a 4 = 0.08 (Schou et al. 1998;Gough 2007). Spiegel & Zahn (1992, SZ92 hereafter) showed that this differential rotation is expected to subsist below the base of the convection zone (at r cz = 0.713 R ), despite the expected reduction in the amplitude of the turbulent stresses. In fact, they showed how the absence of turbulent stresses in the tachocline region would permit the propagation of the latitudinal shear through radiative diffusion, which is clearly at odds with observations. The observed thickness of the tachocline therefore suggests the presence of efficient and anisotropic angular momentum transporters near the radiative-convective interface.

Abstract. The postseismic deformations following subduction megaearthquakes are characterized by a horizontal velocity which, once non-dimensionalized by the coseismic displacement, increases with distance to the trench then presents an almost constant value for distances between 500 and 1500 km. The vertical velocity features a strong narrow peak on the trenchward side of the volcanic arc. Subsidence is observed in the far-field. In order to understand better the implications of these observations, the influence of the geometry of low viscosity regions in subduction zones on the postseismic deformations is analyzed using a 2-D finite element model with viscoelastic rheologies. The slab dip in the top 80 km Θtop, and deeper Θbottom and the locking depth all have a limited impact on the ratio of horizontal postseismic velocity over coseismic displacement. The smaller Θbottom, the smaller the amplitude of the predicted vertical velocity in the middle-field (200–500 km from the trench). The presence of the slab at asthenospheric depths affects very significantly both the horizontal and vertical velocities. Models with an 80 km thick lithosphere, where the relaxation occurs only in the asthenosphere, are characterized by a trenchward horizontal velocity decreasing very moderately in the middle-field and an uplift maximum on the continental side of the volcanic arc, at odds with the observations. A low viscosity channel (LVCh) over the deep parts of the subduction interface or a low viscosity wedge (LVW) have a considerable impact on the middle-field horizontal and vertical velocities: the trenchward horizontal velocities are very significantly increased while the vertical velocities are characterized by strong uplift over the deep parts of the subduction interface. In the case of a low viscosity wedge, a marked subsidence further away from the trench, on the continent side of the volcanic arc is predicted. While the low-viscosity wedge affects little the far-field horizontal velocities, the LVCh increases them significantly. The thicknesses of the lithosphere and the asthenosphere also have a strong impact on both the middle-field and the far-field velocities. The larger they are, the further from the trench are the maxima of the ratio of the postseismic over coseismic horizontal displacement and of the far-field subsidence. 3-D modeling with a geometry as precise as possible of the various zones with postseismic creep associated with each megaearthquake is necessary to derive more precise conclusions. However, the 2-D modeling results obtained here, compared with postseismic data, point towards lithospheres and asthenospheres surprisingly similar in various areas of the world, with thicknesses around 70 and 200 km respectively and towards the presence of a LVW and/or a LVCh. The systematic description of the role of each parameter presented here will facilitate the choice of the parameters to vary in 3-D models.

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