Plate tectonics at an awkward junction: rules for the evolution of Sovanco Ridge area, NE Pacific

Summary. The elegant geometrical rules of plate tectonics do not allow for a gradual shift in plate motion directions, or the gradual, as opposed to sudden, cessation of subduction. At the scale of the small plates in the NE Pacific, imperfections in boundary processes have a large effect on the net torque on the plates, and heavily influence the evolution of the geometry. In this area, the rotation of the spreading directions and the diminution of true subduction along the southern Canadian coast has not occurred by the sudden switching of plate motions from one stable condition to another. Instead, it appears as if the dominant factor for the evolution is the resistance of the ocean floor to formation of new, smoothly slipping transform faults. Compressive deformation of even young lithosphere is not only mechanically unlikely, but is not helpful to the particular configurations found in this area. Instead, a migrating shear zone and an episode of highly en echelon spreading along a new axis nearly perpendicular to the present Juan de Fuca ridge have resulted: the present Sovanco ridge was never a transform fault. Neither is the Nootka fault a shear zone, but the locus of stretching between plates whose motions are congruent at the Juan de Fuca ridge, but diverge toward the continental margin.     

Non-linear altimetric geoid inversion for lithospheric elastic thickness and crustal density

The inversion of high-resolution geoid anomaly maps derived from satellite altimetry should allow one to retrieve the lithospheric elastic thickness, T _e , and crustal density, _c . Indeed, the bending of a lithospheric plate under the load of a seamount depends on both parameters, and the associated geoid anomaly is correspondingly dependent on the two parameters. The difference between the observed and modelled geoid signatures is estimated by a cost function, J , of the two variables, T _e and _c . We show that this cost function forms a valley structure along which many local minima appear, the global minimum of J corresponding to the true values of the lithospheric parameters. Classical gradient methods fail to find this global minimum because they converge to the first local minimum of J encountered, so that the final parameter estimate strongly depends on the starting pair of values ( T _e ,   _c ). We here implement a non-linear optimization algorithm to recover these two parameters from altimetry data. We demonstrate from the inversion of synthetic data that this approach ensures robust estimates of T _e and _c by activating two search phases alternately: a gradient phase to find a local minimum of J , and a tunnelling phase through high values of the cost function. The accuracy of the solution can be improved by a search in an iteratively restricted parameter subspace. Applying our non-linear inversion to the Great Meteor Seamount geoid data, we further show that the inverse problem is intrinsically ill-posed. As a consequence, minute geoid (or gravity) data errors can induce large changes in any recovery of lithospheric elastic thickness and crustal density.     

Slab pull effects from a flexural analysis of the Tonga and Kermadec trenches (Pacific Plate)

Thin-plate flexure models have been frequently used to explain the mechanical behaviour of the lithosphere at oceanic trenches, but little attention has been paid to using them as a way to check the relative importance of different plate-driving mechanisms. A 2-D numerical algorithm accounting for the flexural deflection of the lithosphere controlled by multilayered elastic–plastic rheology (brittle–elastic–ductile) has been applied to the seaward side of the Tonga and Kermadec trenches. This approach gives a better fit to the bathymetry on both trenches than assuming classical homogeneous plate models, and allows the interplate coupling forces and the lithospheric strength profile to be constrained. Our results show that, in order to fit the observed deflection of the lithosphere, a regional tensile horizontal force must act in both regions. This tensile force and its flexural effects are discussed in terms of slab pull as a main plate-driving mechanism. The predicted stress and yielding distributions partially match the outer-rise earthquake hypocentres within the subducting plate, and thus do not invalidate the model.     

The onset of extension during lithospheric shortening:a two-dimensional thermomechanical model for lithospheric unrooting

We model the evolution of the lithosphere during its shortening and consequent gravitational collapse with special emphasis on the induced variations in the surface stress regime and dynamic topography. In particular, we analyse the conditions leading, immediately after lithospheric failure, to local extension, eventually coeval with compression. Different crustal rheologies and kinematic conditions as well as thermally imposed mechanical rupture are considered. Numerical calculations have been performed by using a 2-D finite element code that couples the thermal and mechanical equations for a Newtonian rheology with a temperature-dependent viscosity. The results show that, after the failure of a gravitationally unstable lithospheric root, the replacement of lithospheric mantle by warmer asthenospheric material induces a considerable variation in the dynamic topography and in the surface stress regime. The occurrence of local extension, its intensity and its spatial distribution depend mainly on whether convergence continues throughout the process or ceases after or before the lithospheric failure. Similarly, uplift/subsidence and topographic inversion are controlled by kinematic conditions and crustal rheology. Mechanical rupture produces drastic changes in the surface stress regime and dynamic topography but only for a short time period, after which the system tends to evolve like a continuous model.     

The influence of a stratified rheology on the flexural response of the lithosphere to (un)loading by extensional faulting

We present a two-layered finite difference model for the flexural response of the lithosphere to extensional faulting. The model allows for three modes of flexure: (1) fully coupled, with the upper crust and mantle welded together by the lower crust; (2) fully decoupled, with the upper crust and mantle behaving as independent layers; and (3) partly decoupled, signifying that the response of the upper crust to small-wavelength loads is superimposed on the response of the entire lithosphere to long-wavelength loads. Which of these modes of flexure is to be expected depends on the rheology and especially the thermal state of the lithosphere. Coupled behaviour is related to a cold and strong lithosphere. The Baikal Rift Zone provides a typical example for this mode of flexure. A fully decoupled lithosphere is an exceptional case, related to anomalous high temperatures in the lower crust, and is observed in the Basin and Range province. The most common case is a partly decoupled lithosphere, with the degree of decoupling depending on the thickness and viscosity of the lower crust. This is inferred, for example, for the Bay of Biscay margin.     

塔克拉玛干沙漠腹地高大复杂纵向沙垄区沙丘分形特征

为了探讨塔克拉玛干沙漠小尺度风沙地貌形态特征,对沙漠腹地复杂纵向沙垄横断面的上覆沙丘的分形特征进行了研究。沙丘形态野外测量采用RTK(real-time kinematic)技术,并通过南方测绘软件(South Survey)量算形态特征参数。研究结果表明:(1)沙丘形态具有分形特征,饼状沙堆和沙片的分维数是1.292 2,新月形沙丘的分维数是1.286 6,简单线性沙丘的分维数是1.102 5,新月形沙丘链的分维数是1.085;(2)在不同地貌部位之间,分维数差异不大(1.0~1.3),变异系数为0.06,表明复杂纵向沙垄上覆沙丘形态有自相似性;(3)沙丘的各形态特征参数变异系数的空间变化趋势一致,且与分形维数呈显著的线性正相关(P<0.05),表明沙丘形态分形维数能客观反映沙丘形态特征。在塔克拉玛干沙漠腹地纵向沙垄区,沙丘形态分形维数可以作为反映风沙环境特征的定量指标。     

State of stress within a bending spherical shell and its implications for subducting lithosphere

The state of stress within a bending spherical shell has some special features that are caused by sphericity. While most lithospheres are more like spherical shells than flat plates, our ideas of the state of stress have been dominated by flat-plate models. As a consequence, we might be missing some important aspects of the state of stress within subducting lithospheres. In order to examine this problem, we analyse spherical-shell bending problems from basic equations. We present two approaches to solve spherical-shell bending problems: one by the variational approach, which is suitable for global-scale problems, and the other by the asymptotic equation, which is valid to first order in h/R , where h is the thickness of the lithosphere and R is its curvature radius (i.e. under the assumption of small curvature). The form of the equation for displacement shows that wavelengths of deformation are determined by the spherical (elastic) effect and the gravitational buoyancy effect, for which only the latter effect is included in the usual flat-plate formulations. In the case of the Earth, the buoyancy force is dominant and, consequently, spherical effects are suppressed to a large extent; this explains why flat-plate models have been successful for Earth's lithospheric problems. On the other hand, the state of stress shows interesting spherical effects: while bending (fibre) stress along the subduction zone is always important, bending stress along the trench-strike direction can also be important, in particular when the subduction zone arc is small. Numerical results also indicate that compressive normal stress along the trench-strike direction is important when a subduction zone arc is large. These two stresses, the bending stress and the compressive normal stress, both along the trench-strike direction, may have important implications for intraplate earthquakes at subduction zones.