Stress and temperature in the bending lithosphere as constrained by experimental rock mechanics

Summary. Previous attempts to deduce the stress distribution in the bending lithosphere near a consuming plate margin have relied on the observed bathymetry and an assumed constitutive relation for lithospheric behaviour, e.g. perfectly elastic, viscous/perfectly plastic, or elastic perfectly plastic. From the point of view of rock mechanics, each of these approximations fails to describe one or more of several basic phenomena, including brittle failure of rock, temperature dependence of elasticity, and temperature and/or strain rate dependence of ductile behaviour. In order to formulate a more realistic constitutive relation, a limiting yield strength curve, which is primarily a function of temperature, is constructed from data from brittle failure and ductile flow experiments. The moments which can be supported by plates with this constitutive behaviour are compared to the moments calculated from bathymetric profiles. The comparison indicates that moments required by the bathymetric data are consistent with moments supported by plates with experimentally determined constitutive laws as extrapolated to geologically reasonable temperatures and strain rates. The stresses developed in such models are required to reach values greater than 100 MPa† in the depth range 25–45 km. Geotherms necessary for strength curves consistent with moments calculated from the bathymetric data match those derived from heat flow data for the Aleutian, Bonin, Mariana and Tonga trenches. Of the trenches studied, only the geotherm inferred from the Kuril trench data is significantly different, perhaps implying that the Kuril plate is weaker than the others. The strength curves show that as a first approximation it is better to assume that bending moment is independent of curvature of the plate than to assume that bending moment and curvature are linearly related.     

Impact of regional mantle flow on subducting plate geometry and interplate stress: insights from physical modelling

Physical models of subduction investigate the impact of regional mantle flow on the structure of the subducted slab and deformation of the downgoing and overriding plates. The initial mantle flow direction beneath the overriding plate can be horizontal or vertical, depending on its location with respect to the asthenospheric flow field. Imposed mantle flow produces either over or underpressure on the lower surface of the slab depending on the initial mantle flow pattern (horizontal or vertical, respectively). Overpressure promotes shallow dip subduction while underpressure tends to steepen the slab. Horizontal mantle flow with rates of 1–10 cm yr⁻¹ provides sufficient overpressure on a dense subducting lithosphere to obtain a subduction angle of  ∼60°  , while the same lithospheric slab sinks vertically when no flow is imposed. Vertical drag force (due to downward mantle flow) exerted on a slab can result in steep subduction if the slab is neutrally buoyant but fails to produce steep subduction of buoyant oceanic lithosphere. The strain regime in the overriding plate due to the asthenospheric drag force depends largely on slab geometry. When the slab dip is steeper than the interplate zone, the drag force produces negative additional normal stress on the interplate zone and tensile horizontal stress in the overriding plate. When the slab dip is shallower than the interplate zone, an additional positive normal stress is produced on the interplate zone and the overriding plate experiences additional horizontal compressive stress. However, the impact of the mantle drag force on interplate pressure is small compared to the influence of the slab pull force since these stress variations can only be observed when the slab is dense and interplate pressure is low.     

Comment on 'Consequences of progressive eclogitization on crustal exhumation, a mechanical study' by H. Raimbourg, L. Jolivet and Y. Leroy

Two simple end-member models of a subduction channel have been proposed in the literature: (i) the 'pressure-imposed' model for which the pressure within the channel is assumed to be lithostatic, the channel walls have negligible strength with respect to lateral pressure gradients, and the channel geometry therefore varies with time and (ii) the 'geometry-imposed' model of constant channel geometry, rigid walls and resultant lateral variation in pressure. Neither of these models is realistic, but they provide lower and upper bounds to potential pressure distributions in natural subduction zones. The critical parameter is the relative strength of the confining plates, reflected in the effective viscosity ratio between the channel fill and the walls. The assertion that the 'geometry-imposed' model is internally inconsistent is incorrect—it merely represents one bound to possible behaviour and a bound that may be approached for realistic values of the effective viscosity for weak channel fill (e.g. unconsolidated ocean-floor sediments) and relatively cold and strong subducting and overriding lithospheric plates.     

Numerical comparison of different convergent plate contacts: subduction channel and subduction fault

At convergent plate boundaries, the properties of the actual plate contact are important for the overall dynamics. Convergent plate boundaries both mechanically decouple and link tectonic plates and accommodate large amounts of strain. We investigate two fundamental physical states of the subduction contact: one based on a fault and the other based on a subduction channel. Using a finite element method, we determine the specific signatures of both states of the subduction contact. We pay particular attention to the overriding plate. In a tectonic setting of converging plates, where the subducting plate is freely moving, the subduction channel reduces compression relative to the fault model. In a land-locked basin setting, where the relative motion between the far field of the plates is zero, the subduction channel model produces tensile stress regime in the overriding plate, even though the amount of slab roll-back is small. The fault model shows a stronger development of slab roll-back and a compressive stress regime in the upper plate. Based on a consistent comparison of fault and channel numerical models, we find that the nature of the plate contact is one of the controlling factors in developing or not of backarc extension. We conclude that, the type of plate contact plays a decisive role in controlling the backarc state of stress. To obtain backarc extension, roll-back is required as an underling geodynamic process, but it is not always a sufficient condition.     

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.     

Small-scale mantle flows and induced lithospheric stress near island arcs

Summary. This paper explores the middle ground between complex thermally-coupled viscous flow models and simple corner flow models of island arc environments. The calculation retains the density-driven nature of convection and relaxes the geometrical constraints of corner flow, yet still provides semianalytical solutions for velocity and stress. A novel aspect of the procedure is its allowance for a coupled elastic lithosphere on top of a Newtonian viscous mantle. Initially, simple box-like density drivers illustrate how vertical and horizontal forces are transmitted through the mantle and how the lithosphere responds by trench formation. The flexural strength of the lithosphere spatially broadens the surface topography and gravity anomalies relative to the functional form of the vertical flow stresses applied to the plate base. I find that drivers in the form of inclined subducting slabs cannot induce self-driven parallel flow; however, the necessary flow can be provided by supplying a basal drag of 1–5 MPa to the mantle from the oceanic lithosphere. These basal drag forces create regional lithospheric stress and they should be quantifiable through seismic observations of the neutral surface. The existence of a shallow elevated phase transition is suggested in two slab models of 300 km length where a maximum excess density of 0.2 g cm⁻³ was needed to generate an acceptable mantle flow. A North New Hebrides subduction model which satisfies flow requirements and reproduces general features of topography and gravity contains a high shear stress zone (75 MPa) around the upper slab surface to a depth of 150 km and a deviatoric tensional stress in the back arc to a depth of 70 km. The lithospheric stress state of this model suggests that slab detachment is possible through whole plate fracture.     

Microearthquake swarms: scaling and lacunarity

The continental collision between the African and Eurasian plates in the Iberian peninsula is solved with a NW-SE compression with an extensional basin, the Alboran Sea. To explain this paradox, several models have been proposed, including the subduction process of a lithospheric plate. In this study a relocation of the seismicity of the area using a JHD algorithm for the period 1950–1995 has been performed, which shows a specific hypocentre pattern that is not compatible with plate subduction. In addition, the direction of the stresses acting in the area has been determined through a comprehensive study of all existing focal mechanisms, together with calculations for 19 new earthquakes with sufficient data to determine the focal solution. After considering all these data, the absence of intermediate shocks in the central part of the Alboran basin and the predominantly thrusting mechanisms at the borders of the basin, with pressure axes perpendicular to the front, we consider a delamination process as a possible mechanism acting in the area     

Upper Mantle Velocity Structure Estimated From Ps-Converted Wave Beneath the North-Eastern Japan Arc

Summary. The upper boundary of the descending oceanic plate is located by using PS -waves (converted from P to S at the boundary) in the Tohoku District, the north-eastern part of Honshu, Japan. the observed PS-P time data are well explained by a two-layered oceanic plate model composed of a thin low-velocity upper layer whose thickness is less than 10 km and a thick high-velocity lower layer; the upper and lower layers respectively have 6 per cent lower and 6 per cent higher velocity than the overriding mantle. the estimated location of the upper boundary is just above the upper seismic plane of the double-planed deep seismic zone. This result indicates that events in the upper seismic plane, at least in the depth range from 60 to 150 km, occur within the thin low-velocity layer on the surface of the oceanic plate.     

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.     

Causes of spatially variable tectonic subsidence in the Miocene Bermejo Foreland Basin, Argentina

ABSTRACT Tectonic subsidence in the 20–9 Ma Bermejo basin resulted from spatially variable crustal loading on a lithosphere of spatially variable strength (e.g. elastic thickness). Reconstruction of the crustal loads added between 20 and 9 Ma, and assessment of the effects of these loads on an elastic, isotropic lithosphere confirm this hypothesis. Elastic models effectively explain tectonic subsidence east of the Iglesia–Calingasta basin, but west of it crustal loads were locally compensated. Elastic models also prove that the 20–9 Ma Frontal Cordillera loading is of no importance in the mechanical system of the Bermejo basin. 2D and 3D elastic models of a uniformly strong lithosphere under 20–9 Ma crustal loads corrected for post‐9 Ma erosion successfully replicate the 9 Ma Bermejo basin's proximal palaeotopography. However, they fail to replicate the 9 Ma basin's medial and distal palaeotopography. A 3D finite element model of a lithosphere with bimodal strength (weak below the Bermejo basin and west of the Precordillera, and strong below the Precordillera and east of the Valle Fértil lineament) successfully replicates the 9 Ma basin's palaeotopography. That variable strength model introduces a southward decrease in the wavelength of flexural deformation, which results in a basin that narrows southward, consistent with the 9 Ma Bermejo basin. The preferred 9 Ma lithospheric strength distribution is similar to the present lithospheric strength field derived from gravity data, suggesting that the bimodal strength signature was retained throughout the entire basin's evolution. Late Miocene flattening of the subducting slab, tectonic change to a broken foreland, or deposition of a thick (～8–10 km) sedimentary cover did not affect the strength of the lithosphere underlying the Bermejo basin. The long‐term bimodal strength field does not correlate with the documented thickness of the seismogenic crust.     

Two-dimensional modelling of subduction zone anisotropy with application to southwestern Japan

We present a series of 2-D numerical models of viscous flow in the mantle wedge induced by a subducting lithospheric plate. We use a kinematically defined slab geometry approximating the subduction of the Philippine Sea plate beneath Eurasia. Through finite element modelling we explore the effects of different rheological and thermal constraints (e.g. a low-viscosity region in the wedge corner, power law versus Newtonian rheology, the inclusion of thermal buoyancy forces and a temperature-dependent viscosity law) on the velocity and finite strain field in the mantle wedge. From the numerical flow models we construct models of anisotropy in the wedge by calculating the evolution of the finite strain ellipse and combining its geometry with appropriate elastic constants for effective transversely isotropic mantle material. We then predict shear wave splitting for stations located above the model domain using expressions derived from anisotropic perturbation theory, and compare the predictions to ∼500 previously published shear wave splitting measurements from seventeen stations of the broad-band F-net array located in southwestern Japan. Although the use of different model parameters can have a substantial effect on the character of the finite strain field, the effect on the average predicted splitting parameters is small. However, the variations with backazimuth and ray parameter of individual splitting intensity measurements at a given station for different models are often different, and rigorous analysis of details in the splitting patterns allows us to discriminate among different rheological models for flow in the mantle wedge. The splitting observed in southwestern Japan agrees well with the predictions of trench-perpendicular flow in the mantle wedge along with B-type olivine fabric dominating in a region from the wedge corner to about 125 km from the trench.     

气候和地形对米老排人工林生长和材质的影响

比较分析了米老排人工林胸径和树高生长以及木材品质在不同气候、不同地形条件下的表现差异，结果表明：相同地形条件下生长在南亚热带的米老排人工林林分胸径和树高以及木材密度、顺纹抗压强度和抗弯强度大于生长在中亚热带的，而木材尺寸稳定性小于生长在中亚热带的。相同气候条件下，山谷中的米老排人工林林分胸径和树高以及木材尺寸稳定性大于山脊上的，木材密度、顺纹抗压强度和抗弯强度则小于山脊上的。差异显著性t检验表明：气候和地形对米老排人工林林分胸径和树高影响均极显著，对米老排人工林木材密度、顺纹抗压强度和抗弯强度影响极显著或显著；地形对米老排人工林差异干缩影响极显著或显著，气候对米老排人工林差异干缩影响不显著。综合考虑，要获得优质速生的米老排木材，宜选择南亚热带的山谷进行人工林建设。     

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.     

Anisotropy: a pervasive feature of fault zones?

Summary. Current models of the structure of an active fault zone recognize two important subdivisions – an upper zone, extending to mid-crustal depths, in which processes associated with brittle fracture and friction dominate the fault behaviour, and a lower zone, extending into the mantle, within which stresses may be relieved by ductile flow. Anisotropy directly or indirectly induced by stress might occur throughout the fault zone, especially if caused by some form of stress-induced crack alignment. Dilatancy associated with high stresses is likely to be a very localized phenomenon in the vicinity of high strength regions (asperities), but alignments caused by subcritical crack growth at low stress and strain rate ( extensive-dilatancy anisotropy ) could give rise to anisotropy throughout the fault region.     

A study of shallow global mantle flow due to the accretion and subduction of lithospheric plates

Summary. Models of shallow, global mantle circulation due to the accretion and subduction of lithospheric plates are formulated as potential theory problems on a sphere. Subducting and accreting plate boundaries represent sources and sinks respectively for the sublithospheric flow. Solutions, which are obtained by finite difference approximations, give the instantaneous flow velocities within the asthenosphere compatible with plate boundaries and relative plate motions. Results are presented for present-day plate boundaries and relative plate motions for the case of a uniform viscosity asthenosphere and for that of a low viscosity zone at the base of the lithosphere. These results are discussed in terms of available geophysical data. Some of the implications of a shallow, mantle-wide circulation are also considered.     

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.     

Simple analytic model for subduction zone thermal structure

A new analytic model is presented for the thermal structure of subduction zones. It applies to the deeper regions of a subduction zone, where the overriding mantle is no longer rigid but flows parallel to the slab surface. The model captures the development of one thermal boundary layer out into the mantle wedge, and another into the subducting slab. By combining this model with the analytic model of Royden (1993a , b ), which applies to regions in which the overriding plate is rigid, a nearly complete analytic model for the thermal structure of a steady-state subduction zone can be achieved. A good agreement is demonstrated between the output of the combined analytic model and a numerical finite element calculation. The advantages of this analytic approach include (1) efficiency (only limited computing resources are needed); (2) flexibility (non-linear slab shape, and processes such as erosion, and shear heating are easily incorporated); and (3) transparency (the effect of changes in input variables can be seen directly).     

Free-surface formulation of mantle convection—II. Implication for subduction-zone observables

Viscous and viscoelastic models for a subduction zone with a faulted lithosphere and internal buoyancy can self-consistently and simultaneously predict long-wavelength geoid highs over slabs, short-wavelength gravity lows over trenches, trench-forebulge morphology, and explain the high apparent strength of oceanic lithosphere in trench environments. The models use two different free-surface formulations of buoyancy-driven flows (see, for example, Part I): Lagrangian viscoelastic and pseudo-free-surface viscous formulations. The lower mantle must be stronger than the upper in order to obtain geoid highs at long wavelengths. Trenches are a simple consequence of the negative buoyancy of slabs and a large thrust fault, decoupling the overriding from underthrusting plates. The lower oceanic lithosphere must have a viscosity of less than to²⁴ Pa s in order to be consistent with the flexural wavelength of forebulges. Forebulges are dynamically maintained by viscous flow in the lower lithosphere and mantle, and give rise to apparently stiffer oceanic lithosphere at trenches. With purely viscous models using a pseudo-free-surface formulation, we find that viscous relaxation of oceanic lithosphere, in the presence of rapid trench rollback, leads to wider and shallower back-arc basins when compared to cases without viscous relaxation. Moreover, in agreement with earlier studies, the stresses necessary to generate forebulges are small (∼ 100 bars) compared to the unrealistically high stresses needed in classic thin elastic plate models.     

Asthenospheric counterflow: a kinematic model

Summary. Present-day plate motions imply that about 240 km³ of oceanic lithosphere is created by sea-floor spreading and destroyed by subduction per year. A greater volume of asthenosphere will be dragged along by plate motions. Given the fluxes generated at plate boundaries, the horizontal direction and net rate of counterflow required to maintain mass balance is determined globally by a simple analytical model. Time-dependent calculations indicate that the motions are approximately valid in the hotspot reference frame over the past 5 Myr. Under most plates, the model return flow is opposite to the lithospheric motion in the hotspot frame. The counterflow dominates the resisting stresses to plate motion, so driving force models based on plate drag alone are not valid where the directions of plate motion and counterflow differ. The most marked departure of the two directions is under the North American plate. The model counterflow directions indicate that the sources of mantle hotspots are not located within the asthenosphere. Model flux balances demonstrate exchange of material between asthenospheric reservoirs located beneath different plates. Suggestions of southward asthenospheric motion under the North Atlantic, based on physical features around Iceland and strontium isotope geochemistry, are consistent with the direction of flow predicted by the model.     

Lithospheric structure of the continent–continent collision zone: eastern Turkey

We infer the lithospheric structure in eastern Turkey using teleseismic and regional events recorded by 29 broad-band stations from the Eastern Turkey Seismic Experiment (ETSE). We combine the surface wave group velocities (Rayleigh and Love) with telesesimic receiver functions to jointly invert for the S -wave velocity structure, Moho depth and mantle-lid (lithospheric mantle) thickness. We also estimated the transverse anisotropy due to Love and Rayleigh velocity discrepancies. We found anomalously low shear wave velocities underneath the Anatolian Plateau. Average crustal thickness is 36 km in the Arabian Plate, 44 km in Anatolian Block and 48 km in the Anatolian Plateau. We observe very low shear wave velocities at the crustal portion (30–38 km) of the northeastern part of the Anatolian Plateau. The lithospheric mantle thickness is either not thick enough to resolve it or it is completely removed underneath the Anatolian Plateau. The shear velocities and anisotropy down to 100 km depth suggest that the average lithosphere–asthenosphere boundary in the Arabian Plate is about 90 and 70 km in Anatolian block. Adding the surface waves to the receiver functions is necessary to constrain the trade-off between velocity and the thickness. We find slower velocities than with the receiver function data alone. The study reveals three different lithospheric structures in eastern Turkey: the Anatolian plateau (east of Karliova Triple Junction), the Anatolian block and the northernmost portion of the Arabian plate. The boundary of lithospheric structure differences coincides with the major tectonic boundaries.