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.     

Stress and Flow beneath Island Arcs

Summary. The flow pattern, stress distribution, topography, and gravity anomalies were computed from numerical models having density and viscosity distributions resemblant to the Aleutian arc. The results were compatible with the hypothesis that the excess density of the slab drives its descent and that hydrodynamic forces are responsible for topographic and gravity highs over the outer rise seaward of the trench and the frontal arc and lows over the trench. In models with simple distributions of rheological parameters, the force from the slab was transmitted directly upward producing a negative gravity anomaly over the arc. Material with low resistance to flow was needed along the fault plane above the slab or within the crust of the frontal arc and within the wedge of asthenosphere above the slab to reduce that force and to allow the horizontal lithosphere to move with the slab. Models with the resistance to flow thus reduced had outer rises, deep trenches, horizontal tension seaward of the trench, horizontal compression under the trench, and downdip tension in the slab. Free air gravity anomalies, which are the sum of between deflections of the free surface due to hydrodynamic forces and direct attractions from the masses driving the flow, were not fit excellently by any of the models, in part because the coarse grid used precluded accurate representation of the fault zone above the slab and the frontal arc. An alternate to the hypothesis that about 5 kb of stress on the fault plane is needed to produce an outer rise is offered by these models. Shear stress between the slab and the island arc was always below 700 bars in the more successful models if the density distribution was scaled to match the topography of the trench. This is much less than the 2000 bars stresses needed if frictional heating causes island arc volcanism.     

Gravity constraints on the dynamics of the crust–mantle system during Calabrian subduction

The thermomechanic evolution of the lithosphere–upper mantle system during Calabrian subduction is analysed using a 2-D finite element approach, in which the lithosphere is compositionally stratified into crust and mantle. Gravity and topography predictions are cross-checked with observed gravity and topography patterns of the Calabrian region. Modelling results indicate that the gravity pattern in the arc-trench region is shaped by the sinking of light material, belonging to both the overriding and subduction plates. The sinking of light crustal material, up to depths of the order of 100–150 km is the ultimate responsible for the peculiar gravity signature of subduction, characterized by a minimum of gravity anomaly located at the trench, bounded by two highs located on the overriding and subducting plates, with a variation in magnitude of the order of 200 mGal along a wavelength of 200 km, in agreement with the isostatically compensated component of gravity anomaly observed along a transect crossing the Calabrian Arc, from the Tyrrhenian to the Ionian Seas. The striking agreement between the geodetic retrieved profiles and the modelled ones in the trench region confirms the crucial role of compositional stratification of the lithosphere in the subduction process and the correctness of the kinematic hypotheses considered in our modelling, that the present-day configuration of crust–mantle system below the Calabrian arc results from trench's retreat at a rate of about 3 cm yr⁻¹, followed by gravitational sinking of the subducted slab in the last 5 Myr.     

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.     

Double seismic zones and stresses of intermediate depth earthquakes

Summary. Data from Japanese local seismograph networks suggest that the stresses in double seismic zones are in-plate compression for the upper zone and in-plate tension for the lower zone; the stresses do not necessarily appear to be down-dip. It may therefore be possible to identify other double seismic zones on the basis of data which indicate that events with differing orientations of in-plate stresses occur in a given segment of slab.
A global survey of published focal mechanisms for intermediate depth earthquakes suggests that the stress in the slab is controlled, at least in part, by the age of the slab and the rate of convergence. Old and slow slabs are under in-plate tensile stresses and the amount of in-plate compression in the slab increases with increasing convergence rate or decreasing slab age. Young and fast slabs are an exception to this trend; all such slabs are down-dip tensile. Since these slabs all subduct under continents, they may be bent by continental loading. Double seismic zones are not a feature common to all subduction zones and are only observed in slabs which are not dominated by tensile or compressive stresses.
Unbending of the lithosphere and upper mantle phase changes are unlikely to be the causes of the major features of double zones, although they may contribute to producing some of their characteristics. Sagging or thermal effects, possibly aided by asthenospheric relative motion, may produce the local deviatoric stresses that cause double zones.     

Modelling rates and distribution of subsidence due to dynamic topography over subducting slabs: is it possible to identify dynamic topography from ancient strata?

Dynamic topography formed over subducting oceanic lithosphere has been proposed as a mechanism to explain certain otherwise anomalous long-wavelength patterns of subsidence inferred from ancient strata. Forward modelling of mantle flow in response to a subducting slab predicts amplitudes and distributions of dynamic topography that may occur due to various subducting slab geometries and histories. Plotting calculated dynamic topographies at a point against time produces tectonic subsidence curves. These subsidence curves show features such as evolution from convex to concave shape, amplitudes up to ~2000 m, subsidence rates up to ~220 m Myr⁻¹, and a general decrease in subsidence amplitude away from the subduction zone, over a distance of ~2000 km. On many convergent continental margins, dynamic topography is likely to be superimposed on other subsidence mechanisms. In back-arc basins, subsidence due to dynamic topography should be distinguishable from that due to extensional tectonics based simply on the temporal subsidence evolution expressed in the subsidence curve shapes. In a foreland basin setting, comparing dynamic topography models with forward models of flexural loading suggest the two processes can generate similar temporal subsidence patterns, but that dynamic topography causes subsidence over significantly greater wavelengths. Matches between calculated subsidence due to dynamic topography and backstripped subsidence patterns from Upper Cretaceous strata of the Western Interior Basin, USA, support the hypothesis that a long-wavelength 'background subsidence' was caused by dynamic topography.     

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.     

Stress and temperature in subduction shear zones: Tonga and Mariana

Summary. Because there is secondary sea-floor spreading in the Tonga and Mariana subduction systems, the island arcs are separate plates. Horizontal forces on the two sides of the arc must balance, and the maximum force on the back-arc side can be calculated from a lithostatic ridge model. This, in combination with gravity data, allows calculation of the average shear stress in the top 100 km of the subduction shear zone. Stress in Tonga is 220±100 bar, and in the Mariana it is 165±75 bar. These low stresses are probably made possible by a fluid pore pressure almost equal to the least compressive stress.
Knowledge of stress allows approximate calculation of temperature in the shear zone by integration of a single differential equation. These temperatures are too low to activate most dehydration reactions in the subducted crust. As it approaches the volcanic line, this crust is at 150–350°C in Tonga and 150–300°C in the Mariana. Shear melting of the crust is ruled out, and conductive melting of the slab by contact with the asthenosphere meets with geochemical objections. Magmas in these systems are probably produced by partial melting of asthenosphere, triggered by a sudden release of water from the slab.     

Late Cenozoic tectono‐stratigraphic sequences of the Crotone Basin: insights on the geodynamic history of the Calabrian arc and Tyrrhenian Sea

The Crotone Basin was generated in the late Cenozoic as a forearc basin of the Ionian arc‐trench system. New data are gained through detailed field mapping, high‐resolution stratigraphic analysis of a key area and examination of offshore well data and seismic reflection profiles. Major unconformities divide the basin fill into major sequences, which reveal a three‐stage internal organization thought to reflect geodynamic events of the Calabrian arc and backarc area closely. The first stage is characterized by extensional block faulting and uplift followed by rapid drowning during high subsidence and transtension in the basin along a major NNW‐ to NW‐striking fault system. This stage is interpreted to reflect resumption of rollback after an episode of slab tearing triggered by transitory docking of continental lithosphere in the trench. The initial uplift is inferred to reflect decoupling and rebound after the transitory coupling phase. The second stage is characterized by increased subsidence and continued extension/transtension. This trend presumably reflects a decreasing rate of rollback resulting from a tendency towards viscous coupling after acceleration of slab downwelling. The third stage is characterized by short‐lived transpression along major shear zones and local inversion of former basins. This is inferred to reflect entrance into the trench of buoyant continental lithosphere, resulting in significant deceleration of slab rollback and consequently a break in, or slowing of, backarc extension, and predominance of the effects of compression related to Africa–Europe convergence. Overall, the above evolution resulted in the formation of a progressively narrower and rapidly retreating slab, inducing extreme rates of backarc extension, and may have played a critical role in determining the intermittent nature of the backarc rifting.     

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.     

Effects of active crustal movements on thermal structure in subduction zones

In young suduction zones we observe steady uplift of island arcs. The steady uplift of island arcs is always accompanied by surface erosion. The long duration of uplift and erosion effectively transports heat at depth to shallower parts by advection. If the rates of uplift and erosion are sufficiently large, such a process of heat transportation will strongly affect thermal structure in subduction zones. First, we quantitatively examine the effects of uplift and erosion on thermal structure by using a simple 1-D heat conduction model, based on the assumption that the initial thermal state is in equilibrium. The results show that temperature increase, Δ T  , due to uplift and erosion can be approximately evaluated by Δ T  = ν _e tβ at depth, where ν _e is the rate of uplift (erosion), t is the duration of uplift (erosion), and β is the gradient of the geotherm in the initial state. Next, considering the effects of vertical crustal movements such as uplift and erosion in island arcs and subsidence and sedimentation in ocean trenches, in addition to the effects of radioactive heat generation in the crust, frictional heating at plate boundaries and accretion of oceanic sediments to overriding continental plates, we numerically simulate the evolution process of the thermal structure in subduction zones. The result shows that the temperature beneath the island arc gradually increases as a result of uplift and erosion as plate subduction progresses. Near the ocean trench, on the other hand, the low-temperature region gradually expands as a result of sedimentation and accretion in addition to direct cooling by the cold descending slab. The surface heat flow expected from this model is low in fore-arc basins, high in island arcs and moderately high in back-arc regions.     

The palaeomagnetic field as inferred from magnetic studies on magmatic arc zones

Summary. Processes involved in the generation of arc maginatism, which are associated with the evolution of subduction zones, may in certain cases be able to record the variations of the Earth's magnetic field with time. A mechanism is suggested which may generate lineated magnetic anomaly patterns, similar to those observed over oceanic areas, with bands of alternating normal and reverse polarity parallel to the subduction zone. It is suggested that magmatic arc rocks acquire remanent magnetizations creating a zone of normal or reverse polarity in the magmatic arc zone, and if the geometric arrangement of plate subduction changes, i.e. the region of primary magma generation is displaced normal to the trench by changes of either the Wadati—Benioff zone dip angle or the trench position, then active arc magmatism is displaced accordingly, creating another magnetic anomaly zone. An important factor is the rate of displacement of arc magnatism with time; estimates for the south-western North America magmatic arc gives a value of about 1.2 cm yr^−l for the interval 100–55 Myr ago, which is comparable to sea-floor spreading rates. The elongated patterns of positive and negative magnetic anomalies, trenchward of the Japan trench and the Kurile—Kamchatka trench may have been produced by this process. Elongated intense magnetic anomalies are also observed in other magmatic arc assemblages, such as in western North America. Processes which may obscure these lineated anomaly patterns include, e.g. tectomc rotations within the magmatic arc zone, changes in thermal conditions and igneous activity, remagnetization events and decay of remanent magnetism. The anomalies may be related to, and better preserved by, intrusive rocks or buried rocks.     

Imaging mantle transition zone thickness with SdS-SS finite-frequency sensitivity kernels

We invert differential SdS-SS traveltime residuals measured from stacked waveforms and finite-frequency sensitivity kernels for topography on the 410- and 660-km discontinuities. This approach yields higher resolution images of transition zone thickness than previous stacking methods, which simply average/smooth over topographic features. Apparent structure measured using simple stacking is highly dependent upon the bin size of each stack. By inverting for discontinuity topography with a variety of bin sizes, we can more accurately calculate the true structure. The inverted transition zone model is similar to simple stack models with an average thickness of 242 km, but the lateral variations in thickness are larger in amplitude and smaller in scale. Fast seismic velocities in 3-D mantle models such as SB4L18 correlate with areas of thicker transition zone. The elongated curvilinear regions of thickened transition zone that occur near subduction zones are narrow and high amplitude, which suggests relatively little lateral spreading and warming of subducted lithosphere within the transition zone. The anomalously thin transition zone regions are laterally narrow, and not broadly continuous. If these variations in transition zone thickness are interpreted as thermal in nature, then this model suggests significant temperature variations on small lateral scales.     

A critical assessment of viscous models of trench topography and corner flow

Summary. We obtain stresses for Newtonian viscous flow in simple geometries (e.g. corner flow, bending flow) in order to study the effect of imposed velocity boundary conditions. Stress for a delta function velocity boundary condition decays as 1/ r ²; for a step function velocity, stress goes as 1/ r ; for a discontinuity in curvature, the stress singularity is logarithmic. For corner flow, which has a discontinuity of velocity at a certain point, the corresponding stress has a 1/ r singularity. However, for a more realistic circular-slab model, the stress singularity becomes logarithmic. Thus the stress distribution is very sensitive to the boundary conditions, and in evaluating the applicability of viscous models of trench topography it is essential to use realistic geometries.
Topography and seismicity data from northern Honshu, Japan, were used to construct a finite element model, with flow assumed constant speed and tangent to the top of the grid, for both Newtonian and non-Newtonian flow (power law 3 rheology). Normal stresses at the top of the grid are compared to the observed trench topography. There is poor agreement. Purely viscous models of subducting slabs with simple, geometrically consistent velocity boundary conditions do not predict normal stress patterns compatible with observed topography. Elasticity and plasticity appear to be important in determining trench topography.     

Geometry and brittle deformation of the subducting Nazca Plate, Central Chile and Argentina

We use data from the Chile Argentina Geophysical Experiment (CHARGE) broad-band seismic deployment to refine past observations of the geometry and deformation within the subducting slab in the South American subduction zone between 30°S and 36°S. This region contains a zone of flat slab subduction where the subducting Nazca Plate flattens at a depth of ∼100 km and extends ∼300 km eastward before continuing its descent into the mantle. We use a grid-search multiple-event earthquake relocation technique to relocate 1098 events within the subducting slab and generate contours of the Wadati-Benioff zone. These contours reflect slab geometries from previous studies of intermediate-depth seismicity in this region with some small but important deviations. Our hypocentres indicate that the shallowest portion of the flat slab is associated with the inferred location of the subducting Juan Fernández Ridge at 31°S and that the slab deepens both to the south and the north of this region. We have also determined first motion focal mechanisms for ∼180 of the slab earthquakes. The subhorizontal T -axis solutions for these events are almost entirely consistent with a slab pull interpretation, especially when compared to our newly inferred slab geometry. Deviations of T -axes from the direction of slab dip may be explained with a gap within the subducting slab below 150 km in the vicinity of the transition from flat to normal subducting geometry around 33°S.     

Crustal and upper-mantle structure in the Eastern Mediterranean from the analysis of surface wave dispersion curves

The dispersive properties of surface waves are used to infer earth structure in the Eastern Mediterranean region. Using group velocity maps for Rayleigh and Love waves from 7 to 100 s, we invert for the best 1-D crust and upper-mantle structure at a regular series of points. Assembling the results produces a 3-D lithospheric model, along with corresponding maps of sediment and crustal thickness. A comparison of our results to other studies finds the uncertainties of the Moho estimates to be about 5 km. We find thick sediments beneath most of the Eastern Mediterranean basin, in the Hellenic subduction zone and the Cyprus arc. The Ionian Sea is more characteristic of oceanic crust than the rest of the Eastern Mediterranean region as demonstrated, in particular, by the crustal thickness. We also find significant crustal thinning in the Aegean Sea portion of the backarc, particularly towards the south. Notably slower S -wave velocities are found in the upper mantle, especially in the northern Red Sea and Dead Sea Rift, central Turkey, and along the subduction zone. The low velocities in the upper mantle that span from North Africa to Crete, in the Libyan Sea, might be an indication of serpentinized mantle from the subducting African lithosphere. We also find evidence of a strong reverse correlation between sediment and crustal thickness which, while previously demonstrated for extensional regions, also seems applicable for this convergence zone.     

New insight into the crust and upper mantle structure under Alaska

To better understand the seismic structure of the subducting Pacific plate under Alaska, we determined the three-dimensional P-wave velocity structure to a depth of approximately 200 km beneath Alaska using 438,146 P-wave arrival times from 10,900 earthquakes. In this study an irregular grid parameterization was adopted to express the velocity structure under Alaska. The number of grid nodes increases from north to south in the study area so that the spacing between grid nodes is approximately the same in the longitude direction. Our results suggest that the subducting Pacific slab under Alaska can be divided into three different parts based on its geometry and velocity structure. The western part has features similar to those in other subduction zones. In the central part a thick low-velocity zone is imaged at the top of the subducting Pacific slab beneath north of the Kenai Peninsula, which is believed to be most likely the oceanic crust plus an overlying serpentinized zone and the coupled Yakutat terrane subducted with the Pacific slab. In the eastern part, significant high-velocity anomalies are visible to 60–90 km depth, suggesting that the Pacific slab has only subducted down to that depth.     

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).     

Lithoprobe seismic reflection profiling across Vancouver Island: results from reprocessing

Summary. Multichannel seismic reflection sections recorded across Vancouver Island have revealed two extensive zones of deep seismic reflections that dip gently to the northeast, and a number of moderate northeasterly dipping reflections that can be traced to the surface where major faults are exposed. Based on an integrated interpretation of these data with information from gravity, heat flow, seismicity, seismic refraction, magnetotelluric and geological studies it is concluded that the lower zone of gently dipping reflections is due to underplated oceanic sediments and igneous rocks associated with the current subduction of the Juan de Fuca plate, and that the upper zone represents a similar sequence of accreted rocks associated with an earlier episode of subduction. The high density/high velocity material between the two reflection zones is either an underplated slab of oceanic lithosphere or an imbricated package of mafic rocks. Reprocessing of data from two of the seismic lines has produced a remarkable image of the terrane bounding Leech River fault, with its dip undulating from >60° near the surface to 20° at 3 km depth and ∼38° at 6 km depth.     

Stresses due to phase changes in subduction zones and an empirical equation of state for the mantle

Summary. An empirical equation of state, assuming mineralogical equilibrium, is developed for the top 700 km of the mantle. Assuming a uniform viscosity, this equation of state is used to show that the stresses due to the changes in phase induced in a descending lithospheric plate in a subduction zone are an order of magnitude larger than those due to the negative buoyancy of the slab in the asthenosphere. The stresses predicted are well within the power law creep region for likely mantle materials and so the effective viscosity will vary within the slab. Consequently the stresses will be smaller than those of 7.0 × 10⁸N/m² obtained here using uniform viscosities. These stresses are relatively compressional near the sides of the slab and tensional in the centre.