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.     

The dynamical origin of subduction zone topography

Summary. Subduction zones are expressed topographically by long linear oceanic trenches flanked by a low outer rise on the seaward side and an island arc on the landward side. This topographic structure is reflected in free air gravity anomalies, suggesting that much of the topography originates from dynamical forces applied at the base of the crust. We have successfully reproduced the general topographic features of subduction zones by supposing that the stresses generated by the bending of the viscous lower lithosphere as it subducts are transmitted through the thin elastic upper portion of the lithosphere. The trench is due to a zone of extensional flow (associated with low pressure) in the upper part of the viscous lithosphere.
The stresses in the subducting slab are computed using a finite element technique, assuming a Maxwell viscoelastic constitutive relation. Various dips (10 to 90°) were investigated, as well as depth dependent and non-Newtonian (power law, n = 3) viscosities. Observed subduction zone dimensions are well reproduced by these models. The effective viscosity required at mid-depth in the lithosphere is about 6 × 10²² P. This low value is probably due to the stress dependence of the effective viscosity. However, these models also show that the topography of the subduction zone depends primarily upon the geometry of the subducting slab (dip, radius of curvature of the bend) rather than upon its rheology. Shear stresses beneath the trench reach maxima of approximately 50 MPa. An interesting feature of some solutions is a dynamically supported bench or platform between the trench and island arc.     

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.     

Post-seismic reloading and temporal clustering on a single fault

Geological studies show evidence for temporal clustering of large earthquakes on individual fault systems. Since post-seismic deformation due to the inelastic rheology of the lithosphere may result in a variable loading rate on a fault throughout the interseismic period, it is reasonable to expect that the rheology of the non-seismogenic lower crust and mantle lithosphere may play a role in controlling earthquake recurrence times. We study this phenomenon using a 2-D, finite element method continuum model of the lithosphere containing a single strike-slip fault. This model builds on a previous study using a 1-D spring-dashpot-slider analogue of a single fault system to study the role of Maxwell viscoelastic relaxation in producing non-periodic earthquakes. In our 2-D model, the seismogenic portion of the fault slips when a predetermined yield stress is exceeded; stress accumulated on the seismogenic fault is shed to the viscoelastic layers below and recycled back to the seismogenic fault through viscoelastic relaxation. We find that random variation of the fault yield stress from one earthquake to the next can cause the earthquake sequence to be clustered; the amount of clustering depends on a non-dimensional number, W , called the Wallace number defined as the standard deviation of the randomly varied fault yield stress divided by the effective viscosity of the system times the tectonic loading rate. A new clustering metric based on the bimodal distribution of interseismic intervals allows us to investigate clustering behaviour of systems over a wide range of model parameters and those with multiple viscoelastic layers. For models with   W ≥ 1  clustering increases with increasing W , while those with   W ≤ 1  are unclustered, or quasi-periodic.     

A kinematic viscoelastic model of the San Francisco earthquake of 1906

Summary. We construct a model of the San Andreas fault zone based on a rectangular fault in an elastic layer overlying a viscoelastic half-space. We alllow both steady and episodic aseismic slip at depth on the fault as well as a large-scale relative plate driving force. We use the model to explain the aseismic changes in geodetic triangulation angles observed during the 40 years following the 1906 San Francisco earthquake. The most important results are that viscoelastic relaxation can explain the data very well, and that the driving force of relative plate motion can be characterized by a horizontal distance scale perpendicular to the plate boundary of hundreds of kilometres.     

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.     

State of stress in the Southern Tyrrhenian subduction zone from fault-plane solutions

In this paper we present revised locations and original focal mechanisms computed for intermediate and deep earthquakes that occurred within the Southern Tyrrhenian subduction zone between 1988 and 1994, in order to improve our knowledge of the state of stress for this compressional margin. In particular, we define the stress distribution within a large portion of the descending slab, between 40 and about 450 km depth. The seismicity distribution reveals a continuous 40–50 km thick slab that abruptly increases its dip from subhorizontal in the Ionian Sea to a constant 70° dip in the Tyrrhenian. We computed focal mechanisms for events with magnitudes ranging from 2.7 and 5.7, obtaining the distribution of P - and T -axes for many events for which centroid moment tensor (CMT) solutions are not available, thus enabling the sampling of a larger depth range compared to previous studies. We define three portions of the slab characterized by different distributions of P - and T -axes. A general down-dip compression is found between 165 and 370 km depth, whereas in the upper part of the slab (40–165 km depth) the fault-plane solutions are strongly heterogeneous. Below 370 km the P -axes of the few deep events located further to the north have a shallower dip and are not aligned with the 70° dipping slab, possibly suggesting that they belong to a separated piece of subducted lithosphere. There is a good correspondence between the depth range in which the P -axes plunge closer to the slab dip (∼ 70°) and the interval characterized by the highest seismic energy release (190–370 km).     

Dynamic stress field of a kinematic earthquake source model with k-squared slip distribution

Source models such as the k -squared stochastic source model with k -dependent rise time are able to reproduce source complexity commonly observed in earthquake slip inversions. An analysis of the dynamic stress field associated with the slip history prescribed in these kinematic models can indicate possible inconsistencies with physics of faulting. The static stress drop, the strength excess, the breakdown stress drop and critical slip weakening distance D _c distributions are determined in this study for the kinematic k -squared source model with k -dependent rise time. Several studied k -squared models are found to be consistent with the slip weakening friction law along a substantial part of the fault. A new quantity, the stress delay, is introduced to map areas where the yielding criterion of the slip weakening friction is violated. Hisada's slip velocity function is found to be more consistent with the source dynamics than Boxcar, Brune's and Dirac's slip velocity functions. Constant rupture velocities close to the Rayleigh velocity are inconsistent with the k -squared model, because they break the yielding criterion of the slip weakening friction law. The bimodal character of D _c / D _tot frequency–magnitude distribution was found. D _c approaches the final slip D _tot near the edge of both the fault and asperity. We emphasize that both filtering and smoothing routinely applied in slip inversions may have a strong effect on the space–time pattern of the inferred stress field, leading potentially to an oversimplified view of earthquake source dynamics.     

A New Model for Heat Flow in Extensional Basins: Radiogenic Heat,Asthenospheric Heat,and the McKenzie Model

The McKenzie model proposed in 1978, which is widely used in calculating the thermal history of rift basins and other extensional basins, incorrectly assumes that all heat passing through the lithosphere originates below the lithosphere. In reality, heat from radiogenic sources within the lithosphere, especially in the upper crust, may represent more than half the heat flow at the top of basement. Thinning of the lithosphere during extension does indeed result in an increase of heat flowing from the asthenosphere, but this thinning also reduces the radiogenic heat from within the lithosphere. Because these two effects cancel to a large degree, the direct effects of lithospheric extension on heat flow at the top of basement are smaller than those predicted by the McKenzie model. Because of permanent loss of radiogenic material by lithospheric thinning, the heat flow at the top of basement long after rifting will be lower than the pre-rift heat flow.The McKenzie model predicts an instantaneous increase in heat flow during rifting. The Morgan model proposed in 1983, however, predicts a substantial time delay in the arrival of the higher heat flow from the asthenosphere at the top of basement or within sediments. Using the Morgan model, heat flow during the early stages of rifting will actually be lower than prior to rifting, because the time delay in the loss of radiogenic heat is less than the time delay in arrival of new heat from the asthenosphere.     

A simple model for thermal instability in the asthenosphere

Summary. Motion of the lithosphere over a low viscosity asthenosphere concentrates shear and thus energy dissipation in the asthenosphere. This heat source warms the asthenosphere and, in extreme circumstances, may lead to thermal instabilities. The conditions for thermal stability have been investigated by Melosh who supposed that constant stress acted on the plate, and by Yuen & Schubert who assumed constant velocity boundary conditions. In this paper we investigate a simple analytical model which behaves qualitatively like the more complex systems. This model reproduces the results of Melosh for constant stress and of Yuen & Schubert for constant velocity. The velocity—shear stress characteristic curve for this model shows three branches. The stability of solutions on each branch is a function of the boundary conditions, whether constant stress or constant velocity. The simplicity of the model allows us to investigate stability when neither constant stress nor constant velocity apply and to study the structure of the solutions as these limits are approached. A relation between the velocity of a plate and the driving force is constructed. A loading-line analysis specifies the actual stress and velocity of the plate. Although the solutions are unique for many combinations of the loading-line parameters, there is a region of multiple solutions. These solutions exhibit the characteristics of a 'cusp catastrophe' both a low velocity and a high velocity state are stable, while an intermediate state is unstable. Continental lithosphere may lie in this region, leading to epirogenic movements when the plate changes its velocity with respect to the mantle. Oceanic lithosphere almost certainly moves in the low velocity state.     

Upper mantle heterogeneities beneath Central Europe

Summary. An inversion of ISC travel-time data from selected earthquakes in the distance range 30°-90° to 53 stations in Central Europe has been used to model velocity down to 600 km depth. The model explains 0.1–0.2s of the residuals, as for other array studies, leaving 0.5 s unexplained as noise. The uppermost 100 km of the mantle and crust contains inhomogeneities that correlate remarkably well with the geology. This may be due to deep-seated thermal anomalies or, in some areas, to delays introduced by passage of the rays through sedimentary cover. The deeper anomalies are smaller and unrelated to those in the lithosphere, which suggests that the asthenosphere is decoupled from the rigid lithosphere. The structure at 600 km depth is again quite inhomogeneous and might be due to undulations of the 650 km discontinuity. The models show some suggestion of a high velocity slab trending from east to west beneath the Alps.     

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.     

High-frequency radiation from crack (stress drop) models of earthquake faulting

We present a theory for the radiation of high-frequency waves by earthquake faults. We model the fault as a planar region in which the stress drops to the kinematic friction during slip. This model is entirely equivalent to a shear crack. For two-dimensional fault models we show that the high frequencies originate from the stress and slip velocity concentrations in the vicinity of the fault's edges. These stress concentrations radiate when the crack expands with accelerated motion. The most efficient generation of high-frequency waves occurs when the rupture velocity changes abruptly. In this case, the displacement spectrum has an ω^-2 behaviour at high frequencies. The excitation is proportional to the intensity of the stress concentration near the crack tips and to the change in the focusing factor due to rupture velocity. We extend these two-dimensional results to more general three-dimensional fault models in the case when the rupture velocity changes simultaneously on the rupture front. Results are similar to those described for two-dimensional faults. We apply the theory to the case of a circular fault that grows at constant velocity and stops suddenly. The present theory is in excellent agreement with a numerical solution of the same problem.
Our results provide upper bounds to the high-frequency radiation from more realistic models in which rupture velocity does not change suddenly. The ω^-2 is the minimum possible decay at high frequencies for any crack model of the source.     

State of stress in the oceanic lithosphere in response to loading

Summary. Flexure studies of the oceanic lithosphere constrained by bathymetry and gravity data suggest that the lithosphere behaves elastically over geological time-scales. For loads to be supported, however, large bending stresses (approaching 10 kb in some cases) are required at the top and bottom of the elastic plate.
These stress-differences can be significantly reduced by introducing more complex rheologies: we propose a model of layered lithosphere, consisting of a purely elastic upper layer, a transition zone with viscosity varying with depth and a perfectly plastic lower layer. The transition layer is grossly centred at the bottom of the elastic plate. Such a model results in a noticeable reduction of stress differences; reaching 60 per cent for flow laws representing creep mechanisms in olivine. When applied to a number of seamount loads, this model leads to maximum stress-differences which do not exceed 1–2kb.
The approach used in this study allows us to follow stress relaxation over time. Taking account of the thermal cooling of the lithosphere, we show that the elastic thickness of the lithosphere is stabilized after a given time, while the time required for stabilization is found to be of the order 5—6 per cent of the age of the lithosphere at the date of loading.     

A possible rupture process of slow earthquakes on a frictional fault

Summary. A possible mechanism for the occurrence of slow earthquakes is investigated by calculating numerical solutions for the dynamical rupture process on a quasi-three-dimensional fault with heterogeneous frictional strengths. Experimental friction laws for the dependence of sliding frictional stress on slip velocity, which are based on the cohesive properties of fault asperities, are taken into considerations.
It is found that the applied stress does not drop very rapidly with time and the rupture velocity remarkably decreases as the dependence on slip-velocity becomes smaller. These deceleration effects for the rupture propagation are greatly enhanced with increasing heterogeneities in the distribution of frictional strength and as the initial shear stress has lower levels with respect to the average strength. For these cases, the growth of rupture is extremely slow in a nucleus region with the dimension as large as 10 times the initial rupture length, and gains a terminal velocity dependent on the above factors. The displacement-time function becomes noticeably extended in these cases, and indicates a stick—slip-like phenomena in the extended time interval for a strongly heterogeneous fault.
It seems that these results could explain the characteristic features of slow earthquakes.     

Source mechanism of the deep Colombian earthquake of 1970 July 31 from the free oscillation data

Summary. The method proposed by Mendiguren to determine the source parameters from free oscillation data is applied to the 1970 July 31 deep Colombian earthquake. The results indicate a source propagating horizontally for about 150 km along the lithosphere and cutting across its width. The slab behaves as a guide for source propagation. The horizontal propagation velocity is determined as 3.8 km/s. The intensity of the source grew proportionately to the second power of the propagation distance. This rate of source intensity growth may be interpreted either by a fan-shaped fault model or by a cone-shaped volume source. The average slip and stress drop are estimated as 360 cm and 300 bar for the fault model. For the volume source model the transformational shear strain and stress are estimated as 11 × 10⁻⁵ and 160 bar. There is no evidence of a double couple radiation preceding the P origin time. It is shown that the isotropic and deviatoric components of the moment tensor cannot be uniquely resolved when only observations of a single mode are available. It is observed that, from a statistical basis, the available ₀ S_n data for Colombian shock can be equally well explained by a pure deviatoric source model or by a source model including an isotropic component. Numerical experiments indicate that the inclusion of higher mode data does not change this situation. But, on the other hand, numerical experiments show that the available data and the scheme used for the inversion would not result in a solution including an artificial implosive component if the actual source were pure deviatoric. If the departure from a pure deviatoric source is produced by noise, it has to be non-random, as it could be produced by lateral heterogeneities not included in the inversion scheme.     

Lithospheric structure of the Arabian and Eurasian collision zone in eastern Turkey from S-wave receiver functions

Crustal and upper-mantle seismic discontinuities beneath eastern Turkey are imaged using teleseismic S -to- P converted phases. Three crustal phases are observed: the Moho with depth ranging between 30 and 55 km, indicating variable tectonic regimes within this continental collision zone; an upper-crustal discontinuity at approximately 10 km depth; and various crustal low-velocity zones, possibly associated with recent Quaternary volcanism. Imaging of the upper mantle is complicated by the 3-D geometry of the region, in particular due to the Bitlis–Zagros suture zone. However, several upper-mantle S -to- P converted phase are identified as being the signature of the lithosphere–asthenosphere boundary (LAB). The inferred LAB for the Eastern Anatolian Accretionary Complex indicates that eastern Turkey has an anomalously thin (between ∼60 and 80 km) lithosphere which is consistent with an oceanic slab detachment model. The observed LAB phases for the Arabian shield and Iranian plateau indicate that lithospheric thickness for these stable regions is on the order of 100 to 125 km thick, which is typical of continental margins.     

Deglacial land emergence and lateral upper-mantle heterogeneity in the Svalbard Archipelago—II. Extended results for high-resolution load models

In Paper I (Breuer & Wolf 1995), a preliminary interpretation of the postglacial land emergence observed at a restricted set of six locations in the Svalbard Archipelago was given. The study was based on a simple model of the Barents Sea ice sheet and suggested increases in lithosphere thickness and asthenosphere viscosity with increasing distance from the continental margin.
In the present paper, the newly developed high-resolution load model. BARENTS-2, and land-uplift observations from an extended set of 25 locations are used to study further the possibility of resolving lateral heterogeneity in the upper mantle below the northern Barents Sea. A comparison of the calculated and observed uplift values shows that the lithosphere thickness is not well resolved by the observations, although values above 110 km are most common for this parameter. In contrast to this, there are indications of a lateral variation of asthenosphere viscosity. Whereas values in the range 10¹⁸-10²⁰Pas are inferred for locations close to the continental margin, 10²⁰-10²¹ Pa s are suggested further away from the margin.
A study of the sensitivity of the values found for lithosphere thickness and asthenosphere viscosity to modifications of load model BARENTS-2 shows that such modifications can be largely accommodated by appropriate changes in lithosphere thickness, whereas the suggested lateral variation of asthenosphere viscosity is essentially unaffected. An estimate of the influence of the Fennoscandian. ice sheet leads to the conclusion that its neglect results in an underestimation of the thickness of the Barents Sea ice sheet by about 10 per cent.     

Analytical approach for the toroidal relaxation of viscoelastic earth

This paper is concerned with post-seismic toroidal deformation in a spherically symmetric, non-rotating, linear-viscoelastic, isotropic Maxwell earth model. Analytical expressions for characteristic relaxation times and relaxation strengths are found for viscoelastic toroidal deformation, associated with surface tangential stress, when there are two to five layers between the core–mantle boundary and Earth's surface. The multilayered models can include lithosphere, asthenosphere, upper and lower mantles and even low-viscosity ductile layer in the lithosphere. The analytical approach is self-consistent in that the Heaviside isostatic solution agrees with fluid limit. The analytical solution can be used for high-precision simulation of the toroidal relaxation in five-layer earths and the results can also be considered as a benchmark for numerical methods. Analytical solution gives only stable decaying modes—unstable mode, conjugate complex mode and modes of relevant poles with orders larger than 1, are all excluded, and the total number of modes is found to be just the number of viscoelastic layers between the core–mantle boundary and Earth's surface—however, any elastic layer between two viscoelastic layers is also counted. This confirms previous finding where numerical method (i.e. propagator matrix method) is used. We have studied the relaxation times of a lot of models and found the propagator matrix method to agree very well with those from analytical results. In addition, the asthenosphere and lithospheric ductile layer are found to have large effects on the amplitude of post-seismic deformation. This also confirms the findings of previous works.     

The effects of post-seismic motions on the moment of inertia of a stratified viscoelastic earth with an asthenosphere

Summary. We give the analytical formulation for calculating the transient displacement of fields produced by earthquakes in a stratified, selfgravitating, incompressible, viscoelastic earth. We have evaluated the potential of viscous creep in the asthenosphere in exciting the Chandler wobble by a four-layer model consisting of an elastic lithosphere, a two-layer Maxwell viscoelastic mantle, and an inviscid core. The seismic source is modelled as an inhomogeneous boundary condition, which involves a jump condition of the displacement fields across the fault in the lithosphere. The response fields are derived from the solution of a two-point boundary value problem, using analytical propagator matrices in the Laplace-transformed domain. Transient flows produced by post-seismic rebound are found to be confined within the asthenosphere for local viscosity values less than 10²⁰P. The viscosity of the mantle below the low-viscosity channel is kept at 10²²P. For low-viscosity zones with widths greater than about 100 km and asthenospheric viscosities less than 10¹⁸P, we find that viscoelasticity can amplify the perturbations in the moment of inertia by a factor of 4–5 above the elastic contribution within the time span of the wobble period. We have carried out a comparative study on the changes of the inertia tensor from forcings due to surface loading and to faulting. In general the global responses from faulting are found to be much more sensitive to the viscosity structure of the asthenosphere than those produced from surface loading.