We present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in three dimensions. This finite element formulation is based on the Eulerian description of motion and the transport of the deformation gradient. When modeling a nearly incompressible solid, the transport of the deformation gradient is decomposed into its isochoric part and the Jacobian determinant as independent fields. A homogeneous isotropic hyperelastic solid is assumed and B-splines-based finite elements are used for the spatial discretization. A variational multiscale residual-based approach is employed to stabilize the transport equations. The performance of the scheme is explored for both compressible and nearly incompressible applications. The numerical results are in good agreement with theory illustrating the viability of the computational scheme.

Recent observations and models of continental rifting in magma�¢â�¬��poor environments have led to the concept of multiphase stages of lithospheric extension. In these concepts it is shown that extreme crustal thinning of the crust predates exhumation of lower crustal and subcontinental mantle rocks during final rifting. The Bay of Biscay is a V�¢â�¬��shaped ocean basin that opened in Aptian�¢â�¬��Albian time. In front of this propagating ocean, several rift basins formed that show evidence for extreme crustal thinning and locally also mantle exhumation (the Parentis, Arzacq�¢â�¬��Mauleon, and Cantabrian basins). In this paper we propose, based on geological and geophysical observations and using numerical modeling, a model that can explain the extreme crustal thinning observed in the Arzacq�¢â�¬��Maul���©on and Parentis basins. Our results show that rifting in the Bay of Biscay was initiated by distributed oblique stretching (latest Jurassic to Early Aptian) before it underwent an more orthogonal asymmetric thinning and exhumation phase from Late Aptian to Albian time. These last two stages of deformation are similar to those observed in orthogonal rift systems. We show that thinning is accomplished by the formation of a semibrittle shear zone that allows for the transfer of middle to lower crustal material from the side of the rift collocated with the hanging wall to the side of the rift collocated with the footwall of the detachment system. The main difference with an orthogonal rift system appears to be generated by the formation of flower structures during the distributed oblique phase and the capacity of localizing the deformation in the subsequent stages. These oblique slip faults form very steep normal faults that induce the development of strongly localized, compartmentalized, and asymmetric rift basins. In the case of the Parentis and Arzacq�¢â�¬��Mauleon basins, these strike�¢â�¬��slip faults separate upper plate sag basins to the north from lower plate sag basins to the south. While the northern sag basins do not show any evidence for exhumation, the southern ones are more complex and floored by detachment faults, as indicated by the occurrence of syntectonic and posttectonic sediments onlapping directly onto exhumed lower crustal and mantle rocks.

Prerift salt layers associated with extensional detachment faults exhuming mantle and deeper crustal rocks at the sea floor are observed in the Parentis and Arzacq-Mauleon basins located at the eastern termination of the Bay of Biscay. How detachment faults interact with salt in hyperextended rift systems is yet little understood. Based on field observations and drill-hole and seismic data, we propose a new model to explain the interaction between salt tectonics and extensional detachment systems. We demonstrate that the presence of a thick prerift salt layer in an area undergoing extreme crustal thinning can control the geometry and evolution of rift systems and obscure the rift-related structures in the underlying basement. During an initial stage of rifting, prerift salt layers act as a decoupling horizon between sub- and suprasalt units and hinder crustal detachment faults to cut through the salt layers and form breakaways at the sea floor. As a consequence, they sole out along the ductile salt layer and no subsalt material can be exhumed to the sea floor. Thus, sub- and suprasalt layers deform by different deformation modes, which makes that detachment fault difficult to identify on seismic images. In a later stage, when salt has migrated and thinned out, sub- and suprasalt layers can locally couple and detachment faults can be exposed at the surface, resulting in windows of exhumed basement surrounded by extensional allochthons formed by suprasalt sedimentary units.

We analyse the topography and gravity signature of 39 corrugated surfaces formed over the past 26 myrs in the footwall of axial detachment faults at the eastern Southwest Indian Ridge. These corrugated surfaces appear to have formed at a melt supply about half the global melt supply average for mid-ocean ridges, and we find that their presently elevated topography, relative to adjacent non-corrugated seafloor, was mostly acquired at the end of their formation, at the �termination stage�. This configuration, which also characterizes many off-axis corrugated surfaces in other oceans, suggests that the plate flexural rigidity was very low during the formation of the corrugated surface, and increased significantly at the termination stage. Following Buck (1988), we hypothesize that stresses related to bending of the plate cause internal deformation and damage in the footwall of the fault, which is associated with weakening. As a possible mechanism for enhanced footwall weakening while corrugated surfaces form, we propose the formation of weak shear zones coated with hydrous minerals such as talc, amphibole, chlorite and serpentine, in mantle-derived ultramafics next to gabbro intrusions. If this hypothesis is correct, the amount of footwall weakening and roll-over along axial detachment faults at slow spreading ridges may be controlled both by access to hydrothermal fluids in the footwall of the detachment, and by the abundance and distribution of gabbros intrusions in exhumed ultramafics.

In this paper we describe the tectonosedimentary evolution and its subsequent inversion of a basin that underwent extreme crustal thinning in a transtensional setting ahead of a propagating ocean in the western Pyrenees. The Labourd-Mauléon area situated in the western Pyrenees, at the termination of the V-shaped Bay of Biscay, is an ideal natural laboratory to study how such complex basins evolve in time and space. Because of a mild inversion of the basin during Pyrenean compression, the rift structures and their relations to basement rocks and sediments are exposed and can be directly studied in the field. The basin shows a complex polyphase evolution that starts with left-lateral dominated transtension in latest Jurassic�early Aptian time. This event is overprinted by a late Aptian�early Albian extension that is related to the counterclockwise rotation of Iberia away from Europe leading to the opening of the Bay of Biscay. During this stage, the Late Triassic to Jurassic carbonate platform was stretched, salt migrated, and detachment faults exhumed upper and lower crustal and mantle rocks to the seafloor. The final structure of the basin resembles a sag basin floored by exhumed rocks overlain by extensional allochthons and compartmentalized by N40° to N60° transfer faults. The sedimentary architecture is characterized by late Aptian synrift sediments (e.g., Urgonian limestones) that were deposited in fault-bounded basins and are overlain by thick latest Aptian to Albo-Cenomanian sediments (e.g., Flysch noir) that define a sag sequence. The complex tectonosedimentary evolution of the basin is associated with salt tectonics and overprinted by a major magmatic/thermal event that postdates mantle exhumation.

Seismic and gravity observations from the rifted margin of the eastern Grand Banks, Newfoundland, support a new model for extension of the continental crust from the shelf edge to ODP Site 1277, where mantle rocks are exhumed. We find that the largest decrease in crustal thickness, from about 28 km to 6 km, occurs beneath the continental slope of the Grand Banks over a distance of just 20 km. This rapid decrease in crustal thickness coincides with anomalously high seismic velocities (7.0�7.2 km·s&#8722; 1) in the lower crust of the shelf edge. The thin crust of the continent�ocean transition (COT) in this area has a smooth basement surface, void of upper crustal blocks and prerift sediments. We compare our geophysical results with a geodynamical model that represents rifting of a relatively hot continental lithosphere and with another numerical model that represents rifting of a cold lithosphere. Both geodynamic models suggest that crustal thinning beneath the continental slope was achieved by extensional faulting in the upper crust and ductile shear zones in the middle crust. The geodynamic models provide an explanation for the formation of distinct continental slopes at rifted margins: Beneath the continental shelf of the Grand Banks, the Moho and the strong lower crust rotated upwards toward to a 50° dip without visible internal deformation. The presence of these strong lower crustal rocks at shallow depth in the rift flank subsequently helped to localize the extension farther seaward. With ongoing extension, some high-angle normal faults may have rotated to a sub-horizontal orientation, which would explain the lack of brittle deformation visible in the seismic reflection data. The two geodynamic models produce different amounts of extension of continental crust in the distal margins. The hot rifting model localizes strain much more rapidly, leaving narrow zones of extended continental crust, and it produces a relatively large amount of melt (> 30%) in the final stages of rifting. Continental breakup may occur rapidly in hot lithosphere (< 5 Myr). On the other hand, a cold extension model extends the continental crust to a thickness smaller than 10 km over a width of 50 km in the distal margin, similar to what we inferred at the eastern Grand Banks. The cold lithospheric model requires about 23 Myr of extension before continental breakup, and it predicts much less melting in the mantle (13%). The long rift duration, wide zones of thinned continental crust, and small amount of magmatism make the cold rifting model the most applicable to Newfoundland�Iberia rift.

The mechanics responsible for the initiation of the orthogonal pattern characterizing mid-ocean ridges and transform faults are studied using numerical models. The driving forces are thermal stresses arising from the cooling of young oceanic crust and extensional kinematic boundary conditions. Thermal stress can exert ridge-parallel tension comparable in magnitude to spreading-induced tension when selectively released by ridges and ridge-parallel structure. Two modes of ridge segment growth have been identified in plan view: an overlapping mode where ridge segments overlap and bend toward each other and a connecting mode where two ridge segments are connected by a transform-like fault. As the ratio of thermal stress to spreading-induced stress (γ) increases, the patterns of localized plastic strain change from the overlapping to connecting mode. The orthogonal pattern marks the transition from one mode to the other. Besides the amount of stress from each driving force, the rate of stress accumulation is crucial in determining the emergent pattern. This rate-dependence is characterized by the spreading rate normalized by a reference-cooling rate (Pe&#8242;). When Pe&#8242; is paired with the ratio of thermal stress to the reference spreading-induced stress (γ&#8242;), they unambiguously define stability fields of the two modes. The obliquely connecting, the orthogonally connecting, and the overlapping mode are similar to ridge-transform fault intersections observed in ultra-slow, slow to intermediate, and fast spreading centers, respectively. The patterns are also sensitive to the strain weakening rate. Fracture zones were created in part as a response to thermal stress.

Analysis of new multibeam bathymetry data and seismic Chirp data acquired over the Cape Fear Slide complex on the U.S. Atlantic margin suggests that at least 5 major submarine slides have likely occurred there within the past 30,000 years, indicating that repetitive, large-scale mass wasting and associated tsunamis may be more common in this area than previously believed. Gas hydrate deposits and associated free gas as well as salt tectonics have been implicated in previous studies as triggers for the major Cape Fear slide events. Analysis of the interaction of the gas hydrate phase boundary and the various generations of slides indicates that only the most landward slide likely intersected the phase boundary and inferred high gas pressures below it. For much of the region, we believe that displacement along a newly recognized normal fault led to upward migration of salt, oversteepening of slopes, and repeated slope failures. Using new constraints on slide morphology, we develop the first tsunami model for the Cape Fear Slide complex. Our results indicate that if the most seaward Cape Fear slide event occurred today, it could produce waves in excess of 2 m at the present-day 100 m bathymetric contour.

Although the Iberia�Newfoundland and Alpine Tethys margins are of different age and ultimately had a different fate, they share remarkable similarities. Both pairs of margins show a change from initially distributed and decoupled extension to later localized, coupled and asymmetric extension that results in thinning of the crust and exhumation of subcontinental mantle. The change in the mode of extension together with the localization of deformation reflects an evolution of the bulk rheology of the extending lithosphere. In this paper we summarize the pertinent geological observations for the Iberia�Newfoundland and Alpine Tethys margins. We describe the stratigraphic evolution, the fault geometry, basin architecture, and magmatic and metamophic evolution of the two pairs of margins from initial rifting to final continental breakup. This description forms a basis for understanding the evolution of the bulk rheology and how the various processes interact during progressive lithospheric extension. For the Iberia�Newfoundland and Alpine Tethys margins initial rifting appears to be controlled by inherited heterogeneities and mechanical localization processes, whereas final rifting and lithospheric rupture is controlled by serpentinization, magmatic and thermal weakening. At other margins, these modes may interact in a different way depending on the prerift conditions and the evolution of the rheology during rifting.

Where continental plates break apart, slip along multiple normal faults provides the required space for the Earth's crust to thin and subside1. After initial rifting, however, the displacement on normal faults observed at the sea floor seems not to match the inferred extension2. Here we show that crustal thinning can be accomplished in such extensional environments by a system of conjugate concave downward faults instead of multiple normal faults. Our model predicts that these concave faults accumulate large amounts of extension and form a very thin crust (< 10 km) by exhumation of mid-crustal and mantle material. This transitional crust is capped by sub-horizontal detachment surfaces over distances exceeding 100 km with little visible deformation. Our rift model is based on numerical experiments constrained by geological and geophysical observations from the Alpine Tethys and Iberia/Newfoundland margins3, 4, 5, 6, 7, 8, 9. Furthermore, we suggest that the observed transition from broadly distributed and symmetric extension to localized and asymmetric rifting is directly controlled by the existence of a strong gabbroic lower crust. The presence of such lower crustal gabbros is well constrained for the Alpine Tethys system4, 9. Initial decoupling of upper crustal deformation from lower crustal and mantle deformation by progressive weakening of the middle crust is an essential requirement to reproduce the observed rift evolution. This is achieved in our models by the formation of weak ductile shear zones.

Abyssal-hill-bounding faults that pervade the oceanic crust are the most common tectonic feature on the surface of the Earth. The recognition that these faults form at plate spreading centres came with the plate tectonic revolution. Recent observations reveal a large range of fault sizes and orientations; numerical models of plate separation, dyke intrusion and faulting require at least two distinct mechanisms of fault formation at ridges to explain these observations. Plate unbending with distance from the top of an axial high reproduces the observed dip directions and offsets of faults formed at fast-spreading centres. Conversely, plate stretching, with differing amounts of constant-rate magmatic dyke intrusion, can explain the great variety of fault offset seen at slow-spreading ridges. Very-large-offset normal faults only form when about half the plate separation at a ridge is accommodated by dyke intrusion.

Nearly half of all active subduction zones initiated during the Cenozoic. All subduction zones associated with active back arc extension have initiated since the Eocene, hinting that back arc extension may be intimately associated with an interval (several tens of Myr) following subduction initiation. That such a large proportion of subduction zones are young indicates that subduction initiation is a continuous process in which the net resisting force associated with forming a new subduction zone can be overcome during the normal evolution of plates. Subduction initiation is known to have occurred in a variety of tectonic settings: old fracture zones, transform faults, and extinct spreading centers and through polarity reversal behind active subduction zones. Although occurring within different tectonic settings, four known subduction initiation events (Izu-Bonin-Mariana (IBM) along a fracture zone, Tonga-Kermadec along an extinct subduction boundary, New Hebrides within a back arc, and Puysegur-Fiordland along a spreading center) were typified by rapid uplift within the forearc followed by sudden subsidence. Other constraints corroborate the compressive nature of IBM and Tonga-Kermadec during initiation. Using an explicit finite element method within a two-dimensional domain, we explore the evolving force balance during initiation in which elastic flexure, viscous flow, plastic failure, and heat transport are all considered. In order to tie theory with observation, known tectonic settings of subduction initiation are used as initial and boundary conditions. We systematically explore incipient compression of a homogeneous plate, a former spreading center, and a fracture zone. The force balance is typified by a rapid growth in resisting force as the plate begins bending, reaching a maximum value dependent on plate thickness, but typically ranging from 2 to 3 �� 1012 N/m for cases that become self-sustaining. This is followed by a drop in stress once a shear zone extends through the plate. The formation of a throughgoing fault is associated with rapid uplift on the hanging wall and subsidence on the footwall. Cumulative convergence, not the rate of convergence, is the dominant control on the force balance. Viscous tractions influence the force balance only if the viscosity of the asthenosphere is >1020 Pa s, and then only after plate failure. Following plate failure, buoyancy of the oceanic crust leads to a linear increase with crustal thickness in the work required to initiate subduction. The total work done is also influenced by the rate of lithospheric failure. A self-sustaining subduction zone does not form from a homogeneous plate. A ridge placed under compression localizes subduction initiation, but the resisting ridge push force is not nearly as large as the force required to bend the subducting plate. The large initial bending resistance can be entirely eliminated in ridge models, explaining the propensity for new subduction zones to form through polarity reversals. A fracture zone (FZ) placed in compression leads to subduction initiation with rapid extension of the overriding plate. A FZ must be underthrust by the older plate for &#8764;100�150 km before a transition from forced to self-sustaining states is reached. In FZ models the change in force during transition is reflected by a shift from forearc uplift to subsidence. Subduction initiation is followed by trench retreat and back arc extension. Moderate resisting forces associated with modeled subduction initiation are consistent with the observed youth of Pacific subduction zones. The models provide an explanation for the compressive state of western Pacific margins before and during subduction initiation, including IBM and Tonga-Kermadec in the Eocene, and the association of active back arcs with young subduction zones. On the basis of our dynamic models and the relative poles of rotation between Pacific and Australia during the Eocene, we predict that the northern segment of the Tonga-Kermadec convergent margin would have initiated earlier with a progressive southern migration of the transition between forced and self-sustaining states.

We present a set of self-consistent numerical experiments resulting in the development of local weak zones within a wide region of extending brittle lithosphere overlying viscous asthenosphere. In these two-dimensional models, the brittle yield strength is controlled by a Byerlee's Law friction coefficient and a value for cohesion. A portion of the brittle strength is reduced as a function of plastic strain (strain beyond yield). This strain weakening can result in concentration of strain on spontaneously formed weak zones accommodating dip slip, or model normal faults. The temperature-dependent viscous rheology is based on a laboratory-derived power-law creep flow law for diabase. The initial temperature gradient is taken to be linear with depth, and controls the depth range over which the viscosity decreases beneath the brittle lithosphere. The viscous flow of the transition region below the lithosphere can result in a distributed set of model normal faults, in some cases with regular periodic spacing. The model pattern of deformation depends on a broad range of parameters, including the thickness of the brittle lithosphere, the depth range for the decrease of viscosity with depth, the strength reduction with brittle strain, the rate of strength loss, and the rate of regaining of strength through fault "healing." In this preliminary set of models, we show that the spacing of model basins and ranges can depend on the amount of strain weakening on faults, with wider spacing for larger amounts of strain weakening. For a temperature profile that gives a ~10 km thick brittle layer and about 20 MPa of strength loss with strain on faults, the model results in a pattern of topographic relief that roughly resembles what is seen in profiles across the Basin and Range province of the western United States.

Although the formation of subduction zones plays a central role in plate evolution, the processes and geological settings that lead to the initiation of subduction are poorly understood. Using a visco-elastoplastic model, we show that a fracture zone could be converted into a self-sustaining subduction zone after approximately 100 km of convergence. Modeled initiation is accompanied by rapid extension of the over-riding plate and explains the inferred catastrophic boninitic volcanism associated with Eocene initiation of the Izu-Bonin-Mariana (IBM) subduction zone. Using global plate reconstructions, we suggest that IBM nucleation was associated with a change in plate motion between 55 and 45 Ma. We estimate that the forces resisting IBM subduction initiation were substantially smaller than available driving forces.