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Red abalone Haliotis rufescens is one of the most valuable mollusks in the international market, but it has a low growth rate. A breeding program is being developed to increase its growth rate in Chile. We estimated the changes in direct heritability (h2), maternal/common environments heritability (m2) and genetic correlations (rG) of growth traits (shell length and width, total mass, flesh mass and foot protein as an indicator of meat quality) measured during 2 years (every 4 months) from the juvenile stage (27 months) to the adult harvesting age (51 months), in 60 full-sib red abalone families. Heritabilities for growth traits measured in juveniles and young adults (27–35 months of age), were low (0.07–0.17) and not significant. Initial low h2 were associated with significant amounts of maternal/common environmental effects (m2 = 0.4). In young adults and abalone near the harvest age (39–51 months of age) h2 were much higher (0.32–0.75). These results emphasize the importance of multiple estimations of h2 over time. Among meat quality traits, only the h2 for the flesh mass for adults at harvesting age was significant (0.15). We observed strong positive rG (>0.9) between shell sizes (easy to measure) and total and flesh masses (trait more related to market value than shell sizes but harder to measure) for adults at harvesting age. Thus, if the 5% largest 51 month old abalone were selected from the population as broodstock we expect a positively correlated response on flesh mass of 23.4%.

The links between an early phase of orogenesis, when orogens are commonly wedge shaped, and a later phase, with a plateau geometry, are investigated using coupled thermal-mechanical models with uniform velocity subductionboundary conditions applied to the base of the crust, and simple frictional-plastic and viscous rheologies. Models in which rheological properties do not change with depth or temperature are characterized by growth of back-to-back wedges above the subduction zone. Wedge taper is inversely dependent on the Ramberg number (Rm; gravity stress/basal traction); increasing convergence velocity or crustal strength produces narrower and thicker wedges. Models that are characterized by a decrease in crustal viscosity from η c to η b with depth or temperature, leading to partial or full basal decoupling of the crust from the mantle, display more complex behaviour. For models with a moderate viscosity ratio, η b /η c ∼ 10 - 1 , the crustal wedges have dual tapers with a lower taper in the central region and a higher taper at the edges of the deformed crust. A redaction in the viscosity ratio (η b /η c ∼ 10 - 2 ) is sufficient to cause a transition of the central wedge region to a plateau. This transition depends on the basal traction, therefore the thickness of the weak basal layer also affects the transition. Further reduction of the viscosity ratio (η b /η c ∼ 10 - 4 ) leads to full basal decoupling and the development of plateaux in all cases considered. In most models, the plateaux grow laterally at constant thickness between characteristic edge peaks associated with the transitions from coupled to decoupled lower crust. Where the crust is fully decoupled, large-scale model geometries for both depth- and temperature-dependent rheologies are similar with gravity-driven flow concentrated in the low-viscosity region. However, strong lateral temperature gradients within these models, controlled by the interaction of horizontal and vertical thermal advection, diffusion and heterogeneous thickening of the radioactive crustal layer, lead to differences in the velocity and deformation fields between the two cases, particularly at the plateau margins. The results suggest that simple depth-dependent viscosity models may be reasonable approximations for describing the large-scale geometry of fully developed plateaux, but that they are not appropriate for describing the internal features of large orogenic systems or the transition from wedge to plateau geometry.

Geodynamical numerical modeling has been combined with crustal structural restoration of the central Pyrenees in order to gain insight into fundamental processes that control the evolution of collisional orogens. Models are based on deformation of the crust by stresses transmitted upward from kinematic basal boundary conditions corresponding to the subduction of part of the lithosphere. The influence of inherited crustal heterogeneities, denudation, subcrustal loads, and crustal mechanical properties, consistent with well-constrained crustal partial restored cross sections of the central Pyrenees, is investigated by progressively incorporating them into model experiments. The primary result inferred from the modeling is that the asymmetry of the central Pyrenees double-wedge, seen as strain partitioning and in the morphological evolution, is a consequence of the asymmetric distribution of inherited crustal heterogeneity. The tectonic style of the central Pyrenees is the result of the inversion of the Early Cretaceous extensional fault system, during the early stages of the collision, and the reactivation of Hercynian heterogeneities during the late stages. Most of the upper crustal mass that entered the orogen during the calculated 165 km of convergence was accommodated by an increase of upper crustal cross sectional area or lost by denudation. To explain the upper crustal mass partitioning, as well as the geometry of the foreland basins and the preservation of synorogenic deposits in piggyback basins, a subduction load has to be applied to the models. Lower crust and mantle lithosphere were consumed by the mantle.

The South Island zone of oblique continent-continent convergence occurs along a 400 km-long section of the modern Australia-Pacific plate boundary zone, across which about 50 km of shortening has been accommodated since about 10 Ma. The orogen comprises a central mountain range (Southern Alps) flanked on both sides by what are interpreted to be foreland basins. Two essential features that characterize the orogen are (1) the degree of denudation that accompanied deformation, and (2) a fundamental structural asymmetry. The architectural asymmetry of the orogen can be explained by plane strain, finite element models of continental convergence incorporating mantle subduction. Comparison of model and orogen polarity implies that Pacific plate mantle subducts. The models predict two crustal-scale dipping shear zones that form above the point where the Pacific mantle subducts. The localized one more distant from the incoming plate (retro-step-up shear zone) corresponds to the Alpine fault, whereas its conjugate (pro-step-up shear zone) corresponds to the distributed strain and thrusting along the eastern margin of the mountain belt. Parameters that modify the model boundary conditions (top surface, degree of denudation; basal zone, subduction load, crust-mantle velocity discontinuity, subduction of lower crust, mantle retreat, and distributed decrease in mantle velocity) and the internal strength of the crust (two-layer crust with moderate coupling, temperature distribution, strain weakening) are varied in a series of numerical model calculations that establish the combination of material properties and boundary conditions that lead to different cross sectional architectures of the modeled collision zone. In turn, these are compared with observations about the South Island orogen. The calculations show how the style and extent of deformation across the whole orogen depend on the rheological properties of the crustal layer and on the balance between its internal strength and the combined effects of the boundary and gravitational stresses. North to south along-strike differences in the width and two-dimensional architecture of the orogen, simulated in the experiments by varying the model parameters, can be explained by a combination of southward increases in preconvergent crustal thickness, geothermal gradient, convergence, and potentially subduction retreat, with the added possibility of a southward decrease in the component of lower crustal subduction.

SUMMARY This paper presents and analyses numerical techniques developed to investigate viscoplastic Stokes flows within a model of lithospheric deformation. In particular, the techniques are related to a subduction model of compressional orogens. The driving mechanism in the model corresponds to the near-rigid convergence and subduction of one mantle lithosphere beneath another in plane strain and this boundary condition forces flow in an overlying viscoplastic model crust. The numerical techniques use the arbitrary Eulerian-Lagrangian formulation in which flows with free surfaces and large deformation are computed on an evolving Eulerian finite-element grid that conforms to the material domain. A regridding algorithm allows the associated Lagrangian motion and fields to be followed, and, in addition, coupled back to the Eulerian calculation of the flow. Mass-flux boundary conditions are used so that the effects of erosion and deposition by surface processes, and mass loss by subduction can be included in the model calculation. The evolving model crustal layer is flexurally compensated using a general elastic beam formulation. The applicability of the numerical techniques to problems ranging from accretionary wedges to crustal and lithospheric scale deformation is discussed. Simple flows, a linear viscous subduction model, a whirl flow, and a quasi-convection model are used to show that the mass conservation, regridding and surface tracking errors are small. The broader applicability of the modelling techniques is reviewed.

SUMMARY We investigate the effects of oblique convergence on crustal thickening by modelling the crust as a thin viscous sheet. Crustal deformation is driven by basal velocity boundary conditions representing the kinematics of the underlying convergent mantle lithosphere, which is assumed to detach and subduct. The crustal sheet is coupled to the basal velocity field by a weak simple shear layer, which exerts a traction on the base of the sheet. The use of basal velocity boundary conditions with a thin-sheet model is shown to be valid provided coupling with the base is weak and deformation extends over a horizontally wide zone in comparison to the thickness of the sheet. The effect of the mantle lithosphere on crustal deformation can be shown to depend on the non-dimensional Ampferer number, Am, which represents the relative strengths of the crust and the weak basal shear zone. Analytical and numerical model results for small amounts of normalized convergence show that the ratio of horizontal length-scales for normal and transcurrent crustal deformation is 2, for both linear and non-linear viscous rheologies. The length-scales depend on the relative strength of the crust and the basal shear zone, convolved with a forcing length-scale from the boundary conditions. For obliquely incident velocities, the length-scale ratio is between 2 and 1, the exact value depending on the power-law exponent of the rheology, and the relative magnitude of the normal and transverse velocity components driving deformation. The model results for the ratio of normal to transcurrent deformation length-scales are different from those found by using a side-driven viscous thin-sheet model (England, Houseman & Sonder 1985; Sonder, England & Houseman 1986). We propose that this difference may be used as a test to distinguish the primary driving mechanism for large-scale orogenic deformation. If the deformation mechanism corresponds to pure shear of the whole lithosphere without significant basal tractions, we expect the deformation length-scale to be determined by the scale of the applied boundary conditions and buoyancy forces in the crust. The normal/transcurrent length-scale ratio for this case, in early stages of deformation, will be approximately 4. Alternatively, if the results presented here are more appropriate, then we expect the deformation length-scale to be determined by the intrinsic relative strengths of the crust and underlying basal shear zone. The corresponding normal/transcurrent length-scale ratio for this case, in early stages of deformation, will be between 2 and 1. On the basis of a comparison of the predicted length-scales of deformation with the length-scale over which the velocity boundary conditions are applied, we suggest that long, narrow, linear orogens such as the Andes are controlled by basal boundary conditions, whereas the Himalayan-Tibetan orogen has dimensions consistent with either basally or side-driven deformation.

Crustal-scale deformation is calculated for models in which the driving mechanism corresponds to the asymmetric detachment and underthrusting of the underlying mantle lithosphere. The plane-strain finite-element model results provide indications of the styles of deformation to be expected in small compressional orogens. In particular these styles occur where shortening of the mantle lithosphere is achieved by the nearly rigid convergence between lithospheric mantles and the subduction of one mantle beneath the other. The crust is modelled using Coulomb plastic (frictional) and thermally-activated power-law viscous rheologies and the effects of compositional layering and variable geothermal gradients are included. Results are presented for a range of models in which the strength of the coupling between the model crust and its basal boundary, surface denudation, partial and total subduction of the crust, and compositional layering are examined. The results show the development of inclined step-up shear zones, which are a consequence of conjugate thrusting in regions of Coulomb-controlled rheology. These zones link to sub-horizontal shear zones which occur where composition and temperature render the crust viscously weak. The model strain fields are interpreted in terms of deformation on discrete planes and the seismic reflectivity fabric that may be associated with this discrete deformation. Finally, we ask whether similar seismic reflectivity fabric can be recognized in observations from small compressional orogens.

International audience; We present a new finite element code for the solution of the Stokes and energy (or heat transport) equationsthat has been purposely designed to address crustal-scale to mantle-scale flow problems in three dimensions. Although it is based on an Eulerian description of deformation and flow, the code, which we named DOUAR ('Earth' in Breton language), has the ability to track interfaces and, in particular, the free surface, by using a dual representation based on a set of particles placed on the interface and the computation of a level set function on the nodes of the finite element grid, thus ensuring accuracy and efficiency.The code also makes use of a newmethod to compute the dynamic Delaunay triangulation connecting the particles based on non-Euclidian, curvilinear measure of distance, ensuring that the density of particles remains uniform and/or dynamically adapted to the curvature of the interface. The finite element discretization is based on a non-uniform, yet regular octree division of space within a unit cube that allows efficient adaptation of the finite element discretization, i.e. in regions of strong velocity gradient or high interface curvature. The finite elements are cubes (the leaves of the octree) in which a q1­p0 interpolation scheme is used. Nodal incompatibilities across faces separating elements of differing size are dealt with by introducing linear constraints among nodal degrees of freedom. Discontinuities in material properties across the interfaces are accommodated by the use of a novel method (which we called divFEM) to integrate the finite element equations in which the elemental volume is divided by a local octree to an appropriate depth (resolution).Avariety of rheologies have beenimplemented including linear, non-linear and thermally activated creep and brittle (or plastic) frictional deformation. A simple smoothing operator has been defined to avoid checkerboard oscillations in pressure that tend to develop when using a highly irregular octree discretization and the tri-linear (or q1­p0) finite element. A three-dimensional cloud of particles is used to track material properties that depend on the integrated history of deformation (the integrated strain, for example); its density is variable and dynamically adapted to the computed flow. The large system of algebraic equations that results fromthe finite element discretization and linearization of the basic partial differential equations is solved using a multi-frontal massively parallel direct solver that can efficiently factorize poorly conditioned systems resulting from the highly non-linear rheology and the presence of the free surface. The code is almost entirely parallelized.We present example results including the onset of a Rayleigh­Taylor instability, the indentation of a rigid-plastic material and the formation of a fold beneath a free eroding surface, that demonstrate the accuracy, efficiency and appropriateness of the new code to solve complex geodynamical problems in three dimensions.

International audience; In recent years, much has been done to develop numerical tools to study the three-dimensional nature of the Earth's lithosphere deformation. DOUAR is one of them: it is a new ALE Finite Element code that is based on an adaptive grid, a key feature in the capture of localized deformation. In order to illustrate this, various simulations of punch experiments have been performed on rigid plastic materials with von Mises and Drucker-Prager type of rheologies. We present the grid refinement algorithm based on strain rate measurements and rederive the plane strain punch analytical solution which allows us to test the accuracy of our results. Various 3-D strip punches experiments with different aspect ratios show DOUAR's ability to capture complex fault patterns. We also discuss the degree to which the incompressibility and rigid plasticity constraints are satisfied. Finally, we show the results of a crustal-scale deformation experiment demonstrating the potential of the octree-based mesh refinement algorithm to solve complex three-dimensional geodynamical problems with great efficiency and accuracy.

[1] A model is developed which couples fully saturated porous compaction to the viscous-plastic deformation of the skeleton matrix. The Darcy fluid flow during compaction is described by an advection-diffusion equation for the excess pressure with two source/sink terms that depend on the mechanical compressibility and viscous compaction of the pore space, the latter representing the effect of pressure solution. The incompressible deformation of the composite medium is described by a force balance equation and its rheology can be viscous, plastic, or viscoplastic (Bingham material). For the plastic and viscoplastic cases, the coupling between the compacting and plastically deforming parts of the system is through the Drucker-Prager frictional-plastic yield criterion modified by Terzaghi's principle, so that the yield strength depends on the effective dynamical pressure. The coupled system is solved using a two-dimensional (2-D) finite element method. Two problems are solved to demonstrate the behavior of our theory. The first considers compaction of a uniform sediment layer. The numerical results agree with the predictions of the nondimensional control parameters and previously published results. The second problem concerns 2-D kinematic progradation of deltaic sediments. Substratum and delta sediments have the same compaction properties and a Bingham rheology during deviatoric deformation, such that the delta undergoes linear postyield viscous flow. For certain depositional regimes, overpressure is generated. When pore pressures approach critical values, yielding occurs and the delta front fails and becomes unstable, spreading gravitationally under its own weight. The flow velocity is limited to geological rates by the Bingham viscosity. For the range of parameter values considered, pressure solution is the most effective mechanism for generating near-lithostatic fluid pressures that lead to initial failure, and it appears that mechanical compaction hardly contributes to the fluid overpressure at this stage.

Denudation has long been acknowledged as a process that contributes to the unroofing of compressional orogens. It has, however, mainly been considered as a passive process, not one that can dictate or control the tectonic evolution. This view prevails despite the knowledge that the style of deformation is controlled by the interplay of gravitational and tectonic stresses: an interplay that is sensitive to the mass removed by denudation.

[1] The nature of lithospheric deformation during continental plate collision still remains unresolved. While it has often been proposed that the mantle lithosphere is accommodated by distributed thickening of a viscous root, an alternate hypothesis suggests that significant portions of convergent mantle lithosphere essentially undergo underthrusting or subduction. To further consider this issue, we model the thermochemical evolution of the lithosphere-mantle system using arbitrary Lagrangian-Eulerian finite element techniques. We incorporate a mix of viscous (thermally activated power law creep) and plastic (frictional Coulomb with strain softening) rheologies in the numerical experiments to treat disparate composition in the crust and mantle. A range of rheological and mechanical parameters is explored to determine controls on the style of lithospheric deformation. The models suggest that during the initial stages of plate collision the mantle lithosphere is characterized by plate-like behavior and underthrusting/subduction of the upper region in conjunction with distributed thickening and Rayleigh-Taylor type viscous instability of the lower portion. Depending on the material rheology, temperature regime, and imposed convergence velocity, the deforming mantle lithosphere demonstrates various combinations of these “end-member” behavioral modes. The modeling results are interpreted in the context of observed lithospheric deformation across South Island, New Zealand. A combined style of underthrusting and distributed thickening is consistent with the observed crustal structure in the young collisional orogen as well as seismic imaging of the geometry of the underlying lithosphere.

In studying orogenic processes, the mechanism of viscous Rayleigh-Taylor–type removal of gravitationally unstable lithosphere is often invoked to explain the behavior of the mantle lithosphere. Using numerical models, we consider this mechanism and explore alternate styles of deep lithospheric deformation during tectonic convergence. The numerical experiments incorporate a mix of viscous and plastic rheologies to model the mechanical evolution of the lithosphere-asthenosphere system. Our results suggest that there are a number of deformational modes of the model mantle lithosphere: (1) a dripping or Rayleigh-Taylor–type instability; (2) an asymmetric underthrusting or subduction; (3) symmetric, ablative plate consumption; (4) slab breakoff, the failure and detachment of the strong lithosphere; and (5) mixed modes with combinations of these processes. The development of the modes is controlled by the rate of convergence associated with the background tectonic regime, the density field, and the rheology of the mantle lithosphere. It is important to determine whether these modes occur in the Earth beneath collisional orogens.

Inverted metamorphic sequences are characterized by peak metamorphic temperatures that increase structurally upward, with isograds that are typically parallel to associated thrust faults. A fully coupled thermal-mechanical model for convergent orogens shows how an inverted sequence can be tectonically assembled in a crustal-scale ductile shear zone at moderate to high rates of synorogenic erosion. Model inverted sequences form by tectonic juxtaposition of points with widely differing initial positions that reach peak temperatures at different times and in different places within the model orogen, and thus do not represent metamorphic or thermal gradients. Inverted crustal isotherms are not required to produce model inverted isograds. Model results agree well with metamorphic pressure-temperature data from the Main Central Thrust zone of the central Nepal Himalayas.

A mechanical model of crustal shortening and deformation driven by the relative convergence of rigid, underlying mantle plates explains many features of convergent orogens. Results based on numerical models and supported by sandbox models show that a Coulomb crustal layer subject to basal velocity boundary conditions corresponding to asymmetric detachment and subduction of the underlying mantle passes through three stages of orogenic growth: (1) block uplift bounded by step-up shear zones; (2) development of a low-taper wedge over the underthrusting mantle plate; and (3) development of a low-taperwedge overlying the overthrusting mantle plate and verging in the opposite direction. When modified by isostasy, basal viscous flow, surface erosion and denudation, and sedimentation, the resultant model orogens exhibit a variety of styles with characteristics in common with small, rapidly denuded orogens, large orogens with plateaus and extensional characteristics, and active subduction margins with doubly vergent accretionary wedges and deformed fore-arc basins.

Alpine-type orogens are characterized by three distinct convergent tectonic phases: subduction with deformation that has primarily single vergence, a transition from subduction to collision, and continental collision with double vergence. Although the Cenozoic history of the European Alps has additional complexities, a mechanical explanation for these three phases would provide the necessary crustal-scale framework in which to develop an understanding of the smaller-scale processes. We present results from a simple numerical model, which explain the mechanics of these three phases as a consequence of the changing buoyancy of the lithosphere subducted beneath the orogen. The development and exhumation of a subduction complex, suture zone, and basement nappe stack (Piemont suture, Penninic Nappes); the presence of a crustal-scale back fold and thrust (Insubric Line); and uplift of basement on the pro- (European) side of the orogen (external basement massifs) may be explained as a simple consequence of changing dynamics during the transition from subduction to collision.