The juxtaposition of domains of shortening and extension at different scales in orogens has fueled many debates about driving forces and tectonic interpretations, including timing of deformation. At the orogen scale, gravitational collapse and mass transfer from orogenic plateaux to forelands explain some of these juxtapositions. At a regional scale, structures in gneiss domes are commonly contractional yet are coeval with regional extension and denudation. Here we use three-dimensional numerical experiments to show that crustal flow in orogenic domains does not necessarily conform to plate motion. We document contractional crustal flow associated with the formation of a gneiss dome in an orogenic pull-apart setting where localized extension and crustal thinning focus the exhumation of deep crust. We show that the flow field results in a complex strain pattern in which an extensional strain regime that is collinear with the direction of plate motion is partitioned into the shallow crust, whereas contractional structures and fabrics at a high angle to the direction of imposed transport develop in the deep crust. Advective mass transfer across regions of contrasting yet coeval strain regimes leads to a polyphase tectonic history. We observe structural features remarkably similar to those documented in some natural gneiss domes such as the Montagne Noire, which developed in a dextral pull-apart domain at the southern margin of the French Massif Central.

With the progress of mantle convection modelling over the last decade, it now becomes possible to solve for the dynamics of the interior flow and the surface tectonics to first order. We show here that tectonic data (like surface kinematics and seafloor age distribution) and mantle convection models with plate-like behaviour can in principle be combined to reconstruct mantle convection. We present a sequential data assimilation method, based on suboptimal schemes derived from the Kalman filter, where surface velocities and seafloor age maps are not used as boundary conditions for the flow, but as data to assimilate. Two stages (a forecast followed by an analysis) are repeated sequentially to take into account data observed at different times. Whenever observations are available, an analysis infers the most probable state of the mantle at this time, considering a prior guess (supplied by the forecast) and the new observations at hand, using the classical best linear unbiased estimate. Between two observation times, the evolution of the mantle is governed by the forward model of mantle convection. This method is applied to synthetic 2-D spherical annulus mantle cases to evaluate its efficiency. We compare the reference evolutions to the estimations obtained by data assimilation. Two parameters control the behaviour of the scheme: the time between two analyses, and the amplitude of noise in the synthetic observations. Our technique proves to be efficient in retrieving temperature field evolutions provided the time between two analyses is 10 Myr. If the amplitude of the a priori error on the observations is large (30 per cent), our method provides a better estimate of surface tectonics than the observations, taking advantage of the information within the physics of convection.

Abstract. Recent advances in mantle convection modeling led to the release of a new generation of convection codes, able to self-consistently generate plate-like tectonics at their surface. Those models physically link mantle dynamics to surface tectonics. Combined with plate tectonic reconstructions, they have the potential to produce a new generation of mantle circulation models that use data assimilation methods and where uncertainties in plate tectonic reconstructions are taken into account. We provided a proof of this concept by applying a suboptimal Kalman filter to the reconstruction of mantle circulation (Bocher et al., 2016). Here, we propose to go one step further and apply the ensemble Kalman filter (EnKF) to this problem. The EnKF is a sequential Monte Carlo method particularly adapted to solve high-dimensional data assimilation problems with nonlinear dynamics. We tested the EnKF using synthetic observations consisting of surface velocity and heat flow measurements on a 2-D-spherical annulus model and compared it with the method developed previously. The EnKF performs on average better and is more stable than the former method. Less than 300 ensemble members are sufficient to reconstruct an evolution. We use covariance adaptive inflation and localization to correct for sampling errors. We show that the EnKF results are robust over a wide range of covariance localization parameters. The reconstruction is associated with an estimation of the error, and provides valuable information on where the reconstruction is to be trusted or not.