The building of the Andes results from the subduction of the oceanic Nazca plate underneath the South American continent. However, how and why the Andes and their curvature, the Bolivian orocline, formed in the Cenozoic era (65.5 million years (Myr) ago to present), despite subduction continuing since the Mesozoic era (251.0-65.5 Myr ago), is still unknown. Three-dimensional numerical subduction models demonstrate that variations in slab thickness, arising from the Nazca plate's age at the trench, produce a cordilleran morphology consistent with that observed. The age-dependent sinking of the slab in the mantle drives traction towards the trench at the base of the upper plate, causing it to thicken. Thus, subducting older Nazca plate below the Central Andes can explain the locally thickened crust and higher elevations. Here we demonstrate that resultant thickening of the South American plate modifies both shear force gradients and migration rates along the trench to produce a concave margin that matches the Bolivian orocline. Additionally, the varying forcing along the margin allows stress belts to form in the upper-plate interior, explaining the widening of the Central Andes and the different tectonic styles found on their margins, the Eastern and Western Cordilleras. The rise of the Central Andes and orocline formation are directly related to the local increase of Nazca plate age and an age distribution along the margin similar to that found today; the onset of these conditions only occurred in the Eocene epoch. This may explain the enigmatic delay of the Andean orogeny, that is, the formation of the modern Andes.

Solving the Helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge. This is due to the particular nature of the Helmholtz operator and the sensibility of the solution to small variations of the data. Here a reduced order model is used to determine the scattered solution everywhere in the domain for any incoming wave direction and frequency. Moreover, this is applied to a real engineering problem: water agitation inside real harbors for low to mid-high frequencies.The Proper Generalized Decomposition (PGD) model reduction approach is used to obtain a separable representation of the solution at any point and for any incoming wave direction and frequency. Here, its applicability to such a problem is discussed and demonstrated. More precisely, the contributions of the paper include the PGD implementation into a Perfectly Matched Layer framework to model the unbounded domain, and the separability of the operator which is addressed here using an e cient higher-order projection scheme.Then, the performance of the PGD in this framework is discussed and improved using the higher-order projection and a Petrov-Galerkin approach to construct the separated basis. Moreover, the e ciency of the higherorder projection scheme is demonstrated and compared with the higher-order singular value decomposition.

SUMMARYThe solution of a steady thermal multiphase problem is assumed to be dependent on a set of parameters describing the geometry of the domain, the internal interfaces and the material properties. These parameters are considered as new independent variables. The problem is therefore stated in a multidimensional setup. The Proper Generalized Decomposition (PGD) provides an approximation scheme especially well suited to preclude dramatically increasing the computational complexity with the number of dimensions. The PGD strategy is reviewed for the standard case dealing only with material parameters. Then, the ideas presented in [Ammar et al., "Parametric solutions involving geometry: A step towards efficient shape optimization." Comput. Methods Appl. Mech. Eng., 2014; 268:178-193] to deal with parameters describing the domain geometry are adapted to a more general case including parametrization of the location of internal interfaces. Finally, the formulation is extended to combine the two types of parameters. The proposed strategy is used to solve a problem in applied geophysics studying the temperature field in a cross section of the Earth crust subsurface. The resulting problem is in a 10-dimensional space, but the PGD solution provides a fairly accurate approximation (error  1%) using less that 150 terms in the PGD expansion.

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Simulation-based probabilistic inversions of 3D magnetotelluric (MT) data are arguably the best option to deal with the non-linearity and non-uniqueness of the MT problem. However, the computational cost associated with the modeling of 3D MT data has so far precluded the community from adopting and/or pursuing full probabilistic inversions of large MT datasets. In this contribution, we present a novel and general inversion framework, driven by Markov chain Monte Carlo (MCMC) algorithms, which combines i) an efficient parallel-in-parallel structure to solve the 3D forward problem, ii) a reduced order technique to create fast and accurate surrogate models of the forward problem, and iii) adaptive strategies for both the MCMC algorithm and the surrogate model. In particular, and contrary to traditional implementations, the adaptation of the surrogate is integrated into the MCMC inversion. This circumvents the need of costly offline stages to build the surrogate and further increases the overall efficiency of the method.We demonstrate the feasibility and performance of our approach to invert for large-scale conductivity structures with two numerical examples using different parameterizations and dimensionalities. In both cases, we report staggering gains in computational efficiency compared to traditional MCMC implementations. Our method finally removes the main bottleneck of probabilistic inversions of 3D MT data and opens up new opportunities for both stand-alone MT inversions and multi-observable joint inversions for the physical state of the Earth’s interior.