## Section: New Results

### Seismic Imaging and Inverse Problems

#### hp-adaptive simulation and inversion of magnetotelluric measurements

Participants : Hélène Barucq, Julen Alvarez Aramberri, David Pardo.

The magnetotelluric (MT) method is a passive exploration technique that aims at estimating the resistivity distribution of the Earth's subsurface, and therefore at providing an image of it. This process is divided into two different steps. The first one consists in recording the data. In a second step, recorded measurements are analyzed by employing numerical methods. In this work, we provide a rigorous mathematical setting in the context of the Finite Element Method (FEM) that helps to understand the MT problem and its inversion process. In order to recover a map of the subsurface based on 2D MT measurements, we employ for the first time in MTs a multigoal oriented self adaptive hp-Finite Element Method (FEM). We accurately solve both the full formulation as well as a secondary field formulation where the primary field is given by the solution of a 1D layered medium. To truncate the computational domain, we design a Perfectly Matched Layer (PML) that automatically adapts to high-contrast material properties that appear within the subsurface and on the air-ground interface. For the inversion process, we develop a first step of a Dimensionally Adaptive Method (DAM) by considering the dimension of the problem as a variable in the inversion. Additionally, this dissertation supplies a rigorous numerical analysis for the forward and inverse problems. Regarding the forward modelization, we perform a frequency sensitivity analysis, we study the effect of the source, the convergence of the hp-adaptivity, or the effect of the PML in the computation of the electromagnetic fields and impedance. As far as the inversion is concerned, we study the impact of the selected variable for the inversion process, the different information that each mode provides, and the gains of the DAM approach.

#### Ultrasonic imaging of complex media

Participants : Hélène Barucq, Juliette Chabassier, Marc Duruflé, Julien Diaz, Sébastien Tordeux, Ha Howard Faucher.

In 2015 we have begun a collaborating project with I2M (Physics Acoustics Department of Bordeaux 1 University). We aim at modeling and simulating efficiently the propagation of acoustic waves and later elastodynamic waves in highly heterogeneous media, the final goal is to use topological gradient imaging techniques. Classical techniques as finite elements can be too costly, we propose to design more efficient numerical techniques that exploit the fact that the wavelength is big with respect to the heterogeneities. For instance, we will use numerical upscaling, multiscale homogenization or asymptotic methods. A funding has been obtained for a PhD and a post doctoral position, that have both started in 2015. Our first step is to design a laboratory experiment and a simulation code in order to challenge the limits of the newly derived models and quantify their validity.

#### Impedance transmission conditions for the electric potential across a highly conductive casing

Participants : Hélène Barucq, Aralar Erdozain, David Pardo, Victor Péron.

In this study we present Impedance Transmission Conditions (ITCs) for the electric potential in the framework of borehole through-casing resistivity measurements. Such ITCs substitute the part of the domain corresponding to a highly conductive casing. The naturally small thickness of the casing makes it ideal for exhibiting ITCs. We numerically observe the delivered order of accuracy.

#### An efficient truncated SVD of large matrices based on the low-rank approximation for inverse geophysical problems

Participant : Sébastien Tordeux.

We have proposed a new algorithm to compute a truncated singular value decomposition of the Born matrix based on a low-rank arithmetic. Theoretical background to the low-rank SVD method has been investigated: the Born matrix of an acoustic problem can be approximated by a low-rank approximation derived thanks to a kernel independent multipole expansion. The new algorithm to compute T-SVD approximation consists of four steps, and they are described in detail. The largest singular values and their left and right singular vectors can be approximated numerically without performing any operation with the full matrix. The low-rank approximation is computed due to a dynamic panel strategy of cross approximation technique.

#### Handling clusters with a task-based runtime system: application to Geophysics

Participants : Emmanuel Agullo, Hélène Barucq, Lionel Boillot, George Bosilca, Julien Diaz.

The extreme complexity of hardware platforms makes them harder and harder to program. To fully exploit such machines, the High Performance Computing community often uses a MPI + X (X being pthreads, OpenMP, Cuda ...) programming models. We propose to use an alternative solution consisting of programming at a higher level of abstractions by describing a scientific, high performance computing application as a sequence of tasks whose execution is delegated to a runtime system. We compared MPI-based version and task-based version on Geophysics simulations, especially on the DIVA code of Total. Our previous studies demonstrated the task-based paradigm superiority on shared memory architectures (CPU or MIC), we are now working on distributed and heterogeneous architectures (CPUs+MICs) and, according to our preliminary results, the performances are still better than the MPI-version.

This work has been presented to the conferences PRACEdays [60] , Rice Oil&Gas [43] and PASC [37] .