Missions

Participate in the development of the 3D imaging code FFWI. FFWI is a frequency-domain Full Waveform Inversion (FWI) code.
Interface the iterative solver GMRES (Generalized Minimal RESidual) and the two-level Optimized Restricted Additive Schwarz (ORAS) domain-decomposition based preconditioner in the FFWI code to benefit from the scalability of iterative methods.

Activités

- Interfacing the hybrid direct/iterative solver based on domain-decomposition ORAS preconditioner in 3D frequency-domain FWI code FFWI with PETSc library.
- Development of finite-difference and finite-element schemes for time-harmonic wave equation.
- Coupling between acoustic and elastic schemes for wave simulation in marine environments.
- Assess the performances of the solver against several representative benchmarks when the Helmholtz problem is solved with a hybrid direct/iterative solver preconditioned by the bi-level ORAS domain decomposition method.
- Development of optimal strategies for efficient processing of multiple right-hand sides (Block and recycling strategies such as the Krylov subspace recycling method (GCRO-DR) .

Compétences

- Numerical methods for partial differential equations (linear wave equation).
- Finite-difference and finite-element methods.
- Linear algebra (direct and iterative methods).
- Domain decomposition methods.
- Numerical optimization.
- Parallel computing (MPI, OpenMP)
- Programming languages: Fortran90, C++, MPI, OpenMP.
- Knowledge of the PETSc library.
- Imaging by Full Waveform Inversion (FWI)

Contexte de travail

FWI has many applications including seismic imaging at various scales (near surface for civil engineering, sedimentary basins in oil exploration, deep crust for academic exploration, global earth in earthquake seismology), medical imaging, non destructive control, … FWI aims at estimating the constitutive properties of a medium from acoustic or elastic waves. Wave propagation is triggered by a source device before being recorded by a receiver device. FWI is formulated as the minimization of the misfit between measured data and numerically simulated data with finite-difference or finite-element methods. This nonlinear minimization problem, which can involve large data volume and millions to billions of parameters, is solved with local optimization methods (gradient methods), where the gradient of the objective function is computed with the so-called adjoint-state method. In our case, FWI is implemented in the frequency domain, where wave simulation is a boundary value problem that requires the solution of sparse system of linear equation with multiple right-hand sides (Helmholtz problem). This system can be solved with direct methods for sparse matrices or hybrid direct/iterative methods with domain-decomposition preconditioner. FFWI has been tested so far with direct methods, which are very efficient to tackle a large number of right-hand side but which suffer from their limited scalability to solve very large problems.
In ORAS, each local problem will be solved with the sparse multifrontal direct solver MUMPS. Once this interfacing will have been performed with PETSc library, the computational performance of the solver with be assessed with different realistic benchmarks involving millions to billions of unknowns. Once the accuracy and the computational efficiency of the solver will have been verified, the FFWI code will be applied to an industrial seismic dataset collected by a device of 650 ocean bottom seismometers and triggered by 600,000 sources to image a sedimentary basin in the continental shelf, offshore Australia. These tasks will be supervized by S. Operto and L. Combe at Geoazur Institute of University of Côte d'Azur (UCA) to guide the interfacing of the ORAS solver in FFWI and its assessment with realistic benchmarks. Mathematical and numerical aspects will be co-supervized by V. Dolean (Laboratoire de mathématiques J. A. Dieudonné (LJAD) de l'UCA), P. Jolivet (LIP6, Sorbonne Univesité) et P.-H. Tournier (Laboratoire de mathématiques J.-L. Lions (LJLL) de l'Université Pierre et Marie Curie). Once the ORAS+GMRES+MUMPS solver will have been implemented in FFWI and validated with benchmarks, other developments tasks can be scheduled such as numerical schemes for elastic physics, new optimization algorithm with extended search space and various regularizations based on proximal algorithms.

The recruited ingenieer's work will be carried out at the Geoazur institute (https://geoazur.oca.eu/fr/acc-geoazur) and will be supervised by S. Operto and L. Combe S. Operto is a geophysicist specialized in imaging methods and FWI in particular. L. Combe is a HPC research engineer at Geoazur institute in charge of the development and maintenance of wave simulation/FWI codes. Located at Valbonne-Sophia Antipolis, Geoazur is a multidisciplinary laboratory in Earth Science, which is part of University Côte d'Azur (UCA), CNRS, Observatory of Côte d'Azur (OCA) and Institute for Research and Development (IRD). It hosts 170 persons, researchers, engineers and technicians, PhD students, through seven research teams: SEISMES, MARGES, RISQUES, mouvGS, GeoMAT, Imaging & Waves, ASTROGEO-GPM and different observatories in the field of astronomy, geodesy, seismology and seabed technologies. The researc engineer will belong to the team Imaging & Waves to develop the wave equation solver and interface it with the Full Waveform Inversion (FWI) codes. To develop and run codes, the researcher will have access to several computational infrastructures such as mesocentre SIGAMM hosted by OCA (https://www.oca.eu/fr/mesocentre-sigamm), the CICADA cluster of UCA and the supercomputers of GENCI (http://www.genci.fr/fr). This research will be performed in the framework of the WIND project (https://www.geoazur.fr/WIND) sponsored by a consortium of oil companies gathering AkerBP, ExxonMobil, Petrobras, Shell and SINOPEC and coordinated by S. Operto. The development of the wave equation solver will be performed from existing tools such as the HPDDM library (http://github.com/hpddm/hpddm), FreeFEM (http://www.freefem.org/ff++), PETSc (https://petsc.org/release) under the supervision of V. Dolean (LJAD), P. Jolivet (LIP6) and P.-H. Tournier (LJLL). As a result, the researcher will be part of a multi-disciplinary team gathering applied mathematicians, computer scientists and computational geophysicists and will have the opportunity to develop interactions with both the academic and industrial communities of researchers involved in the field of imaging.

Contraintes et risques

The status of the work will be presented twice by the sponsors of the WIND project as well as at the annual conferences of the EAGE (European Association of Geoscientists & Engineers) and the SEG (Society of Exploration Geophysics).