HAL Id: hal-02076212 scientifjques de niveau recherche, publiés ou non, Perspectives of seismic imaging using FWI with reciprocity misfjt functional. Florian Faucher. To cite this version: Florian Faucher reciprocity misfjt functional Perspectives of seismic imaging using FWI with publics ou privés. recherche français ou étrangers, des laboratoires émanant des établissements d’enseignement et de destinée au dépôt et à la difgusion de documents https://hal.archives-ouvertes.fr/hal-02076212 L’archive ouverte pluridisciplinaire HAL , est abroad, or from public or private research centers. teaching and research institutions in France or The documents may come from lished or not. entifjc research documents, whether they are pub- archive for the deposit and dissemination of sci- HAL is a multi-disciplinary open access Submitted on 22 Mar 2019 Journées Ondes Sud-Ouest (JOSO), Mar 2019, Le Barp, France. hal-02076212
Perspectives of seismic imaging using FWI with reciprocity misfit functional Florian Faucher 1 , Giovanni Alessandrini 2 , H´ ene Barucq 1 , Maarten V. de Hoop 3 , el` Romina Gaburro 4 and Eva Sincich 2 . Journ´ ees Ondes Sud-Ouest, CEA Cesta, France Marth 12 th –14 th , 2019 1Project-Team Magique-3D, Inria Bordeaux Sud-Ouest, France. 2Dipartimento di Matematica e Geoscienze, Universit` a di Trieste, Italy. 3Department of Computational and Applied Mathematics and Earth Science, Rice University, Houston, USA 4Department of Mathematics and Statistics, Health Research Institute (HRI), University of Limerick, Ireland.
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Overview Introduction 1 Time-Harmonic Inverse Problem, FWI 2 Reconstruction procedure using dual-sensors data 3 Numerical experiments 4 Comparison of misfit functions Changing the numerical acquisition with J G Conclusion 5 Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 2/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Plan Introduction 1 Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 3/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Seismic inverse problem Reconstruction of subsurface Earth properties from seismic campaign: collection of wave propagation data at the surface. Surface Γ Source Receivers set Σ Subsurface area of interest Ω Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 4/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Seismic data We work with back-scattered partial data from one-side illumination on large domain. 0 (km s − 1 ) 0 5 depth (km) time (s) 5 1 4 3 2 10 2 3 0 2 4 6 8 15 x (km) 2 4 6 8 position (km) Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 5/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Seismic data We work with back-scattered partial data from one-side illumination on large domain. time (s) Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 5/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Seismic data We work with back-scattered partial data from one-side illumination on large domain. time (s) Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 5/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Seismic data We work with back-scattered partial data from one-side illumination on large domain. time (s) Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 5/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Seismic data Inverse problem : from seismic traces to subsurface? 0 5 time (s) 10 ? 15 2 4 6 8 position (km) nonlinear, ill-posed inverse problem. Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 5/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Plan Time-Harmonic Inverse Problem, FWI 2 Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 6/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Time-harmonic wave equation We consider propagation in acoustic media, given by the Euler’s equations, heterogeneous medium parameters κ and ρ : � − i ωρ ( x ) v ( x ) = −∇ p ( x ) , − i ω p ( x ) = − κ ( x ) ∇ · v ( x ) + f ( x ) . κ : bulk modulus, p : scalar pressure field, v : vectorial velocity field, ρ : density, ω : angular frequency. f : source term, Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 7/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Time-harmonic wave equation We consider propagation in acoustic media, given by the Euler’s equations, heterogeneous medium parameters κ and ρ : � − i ωρ ( x ) v ( x ) = −∇ p ( x ) , − i ω p ( x ) = − κ ( x ) ∇ · v ( x ) + f ( x ) . κ : bulk modulus, p : scalar pressure field, v : vectorial velocity field, ρ : density, ω : angular frequency. f : source term, The system reduces to the Helmholtz equation when ρ is constant, ( − ω 2 c ( x ) − 2 − ∆) p ( x ) = 0 , � κ ( x ) ρ ( x ) − 1 . with c ( x ) = Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 7/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Dual-sensors devices The inverse problem aims the recovery of the subsurface medium parameters from surface measurements of pressure and normal (vertical) velocity: � F : m = ( κ, ρ ) → {F p ; F v } = p ( x 1 ) , p ( x 2 ) , . . . , p ( x n rcv ); � v n ( x 1 ) , v n ( x 2 ) , . . . , v n ( x n rcv ) . Surface Γ Source Receivers set Σ Subsurface area of interest Ω D. Carlson, N. D. Whitmore et al. Increased resolution of seismic data from a dual-sensor streamer cable – Imaging of primaries and multiples using a dual-sensor towed streamer SEG, 2007 – 2010 CGG & Lundun Norway (2017–2018) TopSeis acquisition ( www.cgg.com/en/What-We-Do/Offshore/Products-and-Solutions/TopSeis ) Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 8/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Full Waveform Inversion (FWI) FWI provides a quantitative reconstruction of the subsurface parameters by solving a minimization problem, J ( m ) = 1 2 �F ( m ) − d � 2 . min m ∈M ◮ d are the observed data, ◮ F ( m ) represents the simulation using an initial model m : P. Lailly The seismic inverse problem as a sequence of before stack migrations Conference on Inverse Scattering: Theory and Application, SIAM, 1983 A. Tarantola Inversion of seismic reflection data in the acoustic approximation Geophysics, 1984 A. Tarantola Inversion of travel times and seismic waveforms Seismic tomography, 1987 Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 9/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion FWI, iterative minimization Initial model m 0 Observations k = 0 Forward problem F ω ( m k ) Misfit functional J Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 10/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion FWI, iterative minimization Initial model m 0 Observations k = 0 Forward problem F ω ( m k ) Misfit functional J Optimization procedure k = k + 1 1. Gradient 2. Search direction s k update model Update ω m k +1 = m k + α k s k 3. Line search α k Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 10/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion FWI, iterative minimization Initial model m 0 Observations k = 0 Forward problem F ω ( m k ) Misfit functional J Optimization procedure k = k + 1 1. Gradient 2. Search direction s k update model Update ω m k +1 = m k + α k s k 3. Line search α k Numerical methods ◮ Adjoint-method for the gradient computation, L-BFGS method, ◮ forward problem resolution with Discontinuous Galerkin methods, ◮ parallel computation, HPC, large-scale optimization, ◮ Rk: the code also works for elastic anisotropy and viscous media. Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 10/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion FWI, iterative minimization Initial model m 0 Observations k = 0 Forward problem F ω ( m k ) Misfit functional J Optimization procedure k = k + 1 1. Gradient 2. Search direction s k update model Update ω m k +1 = m k + α k s k 3. Line search α k ◮ > 10 5 : unknowns per physical parameter, ◮ > 10 6 : matrix size for discretization, ◮ we also study stability and convergence of the algorithm . . . Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 10/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Plan Reconstruction procedure using dual-sensors data 3 Florian Faucher – Reciprocity Waveform Inversion – March 12–14, 2019 11/22
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