HAL Id: hal-01928452 émanant des établissements d’enseignement et de Seismic reconstruction using FWI with dual-sensors data.. GDR MecaWave, Nov 2018, Fréjus, France. Maarten V. de Hoop, Florian Faucher, Giovanni Alessandrini, Romina Gaburro, Eva Sincich, et al.. To cite this version: Gaburro, Eva Sincich, Hélène Barucq Maarten V. de Hoop, Florian Faucher, Giovanni Alessandrini, Romina data. Seismic reconstruction using FWI with dual-sensors publics ou privés. recherche français ou étrangers, des laboratoires scientifjques de niveau recherche, publiés ou non, https://hal.archives-ouvertes.fr/hal-01928452v1 destinée au dépôt et à la difgusion de documents 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 20 Nov 2018 (v1), last revised 18 Dec 2019 (v2) hal-01928452v1
Seismic reconstruction using FWI with dual-sensors data. Florian Faucher 1 , Giovanni Alessandrini 2 , H´ ene Barucq 1 , Maarten V. de Hoop 3 , el` Romina Gaburro 4 and Eva Sincich 2 . GdR MecaWave, Fr´ ejus, France November 5 th –9 th , 2018 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 – Seismic inverse problem with dual-sensors – November 5–9, 2018 2/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Plan Introduction 1 Florian Faucher – Seismic inverse problem with dual-sensors – November 5–9, 2018 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 – Seismic inverse problem with dual-sensors – November 5–9, 2018 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 – Seismic inverse problem with dual-sensors – November 5–9, 2018 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 – Seismic inverse problem with dual-sensors – November 5–9, 2018 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 – Seismic inverse problem with dual-sensors – November 5–9, 2018 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 – Seismic inverse problem with dual-sensors – November 5–9, 2018 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 – Seismic inverse problem with dual-sensors – November 5–9, 2018 5/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Plan Time-Harmonic Inverse Problem, FWI 2 Florian Faucher – Seismic inverse problem with dual-sensors – November 5–9, 2018 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, for the recovery of the medium parameters κ and ρ : � − i ωρ v = −∇ p , − i ω p = − κ ∇ · v + f . κ : bulk modulus, p : scalar pressure field, v : vectorial velocity field, ρ : density, f : source term, ω : angular frequency. Florian Faucher – Seismic inverse problem with dual-sensors – November 5–9, 2018 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, for the recovery of the medium parameters κ and ρ : � − i ωρ v = −∇ p , − i ω p = − κ ∇ · v + f . κ : bulk modulus, p : scalar pressure field, v : vectorial velocity field, ρ : density, f : source term, ω : angular frequency. The system reduces to the Helmholtz equation when ρ is constant, ( − ω 2 c − 2 − ∆) p = 0 , � κρ − 1 . with c = Florian Faucher – Seismic inverse problem with dual-sensors – November 5–9, 2018 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 – Seismic inverse problem with dual-sensors – November 5–9, 2018 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 – Seismic inverse problem with dual-sensors – November 5–9, 2018 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 – Seismic inverse problem with dual-sensors – November 5–9, 2018 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 3. Line search α k m k +1 = m k + α k s k Florian Faucher – Seismic inverse problem with dual-sensors – November 5–9, 2018 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 3. Line search α k m k +1 = m k + α k s k Numerical methods ◮ Adjoint-method for the gradient computation, ◮ 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 – Seismic inverse problem with dual-sensors – November 5–9, 2018 10/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Plan Reconstruction procedure using dual-sensors data 3 Florian Faucher – Seismic inverse problem with dual-sensors – November 5–9, 2018 11/22
Intro Inverse Problem Reconstruction procedure Experiments Conclusion Minimization of the cost function The appropriate misfit functional to minimize with pressure and vertical velocity measurements. ◮ Compare the pressure and velocity fields separately: 1 p � 2 + 1 2 �F ( s ) − d ( s ) 2 �F ( s ) − d ( s ) � v � 2 . J L 2 = p v source Florian Faucher – Seismic inverse problem with dual-sensors – November 5–9, 2018 12/22
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