A priori estimates of attraction basins for velocity model reconstruction by time-harmonic Full Waveform Inversion and Data Space Reflectivity formulation

Abstract : Determination of background velocity by Full Waveform Inversion is known to be hampered by the local minima of the data misfit caused by the phase shifts associated to background perturbations. We give in this paper an a priori study of the convergence basins around any nominal velocity model, where the data misfit is guaranteed to have only one local - and hence global - minimum, provided the data error is below a given tolerable error level. The size of the attraction basin gives an upper bound to the error in the initial velocity model which ensures that local optimization algorithm will converge to the global mimimum. We use geometry in the data space in order to compute this size and the associated tolerable error without having to solve any FWI least squares minimization problem. Application is made to the inverse problem associated with wave equations in the time-frequency domain, using reflection data. We study first how, when FWI is used, frequency and search direction geometry influence the size of attraction basins, and how to foster it (e.g. complex frequency progression). Then, we compare the size of attraction basins for background velocities for the classical FWI and the Data Space Reflectivity MBTT formulation. We investigate the domain of validity of the MBTT reformulation, and show that it can increase the size of the background attraction basins by a factor of four to fifteen.
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https://hal.archives-ouvertes.fr/hal-02016373
Contributor : Florian Faucher <>
Submitted on : Thursday, February 14, 2019 - 11:34:19 AM
Last modification on : Friday, April 12, 2019 - 10:46:02 AM
Long-term archiving on : Wednesday, May 15, 2019 - 7:01:47 PM

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  • HAL Id : hal-02016373, version 1

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Hélène Barucq, Henri Calandra, Guy Chavent, Florian Faucher. A priori estimates of attraction basins for velocity model reconstruction by time-harmonic Full Waveform Inversion and Data Space Reflectivity formulation. [Research Report] RR-9253, Magique 3D; Inria Bordeaux Sud-Ouest; Université de Pau et des Pays de l'Adour. 2019. ⟨hal-02016373⟩

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