On the Parametrization of Slope Tomography: Its Implication on the Velocity-position Coupling

Abstract : Seismic tomography seeks to reconstruct the subsurface parameters, mainly wavespeeds. In reflection/diffraction tomography, an additional parameter class is inherently introduced: the scattering positions. The underlying inverse problem is awkward due to the ill-famed velocity-position coupling. We review different optimization strategies in the frame of slope tomography, namely tomographic approaches based on locally coherent seismic events associated with reflection/diffraction from small reflector segments/diffractors. The latter are described by their two-way traveltimes and slopes, the horizontal component of slowness vector at the source and receiver positions). Three plausible inversion strategies exist to address this multi-variate problem: the first consists of alternating between scattering position and wavespeed updates to bypass the coupling issue. The second jointly updates both sought parameters with the risk of ill-posedness. The third one relies on the projection of the model subspace spanned by scattering positions onto the model subspace spanned by velocities leading to a mono-variate reduced-space inversion. This projection is implemented in the adjoint-state method by using two focusing equations satisfied by two observables (one slope and two-way traveltimes) as constraints. Assessing these strategies on synthetic and real cases shows that the reduced-space approach exhibits superior performance while not needing any scaling of the data and model spaces.
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https://hal.archives-ouvertes.fr/hal-02356162
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Submitted on : Friday, November 8, 2019 - 3:48:28 PM
Last modification on : Saturday, November 9, 2019 - 1:51:35 AM

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S. Sambolian, S. Operto, A. Ribodetti, B. Tavakoli F.. On the Parametrization of Slope Tomography: Its Implication on the Velocity-position Coupling. SIAM Conference on Mathematical & Computational Issues in the Geosciences, Mar 2019, Houston, United States. ⟨hal-02356162⟩

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