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Proceedings/Recueil Des Communications Année : 2013

Multi-level, Multi-frequency, compressed Full Waveform Inversion

Résumé

We study the inverse boundary value problem for the wave equation and recovery of the wavespeedupon taking a time-Fourier transform of the data. We design a hierarchical compressed reconstruction in a multi-level scheme for the inverse boundary value problem associated with the Helmholtz equation using the Dirichlet-to-Neumann map, or the single-layer potential operator, at selected frequencies as the data. The compression isbased on a domain partitioning of the subsurface, while the hierarchy is straightforwardedly established throughrefinement. The coefficients are assumed to be piecewise constant functions following the domain partitioning, thusallowing the presence of conormal singularities (causing reflections and diffractions); these guarantee a Lipschitzstability estimate for the inverse problem which gives a radius of convergence, related to the stability constant, of thescheme even in the case of partial data. The stability constant grows exponentially with the number of subdomainsin the domain partitioning, whence the compression. The frequencies are selected to control the approximationerrors in the data due to the compression at the different levels in the scheme. The stability constants (number ofsubdomains) and approximations errors (frequencies) are coupled through a condition between levels for convergenceof the multi-level scheme. We use Haar wavelets for the compression in alternative strategies providing a gradualincrease in the number of subdomains in the domain parititioning via adaptive, local multi-scale refinement. Weinclude visco-acoustic behavior and carry out numerical experiments.
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Dates et versions

hal-01085816 , version 1 (21-11-2014)

Identifiants

  • HAL Id : hal-01085816 , version 1

Citer

Florian Faucher, Maarten V. de Hoop, Henri Calandra, Lingyun Qiu, Christian Rivera. Multi-level, Multi-frequency, compressed Full Waveform Inversion. Proceedings of the Project Review, Geo-Mathematical Imaging Group, Apr 2013, Chicago, United States. 1, pp.1-21, 2013, Proceedings of the Project Review, Geo-Mathematical Imaging Group. ⟨hal-01085816⟩
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