Skip to Main content Skip to Navigation
New interface
Journal articles

Generalized linear sampling method for elastic-wave sensing of heterogeneous fractures

Fatemeh Pourahmadian 1 Bojan B Guzina 1 Houssem Haddar 2 
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : A theoretical foundation is developed for active seismic reconstruction of fractures endowed with spatially-varying interfacial condition (e.g. partially-closed fractures, hydraulic fractures). The proposed indicator functional carries a superior localization property with no significant sensitivity to the fracture's contact condition, measurement errors, and illumination frequency. This is accomplished through the paradigm of the F-factorization technique and the recently developed Generalized Linear Sampling Method (GLSM) applied to elastodynamics. The direct scattering problem is formulated in the frequency domain where the fracture surface is illuminated by a set of incident plane waves, while monitoring the induced scattered field in the form of (elastic) far-field patterns. The analysis of the well-posedness of the forward problem leads to an admissibility condition on the fracture's (linearized) contact parameters. This in turn contributes toward establishing the applicability of the F-factorization method, and consequently aids the formulation of a convex GLSM cost functional whose minimizer can be computed without iterations. Such minimizer is then used to construct a robust fracture indicator function, whose performance is illustrated through a set of numerical experiments. For completeness, the results of the GLSM reconstruction are compared to those obtained by the classical linear sampling method (LSM).
Document type :
Journal articles
Complete list of metadata

Cited literature [36 references]  Display  Hide  Download
Contributor : Houssem Haddar Connect in order to contact the contributor
Submitted on : Friday, December 23, 2016 - 11:26:54 AM
Last modification on : Friday, November 18, 2022 - 9:25:30 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 7:24:47 AM


Files produced by the author(s)


  • HAL Id : hal-01421916, version 1


Fatemeh Pourahmadian, Bojan B Guzina, Houssem Haddar. Generalized linear sampling method for elastic-wave sensing of heterogeneous fractures. Inverse Problems, 2016, pp.28. ⟨hal-01421916⟩



Record views


Files downloads