219 research outputs found
Analysis of new direct sampling indicators for far-field measurements
This article focuses on the analysis of three direct sampling indicators
which can be used for recovering scatterers from the far-field pattern of
time-harmonic acoustic measurements. These methods fall under the category of
sampling methods where an indicator function is constructed using the far-field
operator. Motivated by some recent work, we study the standard indicator using
the far-field operator and two indicators derived from the factorization
method. We show the equivalence of two indicators previously studied as well as
propose a new indicator based on the Tikhonov regularization applied to the
far-field equation for the factorization method. Finally, we give some
numerical examples to show how the reconstructions compare to other direct
sampling methods
Looking back on inverse scattering theory
We present an essay on the mathematical development of inverse scattering theory for time-harmonic waves during the past fifty years together with some personal memories of our participation in these events
Generalized linear sampling method for elastic-wave sensing of heterogeneous fractures
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
-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 -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)
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