Numerical Microlocal analysis of 2-D noisy harmonic plane and circular waves

Jean-David Benamou, Francis Collino and Simon Marmorat

2013

Publication type:

Paper in peer-reviewed journals

Journal:

Asymptotic Analysis, vol. 83, pp. 157-187

Publisher:

IOS Press

DOI:

10.3233/ASY-121157

HAL:

hal-00937691

Keywords :

plane waves, point source, inverse scattering

Abstract:

We present a mathematical and numerical analysis of the stability and accuracy of the NMLA (Numerical MicroLocal Analysis) method and its discretization. We restrict to homogeneous space and focus on the two simplest cases : 1) Noisy plane wave packets, 2) Noisy point source solutions. A stability result is obtained through the introduction of a new impedance observable. The analysis of the point source case leads to a modiﬁed second order (curvature dependent) correction of the algorithm. Since NMLA is local, this second order improved version can be applied to general data (heterogeneous media).

BibTeX:

@article{Ben-Col-Mar-2013,
    author={Jean-David Benamou and Francis Collino and Simon Marmorat },
    title={Numerical Microlocal analysis of 2-D noisy harmonic plane and 
           circular waves },
    doi={10.3233/ASY-121157 },
    journal={Asymptotic Analysis },
    year={2013 },
    volume={83 },
    pages={157--187},
}