Ambient noise correlation-based imaging with moving sensors

Mathias Fink; Josselin Garnier

doi:10.3934/ipi.2017022

Article Contents

2017, Volume 11, Issue 3: 477-500. Doi: 10.3934/ipi.2017022

This issue Previous Article Reconstruction in the partial data Calderón problem on admissible manifolds Next Article Time-invariant radon transform by generalized Fourier slice theorem

Ambient noise correlation-based imaging with moving sensors

Mathias Fink^1, and
Josselin Garnier^2, ,

1.
Institut Langevin, ESPCI and CNRS, PSL Research University, 1 rue Jussieu, 75005 Paris, France
2.
Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France

¹ Corresponding author
¹ Corresponding author

Received: February 29, 2016

Revised: January 31, 2017

Published: August 2017

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Abstract

Waves can be used to probe and image an unknown medium. Passive imaging uses ambient noise sources to illuminate the medium. This paper considers passive imaging with moving sensors. The motivation is to generate large synthetic apertures, which should result in enhanced resolution. However Doppler effects and lack of reciprocity significantly affect the imaging process. This paper discusses the consequences in terms of resolution and it shows how to design appropriate imaging functions depending on the sensor trajectory and velocity.

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Mathematics Subject Classification: Primary: 35R30, 35R60; Secondary: 78A46.

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Figure 1. Experimental set-up for passive Green's function estimation in Section 2. The circles are noise sources (at the surface $\partial B$), the triangle is a receiver at ${\boldsymbol{x}}_{\rm r}(t)$ on a circular trajectory (with radius $R_0$), and the shaded area is a complex medium

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Figure 2. Experimental set-up for passive reflector imaging in Section 3. The circles are noise sources (at the surface $\partial B$), the triangle is a receiver at ${\boldsymbol{x}}_{\rm r}(t)$ on a circular trajectory (with radius $R_0$), andthe diamond is a reflector at ${\boldsymbol{y}}_{\rm ref}$

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Figure 3. xperimental set-up for passive reflector imaging in Section 4. The circles are noise sources (at the surface $\partial B$), the triangle is a receiver on a linear trajectory (with length $a$), andthe diamond is a reflector

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Figure 4. Experimental set-up for passive Green's function estimation in Section 5. The circle is the trajectory of the moving source ${\boldsymbol{x}}_{\rm s}(t)$ and the two triangles are two observation points at $\boldsymbol{x}_1$ and $\boldsymbol{x}_2$

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Figure 5. Experimental set-up for the time-reversal experiment in Appendix A. The source x_s(t) is moving on a circular trajectory (with radius R₀) and the triangles are the sources/receivers of the time-reversal mirror (on ∂B)

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