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Super-resolution in time-reversal focusing on a moving source |
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| Institution: | 1. Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris Diderot, 75205 Paris Cedex 13, France;2. Institut Langevin, UMR 7587, ESPCI ParisTech and CNRS, 1 rue Jussieu, 75238 Paris Cedex 05, France;1. Department of Mathematics and Computer Science, University of Basel, Spiegelgasse 1, CH-4051 Basel, Switzerland;2. CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France;3. UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France;4. INRIA Rocquencourt, Alpines, BP 105, 78153 Le Chesnay Cedex, France;5. Department of Mathematics, Ariel University, 40700, Ariel, Israel;1. Institute of Petroleum Geology and Geophysics, Russian Academy of Sciences, Ac. Koptyug Pr. 3, 630090 Novosibirsk, Russia;2. NTNU, S.P. Andersens veg 15a, 7491 Trondheim, Norway |
| Abstract: | This paper presents a detailed analysis of time-reversal experiments involving a moving point source that emits a pulse. Different configurations are addressed with full-aperture or partial-aperture time-reversal mirrors and with subsonic or supersonic sources. Doppler effects and lack of source-receiver reciprocity significantly affect the time-reversal refocusing when the velocity of the source becomes comparable as or larger than the speed of propagation. The main result is that refocusing can be enhanced when the velocity of the source becomes close to the speed of propagation compared to the classical diffraction-limited refocusing properties when the source does not move, and this super-resolution effect can be quantified by simple and explicit formulas. |
| Keywords: | Time reversal Super-resolution Moving sources |
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