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Sol J, Prod'homme H, Le Magoarou L, Del Hougne P. Experimentally realized physical-model-based frugal wave control in metasurface-programmable complex media. Nat Commun 2024; 15:2841. [PMID: 38565537 PMCID: PMC10987616 DOI: 10.1038/s41467-024-46916-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Accepted: 03/04/2024] [Indexed: 04/04/2024] Open
Abstract
Metasurface-programmable radio environments are considered a key ingredient of next-generation wireless networks. Yet, identifying a metasurface configuration that yields a desired wireless functionality in an unknown complex environment was so far only achieved with closed-loop iterative feedback schemes. Here, we introduce open-loop wave control in metasurface-programmable complex media by estimating the parameters of a compact physics-based forward model. Our experiments demonstrate orders-of-magnitude advantages over deep-learning-based digital-twin benchmarks in terms of accuracy, compactness and required calibration examples. Strikingly, our parameter estimation also works without phase information and without providing measurements for all considered scattering coefficients. These unique generalization capabilities of our pure-physics model unlock unforeseen and previously inaccessible frugal wave control protocols that significantly alleviate the measurement complexity. For instance, we achieve coherent wave control (focusing or perfect absorption) and phase-shift-keying backscatter communications in metasurface-programmable complex media with intensity-only measurements. Our approach is also directly relevant to dynamic metasurface antennas, microwave-based signal processors and emerging in situ reconfigurable nanophotonic, optical and room-acoustical systems.
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Affiliation(s)
- Jérôme Sol
- Univ Rennes, INSA Rennes, CNRS, IETR - UMR 6164, F-35000, Rennes, France
| | - Hugo Prod'homme
- Univ Rennes, INSA Rennes, CNRS, IETR - UMR 6164, F-35000, Rennes, France
| | - Luc Le Magoarou
- Univ Rennes, INSA Rennes, CNRS, IETR - UMR 6164, F-35000, Rennes, France
| | - Philipp Del Hougne
- Univ Rennes, INSA Rennes, CNRS, IETR - UMR 6164, F-35000, Rennes, France.
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2
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Tan T, Godin OA. Rapid emergence of empirical Green's functions from cross-correlations of ambient sound on continental shelfa). THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2023; 154:3784-3798. [PMID: 38109405 DOI: 10.1121/10.0023931] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Accepted: 11/16/2023] [Indexed: 12/20/2023]
Abstract
Applications of acoustic noise interferometry to passive remote sensing of the ocean rely on retrieval of empirical Green's functions (EGFs) from cross-correlations of ambient sound at spatially separated points. At ranges of tens of ocean depths, obtaining stable and accurate EGF estimates usually requires noise averaging periods of hours or days. Using data acquired in the Shallow Water 2006 experiment on the continental shelf off New Jersey, it is found that at ranges of 40-70 ocean depths, the EGFs can be retrieved with noise averaging times as short as 64 s. The phenomenon is observed for various receiver pairs but does not occur simultaneously in all azimuthal directions. The rapidly emerging EGFs have a wider frequency band and a richer normal mode content than the EGFs obtained in previous studies using long averaging times and are better suited for monitoring physical processes in the water column. Available acoustic and environmental data is examined to understand the conditions leading to rapid EGF emergence from diffuse noise. Strong intermittency is observed in the horizontal directionality of ambient sound. Rapid emergence of EGF in shallow-water waveguide is found to occur when the directionality of diffuse ambient noise is favorable.
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Affiliation(s)
- Tsuwei Tan
- Department of Marine Science, ROC Naval Academy, 813 Kaohsiung, Taiwan
| | - Oleg A Godin
- Department of Physics, Naval Postgraduate School, 833 Dyer Road, Monterey, California 93943-5216, USA
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3
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Wapenaar K. Wave-field representations with Green's functions, propagator matrices, and Marchenko-type focusing functions. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2022; 151:587. [PMID: 35105010 DOI: 10.1121/10.0009236] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2021] [Accepted: 12/13/2021] [Indexed: 06/14/2023]
Abstract
Classical acoustic wave-field representations consist of volume and boundary integrals, of which the integrands contain specific combinations of Green's functions, source distributions, and wave fields. Using a unified matrix-vector wave equation for different wave phenomena, these representations can be reformulated in terms of Green's matrices, source vectors, and wave-field vectors. The matrix-vector formalism also allows the formulation of representations in which propagator matrices replace the Green's matrices. These propagator matrices, in turn, can be expressed in terms of Marchenko-type focusing functions. An advantage of the representations with propagator matrices and focusing functions is that the boundary integrals in these representations are limited to a single open boundary. This makes these representations a suitable basis for developing advanced inverse scattering, imaging and monitoring methods for wave fields acquired on a single boundary.
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Affiliation(s)
- Kees Wapenaar
- Department of Geoscience and Engineering, Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands
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4
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Davy M, Besnier P, Del Hougne P, de Rosny J, Richalot E, Sarrazin F, Savin DV, Mortessagne F, Kuhl U, Legrand O. Diffuse field cross-correlations: Scattering theory and electromagnetic experiments. Phys Rev E 2021; 104:044204. [PMID: 34781571 DOI: 10.1103/physreve.104.044204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Accepted: 09/23/2021] [Indexed: 11/07/2022]
Abstract
The passive estimation of impulse responses from ambient noise correlations arouses increasing interest in seismology, acoustics, optics, and electromagnetism. Assuming the equipartition of the noise field, the cross-correlation function measured with noninvasive receiving probes converges towards the difference of the causal and anticausal Green's functions. Here, we consider the case when the receiving field probes are antennas which are well coupled to a complex medium-a scenario of practical relevance in electromagnetism. We propose a general approach based on the scattering matrix formalism to explore the convergence of the cross-correlation function. The analytically derived theoretical results for chaotic systems are confirmed in microwave measurements within a mode-stirred reverberation chamber. This study provides fundamental insight into the Green's function retrieval technique and paves the way for a new technique to characterize electromagnetic antennas.
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Affiliation(s)
- Matthieu Davy
- Univ Rennes, INSA Rennes, CNRS, IETR - UMR 6164, F-35000 Rennes, France
| | - Philippe Besnier
- Univ Rennes, INSA Rennes, CNRS, IETR - UMR 6164, F-35000 Rennes, France
| | - Philipp Del Hougne
- Univ Rennes, INSA Rennes, CNRS, IETR - UMR 6164, F-35000 Rennes, France.,Université Côte d'Azur, CNRS, Institut de Physique de Nice, UMR 7010, 06108 Nice, France
| | - Julien de Rosny
- ESPCI Paris, PSL Research University, Institut Langevin, F-75005 Paris, France
| | - Elodie Richalot
- ESYCOM lab, Univ Gustave Eiffel, CNRS, F-77454 Marne-la-Vallée, France
| | - François Sarrazin
- ESYCOM lab, Univ Gustave Eiffel, CNRS, F-77454 Marne-la-Vallée, France
| | - Dmitry V Savin
- Department of Mathematics, Brunel University London, Uxbridge UB8 3PH, United Kingdom
| | - Fabrice Mortessagne
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, UMR 7010, 06108 Nice, France
| | - Ulrich Kuhl
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, UMR 7010, 06108 Nice, France
| | - Olivier Legrand
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, UMR 7010, 06108 Nice, France
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5
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Meles GA, van der Neut J, van Dongen KWA, Wapenaar K. Wavefield finite time focusing with reduced spatial exposure. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2019; 145:3521. [PMID: 31255146 DOI: 10.1121/1.5110716] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2018] [Accepted: 05/15/2019] [Indexed: 06/09/2023]
Abstract
Wavefield focusing is often achieved by time-reversal mirrors, where wavefields emitted by a source located at the focal point are evaluated at a closed boundary and sent back, after time-reversal, into the medium from that boundary. Mathematically, time-reversal mirrors are derived from closed-boundary integral representations of reciprocity theorems. In heterogeneous media, time-reversal focusing theoretically involves in- and output signals that are infinite in time and the resulting waves propagate through the entire medium. Recently, integral representations have been derived for single-sided wavefield focusing. Although the required input signals for this approach are finite in time, the output signals are not and, similar to time-reversal mirroring, the resulting waves propagate through the entire medium. Here, an alternative solution for double-sided wavefield focusing is derived. This solution is based on an integral representation where in- and output signals are finite in time, and where the energy of the waves propagating in the layer embedding the focal point is smaller than with time-reversal focusing. The potential of the proposed method is explored with numerical experiments involving a head model consisting of a skull enclosing a brain.
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Affiliation(s)
- Giovanni Angelo Meles
- Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, the Netherlands
| | - Joost van der Neut
- Faculty of Applied Sciences, Delft University of Technology, Delft, the Netherlands
| | - Koen W A van Dongen
- Faculty of Applied Sciences, Delft University of Technology, Delft, the Netherlands
| | - Kees Wapenaar
- Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, the Netherlands
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6
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Godin OA. Acoustic noise interferometry in a time-dependent coastal ocean. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2018; 143:595. [PMID: 29495710 DOI: 10.1121/1.5022287] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Interferometry of underwater noise provides a way to estimate physical parameters of the water column and the seafloor without employing any controlled sound sources. In applications of acoustic noise interferometry to coastal oceans, the propagation environment changes appreciably during the averaging times that are necessary for the Green's functions to emerge from noise cross-correlations. Here, a theory is developed to quantify the effects of nonstationarity of the propagation environment on two-point correlation functions of diffuse noise. It is shown that temporal variability of the ocean limits from above the frequency range, where noise cross-correlations approximate the Green's functions. The theoretical predictions are in quantitative agreement with results of the 2012 noise interferometry experiment in the Florida Straits. The loss of coherence at high frequencies constrains the passive acoustic remote sensing to exploiting a low-frequency part of measured noise cross-correlations, thus limiting the resolution of deterministic inversions. On the other hand, the passively measured coherence loss contains information about statistical characteristics of the ocean dynamics at unresolved spatial and temporal scales.
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Affiliation(s)
- Oleg A Godin
- Department of Physics, Naval Postgraduate School, 833 Dyer Road, Monterey, California 93943-5216, USA
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7
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Li X, Chi J, Gao D, Li J, Wang N. Extraction of scattering echo time by surf noise background subtracted autocorrelation. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2017; 142:EL1. [PMID: 28764436 DOI: 10.1121/1.4989996] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Extracting echo time is an important step in scatterer detection by ambient noise, while in general the scattered signal is weak and submerged in the background. An experiment of a Polyvinyl chloride pipe in a coastline surf noise environment is designed to extract the pipe's echo time by noise autocorrelation. As expected, the scattered wave of the pipe is submerged in an autocorrelation signal. A method called background subtracted autocorrelation is proposed in this paper, which can retrieve scattered echo time from autocorrelation signal effectively. And the biggest relative error of extracted echo time is less than 2% in the experiment.
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Affiliation(s)
- Xiaolei Li
- Department of Marine Technology, Ocean University of China, Qingdao 266100, China , , , ,
| | - Jing Chi
- Department of Marine Technology, Ocean University of China, Qingdao 266100, China , , , ,
| | - Dazhi Gao
- Department of Marine Technology, Ocean University of China, Qingdao 266100, China , , , ,
| | - Jie Li
- Department of Marine Technology, Ocean University of China, Qingdao 266100, China , , , ,
| | - Ning Wang
- Department of Marine Technology, Ocean University of China, Qingdao 266100, China , , , ,
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8
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Li X, Yu G, Wang N, Gao D, Wang H. Flux projection beamforming for monochromatic source localization in enclosed space. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2017; 141:EL1. [PMID: 28147621 DOI: 10.1121/1.4973193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Monochromatic sound source localization becomes difficult in enclosed space. According to the reciprocity theorem, a self-consistent method of source localization in enclosed space, referred to as the flux projection beamforming, is proposed, only using the measurement of the sound pressure and normal velocity on the closed boundary at a single frequency. Its validity is examined both by experiment and simulation.
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Affiliation(s)
- Xiaolei Li
- Department of Marine Technology, Ocean University of China, Qingdao 266100, China , , , ,
| | - Gaokun Yu
- Department of Marine Technology, Ocean University of China, Qingdao 266100, China , , , ,
| | - Ning Wang
- Department of Marine Technology, Ocean University of China, Qingdao 266100, China , , , ,
| | - Dazhi Gao
- Department of Marine Technology, Ocean University of China, Qingdao 266100, China , , , ,
| | - Haozhong Wang
- Department of Marine Technology, Ocean University of China, Qingdao 266100, China , , , ,
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9
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Davy M, de Rosny J, Besnier P. Green's Function Retrieval with Absorbing Probes in Reverberating Cavities. PHYSICAL REVIEW LETTERS 2016; 116:213902. [PMID: 27284658 DOI: 10.1103/physrevlett.116.213902] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2015] [Indexed: 06/06/2023]
Abstract
The cross-correlation of a diffuse wave field converges toward the difference between the anticausal and causal Green's functions between two points. This property has paved the way to passive imaging using ambient noise sources. In this Letter, we investigate Green's function retrieval in electromagnetism. Using a model based on the fluctuation dissipation theorem, we demonstrate theoretically that the cross-correlation function strongly depends on the absorption properties of the receivers. This is confirmed in measurements within a reverberation chamber. In contrast to measurements with noninvasive probes, we show that only the anticausal Green's function can be retrieved with a matched antenna. Finally, we interpret this result as an equivalent time-reversal experiment with an electromagnetic sink.
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Affiliation(s)
- Matthieu Davy
- Institut d'Electronique et de Télécommunications de Rennes, UMR CNRS 6164, Université de Rennes 1, Rennes 35042, France
| | - Julien de Rosny
- ESPCI ParisTech, PSL Research University, CNRS, Institut Langevin-1 rue Jussieu, F-75005 Paris, France
| | - Philippe Besnier
- Institut d'Electronique et de Télécommunications de Rennes, UMR CNRS 6164, INSA de Rennes, Rennes 35708, France
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10
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Badon A, Lerosey G, Boccara AC, Fink M, Aubry A. Retrieving time-dependent Green's functions in optics with low-coherence interferometry. PHYSICAL REVIEW LETTERS 2015; 114:023901. [PMID: 25635547 DOI: 10.1103/physrevlett.114.023901] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2014] [Indexed: 06/04/2023]
Abstract
We report on the passive measurement of time-dependent Green's functions in the optical frequency domain with low-coherence interferometry. Inspired by previous studies in acoustics and seismology, we show how the correlations of a broadband and incoherent wave field can directly yield the Green's functions between scatterers of a complex medium. Both the ballistic and multiple scattering components of the Green's function are retrieved. This approach opens important perspectives for optical imaging and characterization in complex scattering media.
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Affiliation(s)
- Amaury Badon
- Institut Langevin, ESPCI ParisTech, PSL Research University, CNRS UMR 7587, 1 rue Jussieu, 75005 Paris, France
| | - Geoffroy Lerosey
- Institut Langevin, ESPCI ParisTech, PSL Research University, CNRS UMR 7587, 1 rue Jussieu, 75005 Paris, France
| | - Albert C Boccara
- Institut Langevin, ESPCI ParisTech, PSL Research University, CNRS UMR 7587, 1 rue Jussieu, 75005 Paris, France
| | - Mathias Fink
- Institut Langevin, ESPCI ParisTech, PSL Research University, CNRS UMR 7587, 1 rue Jussieu, 75005 Paris, France
| | - Alexandre Aubry
- Institut Langevin, ESPCI ParisTech, PSL Research University, CNRS UMR 7587, 1 rue Jussieu, 75005 Paris, France
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11
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Erkol H, Unlu MB. Virtual source method for diffuse optical imaging. APPLIED OPTICS 2013; 52:4933-4940. [PMID: 23852209 DOI: 10.1364/ao.52.004933] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2013] [Accepted: 05/20/2013] [Indexed: 06/02/2023]
Abstract
The Green's function for diffusive wave propagation can be obtained by utilizing the representation theorems of the convolution type and the correlation type. In this work, the Green's function is retrieved by making use of the Robin boundary condition and the representation theorems for diffusive media. The diffusive Green's function between two detectors for photon flux is calculated by combining detector readings due to point light sources and utilizing virtual light sources at the detector positions in optical tomography. Two dimensional simulations for a circular region with eight sources and eight detectors located on the boundary are performed using a finite element method to demonstrate the feasibility of virtual sources. The most important potential application would be the replacement of noisy measurements with synthetic measurements that are provided by the virtual sources. This becomes an important issue in small animal and human studies. In addition, the same method may also be used to reduce the imaging time.
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Affiliation(s)
- Hakan Erkol
- Department of Physics, Bogazici University, Bebek, Istanbul, Turkey.
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12
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Davy M, Fink M, de Rosny J. Green's function retrieval and passive imaging from correlations of wideband thermal radiations. PHYSICAL REVIEW LETTERS 2013; 110:203901. [PMID: 25167409 DOI: 10.1103/physrevlett.110.203901] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2012] [Revised: 03/08/2013] [Indexed: 06/03/2023]
Abstract
We present an experimental demonstration of electromagnetic Green's function retrieval from thermal radiations in anechoic and reverberant cavities. The Green's function between two antennas is estimated by cross correlating milliseconds of decimeter noise. We show that the temperature dependence of the cross-correlation amplitude is well predicted by the blackbody theory in the Rayleigh-Jeans limit. The effect of a nonuniform temperature distribution on the cross-correlation time symmetry is also explored. Finally, we open a new way to image scatterers using ambient thermal radiations.
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Affiliation(s)
- Matthieu Davy
- Institut Langevin, ESPCI ParisTech, CNRS UMR 7587, 1 rue Jussieu, 75005 Paris, France
| | - Mathias Fink
- Institut Langevin, ESPCI ParisTech, CNRS UMR 7587, 1 rue Jussieu, 75005 Paris, France
| | - Julien de Rosny
- Institut Langevin, ESPCI ParisTech, CNRS UMR 7587, 1 rue Jussieu, 75005 Paris, France
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13
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Wapenaar K, Douma H. A unified optical theorem for scalar and vectorial wave fields. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2012; 131:3611-3626. [PMID: 22559339 DOI: 10.1121/1.3701880] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers.
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Affiliation(s)
- Kees Wapenaar
- Department of Geoscience and Engineering, Delft University of Technology, PO Box 5048, 2600 GA Delft, The Netherlands.
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14
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Margerin L, Sato H. Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 130:3674-3690. [PMID: 22225024 DOI: 10.1121/1.3652856] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell T-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell T-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The T-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.
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Affiliation(s)
- Ludovic Margerin
- Institut de Recherche en Astrophysique et Planétologie, Observatoire Midi-Pyrénées, C.N.R.S., 14 Avenue Edouard Belin, Toulouse, France.
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15
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Brown MG. Noise interferometry in an inhomogeneous environment in the geometric limit. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 130:EL173-EL179. [PMID: 21974488 DOI: 10.1121/1.3610260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
An approximation to the transient Green's function G(x(a)∣x(b),t) between points x(a) and x(b) can be estimated by taking the time derivative of the correlation function C(ab)(t) of records of ambient noise measured at locations x(a) and x(b). From the general relationship between C(ab)(t) and G(x(a)∣x(b),t) it is shown, using a stationary-phase-like argument, that in an inhomogeneous environment in the geometric limit C(ab)(t) consists of a superposition of signed step functions and two-sided logarithmic singularities that are delayed in time by the travel times of the rays connecting x(a) and x(b).
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Affiliation(s)
- Michael G Brown
- Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33149, USA.
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16
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Slob E, Weiss CJ. Lagrangian and energy forms for retrieving the impulse response of the Earth due to random electromagnetic forcing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:027601. [PMID: 21929146 DOI: 10.1103/physreve.84.027601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2011] [Revised: 07/05/2011] [Indexed: 05/31/2023]
Abstract
We distinguish between trivial and nontrivial differences in retrieving the real or imaginary parts of the Green's function. Trivial differences come from different Green's function definitions. The energy and lagrangian forms constitute nontrivial differences. Magnetic noise sources suffice to extract the quasistatic electromagnetic-field Earth impulse response in the lagrangian form. This is of interest for Earth subsurface imaging. A numerical example demonstrates that all source vector components are necessary to extract a single-field vector component.
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Affiliation(s)
- Evert Slob
- Department of Geotechnology, Delft University of Technology, Post Office Box 5048, NL-2600 GA Delft, The Netherlands.
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17
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Buckingham MJ. On the two-point cross-correlation function of anisotropic, spatially homogeneous ambient noise in the ocean and its relationship to the Green's function. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 129:3562-3576. [PMID: 21682382 DOI: 10.1121/1.3573989] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
It is well established that the free-space Green's function can be recovered from the two-point cross-correlation function of a random noise field if the noise is white and isotropic. Ambient noise in the ocean rarely satisfies either of these conditions. However, a non-uniform spectrum could be pre-whitened by the application of a suitable filter but anisotropy cannot be so readily eliminated. To investigate the effects of vertical anisotropy, three azimuthally uniform, spatially homogeneous noise fields are analyzed, two of which are idealized, while the third is representative of ambient noise in the deep ocean. In each case, the coherence function, the cross-correlation function, and the derivative of the latter with respect to the correlation delay, are derived for vertical and horizontal alignments of the sensor pair. With vertical sensors, any step-function discontinuity in the directional density function is mapped into a delta function at an appropriate time delay in the derivative (with respect to time delay) of the cross-correlation function. No such mapping occurs with horizontal sensors. In this case, only horizontally traveling noise can generate delta functions in the derivative of the cross-correlation function, and these always appear at the retarded time on either side of the origin.
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Affiliation(s)
- Michael J Buckingham
- Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0238, USA.
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18
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Douma H, Vasconcelos I, Snieder R. The reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 129:2765-2771. [PMID: 21568381 DOI: 10.1121/1.3569728] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
By analyzing correlation-type reciprocity theorems for wavefields in perturbed media, it is shown that the correlation-type reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem. This reciprocity theorem, in contrast to the generalized optical theorem, allows for inhomogeneous background properties and does not make use of a far-field condition. This theorem specializes to the generalized optical theorem when considering a finite-size scatterer embedded in a homogeneous background medium and when utilizing the far-field condition. Moreover, it is shown that the reciprocity theorem for the scattered field is responsible for the cancellation of non-physical (spurious) arrivals in seismic interferometry, and as such provides the mathematical description of such arrivals. Even though here only acoustic waves are treated, the presented treatment is not limited to such wavefields and can be generalized to general wavefields. Therefore, this work provides the framework for deriving equivalents of the generalized optical theorem for general wavefields.
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Affiliation(s)
- Huub Douma
- ION Geophysical∕GXT Imaging Solutions, 225 East 16th Avenue, Suite 1200, Denver, Colorado 80203, USA.
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Snieder R, Fleury C. Cancellation of spurious arrivals in Green's function retrieval of multiple scattered waves. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2010; 128:1598-1605. [PMID: 20968332 DOI: 10.1121/1.3483722] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The Green's function for wave propagation can be extracted by cross-correlating field fluctuations excited on a closed surface that surrounds the employed receivers. This study treats an acoustic multiple scattering medium with discrete scatterers and shows that for a given source the cross-correlation of waves propagating along most combinations of scattering paths gives unphysical arrivals. Because theory predicts that the true Green's function is retrieved, such unphysical arrivals must cancel after integration over all sources. This cancellation occurs because the scattering amplitude of each scatterer satisfies the generalized optical theorem. The cross-correlation of scattered waves with themselves does not lead to the correct retrieval of scattered waves, because the cross-terms between the direct and scattered waves is essential.
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Affiliation(s)
- Roel Snieder
- Center for Wave Phenomena, Colorado School of Mines, Golden, Colorado 80401, USA.
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Curtis A, Halliday D. Source-receiver wave field interferometry. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:046601. [PMID: 20481847 DOI: 10.1103/physreve.81.046601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2009] [Indexed: 05/29/2023]
Abstract
Correlation or convolution of recordings of diffuse fields at a pair of locations have been shown to result in estimates of the Green's function between the two locations. Variously referred to as wave field or seismic interferometry in different fields of research, Green's functions can thus be constructed between either pairs of receivers or pairs of energy sources. Proofs of these results rely on representation theorems. We show how to derive three acoustic and elastic representation theorems that unify existing correlational and convolutional approaches. We thus derive three forms of interferometry that provide Green's functions on source-to-receiver paths, using only energy that has propagated from surrounding sources or to surrounding receivers. The three forms correspond to three possible canonical geometries. We thus allow interferometric theory and methods to be applied to commonly used source-receiver configurations.
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Affiliation(s)
- Andrew Curtis
- School of GeoSciences, The University of Edinburgh, Grant Institute, Kings Buildings, Edinburgh EH9 3JW, United Kingdom
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Shamsalsadati S, Weiss CJ. Retrieving the impulse response of the Earth due to random electromagnetic forcing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:036603. [PMID: 20365892 DOI: 10.1103/physreve.81.036603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2009] [Revised: 12/31/2009] [Indexed: 05/29/2023]
Abstract
A derivation is presented of Green's function in an arbitrary, heterogeneous conductive medium subject to random, ambient, uncorrelated noise sources. The approach for extracting Green's function is based on the correlation of time series of magnetic field components at two independent locations. As in the related case for the electric field, where the volume distribution of noise sources must be spatially correlated with the heterogeneous conductivity distribution, Green's function for magnetic field requires noise sources to be spatially correlated with the volume distribution of magnetic permeability. For applications of electromagnetic imaging of Earth's deep subsurface, the effect of magnetic permeability variations in the subsurface is often assumed to be negligible when compared to the effect of conductivity variations. Hence, the expressions derived here may be useful for passive electromagnetic subsurface imaging, in apparent contrast to their electric field counterparts. Numerical validation exercises are described which validate this theory for Green's function estimation in the low-frequency limit.
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Affiliation(s)
- Sharmin Shamsalsadati
- Department of Geosciences, Virginia Polytechnic Institute and State University, 4044 Derring Hall 0420, Blacksburg, Virginia 24061, USA
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Vasconcelos I, Snieder R, Douma H. Representation theorems and Green's function retrieval for scattering in acoustic media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:036605. [PMID: 19905236 DOI: 10.1103/physreve.80.036605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2009] [Revised: 07/06/2009] [Indexed: 05/28/2023]
Abstract
Reciprocity theorems for perturbed acoustic media are provided in the form of convolution- and correlation-type theorems. These reciprocity relations are particularly useful in the general treatment of both forward and inverse-scattering problems. Using Green's functions to describe perturbed and unperturbed waves in two distinct wave states, representation theorems for scattered waves are derived from the reciprocity relations. While the convolution-type theorems can be manipulated to obtain scattering integrals that are analogous to the Lippmann-Schwinger equation, the correlation-type theorems can be used to retrieve the scattering response of the medium by cross correlations. Unlike previous formulations of Green's function retrieval, the extraction of scattered-wave responses by cross correlations does not require energy equipartitioning. Allowing for uneven energy radiation brings experimental advantages to the retrieval of fields scattered by remote lossless and/or attenuative scatterers. These concepts are illustrated with a number of examples, including analytic solutions to a one-dimensional scattering problem, and a numerical example in the context of seismic waves recorded on the ocean bottom.
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Affiliation(s)
- Ivan Vasconcelos
- ION Geophysical, GXT Imaging Solutions, 1st Floor, Integra House, Vicarage Road, Egham, Surrey TW20 9JZ, United Kingdom
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Halliday D, Curtis A. Generalized optical theorem for surface waves and layered media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:056603. [PMID: 19518578 DOI: 10.1103/physreve.79.056603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2008] [Revised: 03/31/2009] [Indexed: 05/27/2023]
Abstract
We present a generalized optical theorem for surface waves. The theorem also applies to body waves since under many circumstances body waves can be written in terms of surface-wave modal summations. This theorem therefore extends the domain of applicability of the optical theorem from homogeneous background media to a general class of body and surface-wave propagation regimes within layered elastic media.
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Affiliation(s)
- David Halliday
- School of GeoSciences, Grant Institute, University of Edinburgh, Kings Buildings, West Mains Road, Edinburgh EH93JW, United Kingdom
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Godin OA. Retrieval of Green's functions of elastic waves from thermal fluctuations of fluid-solid systems. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2009; 125:1960-1970. [PMID: 19354372 DOI: 10.1121/1.3082101] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Fluctuation-dissipation and flow reversal theorems are used to study long-range correlation of thermal phonons in a stationary heterogeneous mechanical system comprised of arbitrary inhomogeneous fluid flow and anisotropic solid. At thermal equilibrium, with an appropriate choice of physical observables to characterize thermal fluctuations within the fluid and within the solid, the general integral expression for the two-point correlation function of the fluctuations reduces to a linear combination of deterministic Green's functions, which describe wave propagation in opposite directions between the two points. It is demonstrated that the cross-correlation of thermal noise contains as much information about the environment as can be obtained in active reciprocal transmission experiments with transceivers placed at the two points. These findings suggest a possible application of ambient noise cross-correlation to passive acoustic characterization of inhomogeneous flows in fluid-solid systems in laboratory and geophysical settings.
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Affiliation(s)
- Oleg A Godin
- CIRES, University of Colorado, Boulder, Colorado 80309-0216, USA.
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Snieder R, van Wijk K, Haney M, Calvert R. Cancellation of spurious arrivals in Green's function extraction and the generalized optical theorem. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:036606. [PMID: 18851179 DOI: 10.1103/physreve.78.036606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2008] [Indexed: 05/26/2023]
Abstract
The extraction of the Green's function by cross correlation of waves recorded at two receivers nowadays finds much application. We show that for an arbitrary small scatterer, the cross terms of scattered waves give an unphysical wave with an arrival time that is independent of the source position. This constitutes an apparent inconsistency because theory predicts that such spurious arrivals do not arise, after integration over a complete source aperture. This puzzling inconsistency can be resolved for an arbitrary scatterer by integrating the contribution of all sources in the stationary phase approximation to show that the stationary phase contributions to the source integral cancel the spurious arrival by virtue of the generalized optical theorem. This work constitutes an alternative derivation of this theorem. When the source aperture is incomplete, the spurious arrival is not canceled and could be misinterpreted to be part of the Green's function. We give an example of how spurious arrivals provide information about the medium complementary to that given by the direct and scattered waves; the spurious waves can thus potentially be used to better constrain the medium.
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Affiliation(s)
- Roel Snieder
- Center for Wave Phenomena and Department of Geophysics, Colorado School of Mines, Golden, Colorado 80401, USA.
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Snieder R. Extracting the Green's function of attenuating heterogeneous acoustic media from uncorrelated waves. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2007; 121:2637-43. [PMID: 17550163 DOI: 10.1121/1.2713673] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
The Green's function of acoustic or elastic wave propagation can, for loss-less media, be retrieved by correlating the wave field that is excited by random sources and is recorded at two locations. Here the generalization of this idea to attenuating acoustic waves in an inhomogeneous medium is addressed, and it is shown that the Green's function can be retrieved from waves that are excited throughout the volume by spatially uncorrelated injection sources with a power spectrum that is proportional to the local dissipation rate. For a finite volume, one needs both volume sources and sources at the bounding surface for the extraction of the Green's functions. For the special case of a homogeneous attenuating medium defined over a finite volume, the phase and geometrical spreading of the Green's function is correctly retrieved when the volume sources are ignored, but the attenuation is not.
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Affiliation(s)
- Roel Snieder
- Center for Wave Phenomena and Department of Geophysics, Colorado School of Mines, Golden Colorado 80401, USA.
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Snieder R, Wapenaar K, Wegler U. Unified Green's function retrieval by cross-correlation; connection with energy principles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:036103. [PMID: 17500755 DOI: 10.1103/physreve.75.036103] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2006] [Indexed: 05/15/2023]
Abstract
It has been shown theoretically and observationally that the Green's function for acoustic and elastic waves can be retrieved by cross-correlating fluctuations recorded at two locations. We extend the concept of the extraction of the Green's function to a wide class of scalar linear systems. For systems that are not invariant under time reversal, the fluctuations must be excited by volume sources in order to satisfy the energy balance (equipartitioning) that is needed to extract the Green's function. The general theory for retrieving the Green's function is illustrated with examples that include the diffusion equation, Schrödinger's equation, a vibrating string, the acoustic wave equation, a vibrating beam, and the advection equation. Examples are also shown of situations where the Green's function cannot be extracted from ambient fluctuations. The general theory opens up new applications for the extraction of the Green's function from field correlations that include flow in porous media, quantum mechanics, and the extraction of the response of mechanical structures such as bridges.
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Affiliation(s)
- Roel Snieder
- Center for Wave Phenomena and Department of Geophysics, Colorado School of Mines, Golden, Colorado 80401, USA.
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