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191
2004, Emergence of broadband rayleigh waves from correlations of the ambient seismic noise
 Geophysical Research Letters
"... [1] We demonstrate that the coherent information about the Earth structure can be extracted from the ambient seismic noise. We compute crosscorrelations of vertical component records of several days of seismic noise at different pairs of stations separated by distances from about one hundred to mor ..."
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Cited by 201 (18 self)
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[1] We demonstrate that the coherent information about the Earth structure can be extracted from the ambient seismic noise. We compute crosscorrelations of vertical component records of several days of seismic noise at different pairs of stations separated by distances from about one hundred to more than two thousand kilometers. Coherent broadband dispersive wavetrains clearly emerge with group velocities similar to those predicted from the global Rayleighwave tomographic maps that have been constrained using ballistic surface waves. Those results show that coherent Rayleigh waves can be extracted from the ambient seismic noise and that their dispersion characteristics can be measured in a broad range of periods. This provides a source for new types of surfacewave measurements that can be obtained for numerous paths that could not be sampled with the ballistic waves and, therefore, can significantly improve the resolution of
Unified Green’s function retrieval by crosscorrelation; connection with energy principles
"... It has been shown theoretically and observationally that the Green’s function for acoustic and elastic waves can be retrieved by crosscorrelating 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 sys ..."
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Cited by 137 (43 self)
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It has been shown theoretically and observationally that the Green’s function for acoustic and elastic waves can be retrieved by crosscorrelating 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.
SuperResolution in TimeReversal Acoustics
 JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
, 2001
"... We analyze theoretically and with numerical simulations the phenomenon of superresolution in timereversal acoustics. A signal that is recorded and then retransmitted by an array of transducers, propagates back though the medium and refocuses approximately on the source that emitted it. In a homog ..."
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Cited by 106 (17 self)
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We analyze theoretically and with numerical simulations the phenomenon of superresolution in timereversal acoustics. A signal that is recorded and then retransmitted by an array of transducers, propagates back though the medium and refocuses approximately on the source that emitted it. In a homogeneous medium, the refocusing resolution of the timereversed signal is limited by diffraction. When the medium has random inhomogeneities the resolution of the refocused signal can in some circumstances beat the diffraction limit. This is superresolution. We give a theoretical treatment of this phenomenon and present numerical simulations which confirm the theory.
Cluster Computing
, 2002
"... this paper combines very good property for load balancing ..."
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Cited by 85 (1 self)
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this paper combines very good property for load balancing
Statistical Stability in Time Reversal
 SIAM J. APPL. MATH.
, 2004
"... When a signal is emitted from a source, recorded by an array of transducers, timereversed, and reemitted into the medium, it will refocus approximately on the source location. We analyze the refocusing resolution in a high frequency remotesensing regime and show that, because of multiple scatteri ..."
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Cited by 67 (25 self)
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When a signal is emitted from a source, recorded by an array of transducers, timereversed, and reemitted into the medium, it will refocus approximately on the source location. We analyze the refocusing resolution in a high frequency remotesensing regime and show that, because of multiple scattering in an inhomogeneous or random medium, it can improve beyond the diffraction limit. We also show that the backpropagated signal from a spatially localized narrowband source is selfaveraging, or statistically stable, and relate this to the selfaveraging properties of functionals of the Wigner distribution in phase space. Time reversal from spatially distributed sources is selfaveraging only for broadband signals. The array of transducers operates in a remotesensing regime, so we analyze time reversal with the parabolic or paraxial wave equation.
SelfAveraging in Time Reversal for the Parabolic Wave Equation
 Stochastics and Dynamics
, 2002
"... We analyze the selfaveraging properties of timereversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. ..."
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Cited by 56 (20 self)
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We analyze the selfaveraging properties of timereversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation.
Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
, 1998
"... Many transport equations, such as the neutron transport, radiative transfer, and transport equations for waves in random media, have a diffusive scaling that leads to the diffusion equations. In many physical applications, the scaling parameter (mean free path) may differ in several orders of magnit ..."
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Cited by 43 (14 self)
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Many transport equations, such as the neutron transport, radiative transfer, and transport equations for waves in random media, have a diffusive scaling that leads to the diffusion equations. In many physical applications, the scaling parameter (mean free path) may differ in several orders of magnitude from the rarefied regimes to the hydrodynamic (diffusive) regimes within one problem, and it is desirable to develop a class of robust numerical schemes that can work uniformly with respect to this relaxation parameter. In an earlier work [JPT] we handled this numerical problem for discrete velocity kinetic models by reformulating the system into a form commonly used for a relaxation scheme for conservation laws [JX]. Such a reformulation allows us to use the splitting technique for relaxation schemes to design a class of implicit, yet explicitly implementable, schemes that work with high resolution unformly with respect to the relaxation parameter. In this paper we show that such a numerical ...
Hamiltonianpreserving schemes for the Liouville equation with discontinuous potentials
"... When numerically solving the Liouville equation with a discontinuous potential, one faces the problem of selecting a unique, physically relevant solution across the potential barrier, and the problem of a severe time step constraint due to the CFL condition. In this paper, We introduce two classes o ..."
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Cited by 40 (30 self)
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When numerically solving the Liouville equation with a discontinuous potential, one faces the problem of selecting a unique, physically relevant solution across the potential barrier, and the problem of a severe time step constraint due to the CFL condition. In this paper, We introduce two classes of Hamiltonianpreserving schemes for such problems. By using the constant Hamiltonian across the potential barrier, we introduced a selection criterion for a unique, physically relavant solution to the underlying linear hyperbolic equation with singular coefficients. These scheme have a hyperbolic CFL condition, which is a significant improvement over a conventional discretization. We also establish the positivity, and stability in both l 1 and l ∞ norms, of these discretizations, and conducted numerical experiments to study the numerical accuracy. This work is motivated by the wellbalanced kinetic schemes by Perthame and Simeoni for the shallow water equations with a discontinuous bottom topography, and has applications to the level set methods for the computations of multivalued physical observables in the semiclassical limit of the linear Schrödinger equation with a discontinuous potential, among other applications.
The phonon Boltzmann equation, properties and link to weakly anharmonic lattice dynamics
 J. Stat. Phys
"... Abstract: For low density gases the validity of the Boltzmann transport equation is well established. The central object is the oneparticle distribution function, f, which in the BoltzmannGrad limit satisfies the Boltzmann equation. Grad and, much refined, Cercignani argue for the existence of thi ..."
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Cited by 39 (10 self)
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Abstract: For low density gases the validity of the Boltzmann transport equation is well established. The central object is the oneparticle distribution function, f, which in the BoltzmannGrad limit satisfies the Boltzmann equation. Grad and, much refined, Cercignani argue for the existence of this limit on the basis of the BBGKY hierarchy for hard spheres. At least for a short kinetic time span, the argument can be made mathematically precise following the seminal work of Lanford. In this article a corresponding programme is undertaken for weakly nonlinear, both discrete and continuum, wave equations. Our working example is the harmonic lattice with a weakly nonquadratic onsite potential. We argue that the role of the Boltzmann ffunction is taken over by the Wigner function, which is a very convenient device to filter the slow degrees of freedom. The Wigner function, so to speak, labels locally the covariances of dynamically almost stationary measures. One route to the phonon Boltzmann equation is a Gaussian decoupling, which is based on the fact that the purely harmonic dynamics has very good mixing properties. As a further approach the expansion in terms of Feynman diagrams is outlined. Both methods