A passive inverse filter for Green's function retrieval

Passive methods for the recovery of Green's functions from ambient noise require strong hypotheses, including isotropic distribution of the noise sources. Very often, this distribution is nonisotropic, which introduces bias in the Green's function reconstruction. To minimize this bias, a spatiotemporal inverse filter is proposed. The method is tested on a directive noise field computed from an experimental active seismic data set. The results indicate that the passive inverse filter allows the manipulation of the spatiotemporal degrees of freedom of a complex wave field, and it can efficiently compensate for the noise wavefield directivity.     

Unified Green's function retrieval by cross correlation

It has been shown by many authors that the cross correlation of two recordings of a diffuse wave field at different receivers yields the Green's function between these receivers. Recently the theory has been extended for situations where time-reversal invariance does not hold (e.g., in attenuating media) and where source-receiver reciprocity breaks down (in moving fluids). Here we present a unified theory for Green's function retrieval that captures all these situations and, because of the unified form, readily extends to more complex situations, such as electrokinetic Green's function retrieval in poroelastic or piezoelectric media. The unified theory has a wide range of applications in "remote sensing without a source."     

单边噪声源环境下的格林函数提取

对单边噪声源环境下空间中存在散射体时的格林函数到达时间结构提取展开了实验性研究。通过对位于沙滩上的传声器上记录的海浪噪声进行互相关处理,成功提取出两传声器间的格林函数到达时间结构。到达时间结构中观察到伪散射路径,并且伪散射路径在幅值上远高于散射路径。针对上述现象给出了理论及仿真解释:当传声器对受噪声源单边照射时,广义光学定理失效,伪散射路径将会出现;同时,由于伪散射路径由所有方向噪声源贡献,散射路径仅有稳相点附近声源贡献,因此伪散射路径在幅值上可能高于散射路径。结果表明,在单边噪声源环境下,基于互相关技术可以提取伪散射路径。伪散射路径的短时稳定提取可以为散射体无源成像提供更多信息,在海洋声学、地震学等领域具有潜在应用价值。     

复动量格林函数方法对n-α散射研究

在复动量表象下引入格林函数,建立了复动量格林函数方法.把这种方法应用于n-α散射系统,计算其散射相移.提取n-α系统的共振态并研究共振态对能级密度、相移和散射截面的贡献.在不引入任何非物理参数的前提下,离散化薛定谔积分方程得到束缚态、共振态和连续谱.通过分析散射态物理量可以更好地理解共振态以及非共振连续谱态.在n-α系统中的成功应用,证明了该方法的正确性.     

Cancellation of spurious arrivals in Green's function retrieval of multiple scattered waves

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.     

Green's function method for nonequilibrium systems

The causality principle formulated in the paper is offered as a boundary condition for the Schwinger equation. This approach allows study of, in particular, the dynamics of closed, finite systems. An approximate method for solving the equation is offered. A generalization of the Boltzmann equation is obtained for the presence of particle attenuation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 75–80, April, 1973.The author is very grateful to V. L. Bonch-Bruevich for discussion of the work.     

Fourier transform spectrometer instrument lineshape (ILS) retrieval by Fourier deconvolution

This work presents a Fourier deconvolution (FD) technique for retrieving the instrument lineshape (ILS) function of high-resolution Fourier transform infrared (FTIR) spectrometers. The ILS retrieved by FD is compared with the results obtained using the LINEFIT technique of Hase. The effect of a non-ideal ILS function on quantitative analysis of HBr is explored and improvements in the results of quantitative analyses are demonstrated.     

Iterative Wiener deconvolution based method for phase retrieval from noisy intensities

To retrieve the phase from the noisy measured intensities in the diffraction planes, an iterative Wiener deconvolution based method is proposed. With the same iterative scheme as the iterative angular spectrum method (IAS), the propagation of the optical wave function between the input plane and the diffraction planes is calculated by Wiener deconvolution in this method. The angular spectrum convolution kernel used in the iterative angular spectrum method is incorporated into the Wiener filter. The simulation experiments show that the proposed method can reduce the impact of the noise on the retrieved phase and performed better than the pre-denoising method. Furthermore, the proposed method exhibits great advantage compared to IAS for retrieving the complicated phase distribution from two measured intensities.     

Computation of Green's function for radiative transfer

In an accompanying paper, we develop the computational expressions for the higher order perturbation of the radiative transfer equation, and present some numerical results for typical cases. In this article, we discuss a number of issues regarding the implementation of the HOP computation: obtaining the Green's function, its expansion as a double series of Legendre polynomials, and obtaining the adjoint radiance of more general sources such as those for the fluxes at arbitrary altitudes. Examples of Green's function and its expansion coefficients are presented.     

Blind image deconvolution using sparse and redundant representation

This work devotes to the image deconvolution problem that restores clear image from its blurred and noisy measurements with little prior about the blur. A deconvolution method based on sparse and redundant representation theory is developed in this paper. It firstly represents the blur and image over different redundant dictionaries and imposes sparsity constraint to their representation coefficients respectively, then alternately estimates them using an iterative algorithm employing optimization technique. Experimental results on astronomical images show that the proposed method can achieve as good performance as the method requiring a known blur, which demonstrates its effectiveness.     

Relation between phase function and Green's function

A relation is established between the phase of the wave function and Green's function of onedimensional motion. On the basis of this relation, a series of accurate equations are obtained, including a formula for obtaining the Green's function at different one-dimensional coordinates from its form at coinciding one-dimensional coordinates.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 20–24, November, 1979.It remains to thank V. L. Bonch-Bruevich for useful discussions.     

A Green's function method for surface acoustic waves in functionally graded materials

Acoustic wave propagation in anisotropic media with one-dimensional inhomogeneity is discussed. Using a Green's function approach, the wave equation with inhomogeneous variation of elastic property and mass density is transformed into an integral equation, which is then solved numerically. The method is applied to find the dispersion relation of surface acoustic waves for a medium with continuously or discontinuously varying elastic property and mass density profiles.     

Green's function perturbation technique for the Kondo system

The one electron Green's function for the Kondo Hamiltonian is studied by means of diagrammatical perturbation technique. For a modified non zero temperature extension of Doniach's method a linked diagram expansion is established. The resulting diagrams can be rewritten in a form which is useful for partial resummations.     

Green's function perturbation technique for the Kondo system

Zeitschrift für Physik A Hadrons and nuclei - With the aid of a linked diagram expansion for the one electron scattering matrix of the Kondo system the singular log...     

Nonstandard formulation of perturbation theory for Green's function

Perturbation theory is developed for two-variable Green's functions (GF) when the initial GF is linked simultaneously to several higher-order GF. The total mass operator of the initial GF is obtained mathematically correctly in a form convenient for use. As an example of the application of this method, the mass operator of a nuclear spin anticommutator GF is calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 43–49, July, 1988.     

T=0 Green's function for the exciton

The excitons as electronic excitations of an insulator are obtained from the full manybody Hamiltonian by means of T=0Green's function techniques. Exciton amplitudes and energies are obtained via the vertex-part equation from an eigenvalue equation which in the Wannier limit is the effective-mass equation. A formula is obtained for the frequency dependent effective interaction whose static limit (ω=0) goes over into the Haken-Schottky dielectric-constant interaction for excitons of large electron-hole separations. A simple criterion will result to answer the question on when one is allowed to replace the frequency dependent interaction by its ω=0 limit.     

The Green's function moment method

This paper develops a modified moment method for the numerical solution of two “Pocklington Type” integral equations. The first equation arises from the problem of scalar diffraction through a slot; the second from scattering by a straight, thin-wire. Numerical results and comparison with a more conventional method are given.