This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be a...This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.展开更多
The generalized Born approximation is an approximation method that represents the scattering term by the error between the exact Green's function and the approximate Green's function,mainly for the gradient sc...The generalized Born approximation is an approximation method that represents the scattering term by the error between the exact Green's function and the approximate Green's function,mainly for the gradient scattering problem.However,so far,the research on the generalized Born approximation has only stayed in theory,and its implementation techniques are rarely reported.In order to fill this gap,the basic theory of generalized Born approximation is reviewed,and the implementation method of generalized Born approximation is discussed in this paper.In particular,the problem of calculating boundary effect elimination is discussed in detail.Finally,through model trial calculation,the calculation of gradient scattering,by comparing Born approximation and finite difference method,shows that using the generalized Born approximation to calculate gradient scattering achieves higher computational accuracy.展开更多
Rutherford classical scattering theory, as its quantum mechanical analogue, is modified for scattering cross-section and the impact parameter by using quantum mechanical momentum, (de Broglie hypothesis), energy relat...Rutherford classical scattering theory, as its quantum mechanical analogue, is modified for scattering cross-section and the impact parameter by using quantum mechanical momentum, (de Broglie hypothesis), energy relationship for matter oscillator (Einstein’s oscillator) and quantum mechanical wave vectors, and , respectively. It is observed that the quantum mechanical scattering cross-section and the impact parameter depended on inverse square law of quantum action (Planck’s constant). Born approximation is revisited for quantum mechanical scattering. Using Bessel and Neumann asymptotic functions and response of nuclear surface potential barrier, born approximations were modified. The coulombic fields inside the nucleus of the atom are studied for reflection and transmission with corresponding wave vectors, phase shifts and eigenfunctions Bulk quantum mechanical tunneling and reflection scattering, both for ruptured and unruptured nucleus of the atom, are deciphered with corresponding wave vectors, phase shifts and eigenfunction. Similar calculation ware accomplished for quantum surface tunneling and reflection scattering with corresponding wave vectors, phase shifts and eigenfunctions. Such diverse quantum mechanical scattering cross-section with corresponding wave vectors for tunneling and reflection, phase shifts and eigenfunctions will pave a new dimension to understanding the behavior of exchange fields in the nucleus of the atom with insides layers both ruptured and unruptured. Phase shifts, δ<sub>l</sub> for each of the energy profile (partial) will be different and indeed their corresponding wave vectors for exchange energy eigenvalues.展开更多
The multi-parameter inversion of elastic wave equation in a half-space within the Born approximation is studied. A method of simultaneously reconstructing the configurations of the density and Lame parameters of the m...The multi-parameter inversion of elastic wave equation in a half-space within the Born approximation is studied. A method of simultaneously reconstructing the configurations of the density and Lame parameters of the medium was presented by use of a wideband measuring schemes in which transmitters and receivers scan over the half-space surface. It is shown that the reflected waves generated by horizontal and vertical pulses on the surface can be decomposed into P-->P, P-->S, S-->P and S-->S types of scattering components. As is expected, these components contain enough information for desired restruction. From them the density and two Lame parameters are determined explicitly, and the results obtained have the form of filtered back-propagation as in the acoustic diffraction tomography.展开更多
When deriving the Fourier diffraction theorem based on the first-order Born approximation,the difference between wave number of the scattering object and that of the surrounding medium is ignored,causing substantial e...When deriving the Fourier diffraction theorem based on the first-order Born approximation,the difference between wave number of the scattering object and that of the surrounding medium is ignored,causing substantial errors in sound scattering prediction.This paper modifies the Born approximation by taking into account the amplitude and phase changes between the scattering object and the water due to the wave number difference.By changing the radius and center position of the sampling circle in the Fourier domain,accuracy of the predicted sound scattering is improved.With the modified Born approximation,the computed far-field directional pattern of the scattered sound from a circular cylinder is in good agreement with the rigorous solution.Numerical calculations for several objects with different shapes are used to show applicability and effectiveness of the proposed method.展开更多
An efficient approximate scheme is presented for wave-propagation simulation in piecewise heterogeneous media by applying the Born-series approximation to volume-scattering waves. The numerical scheme is tested for di...An efficient approximate scheme is presented for wave-propagation simulation in piecewise heterogeneous media by applying the Born-series approximation to volume-scattering waves. The numerical scheme is tested for dimensionless frequency responses to a heterogeneous alluvial valley where the velocity is perturbed randomly in the range of 5 %–25 %,compared with the full-waveform numerical solution. Then,the scheme is extended to a heterogeneous multilayered model by calculating synthetic seismograms to evaluate approximation accuracies Numerical experiments indicate that the convergence rate of this method decreases gradually with increasing velocity perturbations. The method has a fast convergence for velocity perturbations less than 15 %. However,the convergence becomes slow drastically when the velocity perturbation increases to 20 %. The method can hardly converge for the velocity perturbation up to 25 %.展开更多
本文讨论了 Born 近似与 Rytov 近似的相互关系,并对地面反射、VSP、井间和四周观测系统在异常体速度与背景速度相差5%、10%以及15%的条件下,用这两种近似方法作了重建图像的实验。其结果表明,速度差低于10%时,无论 Born 近似或 Rytov ...本文讨论了 Born 近似与 Rytov 近似的相互关系,并对地面反射、VSP、井间和四周观测系统在异常体速度与背景速度相差5%、10%以及15%的条件下,用这两种近似方法作了重建图像的实验。其结果表明,速度差低于10%时,无论 Born 近似或 Rytov 近似,更射层析均优于透射层析。此时,Rytov 近似的透射层析优势消失,这一结论与传统观点相悖。当速度差大于10%时,Rytov 近似透射层析优于 Born 近似。实验结果还说明,在地面激发、四周观测时,波动理论层析效果最佳,此点与射线理论是一致的。展开更多
基金supported by the Explore Foundation of Weapon Development (Grant No 7130620)
文摘This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.
基金Supported by Project of the National Natural Science Foundation of China(No.41974135)
文摘The generalized Born approximation is an approximation method that represents the scattering term by the error between the exact Green's function and the approximate Green's function,mainly for the gradient scattering problem.However,so far,the research on the generalized Born approximation has only stayed in theory,and its implementation techniques are rarely reported.In order to fill this gap,the basic theory of generalized Born approximation is reviewed,and the implementation method of generalized Born approximation is discussed in this paper.In particular,the problem of calculating boundary effect elimination is discussed in detail.Finally,through model trial calculation,the calculation of gradient scattering,by comparing Born approximation and finite difference method,shows that using the generalized Born approximation to calculate gradient scattering achieves higher computational accuracy.
文摘Rutherford classical scattering theory, as its quantum mechanical analogue, is modified for scattering cross-section and the impact parameter by using quantum mechanical momentum, (de Broglie hypothesis), energy relationship for matter oscillator (Einstein’s oscillator) and quantum mechanical wave vectors, and , respectively. It is observed that the quantum mechanical scattering cross-section and the impact parameter depended on inverse square law of quantum action (Planck’s constant). Born approximation is revisited for quantum mechanical scattering. Using Bessel and Neumann asymptotic functions and response of nuclear surface potential barrier, born approximations were modified. The coulombic fields inside the nucleus of the atom are studied for reflection and transmission with corresponding wave vectors, phase shifts and eigenfunctions Bulk quantum mechanical tunneling and reflection scattering, both for ruptured and unruptured nucleus of the atom, are deciphered with corresponding wave vectors, phase shifts and eigenfunction. Similar calculation ware accomplished for quantum surface tunneling and reflection scattering with corresponding wave vectors, phase shifts and eigenfunctions. Such diverse quantum mechanical scattering cross-section with corresponding wave vectors for tunneling and reflection, phase shifts and eigenfunctions will pave a new dimension to understanding the behavior of exchange fields in the nucleus of the atom with insides layers both ruptured and unruptured. Phase shifts, δ<sub>l</sub> for each of the energy profile (partial) will be different and indeed their corresponding wave vectors for exchange energy eigenvalues.
文摘The multi-parameter inversion of elastic wave equation in a half-space within the Born approximation is studied. A method of simultaneously reconstructing the configurations of the density and Lame parameters of the medium was presented by use of a wideband measuring schemes in which transmitters and receivers scan over the half-space surface. It is shown that the reflected waves generated by horizontal and vertical pulses on the surface can be decomposed into P-->P, P-->S, S-->P and S-->S types of scattering components. As is expected, these components contain enough information for desired restruction. From them the density and two Lame parameters are determined explicitly, and the results obtained have the form of filtered back-propagation as in the acoustic diffraction tomography.
基金supported by the National Natural Science Foundation of China(61071187)Key Laboratory Foundation for Underwater Test and Control Technology(9140c260201110c26)
文摘When deriving the Fourier diffraction theorem based on the first-order Born approximation,the difference between wave number of the scattering object and that of the surrounding medium is ignored,causing substantial errors in sound scattering prediction.This paper modifies the Born approximation by taking into account the amplitude and phase changes between the scattering object and the water due to the wave number difference.By changing the radius and center position of the sampling circle in the Fourier domain,accuracy of the predicted sound scattering is improved.With the modified Born approximation,the computed far-field directional pattern of the scattered sound from a circular cylinder is in good agreement with the rigorous solution.Numerical calculations for several objects with different shapes are used to show applicability and effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41204097 and 41130418)the China National Major Science and Technology Project (2011ZX05023-005-004)
文摘An efficient approximate scheme is presented for wave-propagation simulation in piecewise heterogeneous media by applying the Born-series approximation to volume-scattering waves. The numerical scheme is tested for dimensionless frequency responses to a heterogeneous alluvial valley where the velocity is perturbed randomly in the range of 5 %–25 %,compared with the full-waveform numerical solution. Then,the scheme is extended to a heterogeneous multilayered model by calculating synthetic seismograms to evaluate approximation accuracies Numerical experiments indicate that the convergence rate of this method decreases gradually with increasing velocity perturbations. The method has a fast convergence for velocity perturbations less than 15 %. However,the convergence becomes slow drastically when the velocity perturbation increases to 20 %. The method can hardly converge for the velocity perturbation up to 25 %.
文摘本文讨论了 Born 近似与 Rytov 近似的相互关系,并对地面反射、VSP、井间和四周观测系统在异常体速度与背景速度相差5%、10%以及15%的条件下,用这两种近似方法作了重建图像的实验。其结果表明,速度差低于10%时,无论 Born 近似或 Rytov 近似,更射层析均优于透射层析。此时,Rytov 近似的透射层析优势消失,这一结论与传统观点相悖。当速度差大于10%时,Rytov 近似透射层析优于 Born 近似。实验结果还说明,在地面激发、四周观测时,波动理论层析效果最佳,此点与射线理论是一致的。
