Within the framework of the first-order Born approximation, the triple differential cross sections （TDCSs） for simultaneous ionization and excitation of helium are calculated. The wave function of the ejected electr...Within the framework of the first-order Born approximation, the triple differential cross sections （TDCSs） for simultaneous ionization and excitation of helium are calculated. The wave function of the ejected electron is chosen to be orthogonal or non-orthogonal to the wave function of the bound electron before ionization. It is found that the orthogonality has a strong effect on the TDCS, especially when plane waves and Coulomb waves are used to describe the projectile and the ejected electron.展开更多
Sound velocity inversion problem based on scattering theory is formulated in terms of a nonlinear integral equation associated with scattered field. Because of its nonlinearity, in practice, linearization algorisms （...Sound velocity inversion problem based on scattering theory is formulated in terms of a nonlinear integral equation associated with scattered field. Because of its nonlinearity, in practice, linearization algorisms （Born/ single scattering approximation） are widely used to obtain an approximate inversion solution. However, the linearized strategy is not congruent with seismic wave propagation mechanics in strong perturbation （heterogeneous） medium. In order to partially dispense with the weak perturbation assumption of the Born approximation, we present a new approach from the following two steps： firstly, to handle the forward scattering by taking into account the second- order Born approximation, which is related to generalized Radon transform （GRT） about quadratic scattering poten- tial; then to derive a nonlinear quadratic inversion formula by resorting to inverse GRT. In our formulation, there is a significant quadratic term regarding scattering potential, and it can provide an amplitude correction for inversion results beyond standard linear inversion. The numerical experiments demonstrate that the linear single scattering inversion is only good in amplitude for relative velocity perturbation （3c/c0） of background media up to 10 %, andits inversion errors are unacceptable for the perturbation beyond 10 %. In contrast, the quadratic inversion can give more accurate amplitude-preserved recovery for the per- turbation up to 40 %. Our inversion scheme is able to manage double scattering effects by estimating a trans- mission factor from an integral over a small area, and therefore, only a small portion of computational time is added to the original linear migration/inversion process.展开更多
基金Project supported by the Anhui University Doctoral Research Starting Foundation,China(Grant Nos.02303319 and 33190203)the National Natural Science Foundation of China(Grant No.11274219)
文摘Within the framework of the first-order Born approximation, the triple differential cross sections （TDCSs） for simultaneous ionization and excitation of helium are calculated. The wave function of the ejected electron is chosen to be orthogonal or non-orthogonal to the wave function of the bound electron before ionization. It is found that the orthogonality has a strong effect on the TDCS, especially when plane waves and Coulomb waves are used to describe the projectile and the ejected electron.
基金supported by Innovation Project of Chinese Academy of Sciences and State Key Laboratory of Marine Geology, Tongji University (No. MGK1408)
文摘Sound velocity inversion problem based on scattering theory is formulated in terms of a nonlinear integral equation associated with scattered field. Because of its nonlinearity, in practice, linearization algorisms （Born/ single scattering approximation） are widely used to obtain an approximate inversion solution. However, the linearized strategy is not congruent with seismic wave propagation mechanics in strong perturbation （heterogeneous） medium. In order to partially dispense with the weak perturbation assumption of the Born approximation, we present a new approach from the following two steps： firstly, to handle the forward scattering by taking into account the second- order Born approximation, which is related to generalized Radon transform （GRT） about quadratic scattering poten- tial; then to derive a nonlinear quadratic inversion formula by resorting to inverse GRT. In our formulation, there is a significant quadratic term regarding scattering potential, and it can provide an amplitude correction for inversion results beyond standard linear inversion. The numerical experiments demonstrate that the linear single scattering inversion is only good in amplitude for relative velocity perturbation （3c/c0） of background media up to 10 %, andits inversion errors are unacceptable for the perturbation beyond 10 %. In contrast, the quadratic inversion can give more accurate amplitude-preserved recovery for the per- turbation up to 40 %. Our inversion scheme is able to manage double scattering effects by estimating a trans- mission factor from an integral over a small area, and therefore, only a small portion of computational time is added to the original linear migration/inversion process.
