N-lump solutions of the Kadomtsev-Petviashvili I equation in non-uniform media are derived through the inverse scattering transform. The obtained solutions describe lump waves with time-dependent amplitudes and veloci...N-lump solutions of the Kadomtsev-Petviashvili I equation in non-uniform media are derived through the inverse scattering transform. The obtained solutions describe lump waves with time-dependent amplitudes and velocities. Dynamics of l-lump wave and interactions of two lump wave are illustrated.展开更多
The scattering of plane time-harmonic electromagnetic waves propagating in a homogeneous chiral environment by a perfectly conducting grating is studied.The problem is simplified to a two-dimensional scattering proble...The scattering of plane time-harmonic electromagnetic waves propagating in a homogeneous chiral environment by a perfectly conducting grating is studied.The problem is simplified to a two-dimensional scattering problem,and the existence and uniqueness of solutions are discussed by an integral equation approach.展开更多
Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media.Combining inverse scattering theory,perturbation theory and stationary phase approximation,we derive the P...Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media.Combining inverse scattering theory,perturbation theory and stationary phase approximation,we derive the P-wave seismic scattering coefficient equation in terms of fluid factor,shear modulus and density of background homogeneous media and perturbation media.With this equation as forward solver,a pre-stack seismic Bayesian inversion method is proposed to estimate the fluid factor of heterogeneous media.In this method,Cauchy distribution is utilized to the ratios of fluid factors,shear moduli and densities of perturbation media and background homogeneous media,respectively.Gaussian distribution is utilized to the likelihood function.The introduction of constraints from initial smooth models enhances the stability of the estimation of model parameters.Model test and real data example demonstrate that the proposed method is able to estimate the fluid factor of heterogeneous media from pre-stack seismic data directly and reasonably.展开更多
An iterative strategy combining Kirchhoff approximation （KA） method is presented in this paper to study the interactions between KA is applied to study scattering from underlying rough surfaces with the hybrid finit...An iterative strategy combining Kirchhoff approximation （KA） method is presented in this paper to study the interactions between KA is applied to study scattering from underlying rough surfaces with the hybrid finite element-boundary integral （FE-BI） the inhomogeneous object and the underlying rough surface. whereas FE-BI deals with scattering from the above target. Both two methods use updated excitation sources. Huygens equivalence principle and an iterative strategy are employed to consider the multi-scattering effects. This hybrid FE-BI-KA scheme is an improved and generalized version of previous hybrid Kirchhoff approximation-method of moments （KA-MoM）. This newly presented hybrid method has the following advantages： （1） the feasibility of modeling multi-scale scattering problems （large scale underlying surface and small scale target）; （2） low memory requirement as in hybrid KA-MoM; （3） the ability to deal with scattering from inhomogeneous （including coated or layered） scatterers above rough surfaces. The numerical results are given to evaluate the accuracy of the multi-hybrid technique; the computing time and memory requirements consumed in specific numerical simulation of FE-BI-KA are compared with those of MoM. The convergence performance is analyzed by studying the iteration number variation caused by related parameters. Then bistatic scattering from inhomogeneous object of different configurations above dielectric Gaussian rough surface is calculated and the influences of dielectric compositions and surface roughness on the scattering pattern are discussed.展开更多
Consider the reconstruction of the complex refraction index of an object, which is immersed in a known homogeneous background, from the knowledge of scattered waves of the point sources outside of the object. We first...Consider the reconstruction of the complex refraction index of an object, which is immersed in a known homogeneous background, from the knowledge of scattered waves of the point sources outside of the object. We firstly establish the uniqueness for this inverse problem, which provides the theoretical basis for the reconstruction scheme. Then based on the contrast source inversion(CSI) method, we propose an algorithm determining the refraction index and the artificial wave sources alternately by a dynamic iterative scheme. The algorithm defines the iterates by solving a series of minimization problems with uniformly convex penalty terms, which are allowed to be non-smooth to include L1 and total variation like functionals, ensuring the reconstruction quality when the unknown refraction index has the special features such as sparsity and discontinuity. By choosing the regularizing parameter automatically, the algorithm is terminated in terms of discrepancy principle. The convergence property of the iterative sequence is rigorously proven. Numerical implementations demonstrate the validity of the proposed algorithm.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.11071157Shanghai Leading Academic Discipline Project under Grant No.J50101
文摘N-lump solutions of the Kadomtsev-Petviashvili I equation in non-uniform media are derived through the inverse scattering transform. The obtained solutions describe lump waves with time-dependent amplitudes and velocities. Dynamics of l-lump wave and interactions of two lump wave are illustrated.
文摘The scattering of plane time-harmonic electromagnetic waves propagating in a homogeneous chiral environment by a perfectly conducting grating is studied.The problem is simplified to a two-dimensional scattering problem,and the existence and uniqueness of solutions are discussed by an integral equation approach.
基金supported by the National Basic Research Program of China(Grant No.2013CB228604)the National Grand Project for Science and Technology(Grant Nos.2011ZX05030-004-002,2011ZX05019-003&2011ZX05006-002)
文摘Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media.Combining inverse scattering theory,perturbation theory and stationary phase approximation,we derive the P-wave seismic scattering coefficient equation in terms of fluid factor,shear modulus and density of background homogeneous media and perturbation media.With this equation as forward solver,a pre-stack seismic Bayesian inversion method is proposed to estimate the fluid factor of heterogeneous media.In this method,Cauchy distribution is utilized to the ratios of fluid factors,shear moduli and densities of perturbation media and background homogeneous media,respectively.Gaussian distribution is utilized to the likelihood function.The introduction of constraints from initial smooth models enhances the stability of the estimation of model parameters.Model test and real data example demonstrate that the proposed method is able to estimate the fluid factor of heterogeneous media from pre-stack seismic data directly and reasonably.
基金supported by the National Natural Science Foundation of China(Grant No.60971067)the Specialized Research Fund for the Doctoral Program of Higher Education,China(Grant No.20100203110016)the Fundamental Research Funds for the Central Universities,China
文摘An iterative strategy combining Kirchhoff approximation （KA） method is presented in this paper to study the interactions between KA is applied to study scattering from underlying rough surfaces with the hybrid finite element-boundary integral （FE-BI） the inhomogeneous object and the underlying rough surface. whereas FE-BI deals with scattering from the above target. Both two methods use updated excitation sources. Huygens equivalence principle and an iterative strategy are employed to consider the multi-scattering effects. This hybrid FE-BI-KA scheme is an improved and generalized version of previous hybrid Kirchhoff approximation-method of moments （KA-MoM）. This newly presented hybrid method has the following advantages： （1） the feasibility of modeling multi-scale scattering problems （large scale underlying surface and small scale target）; （2） low memory requirement as in hybrid KA-MoM; （3） the ability to deal with scattering from inhomogeneous （including coated or layered） scatterers above rough surfaces. The numerical results are given to evaluate the accuracy of the multi-hybrid technique; the computing time and memory requirements consumed in specific numerical simulation of FE-BI-KA are compared with those of MoM. The convergence performance is analyzed by studying the iteration number variation caused by related parameters. Then bistatic scattering from inhomogeneous object of different configurations above dielectric Gaussian rough surface is calculated and the influences of dielectric compositions and surface roughness on the scattering pattern are discussed.
基金supported by National Natural Science Foundation of China(Grant Nos.11421110002,11531005 and 11501102)National Science Foundation of Jiangsu Province(Grant No.BK20150594)
文摘Consider the reconstruction of the complex refraction index of an object, which is immersed in a known homogeneous background, from the knowledge of scattered waves of the point sources outside of the object. We firstly establish the uniqueness for this inverse problem, which provides the theoretical basis for the reconstruction scheme. Then based on the contrast source inversion(CSI) method, we propose an algorithm determining the refraction index and the artificial wave sources alternately by a dynamic iterative scheme. The algorithm defines the iterates by solving a series of minimization problems with uniformly convex penalty terms, which are allowed to be non-smooth to include L1 and total variation like functionals, ensuring the reconstruction quality when the unknown refraction index has the special features such as sparsity and discontinuity. By choosing the regularizing parameter automatically, the algorithm is terminated in terms of discrepancy principle. The convergence property of the iterative sequence is rigorously proven. Numerical implementations demonstrate the validity of the proposed algorithm.
