By means of some algebraic techniques,especially the Binet-Cauchy formula,an explicit multi-soliton solution of the derivative nonlinear Schrdinger equation with vanishing boundary condition is attained based on a pur...By means of some algebraic techniques,especially the Binet-Cauchy formula,an explicit multi-soliton solution of the derivative nonlinear Schrdinger equation with vanishing boundary condition is attained based on a pure Marchenko formalism without needing the usual scattering data except for given N simple poles. The one-and two-soliton solutions are given as two special examples in illustration of the general formula of multi-soliton solution. Their effectiveness and equivalence to other approaches are also demonstrated. Meanwhile,the asymptotic behavior of the multi-soliton solution is discussed in detail. It is shown that the N-soliton solution can be viewed as a summation of N one-soliton solutions with a definite displacement and phase shift of each soliton in the whole process（from t →∞ to t → ＋∞ ） of the elastic collisions.展开更多
Marchenko imaging obtains the subsurface reflectors using one-way Green’s functions,which are retrieved by solving the Marchenko equation.This method generates an image that is free of spurious artifacts due to inter...Marchenko imaging obtains the subsurface reflectors using one-way Green’s functions,which are retrieved by solving the Marchenko equation.This method generates an image that is free of spurious artifacts due to internal multiples.The Marchenko imaging method is a target-oriented technique;thus,it can image a user specified area.In the traditional Marchenko method,an accurate velocity model is critical for estimating direct waves from imaging points to the surface.An error in the velocity model results in the inaccurate estimation of direct waves.In turn,this leads to errors in computation of one-way Green’s functions,which then affects the final Marchenko images.To solve this problem,in this paper,we propose a self-adaptive traveltime updating technique based on the principle of equal traveltime to improve the Marchenko imaging method.The proposed method calculates the time shift of direct waves caused by the error in the velocity model,and corrects the wrong direct wave according to the time shift and reconstructs the correct Green’s functions.The proposed method improves the results of imaging using an inaccurate velocity model.By comparing the results from traditional Marchenko and the new method using synthetic data experiments,we demonstrated that the adaptive traveltime updating Marchenko imaging method could restore the image of geological structures to their true positions.展开更多
Using the integral representation of the Jost solution,we deduce some conditions as the kernel functionN(x,y,t)if the Jost solution satisfies the two Lax equations.Then we verify the multi-soliton solution of NLS equa...Using the integral representation of the Jost solution,we deduce some conditions as the kernel functionN(x,y,t)if the Jost solution satisfies the two Lax equations.Then we verify the multi-soliton solution of NLS equationwith non-vanishing boundary conditions if we prove that these conditions can be demonstrated by the GLM equation,which determines the kernel function N(x,y,t)in according to the inverse scattering method.展开更多
基金Supported by the National Natural Science Foundation of China (10775105)
文摘By means of some algebraic techniques,especially the Binet-Cauchy formula,an explicit multi-soliton solution of the derivative nonlinear Schrdinger equation with vanishing boundary condition is attained based on a pure Marchenko formalism without needing the usual scattering data except for given N simple poles. The one-and two-soliton solutions are given as two special examples in illustration of the general formula of multi-soliton solution. Their effectiveness and equivalence to other approaches are also demonstrated. Meanwhile,the asymptotic behavior of the multi-soliton solution is discussed in detail. It is shown that the N-soliton solution can be viewed as a summation of N one-soliton solutions with a definite displacement and phase shift of each soliton in the whole process（from t →∞ to t → ＋∞ ） of the elastic collisions.
基金supported by the National Natural Science Foundation of China(No.41874167)the National Science and Technology Major Project of China(No.2017YFB0202904)the National Natural Science Foundation of China(No.41904130)。
文摘Marchenko imaging obtains the subsurface reflectors using one-way Green’s functions,which are retrieved by solving the Marchenko equation.This method generates an image that is free of spurious artifacts due to internal multiples.The Marchenko imaging method is a target-oriented technique;thus,it can image a user specified area.In the traditional Marchenko method,an accurate velocity model is critical for estimating direct waves from imaging points to the surface.An error in the velocity model results in the inaccurate estimation of direct waves.In turn,this leads to errors in computation of one-way Green’s functions,which then affects the final Marchenko images.To solve this problem,in this paper,we propose a self-adaptive traveltime updating technique based on the principle of equal traveltime to improve the Marchenko imaging method.The proposed method calculates the time shift of direct waves caused by the error in the velocity model,and corrects the wrong direct wave according to the time shift and reconstructs the correct Green’s functions.The proposed method improves the results of imaging using an inaccurate velocity model.By comparing the results from traditional Marchenko and the new method using synthetic data experiments,we demonstrated that the adaptive traveltime updating Marchenko imaging method could restore the image of geological structures to their true positions.
基金the Huazhong University of Science and Technology under Grant No.0101011110National Natural Science Foundation of China under Grant No.10375041
文摘Using the integral representation of the Jost solution,we deduce some conditions as the kernel functionN(x,y,t)if the Jost solution satisfies the two Lax equations.Then we verify the multi-soliton solution of NLS equationwith non-vanishing boundary conditions if we prove that these conditions can be demonstrated by the GLM equation,which determines the kernel function N(x,y,t)in according to the inverse scattering method.
