Using staggered-grid finite difference method to solve seismic wave equation,large spatial grid and high dominant frequency of source cause numerical dispersion,staggeredgrid finite difference method,which can reduce ...Using staggered-grid finite difference method to solve seismic wave equation,large spatial grid and high dominant frequency of source cause numerical dispersion,staggeredgrid finite difference method,which can reduce the step spatial size and increase the order of difference,will multiply the calculation amount and reduce the efficiency of solving wave equation.The optimal nearly analytic discrete(ONAD)method can accurately solve the wave equation by using the combination of displacement and gradient of spatial nodes to approach the spatial partial derivative under rough grid and high-frequency condition.In this study,the ONAD method is introduced into the field of reverse-time migration(RTM)for performing forward-and reverse-time extrapolation of a two-dimensional acoustic equation,and the RTM based on ONAD method is realized via normalized cross-correlation imaging condition,effectively suppressed the numerical dispersion and improved the imaging accuracy.Using ONAD method to image the groove model and SEG/EAGE salt dome model by RTM,and comparing with the migration sections obtained by staggered-grid finite difference method with the same time order 2 nd and space order 4 th,results show that the RTM based on ONAD method can effectively suppress numerical dispersion caused by the high frequency components in source and shot records,and archive accurate imaging of complex geological structures especially the fine structure,and the migration sections of the measured data show that ONAD method has practical application value.展开更多
Full-waveform velocity inversion based on the acoustic wave equation in the time domain is investigated in this paper. The inversion is the iterative minimization of the misfit between observed data and synthetic data...Full-waveform velocity inversion based on the acoustic wave equation in the time domain is investigated in this paper. The inversion is the iterative minimization of the misfit between observed data and synthetic data obtained by a numerical solution of the wave equation. Two inversion algorithms in combination with the CG method and the BFGS method are described respectively. Numerical computations for two models including the benchmark Marmousi model with complex structure are implemented. The inversion results show that the BFGS-based algorithm behaves better in inversion than the CG-based algorithm does. Moreover, the good inversion result for Marmousi model with the BFGS-based algorithm suggests the quasi-Newton methods can provide an important tool for large-scale velocity inversion. More computations demonstrate the correctness and effectives of our inversion algorithms and code.展开更多
The inverse problem of wave equation is the importance of study not only in seismic prospecting but also in applied mathematics. With the development of the research, the inverse methods of 1 - D wave equations have b...The inverse problem of wave equation is the importance of study not only in seismic prospecting but also in applied mathematics. With the development of the research, the inverse methods of 1 - D wave equations have been trending towards the multiple parameters inversion . We have obtained an inverse method with double -parameter, in which medium density and wave velocity can be derived simultaneously. In this paper, to increase the inverse accuracy, the method is improved as follows. Firstly, the formula in which the Green Function is omitted are derived and used. Secondly, the regularizing method is reasonable used by choosing the stable function. With the new method, we may derive elastic parameter and medium density or medium density and wave velocity. Thus, lithology parameters for seismic prospecting may be obtained.After comparing the derived values from the new method with that from previous method, we obtain the new method through which substantially improve the derived accuracy . The new method has been applied to real depths inversion for sedimentary strata and volcanic rock strata in Chaoyanggou Terrace of Songliao Basin in eastern China. According to the inverse results,the gas - bearing beds are determlned.展开更多
In this paper,the Cauchy problem of biharmonic equation is considered.This problem is ill-posed,i.e.,the solution(if exists)does not depend on the measurable data.Firstly,we give the conditional stability result under...In this paper,the Cauchy problem of biharmonic equation is considered.This problem is ill-posed,i.e.,the solution(if exists)does not depend on the measurable data.Firstly,we give the conditional stability result under the a priori bound assumption for the exact solution.Secondly,a modified Tikhonov regularization method is used to solve this ill-posed problem.Under the a priori and the a posteriori regularization parameter choice rule,the error estimates between the regularization solutions and the exact solution are obtained.Finally,some numerical examples are presented to verify that our method is effective.展开更多
This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is...This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is introduced and applied to the inversion of Maxwell equations. The inverse problem is decomposed into multiple scales with wavelet transform, and hence the original problem is reformulated to a set of sub-inverse problems corresponding to different scales, which can be solved successively according to the size of scale from the shortest to the longest. The stable and fast regularized Gauss-Newton method is applied to each scale. Numerical results show that the proposed method is effective, especially in terms of wide convergence, computational efficiency and precision.展开更多
Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based ...Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.展开更多
By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at t...By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.展开更多
The mixed covolume method for the regularized long wave equation is devel- oped and studied. By introducing a transfer operator γh, which maps the trial function space into the test function space, and combining the ...The mixed covolume method for the regularized long wave equation is devel- oped and studied. By introducing a transfer operator γh, which maps the trial function space into the test function space, and combining the mixed finite element with the finite volume method, the nonlinear and linear Euler fully discrete mixed covolume schemes are constructed, and the existence and uniqueness of the solutions are proved. The optimal error estimates for these schemes are obtained. Finally, a numerical example is provided to examine the efficiency of the proposed schemes.展开更多
We develop a new full waveform inversion (FWI) method for slowness with the crosshole data based on the acoustic wave equation in the time domain. The method combines the total variation (TV) regularization with the c...We develop a new full waveform inversion (FWI) method for slowness with the crosshole data based on the acoustic wave equation in the time domain. The method combines the total variation (TV) regularization with the constrained optimization together which can inverse the slowness effectively. One advantage of slowness inversion is that there is no further approximation in the gradient derivation. Moreover, a new algorithm named the skip method for solving the constrained optimization problem is proposed. The TV regularization has good ability to inverse slowness at its discontinuities while the constrained optimization can keep the inversion converging in the right direction. Numerical computations both for noise free data and noisy data show the robustness and effectiveness of our method and good inversion results are yielded.展开更多
This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the...This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.展开更多
The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged non- thermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzma...The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged non- thermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold （hot） dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space-time fractional KdV-Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.展开更多
Based on the embedding thought, a method of wide convergence region for solving the coefficient inverse problem of wave equations in the space-time variable domain is presented. The numerical simulation shows that the...Based on the embedding thought, a method of wide convergence region for solving the coefficient inverse problem of wave equations in the space-time variable domain is presented. The numerical simulation shows that the method is feasible and effective.展开更多
The element-free Galerkin （EFG） method is used in this paper to find the numerical solution to a regularized long-wave （RLW） equation. The Galerkin weak form is adopted to obtain the discrete equations, and the es...The element-free Galerkin （EFG） method is used in this paper to find the numerical solution to a regularized long-wave （RLW） equation. The Galerkin weak form is adopted to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. The effectiveness of the EFG method of solving the RLW equation is investigated by two numerical examples in this paper.展开更多
This paper presents a meshless method for the nonlinear generalized regularized long wave （GRLW） equation based on the moving least-squares approximation. The nonlinear discrete scheme of the GRLW equation is obtain...This paper presents a meshless method for the nonlinear generalized regularized long wave （GRLW） equation based on the moving least-squares approximation. The nonlinear discrete scheme of the GRLW equation is obtained and is solved using the iteration method. A theorem on the convergence of the iterative process is presented and proved using theorems of the infinity norm. Compared with numerical methods based on mesh, the meshless method for the GRLW equation only requires the.scattered nodes instead of meshing the domain of the problem. Some examples, such as the propagation of single soliton and the interaction of two solitary waves, are given to show the effectiveness of the meshless method.展开更多
The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate reg...The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate regularized solutions is discussed. As an application of the method, an inverse problem in the two-dimensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given.展开更多
Direct and inverse scattering problems connected with the wave equation in non-homogeneous bounded domains constitute challenging actual subjects for both mathematicians and engineers. Among them one can mention, for ...Direct and inverse scattering problems connected with the wave equation in non-homogeneous bounded domains constitute challenging actual subjects for both mathematicians and engineers. Among them one can mention, for example, inverse source problems in seismology, nondestructive archeological probing, mine prospecting, inverse initial-value problems in acoustic tomography, etc. In spite of its crucial importance, almost all of the available rigorous investigations concern the case of unbounded simple domains such as layered planar or cylindrical or spherical structures. The main reason for the lack of the works related to non-homogeneous bounded structures is the extreme complexity of the explicit expressions of the Green’s functions. The aim of the present work consists in discovering some universal properties of the Green’s functions in question, which reduce enormously the difficulties arising in various applications. The universality mentioned here means that the properties are not depend on the geometrical and physical properties of the configuration. To this end one considers first the case when the domain is partially-homogeneous. Then the results are generalized to the most general case. To show the importance of the universal properties in question, they are applied to an inverse initial-value problem connected with photo-acoustic tomography.展开更多
The ion-acoustic solitary wave in collisionless unmagnetized plasma consisting of warm ions-fluid and isothermal electrons is studied using the time fractional KdV equation. The reductive perturbation method has been ...The ion-acoustic solitary wave in collisionless unmagnetized plasma consisting of warm ions-fluid and isothermal electrons is studied using the time fractional KdV equation. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude ion-acoustic wave in warm plasma. The Lagrangian of the time fractional KdV equation is used in a similar form to the Lagrangian of the regular KdV equation with fractional derivative for the time differentiation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that gives the time fractional KdV equation. The variational-iteration method is used to solve the derived time fractional KdV equation. The calculations of the solution are carried out for different values of the time fractional order. These calculations show that the time fractional can be used to modulate the electrostatic potential wave instead of adding a higher order dissipation term to the KdV equation. The results of the present investigation may be applicable to some plasma environments, such as the ionosphere plasma.展开更多
Full waveform inversion size of full waveform inversion will and the limitation of full waveform is mainly used to obtain high resolution velocity models of subsurface. The lead to a gigantic computation cost. Under t...Full waveform inversion size of full waveform inversion will and the limitation of full waveform is mainly used to obtain high resolution velocity models of subsurface. The lead to a gigantic computation cost. Under the available computer resource inversion, the authors propose L-BFGS algorithm as the optimization method to solve this problem. In order to demonstrate the flexibility of the method, three different numerical experi- ments have been done to analyze the properties of full waveform inversion based on L-BFGS.展开更多
The gradient preconditioning approach based on seismic wave energy can effectively avoid the huge memory consumption of the gradient preconditioning algorithms based on the Hessian matrix. However, the accuracy of thi...The gradient preconditioning approach based on seismic wave energy can effectively avoid the huge memory consumption of the gradient preconditioning algorithms based on the Hessian matrix. However, the accuracy of this approach is prone to be influ- enced by the energy of reflected waves. To tackle this problem, the paper proposes a new gradient preconditioning method based on the energy of transmitted waves. The approach scales the gradient through a precondition factor, which is calculated by the ‘ap- proximate transmission wavefield’ simulation based on the nonreflecting acoustic wave equation. The method requires no computing nor storing of the Hessian matrix and its inverse matrix. Furthermore, the proposed method can effectively eliminate the effects of geometric spreading and disproportionality in the gradient illumination. The results of model experiments show that the time-domain full waveform inversion (FWI) using the gradient preconditioning based on transmitted wave energy can achieve higher inversion accuracy for deep high-velocity bodies and their underlying strata in comparison with the one using the gradient preconditioning based on seismic wave energy. The field marine seismic data test shows that our proposed method is also highly applicable to the FWI of field marine seismic data.展开更多
基金financially supported by the National Key R&D Program of China(No.2018YFC1405900)the National Natural Science Foundation of China(No.41674118)+1 种基金the Fundamental Research Funds for the Central Universities(No.201822011)the National Science and Technology Major Project(No.2016ZX05027-002)。
文摘Using staggered-grid finite difference method to solve seismic wave equation,large spatial grid and high dominant frequency of source cause numerical dispersion,staggeredgrid finite difference method,which can reduce the step spatial size and increase the order of difference,will multiply the calculation amount and reduce the efficiency of solving wave equation.The optimal nearly analytic discrete(ONAD)method can accurately solve the wave equation by using the combination of displacement and gradient of spatial nodes to approach the spatial partial derivative under rough grid and high-frequency condition.In this study,the ONAD method is introduced into the field of reverse-time migration(RTM)for performing forward-and reverse-time extrapolation of a two-dimensional acoustic equation,and the RTM based on ONAD method is realized via normalized cross-correlation imaging condition,effectively suppressed the numerical dispersion and improved the imaging accuracy.Using ONAD method to image the groove model and SEG/EAGE salt dome model by RTM,and comparing with the migration sections obtained by staggered-grid finite difference method with the same time order 2 nd and space order 4 th,results show that the RTM based on ONAD method can effectively suppress numerical dispersion caused by the high frequency components in source and shot records,and archive accurate imaging of complex geological structures especially the fine structure,and the migration sections of the measured data show that ONAD method has practical application value.
文摘Full-waveform velocity inversion based on the acoustic wave equation in the time domain is investigated in this paper. The inversion is the iterative minimization of the misfit between observed data and synthetic data obtained by a numerical solution of the wave equation. Two inversion algorithms in combination with the CG method and the BFGS method are described respectively. Numerical computations for two models including the benchmark Marmousi model with complex structure are implemented. The inversion results show that the BFGS-based algorithm behaves better in inversion than the CG-based algorithm does. Moreover, the good inversion result for Marmousi model with the BFGS-based algorithm suggests the quasi-Newton methods can provide an important tool for large-scale velocity inversion. More computations demonstrate the correctness and effectives of our inversion algorithms and code.
文摘The inverse problem of wave equation is the importance of study not only in seismic prospecting but also in applied mathematics. With the development of the research, the inverse methods of 1 - D wave equations have been trending towards the multiple parameters inversion . We have obtained an inverse method with double -parameter, in which medium density and wave velocity can be derived simultaneously. In this paper, to increase the inverse accuracy, the method is improved as follows. Firstly, the formula in which the Green Function is omitted are derived and used. Secondly, the regularizing method is reasonable used by choosing the stable function. With the new method, we may derive elastic parameter and medium density or medium density and wave velocity. Thus, lithology parameters for seismic prospecting may be obtained.After comparing the derived values from the new method with that from previous method, we obtain the new method through which substantially improve the derived accuracy . The new method has been applied to real depths inversion for sedimentary strata and volcanic rock strata in Chaoyanggou Terrace of Songliao Basin in eastern China. According to the inverse results,the gas - bearing beds are determlned.
基金Supported by the National Natural Science Foundation of China(Grant No.11961044)。
文摘In this paper,the Cauchy problem of biharmonic equation is considered.This problem is ill-posed,i.e.,the solution(if exists)does not depend on the measurable data.Firstly,we give the conditional stability result under the a priori bound assumption for the exact solution.Secondly,a modified Tikhonov regularization method is used to solve this ill-posed problem.Under the a priori and the a posteriori regularization parameter choice rule,the error estimates between the regularization solutions and the exact solution are obtained.Finally,some numerical examples are presented to verify that our method is effective.
基金supported by the Program of Excellent Team of Harbin Institute of Technology
文摘This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is introduced and applied to the inversion of Maxwell equations. The inverse problem is decomposed into multiple scales with wavelet transform, and hence the original problem is reformulated to a set of sub-inverse problems corresponding to different scales, which can be solved successively according to the size of scale from the shortest to the longest. The stable and fast regularized Gauss-Newton method is applied to each scale. Numerical results show that the proposed method is effective, especially in terms of wide convergence, computational efficiency and precision.
基金supported by the China State Key Science and Technology Project on Marine Carbonate Reservoir Characterization (No. 2011ZX05004-003)the Basic Research Programs of CNPC during the 12th Five-Year Plan Period (NO.2011A-3603)+1 种基金the Natural Science Foundation of China (No.41104066)the RIPED Young Professional Innovation Fund (NO.2010-13-16-02, 2010-A-26-02)
文摘Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.
基金Project supported by the National Natural Science Foundation of China (No. 10172038).
文摘By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.
基金supported by the National Natural Science Fundation of China (No. 11061021)the Science Research of Inner Mongolia Advanced Education (Nos. NJ10006, NJ10016, and NJZZ12011)the National Science Foundation of Inner Mongolia (Nos. 2011BS0102 and 2012MS0106)
文摘The mixed covolume method for the regularized long wave equation is devel- oped and studied. By introducing a transfer operator γh, which maps the trial function space into the test function space, and combining the mixed finite element with the finite volume method, the nonlinear and linear Euler fully discrete mixed covolume schemes are constructed, and the existence and uniqueness of the solutions are proved. The optimal error estimates for these schemes are obtained. Finally, a numerical example is provided to examine the efficiency of the proposed schemes.
文摘We develop a new full waveform inversion (FWI) method for slowness with the crosshole data based on the acoustic wave equation in the time domain. The method combines the total variation (TV) regularization with the constrained optimization together which can inverse the slowness effectively. One advantage of slowness inversion is that there is no further approximation in the gradient derivation. Moreover, a new algorithm named the skip method for solving the constrained optimization problem is proposed. The TV regularization has good ability to inverse slowness at its discontinuities while the constrained optimization can keep the inversion converging in the right direction. Numerical computations both for noise free data and noisy data show the robustness and effectiveness of our method and good inversion results are yielded.
基金Project supported by the National Natural Science Foundation of China(No.11074170)the State Key Laboratory Foundation of Shanghai Jiao Tong University(No.MSVMS201105)
文摘This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.
文摘The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged non- thermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold （hot） dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space-time fractional KdV-Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.
文摘Based on the embedding thought, a method of wide convergence region for solving the coefficient inverse problem of wave equations in the space-time variable domain is presented. The numerical simulation shows that the method is feasible and effective.
基金supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y6110007)
文摘The element-free Galerkin （EFG） method is used in this paper to find the numerical solution to a regularized long-wave （RLW） equation. The Galerkin weak form is adopted to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. The effectiveness of the EFG method of solving the RLW equation is investigated by two numerical examples in this paper.
基金supported by the National Natural Science Foundation of China (Grant No. 10871124)the Innovation Program of the Shanghai Municipal Education Commission,China (Grant No. 09ZZ99)
文摘This paper presents a meshless method for the nonlinear generalized regularized long wave （GRLW） equation based on the moving least-squares approximation. The nonlinear discrete scheme of the GRLW equation is obtained and is solved using the iteration method. A theorem on the convergence of the iterative process is presented and proved using theorems of the infinity norm. Compared with numerical methods based on mesh, the meshless method for the GRLW equation only requires the.scattered nodes instead of meshing the domain of the problem. Some examples, such as the propagation of single soliton and the interaction of two solitary waves, are given to show the effectiveness of the meshless method.
文摘The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate regularized solutions is discussed. As an application of the method, an inverse problem in the two-dimensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given.
文摘Direct and inverse scattering problems connected with the wave equation in non-homogeneous bounded domains constitute challenging actual subjects for both mathematicians and engineers. Among them one can mention, for example, inverse source problems in seismology, nondestructive archeological probing, mine prospecting, inverse initial-value problems in acoustic tomography, etc. In spite of its crucial importance, almost all of the available rigorous investigations concern the case of unbounded simple domains such as layered planar or cylindrical or spherical structures. The main reason for the lack of the works related to non-homogeneous bounded structures is the extreme complexity of the explicit expressions of the Green’s functions. The aim of the present work consists in discovering some universal properties of the Green’s functions in question, which reduce enormously the difficulties arising in various applications. The universality mentioned here means that the properties are not depend on the geometrical and physical properties of the configuration. To this end one considers first the case when the domain is partially-homogeneous. Then the results are generalized to the most general case. To show the importance of the universal properties in question, they are applied to an inverse initial-value problem connected with photo-acoustic tomography.
文摘The ion-acoustic solitary wave in collisionless unmagnetized plasma consisting of warm ions-fluid and isothermal electrons is studied using the time fractional KdV equation. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude ion-acoustic wave in warm plasma. The Lagrangian of the time fractional KdV equation is used in a similar form to the Lagrangian of the regular KdV equation with fractional derivative for the time differentiation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that gives the time fractional KdV equation. The variational-iteration method is used to solve the derived time fractional KdV equation. The calculations of the solution are carried out for different values of the time fractional order. These calculations show that the time fractional can be used to modulate the electrostatic potential wave instead of adding a higher order dissipation term to the KdV equation. The results of the present investigation may be applicable to some plasma environments, such as the ionosphere plasma.
文摘Full waveform inversion size of full waveform inversion will and the limitation of full waveform is mainly used to obtain high resolution velocity models of subsurface. The lead to a gigantic computation cost. Under the available computer resource inversion, the authors propose L-BFGS algorithm as the optimization method to solve this problem. In order to demonstrate the flexibility of the method, three different numerical experi- ments have been done to analyze the properties of full waveform inversion based on L-BFGS.
基金support of the NSFCShandong Joint Fund for Marine Science Research Centers (No. U1606401)the National Natural Science Foundation of China (Nos. 41574105 and 41704114)+1 种基金the National Science and Technology Major Project of China (No.2016ZX05027-002)Taishan Scholar Project Funding (No. tspd20161007)
文摘The gradient preconditioning approach based on seismic wave energy can effectively avoid the huge memory consumption of the gradient preconditioning algorithms based on the Hessian matrix. However, the accuracy of this approach is prone to be influ- enced by the energy of reflected waves. To tackle this problem, the paper proposes a new gradient preconditioning method based on the energy of transmitted waves. The approach scales the gradient through a precondition factor, which is calculated by the ‘ap- proximate transmission wavefield’ simulation based on the nonreflecting acoustic wave equation. The method requires no computing nor storing of the Hessian matrix and its inverse matrix. Furthermore, the proposed method can effectively eliminate the effects of geometric spreading and disproportionality in the gradient illumination. The results of model experiments show that the time-domain full waveform inversion (FWI) using the gradient preconditioning based on transmitted wave energy can achieve higher inversion accuracy for deep high-velocity bodies and their underlying strata in comparison with the one using the gradient preconditioning based on seismic wave energy. The field marine seismic data test shows that our proposed method is also highly applicable to the FWI of field marine seismic data.
