In 3D frequency domain seismic forward and inversion calculation,the huge amount of calculation and storage is one of the main factors that restrict the processing speed and calculation efficiency.The frequency domain...In 3D frequency domain seismic forward and inversion calculation,the huge amount of calculation and storage is one of the main factors that restrict the processing speed and calculation efficiency.The frequency domain finite-difference forward simulation algorithm based on the acoustic wave equation establishes a large bandwidth complex matrix according to the discretized acoustic wave equation,and then the frequency domain wave field value is obtained by solving the matrix equation.In this study,the predecessor's optimized five-point method is extended to a 3D seven-point finite-difference scheme,and then a perfectly matched layer absorbing boundary condition(PML)is added to establish the corresponding matrix equation.In order to solve the complex matrix,we transform it to the equivalent real number domain to expand the solvable range of the matrix,and establish two objective functions to transform the matrix solving problem into an optimization problem that can be solved using gradient methods,and then use conjugate gradient algorithm to solve the problem.Previous studies have shown that in the conjugate gradient algorithm,the product of the matrix and the vector is the main factor that affects the calculation efficiency.Therefore,this study proposes a method that transform bandwidth matrix and vector product problem into some equivalent vector and vector product algorithm,thereby reducing the amount of calculation and storage.展开更多
Green's functions for Blot's dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics,...Green's functions for Blot's dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green's functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term "decoupling coefficient" for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green's functions. The correct- ness of the solution is demonstrated by numerically comparing the current solution with Cheng's previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green's functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method (BEM) and other applications.展开更多
The basic objective of time-scale transformation is to compress or expand the signal in time field while keeping the same spectral properties. This paper presents two methods to derive time-scale transformation formul...The basic objective of time-scale transformation is to compress or expand the signal in time field while keeping the same spectral properties. This paper presents two methods to derive time-scale transformation formula based on continuous wavelet transform. For an arbitrary given square-integrable function f(t),g(t) = f(t/λ) is derived by continuous wavelet transform and its inverse transform. The result shows that time-scale transformation may be obtained through the modification of the time-scale of wavelet function filter using equivalent substitution. The paper demonstrates the result by theoretic derivations and experimental simulation.展开更多
In this paper,a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies.The computing scheme is based on the Boundary Integra...In this paper,a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies.The computing scheme is based on the Boundary Integral Equation and derived in the time domain;thus,the time-harmonic Neumann boundary condition can be imposed.By the present method,the values of the initial conditions are set to zero,and the approach process is carried forward in a loop from the first time step to the last.At each time step,the radiated pressure on each element is updated.After several loops,the correct radiated pressures can be obtained.A sphere pulsating with a monopole frequency in an infinite acoustic domain is calculated first.This result is compared with the analytical solution,and both of them are in good agreement.Then,a complex-shaped radiator is taken as the studied case.The pulsating frequency of this case is multiple,and the waves propagate in half space.It is shown that the present method can treat multiple-frequency pulsation well,even when the radiator is a complex shape,and a robust convergence can be attained quickly.展开更多
Reverse Time Migration(RTM) is a high precision imaging method of seismic wavefield at present,but low-frequency noises severely affect its imaging results.Thus one of most important aspect of RTM is to select the pro...Reverse Time Migration(RTM) is a high precision imaging method of seismic wavefield at present,but low-frequency noises severely affect its imaging results.Thus one of most important aspect of RTM is to select the proper noise suppression method.The wavefield characteristics of the Poynting vector are analyzed and the upgoing,downgoing,leftgoing and rightgoing waves are decomposed using the Poynting vector of the acoustic wave equation.The normalized wavefield decomposition cross-correlation imaging condition is used to suppress low-frequency noises in RTM and improve the imaging precision.Numerical experiments using the Mamousi velocity model are performed and the results demonstrate that the upgoing,downgoing,leftgoing and rightgoing waves are well decomposed using the Poynting vector.Compared with the normalized cross-correlation imaging and Laplacian filtering method,the results indicate that the low-frequency noises are well suppressed by using the normalized wavefield decomposition cross-correlation imaging condition.展开更多
The finite-difference time-domain (FDTD) method is proposed for analyzing the surface acoustic wave (SAW) propagation in two-dimensional (2D) piezoelectric phononic crystals (PCs) at radio frequency (RF), an...The finite-difference time-domain (FDTD) method is proposed for analyzing the surface acoustic wave (SAW) propagation in two-dimensional (2D) piezoelectric phononic crystals (PCs) at radio frequency (RF), and also experiments are established to demonstrate its analysis result of the PCs' band gaps. The FDTD method takes the piezoelectric effect of PCs into account, in which periodic boundary conditions are used to decrease memory/time consumption and the perfectly matched layer boundary conditions are adopted as the SAW absorbers to attenuate artificial reflections. Two SAW delay lines are established with/without piezoelectric PCs located between interdigital transducers. By removing several echoes with window gating function in time domain, delay lines transmission function is achieved. The PCs' transmission functions and band gaps are obtained by comparing them in these two delay lines. When Aluminum/128°YX-LiNbO3 is adopted as scatter and substrate material, the PCs' band gap is calculated by this FDTD method and COMSOL respectively. Results show that computational results of FDTD agree well with experimental results and are better than that of COMSOL.展开更多
When the rotatory inertia is taken into account, vibrations of a linear plate can be described by the Kirchhoff plate equation. Consider this equation with locally distributed control forces and some boundary conditio...When the rotatory inertia is taken into account, vibrations of a linear plate can be described by the Kirchhoff plate equation. Consider this equation with locally distributed control forces and some boundary condition which is the simply supported boundary condition for a rectangular plate. In this paper, the authors establish exact controllability of the system in terms of the equivalence to exact internal controllability of the wave equation, by means of a frequency domain characterization of exact controllability introduced recently in [11].展开更多
基金supported by the National Natural Science Foundation of China(Project U1901602&41790465)Key Special Project for Introduced Talents Team of Southern Marine Science and Engineering Guangdong Laboratory(Guangzhou)(GML2019ZD0203)+2 种基金Shenzhen Key Laboratory of Deep Offshore Oil and Gas Exploration Technology(Grant No.ZDSYS20190902093007855)Shenzhen Science and Technology Program(Grant No.KQTD20170810111725321)the leading talents of Guangdong province program(Grant No.2016LJ06N652).
文摘In 3D frequency domain seismic forward and inversion calculation,the huge amount of calculation and storage is one of the main factors that restrict the processing speed and calculation efficiency.The frequency domain finite-difference forward simulation algorithm based on the acoustic wave equation establishes a large bandwidth complex matrix according to the discretized acoustic wave equation,and then the frequency domain wave field value is obtained by solving the matrix equation.In this study,the predecessor's optimized five-point method is extended to a 3D seven-point finite-difference scheme,and then a perfectly matched layer absorbing boundary condition(PML)is added to establish the corresponding matrix equation.In order to solve the complex matrix,we transform it to the equivalent real number domain to expand the solvable range of the matrix,and establish two objective functions to transform the matrix solving problem into an optimization problem that can be solved using gradient methods,and then use conjugate gradient algorithm to solve the problem.Previous studies have shown that in the conjugate gradient algorithm,the product of the matrix and the vector is the main factor that affects the calculation efficiency.Therefore,this study proposes a method that transform bandwidth matrix and vector product problem into some equivalent vector and vector product algorithm,thereby reducing the amount of calculation and storage.
基金Project supported by the National Natural Science Foundation of China(Nos.51478435,11402150,and 11172268)
文摘Green's functions for Blot's dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green's functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term "decoupling coefficient" for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green's functions. The correct- ness of the solution is demonstrated by numerically comparing the current solution with Cheng's previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green's functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method (BEM) and other applications.
文摘The basic objective of time-scale transformation is to compress or expand the signal in time field while keeping the same spectral properties. This paper presents two methods to derive time-scale transformation formula based on continuous wavelet transform. For an arbitrary given square-integrable function f(t),g(t) = f(t/λ) is derived by continuous wavelet transform and its inverse transform. The result shows that time-scale transformation may be obtained through the modification of the time-scale of wavelet function filter using equivalent substitution. The paper demonstrates the result by theoretic derivations and experimental simulation.
文摘In this paper,a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies.The computing scheme is based on the Boundary Integral Equation and derived in the time domain;thus,the time-harmonic Neumann boundary condition can be imposed.By the present method,the values of the initial conditions are set to zero,and the approach process is carried forward in a loop from the first time step to the last.At each time step,the radiated pressure on each element is updated.After several loops,the correct radiated pressures can be obtained.A sphere pulsating with a monopole frequency in an infinite acoustic domain is calculated first.This result is compared with the analytical solution,and both of them are in good agreement.Then,a complex-shaped radiator is taken as the studied case.The pulsating frequency of this case is multiple,and the waves propagate in half space.It is shown that the present method can treat multiple-frequency pulsation well,even when the radiator is a complex shape,and a robust convergence can be attained quickly.
文摘Reverse Time Migration(RTM) is a high precision imaging method of seismic wavefield at present,but low-frequency noises severely affect its imaging results.Thus one of most important aspect of RTM is to select the proper noise suppression method.The wavefield characteristics of the Poynting vector are analyzed and the upgoing,downgoing,leftgoing and rightgoing waves are decomposed using the Poynting vector of the acoustic wave equation.The normalized wavefield decomposition cross-correlation imaging condition is used to suppress low-frequency noises in RTM and improve the imaging precision.Numerical experiments using the Mamousi velocity model are performed and the results demonstrate that the upgoing,downgoing,leftgoing and rightgoing waves are well decomposed using the Poynting vector.Compared with the normalized cross-correlation imaging and Laplacian filtering method,the results indicate that the low-frequency noises are well suppressed by using the normalized wavefield decomposition cross-correlation imaging condition.
基金supported by the National Natural Science Foundation of China(11174318,11304346,61106081)Chinese Postdoctoral Science Foundation(2011M501204,2013T60718)+2 种基金National High Technology Research and Development Program(863 Program)(SS2013AA041103)Beijing Municipal Science and Technology Commission Project(Z141100003814016)the Fundamental Research Funds for the Central Universities(HUST:2013QN038)
文摘The finite-difference time-domain (FDTD) method is proposed for analyzing the surface acoustic wave (SAW) propagation in two-dimensional (2D) piezoelectric phononic crystals (PCs) at radio frequency (RF), and also experiments are established to demonstrate its analysis result of the PCs' band gaps. The FDTD method takes the piezoelectric effect of PCs into account, in which periodic boundary conditions are used to decrease memory/time consumption and the perfectly matched layer boundary conditions are adopted as the SAW absorbers to attenuate artificial reflections. Two SAW delay lines are established with/without piezoelectric PCs located between interdigital transducers. By removing several echoes with window gating function in time domain, delay lines transmission function is achieved. The PCs' transmission functions and band gaps are obtained by comparing them in these two delay lines. When Aluminum/128°YX-LiNbO3 is adopted as scatter and substrate material, the PCs' band gap is calculated by this FDTD method and COMSOL respectively. Results show that computational results of FDTD agree well with experimental results and are better than that of COMSOL.
基金National Key Project of ChinaNational Natural Science Foundation of China! (No. 69874034).
文摘When the rotatory inertia is taken into account, vibrations of a linear plate can be described by the Kirchhoff plate equation. Consider this equation with locally distributed control forces and some boundary condition which is the simply supported boundary condition for a rectangular plate. In this paper, the authors establish exact controllability of the system in terms of the equivalence to exact internal controllability of the wave equation, by means of a frequency domain characterization of exact controllability introduced recently in [11].