Angle domain common imaging gathers(ADCIGs)serve as not only an ideal approach for tomographic velocity modeling but also as a crucial means of mitigating low-frequency noise.Thus,they play a significant role in seism...Angle domain common imaging gathers(ADCIGs)serve as not only an ideal approach for tomographic velocity modeling but also as a crucial means of mitigating low-frequency noise.Thus,they play a significant role in seismic data processing.Recently,the Poynting vector method,due to its lower computational requirements and higher resolution,has become a commonly used approach for obtaining ADCIGs.However,due to the viscoelastic properties of underground media,attenuation effects(phase dispersion and amplitude attenuation)have become a factor,which is important in seismic data processing.However,the primary applications of ADCIGs are currently confined to acoustic and elastic media.To assess the influence of attenuation and elastic effects on ADCIGs,we introduce an extraction method for ADCIGs based on fractional viscoelastic equations.This method enhances ADCIGs accuracy by simultaneously considering both the attenuation and elastic properties of underground media.Meanwhile,the S-wave quasi tensor is used to reduce the impact of P-wave energy on S-wave stress,thus further increasing the accuracy of PS-ADCIGs.In conclusion,our analysis examines the impact of the quality factor Q on ADCIGs and offers theoretical guidance for parameter inversion.展开更多
In this paper, we consider a system of coupled quasilinear viscoelastic equa- tions with nonlinear damping. We use the perturbed energy method to show the general decay rate estimates of energy of solutions, which ext...In this paper, we consider a system of coupled quasilinear viscoelastic equa- tions with nonlinear damping. We use the perturbed energy method to show the general decay rate estimates of energy of solutions, which extends some existing results concerning a general decay for a single equation to the case of system, and a nonlinear system of viscoelastic wave equations to a quasilinear system.展开更多
This paper is concerned with a system of nonlinear viscoelastic wave equations with degenerate nonlocal damping and memory terms.We will prove that the energy associated to the system is unbounded.In fact,it will be p...This paper is concerned with a system of nonlinear viscoelastic wave equations with degenerate nonlocal damping and memory terms.We will prove that the energy associated to the system is unbounded.In fact,it will be proved that the energy will grow up as an exponential function as time goes to infinity,provided that the initial data are positive initial energy.展开更多
A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay result...A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.展开更多
A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions ira- posed on the source and the damping, we establish ...A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions ira- posed on the source and the damping, we establish uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.展开更多
The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, fo...The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.展开更多
H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and unique...H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.展开更多
基金supported by the National Natural Science Foundation of China(NSFC)under contract number 42274147 and 41874144。
文摘Angle domain common imaging gathers(ADCIGs)serve as not only an ideal approach for tomographic velocity modeling but also as a crucial means of mitigating low-frequency noise.Thus,they play a significant role in seismic data processing.Recently,the Poynting vector method,due to its lower computational requirements and higher resolution,has become a commonly used approach for obtaining ADCIGs.However,due to the viscoelastic properties of underground media,attenuation effects(phase dispersion and amplitude attenuation)have become a factor,which is important in seismic data processing.However,the primary applications of ADCIGs are currently confined to acoustic and elastic media.To assess the influence of attenuation and elastic effects on ADCIGs,we introduce an extraction method for ADCIGs based on fractional viscoelastic equations.This method enhances ADCIGs accuracy by simultaneously considering both the attenuation and elastic properties of underground media.Meanwhile,the S-wave quasi tensor is used to reduce the impact of P-wave energy on S-wave stress,thus further increasing the accuracy of PS-ADCIGs.In conclusion,our analysis examines the impact of the quality factor Q on ADCIGs and offers theoretical guidance for parameter inversion.
基金supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education,Science and Technology (2011-0007870)
文摘In this paper, we consider a system of coupled quasilinear viscoelastic equa- tions with nonlinear damping. We use the perturbed energy method to show the general decay rate estimates of energy of solutions, which extends some existing results concerning a general decay for a single equation to the case of system, and a nonlinear system of viscoelastic wave equations to a quasilinear system.
基金Supported by the National Natural Science Foundation of China(Grant No.11801145)。
文摘This paper is concerned with a system of nonlinear viscoelastic wave equations with degenerate nonlocal damping and memory terms.We will prove that the energy associated to the system is unbounded.In fact,it will be proved that the energy will grow up as an exponential function as time goes to infinity,provided that the initial data are positive initial energy.
文摘A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.
文摘A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions ira- posed on the source and the damping, we establish uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.
文摘The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.
基金Supported by NNSF(10601022,11061021)Supported by NSF of Inner Mongolia Au-tonomous Region(200607010106)Supported by SRP of Higher Schools of Inner Mongolia(NJ10006)
文摘H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.
