In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linea...In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.展开更多
We establish new identities for Moore-Penrose inverses of some operator products,and prove their associated reverse-order laws.Moreover,our results concerning the Moore-Penrose inverse of a product of two operators le...We establish new identities for Moore-Penrose inverses of some operator products,and prove their associated reverse-order laws.Moreover,our results concerning the Moore-Penrose inverse of a product of two operators lead in finding a relation between the operators in the case where Greville's inclusions are made into equalities.展开更多
Time reversal is a key component of time-reverse migration and source location using wavefield extrapolation.The implementation of time reversal depends on the time symmetry of wave equations in acoustic and elastic m...Time reversal is a key component of time-reverse migration and source location using wavefield extrapolation.The implementation of time reversal depends on the time symmetry of wave equations in acoustic and elastic media.This symmetry in time is no longer valid in attenuative medium.Not only the velocity is anisotropic in shale oil and gas reservoirs,but also the attenuation is usually anisotropic,which can be characterized by viscoelastic orthotropic media.In this paper,the fractional order viscoelastic anisotropic wave equation is used to decouple the energy dissipation and the velocity dispersion.By changing the sign of the dissipation term during backpropagation,the anisotropic attenuation is compensated and the time symmetry is restored.The attenuation compensation time-reverse location algorithm can eff ectively locate the source in viscoelastic orthotropic media.Compared to cases without attenuation compensation or using isotropic attenuation compensation,this method can remove location error caused by anisotropic attenuation and improve the imaging eff ect of the source.This paper verifi es the eff ectiveness of the method through theoretical analysis and model testing.展开更多
基金supported by the NNSF of China(12261065)the NSF of Inner Mongolia(2022MS01005)+1 种基金the Basic Science Research Fund of the Universities Directly under the Inner Mongolia Autonomous Re-gion(JY20220084)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(NMGIRT2317).
文摘In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.
基金This work has been financially supported by the research deputy of education and Research University of Torbat Heydarieh,the grant number is UTH:1399/8/2483。
文摘We establish new identities for Moore-Penrose inverses of some operator products,and prove their associated reverse-order laws.Moreover,our results concerning the Moore-Penrose inverse of a product of two operators lead in finding a relation between the operators in the case where Greville's inclusions are made into equalities.
基金This work was supported by National Natural Science Foundation of China(No.41504097,41874153).
文摘Time reversal is a key component of time-reverse migration and source location using wavefield extrapolation.The implementation of time reversal depends on the time symmetry of wave equations in acoustic and elastic media.This symmetry in time is no longer valid in attenuative medium.Not only the velocity is anisotropic in shale oil and gas reservoirs,but also the attenuation is usually anisotropic,which can be characterized by viscoelastic orthotropic media.In this paper,the fractional order viscoelastic anisotropic wave equation is used to decouple the energy dissipation and the velocity dispersion.By changing the sign of the dissipation term during backpropagation,the anisotropic attenuation is compensated and the time symmetry is restored.The attenuation compensation time-reverse location algorithm can eff ectively locate the source in viscoelastic orthotropic media.Compared to cases without attenuation compensation or using isotropic attenuation compensation,this method can remove location error caused by anisotropic attenuation and improve the imaging eff ect of the source.This paper verifi es the eff ectiveness of the method through theoretical analysis and model testing.
