The regularization contributes to the resolution and stability in geophysical inversion. The authors apply dual-parameter shaping regularization to full waveform inversion, aiming at two points ： （ 1 ） improving th...The regularization contributes to the resolution and stability in geophysical inversion. The authors apply dual-parameter shaping regularization to full waveform inversion, aiming at two points ： （ 1 ） improving the boundary resolution, and （2） increasing convergence. Firstly, the forward modeling is done, and the inversion is processed with the optimal solution. Compared with classical Tikhonov regularization scheme, the method re fleets better resolution and stronger convergence. Then, Marmousi model is experimented and inversed, and the deep structure has a sharper outline. The phase residual comparison illustrates weaker cycle-slipping. And a choice scheme of parameter is applied in FWI.展开更多
Let Rn be an n-dimensional Euclidean space with n≥ 3. Denote by Ωn the unit sphere in Rn. For a function f∈L(Ωn) we denote by ENδ(f) the equiconvergent operator of Cesaro means of order δ of the Fourier-Laplace ...Let Rn be an n-dimensional Euclidean space with n≥ 3. Denote by Ωn the unit sphere in Rn. For a function f∈L(Ωn) we denote by ENδ(f) the equiconvergent operator of Cesaro means of order δ of the Fourier-Laplace series of f. The special value λ:= (n-2)/2 of δ is known as the critical index. For 0 < δ≤λ, we set p0 := 2λ/(λ+δ). The main aim of this paper is to prove thatwith l > 1.展开更多
The authors introduce the Hausdorff convergence to discuss the differentiable sphere theorem with excess pinching. Finally, a type of rigidity phenomenon on Riemannian manifolds is derived.
In this paper, we discuss the convergence of the Broyden algorithms withrevised search direction. Under some inexact line searches, we prove that the algorithms areglobally convergent for continuously differentiable f...In this paper, we discuss the convergence of the Broyden algorithms withrevised search direction. Under some inexact line searches, we prove that the algorithms areglobally convergent for continuously differentiable functions and the rate of convergence of thealgorithms is one-step superlinear and n-step second-order for uniformly convex objective functions.展开更多
In this paper,the motion of inverse mean curvature flow which starts from a closed star-sharped hypersurface in special rotationally symmetric spaces is studied.It is proved that the flow converges to a unique geodesi...In this paper,the motion of inverse mean curvature flow which starts from a closed star-sharped hypersurface in special rotationally symmetric spaces is studied.It is proved that the flow converges to a unique geodesic sphere,i.e.,every principle curvature of the hypersurfaces converges to a same constant under the flow.展开更多
Given a continuous boundary value on the boundary of a ＂simply closed surface＂ as that encloses the whole Earth, a regular harmonic fictitious field V＊（P） in the domain outside an inner sphere Ki that lies inside...Given a continuous boundary value on the boundary of a ＂simply closed surface＂ as that encloses the whole Earth, a regular harmonic fictitious field V＊（P） in the domain outside an inner sphere Ki that lies inside the Earth could be determined, and it is proved that V＊（P） coincides with the Earth＇s real field V（P） in the whole domain outside the Earth. Since in the domain outside the inner sphere Ki and the fictitious regular harmonic function V＊（P） could be expressed as a uniformly convergent spherical harmonic series, it is concluded that the Earth＇s potential field could be expressed as a uniformly convergent spherical harmonic expansion series in the whole domain outside the Earth.展开更多
文摘The regularization contributes to the resolution and stability in geophysical inversion. The authors apply dual-parameter shaping regularization to full waveform inversion, aiming at two points ： （ 1 ） improving the boundary resolution, and （2） increasing convergence. Firstly, the forward modeling is done, and the inversion is processed with the optimal solution. Compared with classical Tikhonov regularization scheme, the method re fleets better resolution and stronger convergence. Then, Marmousi model is experimented and inversed, and the deep structure has a sharper outline. The phase residual comparison illustrates weaker cycle-slipping. And a choice scheme of parameter is applied in FWI.
文摘Let Rn be an n-dimensional Euclidean space with n≥ 3. Denote by Ωn the unit sphere in Rn. For a function f∈L(Ωn) we denote by ENδ(f) the equiconvergent operator of Cesaro means of order δ of the Fourier-Laplace series of f. The special value λ:= (n-2)/2 of δ is known as the critical index. For 0 < δ≤λ, we set p0 := 2λ/(λ+δ). The main aim of this paper is to prove thatwith l > 1.
基金supported by the National Natural Science Foundation of China (No. 10671066)the Scientific Research Foundation of Qufu Normal University and the Shanghai and Shandong Priority Academic Discipline
文摘The authors introduce the Hausdorff convergence to discuss the differentiable sphere theorem with excess pinching. Finally, a type of rigidity phenomenon on Riemannian manifolds is derived.
基金This research is supported by Ministry of Education P. R. C.
文摘In this paper, we discuss the convergence of the Broyden algorithms withrevised search direction. Under some inexact line searches, we prove that the algorithms areglobally convergent for continuously differentiable functions and the rate of convergence of thealgorithms is one-step superlinear and n-step second-order for uniformly convex objective functions.
文摘In this paper,the motion of inverse mean curvature flow which starts from a closed star-sharped hypersurface in special rotationally symmetric spaces is studied.It is proved that the flow converges to a unique geodesic sphere,i.e.,every principle curvature of the hypersurfaces converges to a same constant under the flow.
基金Supported by the National Natural Science Foundation of China （No.40637034, No. 40574004）, the National 863 Program of China （No. 2006AA12Z211）. The author thanks Prof. Dr. Sjoberg for his valuable comments on the original manuscript.
文摘Given a continuous boundary value on the boundary of a ＂simply closed surface＂ as that encloses the whole Earth, a regular harmonic fictitious field V＊（P） in the domain outside an inner sphere Ki that lies inside the Earth could be determined, and it is proved that V＊（P） coincides with the Earth＇s real field V（P） in the whole domain outside the Earth. Since in the domain outside the inner sphere Ki and the fictitious regular harmonic function V＊（P） could be expressed as a uniformly convergent spherical harmonic series, it is concluded that the Earth＇s potential field could be expressed as a uniformly convergent spherical harmonic expansion series in the whole domain outside the Earth.
