针对常规大地电磁(Magnetotelluric,MT)反演方法对电阻率异常体边界不太敏感的问题,本文尝试基于贝叶斯理论开展二维大地电磁电阻率尖锐边界反演研究.在反演中,模型参数由边界位置及内部电阻率组成,通过贝叶斯理论将模型参数与数据相联...针对常规大地电磁(Magnetotelluric,MT)反演方法对电阻率异常体边界不太敏感的问题,本文尝试基于贝叶斯理论开展二维大地电磁电阻率尖锐边界反演研究.在反演中,模型参数由边界位置及内部电阻率组成,通过贝叶斯理论将模型参数与数据相联系,采用Markov Chain Monte Carlo(MCMC)的Metropolis-Hastings(MH)方法对后验概率密度函数(Posteriori Probability Density,PDD)进行采样.采样过程中无罚值函数约束,完全以数据自身所包含的信息对模型进行约束,同时与有限约束进行比较,并考虑不同起始采样点对结果的影响.以接受率为参考,用模型算例说明MH方法中建议分布函数选择的重要性.当模型参数间相关性较弱时,使用边缘概率分布对采样结果进行分析.该方法能给出模型参数的分布范围,并给出该模型参数范围对应的数据范围.通过与已知模型的对比及数据拟合情况分析检验了该反演方法的有效性.该方法有助于提高大地电磁尖锐边界反演的分辨能力.展开更多
This paper obtain that the radius of starlikeness for class s(α,n)in[1] is,repectively,r1(α,n)=｛√[(1+n)α-n]^2+1-2α+(1+n)α-n/1-2α｝^1/n,0≤α≤α0,r2(α,n）=｛4[n√α（1-α）-α/（1+n)^2(1-α）-4α｝^1/(2n>,...This paper obtain that the radius of starlikeness for class s(α,n)in[1] is,repectively,r1(α,n)=｛√[(1+n)α-n]^2+1-2α+(1+n)α-n/1-2α｝^1/n,0≤α≤α0,r2(α,n）=｛4[n√α（1-α）-α/（1+n)^2(1-α）-4α｝^1/(2n>,α0≤α≤1,where α0 is unique solution of equation √αα=σ with α in(0,1),and α=[1+(1-2α）r^2n]/(1-r^2n),σ=[1-(1-2α)r^n]/(1+r^n）。Futhermore,we consider an extension of class S(α,n):Let S(α，β，n）denote the elass of funetions f(z)=z+αn+1z^n+1+…(n≥0) that are analytie in |z|<1 such that f(z)/g(z)∈p(α,n）[1],where g(z)∈S^*(β)[2].This paper prove that the radius of starlikeness of class S(α,β，n）is given by the smallest positive root (less than 1) of the following equations (1-2α)(1-2β）r^2n-2[1-α-β-n(1-α)]r^n+1=0,0≤α≤α0,(1-α）[1-(1-2β)r^n]-n[(√α-√α）^2(1+r^n)=0,,α0≤α<1,where α=[1+(1-2α)r^2n]/(1-r^2n)(0≤r<1),α0∈(0,1) is some fixed number.This result is also the extension of well-known results [T,Th3] and [8,Th3].展开更多
基金National High Technology Research and Development Porject (863)(2008AA093001)National Science and Technology Major Project (2008ZX05005-005-010HZ)+2 种基金the National Natural Science Foundation of China (40674063)National Key Foundation Research Development Project (973)(2007CB411706-02)&(2007CB411702)Project (MG20080203) of State Key Laboratory of Marine Geology, Tongji University
文摘针对常规大地电磁(Magnetotelluric,MT)反演方法对电阻率异常体边界不太敏感的问题,本文尝试基于贝叶斯理论开展二维大地电磁电阻率尖锐边界反演研究.在反演中,模型参数由边界位置及内部电阻率组成,通过贝叶斯理论将模型参数与数据相联系,采用Markov Chain Monte Carlo(MCMC)的Metropolis-Hastings(MH)方法对后验概率密度函数(Posteriori Probability Density,PDD)进行采样.采样过程中无罚值函数约束,完全以数据自身所包含的信息对模型进行约束,同时与有限约束进行比较,并考虑不同起始采样点对结果的影响.以接受率为参考,用模型算例说明MH方法中建议分布函数选择的重要性.当模型参数间相关性较弱时,使用边缘概率分布对采样结果进行分析.该方法能给出模型参数的分布范围,并给出该模型参数范围对应的数据范围.通过与已知模型的对比及数据拟合情况分析检验了该反演方法的有效性.该方法有助于提高大地电磁尖锐边界反演的分辨能力.
文摘This paper obtain that the radius of starlikeness for class s(α,n)in[1] is,repectively,r1(α,n)=｛√[(1+n)α-n]^2+1-2α+(1+n)α-n/1-2α｝^1/n,0≤α≤α0,r2(α,n）=｛4[n√α（1-α）-α/（1+n)^2(1-α）-4α｝^1/(2n>,α0≤α≤1,where α0 is unique solution of equation √αα=σ with α in(0,1),and α=[1+(1-2α）r^2n]/(1-r^2n),σ=[1-(1-2α)r^n]/(1+r^n）。Futhermore,we consider an extension of class S(α,n):Let S(α，β，n）denote the elass of funetions f(z)=z+αn+1z^n+1+…(n≥0) that are analytie in |z|<1 such that f(z)/g(z)∈p(α,n）[1],where g(z)∈S^*(β)[2].This paper prove that the radius of starlikeness of class S(α,β，n）is given by the smallest positive root (less than 1) of the following equations (1-2α)(1-2β）r^2n-2[1-α-β-n(1-α)]r^n+1=0,0≤α≤α0,(1-α）[1-(1-2β)r^n]-n[(√α-√α）^2(1+r^n)=0,,α0≤α<1,where α=[1+(1-2α)r^2n]/(1-r^2n)(0≤r<1),α0∈(0,1) is some fixed number.This result is also the extension of well-known results [T,Th3] and [8,Th3].
