The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matri...The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.展开更多
This article considers a risk model as in Yuen et al. （2002）. Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is ...This article considers a risk model as in Yuen et al. （2002）. Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.展开更多
The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, ...The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.展开更多
We collected waveforms of a teleseismic event which occurred from January 2007 to October 2011 from 174 broadband seismic stations deployed in Hebei and its adjacent areas. Using the H-k stacking method,the average th...We collected waveforms of a teleseismic event which occurred from January 2007 to October 2011 from 174 broadband seismic stations deployed in Hebei and its adjacent areas. Using the H-k stacking method,the average thickness and Poisson's ratio of the crust are acquired. In order to obtain reliable receiver functions, the broadband seismograms of 488 teleseismic earthquakes occurring in the epicentral distance range from 30° to 90° with magnitudes larger than Mb6. 0 are collected. The results show that crustal thickness have conspicuous lateral heterogeneity and have good correlation to the regional geological tectonic features. Poisson ratio's value is equated with the global models estimates which fluctuate at about 0. 25. Crustal thickness has positive correlation to the topography and the Taihang Mountains form the transition zone of thick and thin crustal thickness. There is an obvious difference in crustal thickness beneath the north and south of the Shanxi earthquake zone and the Poisson ratio of Datong,Ningwu and Anze basins is greater than 0. 3. The crustal thickness beneath the Zhang-Bo( Zhangjiakou-Bohai Sea)earthquake zone decreases from west to north and its Poisson ratio shows conspicuous lateral heterogeneity. The thin crust and low Poisson ratio in the Huabei( North China)basin may correlate with the delamination of the North China craton.展开更多
The Xing’an Mongolian Orogenic Belt(XMOB) and the northern margin of North China Craton(NCC) have undergone multistage tectonic superimposition and the tectonic evolution is extremely complicated. We collect the tele...The Xing’an Mongolian Orogenic Belt(XMOB) and the northern margin of North China Craton(NCC) have undergone multistage tectonic superimposition and the tectonic evolution is extremely complicated. We collect the teleseismic data of 44 temporary broadband seismic stations deployed in the XMOB and the northern margin of NCC to calculate the P wave receiver functions. The crustal thickness and average crustal ratio as well as the Poisson’s ratios beneath 33 stations are estimated using the H-κ stacking method. The results show:(1) the crustal thickness of the study area ranges from 38.7 to 42.7 km, with an average thickness of 41.2 km. There is a great difference in crustal thickness on both sides of Solonker suture zone. The characteristics of crustal thickness support the geodynamic model that the Paleo-Asian Ocean subducted and closed at the Solonker suture zone.(2) The Poisson’s ratios in the study area are low, ranging from 0.215 to 0.277, with an average value of 0.243, suggesting that the rock composition of the area is dominated by felsic-acid rocks.(3) There exists a negative correlation between the Poisson’s ratio and the crustal thickness. Combined with the lower values of Poisson’s ratio, we speculate that the delamination is the major mechanism in crustal extension and thinning in the study area.展开更多
With the help of the method of separation of variables and the Debye-Hüchel approximation, the Poisson-Boltzmann equation that describes the distribution of the potential in the electrical double layer of a cylin...With the help of the method of separation of variables and the Debye-Hüchel approximation, the Poisson-Boltzmann equation that describes the distribution of the potential in the electrical double layer of a cylindrical particle with a limited length has been firstly solved under a very low potential condition. Then with the help of the functional analysis theory this equation has been further analytically solved under general potential conditions and consequently, the corresponding surface charge densities have been obtained. Both the potential and the surface charge densities cointide with those results obtained from the Debye-Hüchel approximation when the very low potential of zeψ〈〈kT is introduced.展开更多
de Casteljau算法可以递推地定义一条具有限个控制顶点的Bzier曲线,在此基础上文中提出了基于de Casteljau算法的Poisson细分曲线逼近算法,Poisson曲线完全具备了Bzier曲线的重要性质,并且比Bzier曲线有更广泛的应用范围。最后还...de Casteljau算法可以递推地定义一条具有限个控制顶点的Bzier曲线,在此基础上文中提出了基于de Casteljau算法的Poisson细分曲线逼近算法,Poisson曲线完全具备了Bzier曲线的重要性质,并且比Bzier曲线有更广泛的应用范围。最后还给出了n阶Poisson曲线的细分。展开更多
基金supported by the National Natural Science Foundation of China (Nos.41374023,41131067,41474019)the National 973 Project of China (No.2013CB733302)+2 种基金the China Postdoctoral Science Foundation (No.2016M602301)the Key Laboratory of Geospace Envi-ronment and Geodesy,Ministry of Education,Wuhan University (No.15-02-08)the State Scholarship Fund from Chinese Scholarship Council (No.201306270014)
文摘The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.
基金This work was supported in part by the National Natural Science Foundation of China (10071058, 70273029) the Ministry of Education of China.
文摘This article considers a risk model as in Yuen et al. （2002）. Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.
文摘The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.
基金funded by the Seismic Situation Tracing Orientation Task,China Earthquake Administration(2014020120)the Science and Technology Support Program of Hebei Province(2014020120)
文摘We collected waveforms of a teleseismic event which occurred from January 2007 to October 2011 from 174 broadband seismic stations deployed in Hebei and its adjacent areas. Using the H-k stacking method,the average thickness and Poisson's ratio of the crust are acquired. In order to obtain reliable receiver functions, the broadband seismograms of 488 teleseismic earthquakes occurring in the epicentral distance range from 30° to 90° with magnitudes larger than Mb6. 0 are collected. The results show that crustal thickness have conspicuous lateral heterogeneity and have good correlation to the regional geological tectonic features. Poisson ratio's value is equated with the global models estimates which fluctuate at about 0. 25. Crustal thickness has positive correlation to the topography and the Taihang Mountains form the transition zone of thick and thin crustal thickness. There is an obvious difference in crustal thickness beneath the north and south of the Shanxi earthquake zone and the Poisson ratio of Datong,Ningwu and Anze basins is greater than 0. 3. The crustal thickness beneath the Zhang-Bo( Zhangjiakou-Bohai Sea)earthquake zone decreases from west to north and its Poisson ratio shows conspicuous lateral heterogeneity. The thin crust and low Poisson ratio in the Huabei( North China)basin may correlate with the delamination of the North China craton.
基金supported by the National Natural Science Foundation of China (No. 41774066)Central Public-interest Scientific Institution Basal Research special(No. DQJB16A0305)
文摘The Xing’an Mongolian Orogenic Belt(XMOB) and the northern margin of North China Craton(NCC) have undergone multistage tectonic superimposition and the tectonic evolution is extremely complicated. We collect the teleseismic data of 44 temporary broadband seismic stations deployed in the XMOB and the northern margin of NCC to calculate the P wave receiver functions. The crustal thickness and average crustal ratio as well as the Poisson’s ratios beneath 33 stations are estimated using the H-κ stacking method. The results show:(1) the crustal thickness of the study area ranges from 38.7 to 42.7 km, with an average thickness of 41.2 km. There is a great difference in crustal thickness on both sides of Solonker suture zone. The characteristics of crustal thickness support the geodynamic model that the Paleo-Asian Ocean subducted and closed at the Solonker suture zone.(2) The Poisson’s ratios in the study area are low, ranging from 0.215 to 0.277, with an average value of 0.243, suggesting that the rock composition of the area is dominated by felsic-acid rocks.(3) There exists a negative correlation between the Poisson’s ratio and the crustal thickness. Combined with the lower values of Poisson’s ratio, we speculate that the delamination is the major mechanism in crustal extension and thinning in the study area.
基金Supported by the National Natural Science Foundation of China(No.20473034) the Taihu Scholar Foundation of SouthernYangtze University(2003).
文摘With the help of the method of separation of variables and the Debye-Hüchel approximation, the Poisson-Boltzmann equation that describes the distribution of the potential in the electrical double layer of a cylindrical particle with a limited length has been firstly solved under a very low potential condition. Then with the help of the functional analysis theory this equation has been further analytically solved under general potential conditions and consequently, the corresponding surface charge densities have been obtained. Both the potential and the surface charge densities cointide with those results obtained from the Debye-Hüchel approximation when the very low potential of zeψ〈〈kT is introduced.
