On the eve of the occurrence of geological hazards,part of the rock and soil body begins to burst,rub,and fracture,generating infrasound signals propagating outward.3D advanced positioning of the landslide has remaine...On the eve of the occurrence of geological hazards,part of the rock and soil body begins to burst,rub,and fracture,generating infrasound signals propagating outward.3D advanced positioning of the landslide has remained unsolved,which is important for disaster prevention.Through the Fourier transform and Hankel transform of the wave equation in cylindrical coordinates,this work established a three-dimensional axisymmetric sound field model based on normal waves,and designed a 4-element helix triangular pyramid array with vertical and horizontal sampling capabilities.Based on this,the three-dimensional matching localization algorithm of infrasound for geological hazards is proposed.Applying the algorithm to the infrasound signal localization of rock and soil layers,it was found that the helix triangular pyramid array can achieve accurate estimation of depth and distance with a smaller number of array elements than the traditional array,and may overcome the azimuth symmetry ambiguity.This study shows the application prospects of this method for predicting geohazards position several hours in advance.展开更多
Let {（ξni, ηni）, 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as （S1,ρnS1 ＋ √1- ρ2nS2）, ρn ∈（0, 1）, where （S1,S2） is...Let {（ξni, ηni）, 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as （S1,ρnS1 ＋ √1- ρ2nS2）, ρn ∈（0, 1）, where （S1,S2） is a bivariate spherical random vector. For the distribution function of radius√S12 ＋ S22 belonging to the max-domain of attraction of the Weibull distribution, the limiting distribution of maximum of this triangular array is known as the convergence rate of p~ to 1 is given. In this paper, under the refinement of the rate of convergence of p~ to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.展开更多
基金Project(41877219)supported by the National Natural Science Foundation of ChinaProject(cstc2019jcyj-msxmX0585)supported by Natural Science Foundation of Chongqing,ChinaProject(KJ-2018016)supported by Science and Technology Project of Planning and Natural Resources Bureau of Chongqing Government,China。
文摘On the eve of the occurrence of geological hazards,part of the rock and soil body begins to burst,rub,and fracture,generating infrasound signals propagating outward.3D advanced positioning of the landslide has remained unsolved,which is important for disaster prevention.Through the Fourier transform and Hankel transform of the wave equation in cylindrical coordinates,this work established a three-dimensional axisymmetric sound field model based on normal waves,and designed a 4-element helix triangular pyramid array with vertical and horizontal sampling capabilities.Based on this,the three-dimensional matching localization algorithm of infrasound for geological hazards is proposed.Applying the algorithm to the infrasound signal localization of rock and soil layers,it was found that the helix triangular pyramid array can achieve accurate estimation of depth and distance with a smaller number of array elements than the traditional array,and may overcome the azimuth symmetry ambiguity.This study shows the application prospects of this method for predicting geohazards position several hours in advance.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11501113,11601330 and 11701469)the Key Project of Fujian Education Committee(Grant No.JA15045)the Funding Program for Junior Faculties of College and Universities of Shanghai Education Committee(Grant No.ZZslg16020)
文摘Let {（ξni, ηni）, 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as （S1,ρnS1 ＋ √1- ρ2nS2）, ρn ∈（0, 1）, where （S1,S2） is a bivariate spherical random vector. For the distribution function of radius√S12 ＋ S22 belonging to the max-domain of attraction of the Weibull distribution, the limiting distribution of maximum of this triangular array is known as the convergence rate of p~ to 1 is given. In this paper, under the refinement of the rate of convergence of p~ to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.
