针对Mogi模型垂直位移与水平位移联合反演中的病态问题,改进火山形变总体最小二乘(Total Least Squares,TLS)联合反演的虚拟观测法,并使用方差分量估计(Variance Components Estimation,VCE)方法确定病态问题的正则化参数.将附有先验信...针对Mogi模型垂直位移与水平位移联合反演中的病态问题,改进火山形变总体最小二乘(Total Least Squares,TLS)联合反演的虚拟观测法,并使用方差分量估计(Variance Components Estimation,VCE)方法确定病态问题的正则化参数.将附有先验信息的参数作为观测方程,与垂直位移和水平位移的观测方程联合解算,推导了三类观测方程联合反演的求解公式及基于总体最小二乘方差分量估计确定正则化参数的表达式,给出了算法的迭代流程.通过算例实验,研究了总体最小二乘联合反演的虚拟观测法在火山Mogi模型形变反演中的应用;算例结果表明,三类数据的联合平差及方差分量估计方法可以确定权比因子并得到修正后的压力源参数,具有一定的实际参考价值.展开更多
Deep wellbores/boreholes are generally drilled into rocks for oil and gas exploration,monitoring of tectonic stresses purposes.Wellbore and tunnel in depth are generally in true triaxial stress state,even if the groun...Deep wellbores/boreholes are generally drilled into rocks for oil and gas exploration,monitoring of tectonic stresses purposes.Wellbore and tunnel in depth are generally in true triaxial stress state,even if the ground is under axisymmetric loading condition.Stability of such wellbores is very critical and collapse of wellbore must be avoided.Mogi-Coulomb failure criterion is a better representation of rock strength under true triaxial condition.In this paper,an analytical solution is proposed using Mogi-Coulomb failure criterion.The solution is obtained for rock mass exhibiting elastic-perfectly plastic or elastic-brittle-plastic behaviour considering in-plane isotropic stresses.The proposed solution is then compared with exact analytical solution for incompressible material and experimental results of thickwall cylinder.It is shown that the results obtained by the proposed analytical solution are in good agreement with the experimental results and exact analytical solution.A reduction of about 13%e20%in plastic zone from the proposed closed-form solution is observed,as compared to the results from the finite element method(FEM)based Mohr-Coulomb criterion.Next,the influences of various parameters such as Poisson’s ratio,internal pressure(mud weight),dilation angle,and out-of-plane stress are studied in terms of stress and deformation responses of wellbore.The results of the parametric study reveal that variation in the out-of-plane stress has an inverse relation with the radius of plastic zone.Poisson’s ratio does not have an appreciable influence on the tangential stress,radial stress and radial deformation.Dilation angle has a direct relation with the deformation.Internal pressure is found to have an inverse relation with the radial deformation and the radius of plastic zone.展开更多
针对垂直位移与水平位移的Mogi模型,提出采用总体最小二乘联合（total least squares joint,TLS-J）平差方法进行求解。该方法可同时顾及联合平差函数模型中观测向量与系数矩阵的误差项,且采用3种判别函数最小化法确定相对权比,用以权...针对垂直位移与水平位移的Mogi模型,提出采用总体最小二乘联合（total least squares joint,TLS-J）平差方法进行求解。该方法可同时顾及联合平差函数模型中观测向量与系数矩阵的误差项,且采用3种判别函数最小化法确定相对权比,用以权衡垂直位移与水平位移观测数据在联合求解过程中所占的比重。针对平差过程中出现的病态问题,结合L曲线法确定岭参数。通过实际算例,系统研究了总体最小二乘联合平差方法在长白山天池火山Mogi模型反演中的应用。研究结果表明,以判别函数为∑n1i=1｜e1i｜＋∑n2j=1｜e2j｜的函数最小化能获得合理的压力源参数估值结果和相对权比大小,具有一定的实际参考价值。展开更多
文摘针对Mogi模型垂直位移与水平位移联合反演中的病态问题,改进火山形变总体最小二乘(Total Least Squares,TLS)联合反演的虚拟观测法,并使用方差分量估计(Variance Components Estimation,VCE)方法确定病态问题的正则化参数.将附有先验信息的参数作为观测方程,与垂直位移和水平位移的观测方程联合解算,推导了三类观测方程联合反演的求解公式及基于总体最小二乘方差分量估计确定正则化参数的表达式,给出了算法的迭代流程.通过算例实验,研究了总体最小二乘联合反演的虚拟观测法在火山Mogi模型形变反演中的应用;算例结果表明,三类数据的联合平差及方差分量估计方法可以确定权比因子并得到修正后的压力源参数,具有一定的实际参考价值.
文摘Deep wellbores/boreholes are generally drilled into rocks for oil and gas exploration,monitoring of tectonic stresses purposes.Wellbore and tunnel in depth are generally in true triaxial stress state,even if the ground is under axisymmetric loading condition.Stability of such wellbores is very critical and collapse of wellbore must be avoided.Mogi-Coulomb failure criterion is a better representation of rock strength under true triaxial condition.In this paper,an analytical solution is proposed using Mogi-Coulomb failure criterion.The solution is obtained for rock mass exhibiting elastic-perfectly plastic or elastic-brittle-plastic behaviour considering in-plane isotropic stresses.The proposed solution is then compared with exact analytical solution for incompressible material and experimental results of thickwall cylinder.It is shown that the results obtained by the proposed analytical solution are in good agreement with the experimental results and exact analytical solution.A reduction of about 13%e20%in plastic zone from the proposed closed-form solution is observed,as compared to the results from the finite element method(FEM)based Mohr-Coulomb criterion.Next,the influences of various parameters such as Poisson’s ratio,internal pressure(mud weight),dilation angle,and out-of-plane stress are studied in terms of stress and deformation responses of wellbore.The results of the parametric study reveal that variation in the out-of-plane stress has an inverse relation with the radius of plastic zone.Poisson’s ratio does not have an appreciable influence on the tangential stress,radial stress and radial deformation.Dilation angle has a direct relation with the deformation.Internal pressure is found to have an inverse relation with the radial deformation and the radius of plastic zone.
文摘针对垂直位移与水平位移的Mogi模型,提出采用总体最小二乘联合（total least squares joint,TLS-J）平差方法进行求解。该方法可同时顾及联合平差函数模型中观测向量与系数矩阵的误差项,且采用3种判别函数最小化法确定相对权比,用以权衡垂直位移与水平位移观测数据在联合求解过程中所占的比重。针对平差过程中出现的病态问题,结合L曲线法确定岭参数。通过实际算例,系统研究了总体最小二乘联合平差方法在长白山天池火山Mogi模型反演中的应用。研究结果表明,以判别函数为∑n1i=1｜e1i｜＋∑n2j=1｜e2j｜的函数最小化能获得合理的压力源参数估值结果和相对权比大小,具有一定的实际参考价值。
