With deep mining of coal mines, prospecting multilayer water-filled goaf has become a new content that results from geophysical exploration in coalfields. The central loop transient electromagnetic （TEM） method is f...With deep mining of coal mines, prospecting multilayer water-filled goaf has become a new content that results from geophysical exploration in coalfields. The central loop transient electromagnetic （TEM） method is favorable for prospecting conductive layers because of the coupling relationship between its field structure and formation. However, the shielding effect of conductive overburden would not only require a longer observation time when prospecting the same depth but also weaken the anomalous response of underlying layers. Through direct time domain numerical simulation and horizontal layered earth forward modeling, this paper estimates the length of observation time required to prospect the target, and the distinguishable criterion of multilayer water-filled goal is presented with observation error according to the effect of noise on observation data. The observed emf curves from Dazigou Coal Mine, Shanxi Province can distinguish multilayer water-filled goaf. In quantitative inversion interpretation of observed curves, using electric logging data as initial parameters restrains the equivalence caused by coal formation thin layers. The deduced three-layer and two-layer water-filled goals are confirmed by the drilling hole. The result suggests that when observation time is long enough and with the anomalous situation of underlying layers being greater than the observation error, the use of the central loop TEM method to orosoect a multilaver water-filled goaf is feasible.展开更多
We analyze an h-p version Petrov-Galerkin finite element method for linear Volterra integrodifferential equations. We prove optimal a priori error bounds in the L2- and H1-norm that are explicit in the time steps,the ...We analyze an h-p version Petrov-Galerkin finite element method for linear Volterra integrodifferential equations. We prove optimal a priori error bounds in the L2- and H1-norm that are explicit in the time steps,the approximation orders and in the regularity of the exact solution. Numerical experiments confirm the theoretical results. Moreover,we observe that the numerical scheme superconverges at the nodal points of the time partition.展开更多
A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The s...A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The stability and error estimates of the temporal semidiscrete scheme are rigorously discussed,and the convergence order of the proposed method is proved to be O(τ2+Nα-m)in L2-norm,whereτ,N,αand m are the time step size,polynomial degree,fractional derivative index and regularity of the exact solution,respectively.Numerical experiments are carried out to demonstrate the theoretical analysis.展开更多
基金supported by the National Science Foundation of China(No.41374129)Science and Technology Project of Shanxi Province(No.20100321066)Research and Development Project of National Major Scientifi c Research Equipment(No.ZDYZ2012-1-05-04)
文摘With deep mining of coal mines, prospecting multilayer water-filled goaf has become a new content that results from geophysical exploration in coalfields. The central loop transient electromagnetic （TEM） method is favorable for prospecting conductive layers because of the coupling relationship between its field structure and formation. However, the shielding effect of conductive overburden would not only require a longer observation time when prospecting the same depth but also weaken the anomalous response of underlying layers. Through direct time domain numerical simulation and horizontal layered earth forward modeling, this paper estimates the length of observation time required to prospect the target, and the distinguishable criterion of multilayer water-filled goal is presented with observation error according to the effect of noise on observation data. The observed emf curves from Dazigou Coal Mine, Shanxi Province can distinguish multilayer water-filled goaf. In quantitative inversion interpretation of observed curves, using electric logging data as initial parameters restrains the equivalence caused by coal formation thin layers. The deduced three-layer and two-layer water-filled goals are confirmed by the drilling hole. The result suggests that when observation time is long enough and with the anomalous situation of underlying layers being greater than the observation error, the use of the central loop TEM method to orosoect a multilaver water-filled goaf is feasible.
基金supported by National Natural Science Foundation of China(Grant Nos.11226330 and 11301343)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20113127120002)+3 种基金the Research Fund for Young Teachers Program in Shanghai(GrantNo.shsf018)the Fund for E-institute of Shanghai Universities(Grant No.E03004)supported by the Natural Sciences and Engineering Research Council of Canada(Grant No.OGP0046726)Shanghai University under Leading Academic Discipline Project of Shanghai MunicipalEducation Commission(Grant No.J50101)
文摘We analyze an h-p version Petrov-Galerkin finite element method for linear Volterra integrodifferential equations. We prove optimal a priori error bounds in the L2- and H1-norm that are explicit in the time steps,the approximation orders and in the regularity of the exact solution. Numerical experiments confirm the theoretical results. Moreover,we observe that the numerical scheme superconverges at the nodal points of the time partition.
基金supported by National Center for Mathematics and Interdisciplinary Sciences,CASNational Natural Science Foundation of China (Grant Nos. 60931002 and 91130019)
文摘A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The stability and error estimates of the temporal semidiscrete scheme are rigorously discussed,and the convergence order of the proposed method is proved to be O(τ2+Nα-m)in L2-norm,whereτ,N,αand m are the time step size,polynomial degree,fractional derivative index and regularity of the exact solution,respectively.Numerical experiments are carried out to demonstrate the theoretical analysis.
