We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion,where both fast and slow components are influenced by white noise.Furthermore,we verify the exponential tracking property for the ...We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion,where both fast and slow components are influenced by white noise.Furthermore,we verify the exponential tracking property for the established random slow manifold,which leads to a lower dimensional reduced system.Alongside this we consider a parameter estimation method for a nonlocal fast-slow stochastic dynamical system,where only the slow component is observable.In terms of quantifying parameters in stochastic evolutionary systems,the provided method offers the advantage of dimension reduction.展开更多
The conventional acoustic logging interpretation method, which is based on vertical wells that penetrate isotropic formations, is not suitable for horizontal and deviated wells penetrating anisotropic formations. This...The conventional acoustic logging interpretation method, which is based on vertical wells that penetrate isotropic formations, is not suitable for horizontal and deviated wells penetrating anisotropic formations. This unsuitability is because during horizontal and deviated well drilling, cuttings will splash on the well wall or fall into the borehole bottom and form a thin bed of cuttings. In addition, the high velocity layers at different depths and intrinsic anisotropy may affect acoustic logging measurements. In this study, we examine how these factors affect the acoustic wave slowness measured in horizontal and deviated wells that are surrounded by an anisotropic medium using numerical simulation. We use the staggered-grid finite difference method in time domain （FDTD） combined with hybrid-PML. First, we acquire the acoustic slowness using a simulated array logging system, and then, we analyze how various factors affect acoustic slowness measurements and the differences between the effects of these factors. The factors considered are high-velocity layers, thin beds of cuttings, dipping angle, formation thickness, and anisotropy. The simulation results show that these factors affect acoustic wave slowness measurements differently. We observe that when the wavelength is much smaller than the distance between the borehole wall and high velocity layer, the true slowness of the formation could be acquired. When the wavelengths are of the same order （i.e., in the near-field scenarios）, the geometrical acoustics theory is no longer applicable. Furthermore, when a thin bed of cuttings exists at the bottom of the borehole, Fermat＇s principle is still applicable, and true slowness can be acquired. In anisotropic formations, the measured slowness changes with increments in the dipping angle. Finally, for a measurement system with specific spacing, the slowness of a thin target layer can be acquired when the distance covered by the logging tool is sufficiently long. Based on systematical simulations with different dipping angles and anisotropy in homogenous TI media, slowness estimation charts are established to quantitatively determine the slowness at any dipping angle and for any value of the anisotropic ratio. Synthetic examples with different acoustic logging tools and different elastic parameters demonstrate that the acoustic slowness estimation method can be conveniently applied to horizontal and deviated wells in TI formations with high accuracy.展开更多
基金supported by NSF (1620449)NSFC (11531006 and 11771449)
文摘We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion,where both fast and slow components are influenced by white noise.Furthermore,we verify the exponential tracking property for the established random slow manifold,which leads to a lower dimensional reduced system.Alongside this we consider a parameter estimation method for a nonlocal fast-slow stochastic dynamical system,where only the slow component is observable.In terms of quantifying parameters in stochastic evolutionary systems,the provided method offers the advantage of dimension reduction.
基金supported by National Natural Science Foundation of China(No.41204094)Science Foundation of China University of Petroleum,Beijing(No.2462015YQ0506)
文摘The conventional acoustic logging interpretation method, which is based on vertical wells that penetrate isotropic formations, is not suitable for horizontal and deviated wells penetrating anisotropic formations. This unsuitability is because during horizontal and deviated well drilling, cuttings will splash on the well wall or fall into the borehole bottom and form a thin bed of cuttings. In addition, the high velocity layers at different depths and intrinsic anisotropy may affect acoustic logging measurements. In this study, we examine how these factors affect the acoustic wave slowness measured in horizontal and deviated wells that are surrounded by an anisotropic medium using numerical simulation. We use the staggered-grid finite difference method in time domain （FDTD） combined with hybrid-PML. First, we acquire the acoustic slowness using a simulated array logging system, and then, we analyze how various factors affect acoustic slowness measurements and the differences between the effects of these factors. The factors considered are high-velocity layers, thin beds of cuttings, dipping angle, formation thickness, and anisotropy. The simulation results show that these factors affect acoustic wave slowness measurements differently. We observe that when the wavelength is much smaller than the distance between the borehole wall and high velocity layer, the true slowness of the formation could be acquired. When the wavelengths are of the same order （i.e., in the near-field scenarios）, the geometrical acoustics theory is no longer applicable. Furthermore, when a thin bed of cuttings exists at the bottom of the borehole, Fermat＇s principle is still applicable, and true slowness can be acquired. In anisotropic formations, the measured slowness changes with increments in the dipping angle. Finally, for a measurement system with specific spacing, the slowness of a thin target layer can be acquired when the distance covered by the logging tool is sufficiently long. Based on systematical simulations with different dipping angles and anisotropy in homogenous TI media, slowness estimation charts are established to quantitatively determine the slowness at any dipping angle and for any value of the anisotropic ratio. Synthetic examples with different acoustic logging tools and different elastic parameters demonstrate that the acoustic slowness estimation method can be conveniently applied to horizontal and deviated wells in TI formations with high accuracy.
文摘提出一种基于符号高阶统计量(HOS,high-order statistics)的MPSK调制信道衰落系数盲估计算法。针对平坦慢衰落信道模型,首先分析了MPSK调制符号高阶统计量特征,证明了MPSK调制符号的M次方符号的值是唯一的,而当1≤M′<M时,调制符号的M′次方符号在复平面上是对称分布的;之后利用此特征推导出MPSK调制阶数、初始相位和衰落系数估计算法。仿真实验表明,信噪比高于12 d B条件下,HOS算法估计性能与目前平坦慢衰落信道盲估计的主流方法 Lloyd-Max算法相同,而算法复杂度为Lloyd-Max算法的1/50,并且在接收样本符号较少的条件下HOS算法的均方误差曲线收敛于最小二乘估计理论下界。
