Analysis of a numerical solution to the one-dimensional stochastic convection equation

Under certain conditions the concentration and flux of a substance moving in a stochastic flow field are described by the stochastic convection equation. A numerical method for solving the one-dimensional problem is studied here. The differential operator is replaced by a discrete linear operator based on finite differences. The resulting system of stochastic equations is then replaced by a system of equations whose solution is the mean concentration or mean flux. This final system is analysed and conditions for a stable numerical solution are obtained. Finally, numerical examples are given and are compared to an approximate analytical solution to the stochastic convection equation.     

基于结构导向的梯度属性边缘检测技术

地震数据中的不连续性检测对于识别和刻画地下地质体边界具有重要意义.随着勘探目标向岩性油藏和复杂断块油藏的转变,解释人员需要对小断裂、微裂缝等微幅地质体边界信息进行精细刻画.常规边缘检测算子由于算法的局限性不能满足上述需求.本文通过引入能量归一化和沿层检测思想对常规检测算子进行改进,提出一种基于结构导向的梯度属性边缘检测技术.该技术通过结构张量估计得到局部地层区域的倾角和方位角,利用得到的倾角和方位角信息作为约束,使用二维边缘检测算子实现三维数据中的沿层不连续性检测.经过实际资料处理,并与结构导向方差属性对比分析,证实该方法在地层不连续性检测方面具有很好效果,检测得到的不连续性信息在细节上表现更丰富,可以作为地层横向差异和地质体边界识别的有力工具.     

海南岛海风雷暴结构的数值模拟

本文利用高分辨率WRF模式对2012年7月20日发生在海南地区的一次海风雷暴过程进行模拟,探讨了海南岛复杂地形下海风雷暴的结构、发展演变过程及其触发机制.结果表明,海南岛北部向内陆传播的海风与南部受地形阻挡的海风相遇后会形成海风辐合带,辐合带能影响当地的散度和涡旋特征,为雷暴的发生发展提供有利的动力和热力学条件.海南岛受热带海洋的影响较大,当地的水汽条件和对流潜势长期保持着有利于对流发展的状态,自由对流高度始终处于较低的位置,一旦海风辐合带来的抬升运动克服对流抑制到达自由对流高度后,对流就能自主地发展起来,所以单纯的海风辐合也常常能触发当地的强雷暴.雷暴发生发展过程中对流参数存在明显的变化,其演变曲线的突变位置对雷暴的发生有一定的指示作用.海南岛的海风雷暴过程与当地的复杂地形密切相关,地形的动力阻挡作用影响着低层海风的辐合以及对流的发展.     

Mean-field equations for weakly nonlinear two-scale perturbations of forced hydromagnetic convection in a rotating layer

We consider stability of regimes of hydromagnetic thermal convection in a rotating horizontal layer with free electrically-conducting boundaries, to perturbations involving large spatial and temporal scales. Equations governing the evolution of weakly nonlinear mean perturbations are derived under the assumption that the α-effect is insignificant in the leading-order (e.g. due to a symmetry of the system). The mean-field equations generalise the standard equations of hydromagnetic convection: New terms emerge – a second-order linear operator representing the combined eddy diffusivity and quadratic terms associated with the eddy advection. If the perturbed CHM regime is nonsteady and insignificance of the α-effect in the system does not rely on the presence of a spatial symmetry, the combined eddy diffusivity operator also involves a nonlocal pseudodifferential operator. If the perturbed CHM state is almost symmetric, α-effect terms appear in the mean-field equations as well. Near a point of a symmetry-breaking bifurcation, cubic nonlinearity emerges in the equations. All the new terms are in general anisotropic. A method for evaluation of their coefficients is presented; it requires solution of a significantly smaller number of auxiliary problems than in a straightforward approach.     

Fourier finite-difference migration for steeply dipping reflectors with complex overburden1

The improvement in accuracy and efficiency of wave-equation migration techniques is an ongoing topic of research. The main problem is the correct imaging of steeply dipping reflectors in media with strong lateral velocity variations. We propose an improved migration method which is based on cascading phase-shift and finite-difference operators for downward continuation. Due to these cascaded operators we call this method‘Fourier finite-difference migration’(FFD migration). In our approach we try to generalize and improve the split-step Fourier migration method for strong lateral velocity variations using an additional finite-difference correction term. Like most of the current migration methods in use today, our method is based on the one-way wave equation. It is solved by first applying the square-root operator but using a constant velocity at each depth step which has to be the minimum velocity. In a second step, the approximate difference between the correct square-root operator and this constant-velocity squareroot operator (the error made in the first step) is implemented as an implicit FD migration scheme, part of which is the split-step Fourier correction term. Some practical aspects of the new FFD method are discussed. Its performance is compared with that of split-step and standard FD migration schemes. First applications to synthetic and real data sets are presented. They show that the superiority of FFD migration becomes evident by migrating steeply dipping reflectors with complex overburden having strong lateral velocity variations. If velocity is laterally constant, FFD migration has the accuracy of the phase-shift method. The maximum migration angle is velocity adaptive, in contrast to conventional FD migration schemes. It varies laterally depending on the local level of velocity variation. FFD migration is more efficient than higher-order implicit FD schemes. These schemes use two cascaded downward-continuation steps in order to attain comparable migration performance.     

A finite element model for the diffusion—convection equation with applications to air pollution problems

A method of solution for the diffusion-convection equation in one spatial dimension has been developed previously. The generalization of this method into two-spatial dimensions will be presented. The method employs space-time volume elements with edges joining the nodes at subsequent time levels oriented along the characteristics of the associated pure convection problem. The accuracy and utility of the method are demonstrated by solving several examples and results are compared with the exact solutions.     

Parameterized thermal model of a mixed mantle convection

IntroductionTectonicevolutionisinfluencedbythermalhistoryoftheEarth.TheEarthhasabout4.6Gahistory.ThermalenergyfromtheinterioroftheEachprovidesthemainpowerfortectonicevolution.ItnotonlycontrolstheformationofthelayeredstructuresinsidetheEarth,butalsopromotesthetectonicmovementsofthesurfaceplatesduringthegeologicalera.ThestudyofthethermalhistoryoftheEarthhaspassedseveralstages.Inearlystudies,onlyconductivemechanism(Lubimova,1958)isdiscussedinthethermalevolution.However,theimpotalceofthermalco…     

基于随温度变化的热系数模拟板块俯冲动力学过程

热传导系数和热膨胀系数是影响板块俯冲动力学过程的两个重要参数. 由于地球介质的不均匀性,热系数也会随深度发生变化.然而,这种变化在地球动力学模拟研究中往往被忽略.本文针对随温度变化的热传导系数和热膨胀系数, 模拟板块俯冲的动力学过程,分析热系数、黏度对板块俯冲形态的影响及其对应的地幔对流特征.结果表明,依温度变化的热传导系数和热膨胀系数会影响地幔温度及黏度分布,进而改变板块的俯冲角度;黏度是控制板块俯冲动力学演化过程的重要因素;地幔对流受黏度结构的影响,呈现分层对流及局部多个对流环等多种不同形态的对流场特征.      

A numerical procedure for obtaining the mean solution and variance of the two-dimensional stochastic convection equation

Under certain conditions the concentration of a substance moving in a stochastic flow field is described by the stochastic convection equation. A numerical method yielding the mean solution and variance of the two-dimensional problem is described here. First, the differential operator is replaced by a discrete linear operator based on finite differences. The resulting system of stochastic equations is then replaced by a system of equations whose solution is the mean concentration. The variance of the concentration can then be calculated. In addition, and example is given for which an approximate analytical solution and its variance is known. The numerical method is applied to the example and results compared to the approximate analytical solution and variance.     

The response of the high-latitude ionosphere to IMF variations

The convection of plasma in the high-latitude ionosphere is strongly affected by the interplanetary magnetic field (IMF) carried by the solar wind. From numerous statistical studies, it is known that the plasma circulation conforms to patterns that are characteristic of particular IMF states. Following a change in the IMF, the convection responds by reconfiguring into a pattern that is more consistent with the new IMF. Some early studies reported that the convection first begins to change near noon while on the dawn and dusk flanks and on the nightside it remains relatively unaffected for tens of minutes. Work by Ridley et al. (J. Geophys. Res. 103 (1998) 4023–4039) and Ruohoniemi and Greenwald (Geophys. Res. Lett. 25 (1998) 2913–2916) that was based on measurements with more global sets of instruments challenged this view. A debate ensued as to the true nature of the convection response. We follow the arguments of Lockwood and Cowley (J. Geophys. Res. 104 (1999) 4387–4391) and Ridley et al. (J. Geophys. Res. 104 (1999) 4393–4396) by reviewing recent results on the timing of the onset of the convection response to the changed IMF. We discuss the timing problem from the perspectives of observations and modeling. In our view, the onset of the ionospheric response to changed IMF is globally simultaneous on time scales of a few minutes. A physical basis for the rapid communication of effects in the dayside convection to the nightside has been demonstrated in magnetohydrodynamic simulations. We also offer some cautionary notes on the timing of convection changes and the use of global assimilative techniques to study local behavior.     

Linear Stability of Thermal Convection in Rotating Systems with Fixed Heat Flux Boundaries

Linear stability of rotating thermal convection in a horizontal layer of Boussinesq fluid under the fixed heat flux boundary condition is examined by the use of a vertically truncated system up to wavenumber one. When the rotation axis is in the vertical direction, the asymptotic behavior of the critical convection for large rotation rates is almost the same as that under the fixed temperature boundary condition. However, when the rotation axis is horizontal and the lateral boundaries are inclined, the mode with zero horizontal wavenumber remains as the critical mode regardless of the rotation rate. The neutral curve has another local minimum at a nonzero horizontal wavenumber, whose asymptotic behavior coincides with the critical mode under the fixed temperature condition. The difference of the critical horizontal wavenumber between those two geometries is qualitatively understood by the difference of wave characteristics; inertial waves and Rossby waves, respectively.     

Two-dimensional electric field measurements in the ionospheric footprint of a flux transfer event

Line-of-sight Doppler velocities from the SuperDARN CUTLASS HF radar pair have been combined to produce the first two-dimensional vector measurements of the convection pattern throughout the ionospheric footprint of a flux transfer event (a pulsed ionospheric flow, or PIF). Very stable and moderate interplanetary magnetic field conditions, along with a preceding prolonged period of northward interplanetary magnetic field, allow a detailed study of the spatial and the temporal evolution of the ionospheric response to magnetic reconnection. The flux tube footprint is tracked for half an hour across six hours of local time in the auroral zone, from magnetic local noon to dusk. The motion of the footprint of the newly reconnected flux tube is compared with the ionospheric convection velocity. Two primary intervals in the PIFs evolution have been determined. For the first half of its lifetime in the radar field of view the phase speed of the PIF is highly variable and the mean speed is nearly twice the ionospheric convection speed. For the final half of its lifetime the phase velocity becomes much less variable and slows down to the ionospheric convection velocity. The evolution of the flux tube in the magnetosphere has been studied using magnetic field, magnetopause and magnetosheath models. The data are consistent with an interval of azimuthally propagating magnetopause reconnection, in a manner consonant with a peeling of magnetic flux from the magnetopause, followed by an interval of anti-sunward convection of reconnected flux tubes.     

On the using cumulant expansion method and van Kampen’s lemma for stochastic differential equations with forcing

Second-order exact ensemble averaged equation for linear stochastic differential equations with multiplicative randomness and random forcing is obtained by using the cumulant expansion ensemble averaging method and by taking the time dependent sure part of the multiplicative operator into account. It is shown that the satisfaction of the commutativity and the reversibility requirements proposed earlier for linear stochastic differential equations without forcing are necessary for the linear stochastic differential equations with forcing when the cumulant expansion ensemble averaging method is used. It is shown that the applicability of the operator equality, which is used for the separation of operators in the literature, is also subjected to the satisfaction of the commutativity and the reversibility requirements. The van Kampen’s lemma, which is proposed for the analysis of nonlinear stochastic differential equations, is modified in order to make the probability density function obtained through the lemma depend on the forcing terms too. The second-order exact ensemble averaged equation for linear stochastic differential equations with multiplicative randomness and random forcing is also obtained by using the modified van Kampen’s lemma in order to validate the correctness of the modified lemma. Second-order exact ensemble averaged equation for one dimensional convection diffusion equation with reaction and source is obtained by using the cumulant expansion ensemble averaging method. It is shown that the van Kampen’s lemma can yield the cumulant expansion ensemble averaging result for linear stochastic differential equations when the lemma is applied to the interaction representation of the governing differential equation. It is found that the ensemble averaged equations given for one the dimensional convection diffusion equation with reaction and source in the literature obtained by applying the lemma to the original differential equation are restricted with small sure part of multiplicative operator. Second-order exact differential equations for the evolution of the probability density function for the one dimensional convection diffusion equation with reaction and source and one dimensional nonlinear overland flow equation with source are obtained by using the modified van Kampen’s lemma. The equation for the evolution of the probability density function for one dimensional nonlinear overland flow equation with source given in the literature is found to be not second-order exact. It is found that the differential equations for the evolution of the probability density functions for various hydrological processes given in the literature are not second-order exact. The significance of the new terms found due to the second-order exact ensemble averaging performed on the one dimensional convection diffusion equation with reaction and source and during the application of the van Kampen’s lemma to the one dimensional nonlinear overland flow equation with source is investigated.     

Influences of local factors on permafrost occurrence and their implications for Qinghai-Xizang Railway design

Permafrost is a product of long-term energy ex-change between the atmosphere and the ground. Macro-scale distribution of permafrost is controlled overall by climate. However, site-specific variables such as terrain conditions, snow cover, soil/rock type, and moisture content can significantly modify the ef-fect of climate, resulting in localized anomalies in permafrost distribution[1,2]. These factors cause distur-bances to normal thermal regimes and can determine the presence and absence of p…     

A benchmark comparison of numerical methods for infinite Prandtl number thermal convection in two-dimensional Cartesian geometry

Abstract

A comparison is made between seven different numerical methods for calculating two-dimensional thermal convection in an infinite Prandtl number fluid. Among the seven methods are finite difference and finite element techniques that have been used to model thermal convection in the Earth's mantle. We evaluate the performance of each method using a suite of four benchmark problems, ranging from steady-state convection to intrinsically time-dependent convection with recurring thermal boundary layer instabilities. These results can be used to determine the accuracy of other computational methods, and to assist in the development of new ones.     

3D TABLE-DRIVEN MIGRATION1

An efficient full 3D wavefield extrapolation technique is presented. The method can be used for any type of subsurface structure and the degree of accuracy and dip-angle performance are user-defined. The extrapolation is performed in the space-frequency domain as a space-dependent spatial convolution with recursive Kirchhoff extrapolation operators. To get a high level of efficiency the operators are optimized such that they have the smallest possible size for a specified accuracy and dip-angle performance. As both accuracy and maximum dip-angle are input parameters for the operator calculation, the method offers the possibility of a trade-off between these quantities and efficiency. The operators are calculated in advance and stored in a table for a range of wavenumbers. Once they have been calculated they can be used many times. At the basis of the operator design is the well-known phase-shift operator. Although this operator is exact for homogeneous media only, it is assumed that it may be applied locally in case of inhomogeneities. Lateral velocity variations can then be handled by choosing the extrapolation operator according to the local value of the velocity. Optionally the operators can be designed such that they act as spatially variant high-cut filters. This means that the evanescent field can be suppressed in one pass with the extrapolation. The extrapolation method can be used both in prestack and post-stack applications. In this paper we use it in zero-offset migration. Tests on 2D and 3D synthetic and 2D real data show the excellent quality of the method. The full 3D result is much better then the result of two-pass migration, which has been applied to the same data. The implementation yields a code that is fully vectorizable, which makes the method very suitable for vector computers.     

用近垂直地震反射方法研究莫霍面的特征与成因

利用近垂直地震反射方法研究了在中国满洲里－绥芬河地学断面域内泰康－哈尔滨约１３０ｋｍ范围内地壳结构和莫霍面特征．通过数据采集,定量处理和综合分析,得到以下认识：在野外观测中激发井深和震源能量是主要参数;在资料处理中速度分析与共反射点分布的处理是主要技术．分析莫霍震相可以得到它的层状与似层状内部结构以及起伏、断裂等外形特征．利用傅立叶谱、时频分析与瞬时信息可更细致地研究莫霍特征．影响莫霍特征与成因的因素主要为分异作用、地幔对流、相变、地球转动和板块运动;其中地幔对流和相变是形成莫霍的主要因素．     

地震数据互相关驱动的多道反演方法

地震反演是储层定量描述和地震油气识别的关键技术,反演结果在复杂构造区域的横向连续性和保真性是影响地震资料定量解释精度的重要因素.基于此,本文发展了地震数据互相关驱动的多道反演方法.考虑地层反射系数与地震数据在结构上具有相似性的特点,基于地震数据互相关描述地层反射系数的结构特征,并将其作为多道地震反演的横向约束条件;此外,为改善地震数据本身横向连续性差对反演结果的影响,在目标泛函的惩罚项中引入局部优化算子,构建了一个易于求解的多道地震反演目标泛函.与常规多道地震反演方法相比,本文方法能够设计更合理、更符合实际情况的横向约束算子,提高反演结果的横向连续性,并且能有效降低地震资料质量对反演结果的影响.模型测试和实际应用验证了本方法的可靠性和稳定性.     

The influence of surface layer salinity on wintertime convection in Wilkinson Basin,Gulf of Maine

Observations suggest that the interannual variability of wintertime convection in Wilkinson Basin (WB) during 1977–2005 is related to the variation in the surface layer salinity in the western Gulf of Maine (wGOM). When the winter convection is stronger (weaker), the resulting deep-layer temperatures in the wGOM are colder (warmer), and the likelihood of deep winter mixing is greater when the wGOM salinities are high. This hypothesis was tested using a one-dimensional mixed layer model to simulate the water column structure over the cooling period. Comparisons were made between the convection potential for the range of observed late-fall salinity values. Model results indicated that the mixed layer depth could deepen by as much as 50% when the surface layer salinities in the wGOM were high. Sensitivity tests revealed that the surface layer salinity variability, and its influence on the water column density structure, was a significant factor, along with local climate variability, in determining the observed time series trend in springtime bottom layer temperatures.