An approximate method for determining the stability of two-scale flow in the mantle

Summary An approximate method of calculating the stability of two-dimensional convection rolls to cross-roll disturbances is evaluated by comparison with the results from exact analyses and good agreement is obtained. In particular, investigation of the second mode of the disturbance provides a qualitative estimate of the terms excluded in making the approximation. We conclude that this approximate method, sensibly used, gives a good indication of the stability of rolls to cross-roll disturbances.Application of this method is made to convection rolls heated partially or wholly from within, and to rolls in the presence of a longitudinal shear flow. The approximation indicates that, at high Rayleigh Numbers, growth rates are underestimated and so the amount of shear calculated to stabilise longitudinal rolls is a lower bound. Our results suggest that two-dimensional rolls are unlikely to be a stable flow pattern beneath even the fastest moving plates.     

An approximate method for soil-structure interaction for sh-waves—the born approximation

An approximate method is proposed for the scattering of SH-waves by foundations of irregular shape and the resulting soil-structure interaction problems. The scattering of elastic waves by the rigid foundation embedded in half-space is solved approximately by using integral representation of the wave equation. The procedure is the Born approximation which has been widely used in quantum mechanics for collision and scattering theory though not well-known in elastodynamics. This paper extends the previous work of the authors on the scattering of waves to account for soil-structure interaction. The motion of the foundation is evaluated by the balance of momentum under stresses due to the incident waves as well as the waves generated by its own motion and the forces coming from the superstructure. The model investigated consists of an infinitely long elastic shear wall of height H and thickness h erected on a rigid infinitely long foundation. Results are presented for the cases with circular, elliptical and rectangular foundations. For a circular foundation, excellent agreement is found with the exact solutions for the foundation displacement and the relative displacement between the top and bottom of the structure for the entire range of wave numbers. For an elliptical foundation, accuracy decreases with increasing wave numbers. Foundation displacements are compared for foundation shapes that are shallow elliptical, deep elliptical, rectangular and circular. It is observed that foundation displacements are dependent on the angle of incidence except for a semi-circle. The results on the details of the scattered field are, however, not as accurate.     

An approximate method for joint sequential simulation of multiple spatial variables

Multivariate simulation is an important longstanding problem in geostatistics. Fitting a model of coregionalization to many variables is intractable and often not permitted; however, the matrix of collocated correlation coefficients is often well informed. Performing a matrix simulation with LU decomposition of the correlation matrix at each step of sequential simulation is implemented in some software. The target correlation matrix is not reproduced because of conditioning to local data and the particular variable ordering in the sequential/LU decomposition. A correction procedure is developed to calculate a modified correlation matrix that leads to reproduction of the target correlation matrix. The theoretical and practical aspects of this correction are developed.     

近钻头井斜动态测量重力加速度信号提取方法研究

利用加速度计进行近钻头井斜动态测量时,钻具的高速旋转,井下强振动、强冲击环境给重力加速度测量带来极大干扰,如何从干扰噪声中有效提取重力加速度信号对于提高井斜角和工具面角的测量精度至关重要.根据重力加速度径向和切向分量为周期性信号,轴向分量为近似直流信号,离心加速度为缓慢变化信号,振动和冲击加速度为随机信号的特征,提出一种基于互相关检测的重力加速度信号提取方法,选择径向或切向磁力计信号作为参考信号.利用相关检测方法分别对仿真数据、实验室旋转测试数据和振动测试数据进行处理,并计算了井斜角和工具面角,结果表明相关检测方法可以有效提取重力加速度信号,基于MEMS加速度计的井斜角测量精度优于0.5°,工具面角变化连续平滑,满足井斜动态测量需求.通过进一步开展实际钻井环境测试,该方法有望应用于近钻头地质导向系统或旋转导向钻井系统等需要近钻头井斜动态测量的场合.

     

An optimised method for calculating the O+-O collision parameter from aeronomical measurements

A study has been made of the interaction between the thermosphere and the ionosphere at high latitudes, with particular regard to the value of the O⁺-O collision parameter. The European incoherent scatter radar (EISCAT) was used to make tristatic measurements of plasma parameters at F-region altitudes while simultaneous measurements of the neutral wind were made by a Fabry-Perot interferometer (FPI). The radar data were used to derive the meridional neutral winds in a way similar to that used by previous authors. The accuracy of this technique at high latitudes is reduced by the dynamic nature of the auroral ionosphere and the presence of significant vertical winds. The derived winds were compared with the meridional winds measured by the FPI. For each night, the value of the O⁺-O collision parameter which produced the best agreement between the two data sets was found. The precision of the collision frequency found in this way depends on the accuracy of the data. The statistical method was critically examined in an attempt to account for the variability in the data sets. This study revealed that systematic errors in the data, if unaccounted for by the analysis, have a tendency to increase the value of the derived collision frequency. Previous analyses did not weight each data set in order to account for the quality of the data; an improved method of analysis is suggested.     

On a method of computing the gravitational fields of inhomogeneous bodies

Summary A solution of the direct gravity problem for a finite body with variable density is given. The method is based on Green's formula and is applicable when a particular solution of Poisson's equation is known. The attraction due to the body is expressed by integrals over its surface The exact solution of the direct gravity problem, as known from the theory of two-dimensional fields [1–3], is closely connected with the problem of the analytic continuation of the exterior field of the attracting mass system into its interior. In the first place, this is a problem of determining the singularities of the exterior field, their distribution within the system and their nature. This approach to the solution of the direct problem is also meaningful from the point of view of determining the characteristics of the attracting system and, therefore, also of solving the inverse problem. In the case of two-dimensional fields the methods of analytical continuation were widely developed in a series of well-known papers by V. N. Strakhov, and they are mainly based on the methods of the theory of the functions of the complex variable. These methods were also successfully applied by Tsirulskii and Golizdra [1, 2] in treating the homogeneous and inhomogeneous, two-dimensional direct problem by means of Cauchy's integrals. However, as regards three-dimensional fields a number of fundamental problems has not been solved in this respect.Dedicated to 90th Birthday of Professor Frantiek Fiala     

多肢剪力墙自振频率传递矩阵法简化计算

基于连续体系模型与传递矩阵法的结合,提出了一种简化方法来计算多肢剪力墙的动力特性。整个结构体系等效模拟为一个夹层结构梁;建立了相应的基本微分方程;通过求解微分方程得到了楼层间变形函数;利用边界条件及层间变形函数导出了层间传递矩阵;据此计算出了体系的振型与自振频率。算例分析表明本文方法计算结果与文献给出的解是比较吻合的。     

Kinematic dynamo action in a sphere: Effects of periodic time-dependent flows on solutions with axial dipole symmetry

Choosing a simple class of flows, with characteristics that may be present in the Earth's core, we study the ability to generate a magnetic field when the flow is permitted to oscillate periodically in time. The flow characteristics are parameterised by D, representing a differential rotation, M, a meridional circulation, and C, a component characterising convective rolls. The dynamo action of all solutions with fixed parameters (steady flows) is known from earlier studies. Dynamo action is sensitive to these flow parameters and fails spectacularly for much of the parameter space where magnetic flux is concentrated into small regions, leading to high diffusion. In addition, steady flows generate only steady or regularly reversing oscillatory fields and cannot therefore reproduce irregular geomagnetic-type reversal behaviour. Oscillations of the flow are introduced by varying the flow parameters in time, defining a closed orbit in the space ( D,?M ). When the frequency of the oscillation is small, the net growth rate of the magnetic field over one period approaches the average of the growth rates for steady flows along the orbit. At increased frequency time-dependence appears to smooth out flux concentrations, often enhancing dynamo action. Dynamo action can be impaired, however, when flux concentrations of opposite signs occur close together as smoothing destroys the flux by cancellation. It is possible to produce geomagnetic-type reversals by making the orbit stray into a region where the steady flows generate oscillatory fields. In this case, however, dynamo action was not found to be enhanced by the time-dependence. A novel approach is being taken to solve the time-dependent eigenvalue problem where, by combining Floquet theory with a matrix-free Krylov-subspace method, we can avoid large memory requirements for storing the matrix required by the standard approach.     

An analytical method of analysing the oscillatory pressure head measured at any depth in a well casing

When a slug test is conducted in a highly permeable aquifer, a shallow pressure transducer in the well casing produces an oscillatory pressure head that is representative of the water level fluctuation, whereas a deep pressure transducer in the well casing yields an oscillatory pressure head that is different from the water level change. Although the solutions for shallow and deep pressure head are different, it is found that the ratios of the subsequent extremity displacements are in an identical relationship (an extremity can be a maximum or a minimum in the oscillatory pressure head). Based on this relationship, an analytical data analysis method for the determination of the hydraulic conductivity is developed for both shallow and deep pressure transducer data. This analytical method is applied to the pressure head measured at different depths in the well casing of a well partially penetrating an unconfined coarse sand aquifer. Satisfactory results are obtained, validating the applicability of this analytical method for pressure transducer data at any depth in a well casing. Copyright © 2007 John Wiley & Sons, Ltd.     

基于射线追踪技术计算地震定位中震源轨迹的改进方法

使用震源轨迹确定震源位置不仅稳健而且直观,但当介质复杂时震源轨迹难以给出解析解.基于最小走时树射线追踪技术计算震源轨迹的方法(以轨迹所在的残差场中残差最小的点(初始点)至残差较小的点(震源轨迹代表点)的射线路径表示震源轨迹)适用于复杂速度模型,但尚不能正确计算由多段组成的震源轨迹,同时兼顾计算轨迹的完整性和精细性较为困难,计算参数设置烦琐不适于大批量数据的自动处理.针对该方法存在的问题,本文对其进行了改进:(1)采用一种"削皮"算法选取震源轨迹所经过的模型单元的节点作为轨迹代表点;(2)将残差较小的区域作为震源轨迹计算区域(该区域依轨迹分布自适应地划分为若干个连通区域),从未计算的轨迹代表点中选取残差最小者作为射线路径初始点,利用最小走时树算法依次计算所有连通区域内的震源轨迹;(3)通过去掉较短的不再分叉的射线路径使震源轨迹更为精细.虚拟和真实事件的算例表明,改进方法有效克服了原方法的不足,可便捷地计算复杂速度模型中事件的震源轨迹,计算的轨迹精细且较完整.     

Numerical method for calculating the surface wave field in the presence of caustics

Due to the lateral heterogeneity of the upper layers of the Earth, paths of surface waves deviate from arcs of great circles. Because of the sphericity of the Earth, the paths intersect on a hemisphere opposite to the epicenter and form caustics consisting of two branches, with their tangent point being a cusp. For this reason, the field of surface waves cannot be analyzed in terms of the ray theory at distances larger than 90°. The asymptotic approach to the analysis of the field in the vicinity of such caustics is very ill-suited for numerical implementation. The difficulties of such an approach to the field calculation are aggravated by the fact that such caustics are superimposed in some regions. Therefore, it is suggested to use the theorem of representation, according to which the field within a certain contour is expressed as an integral whose integrand contains values of the function itself, its derivative along the normal to the contour, and Green’s function. The field on the contour (the circle bounding a hemisphere centered at the epicenter) is calculated by the ray method because rays do not intersect on this hemisphere. These data are used for the construction of the field on the opposite hemisphere assumed to be homogeneous, which enables the construction of Green’s function for this hemisphere. This limitation is not very stringent because the configuration of rays and caustics on this hemisphere is mainly determined by the field on the circle. The integral in the representation theorem is calculated numerically. Numerical examples are presented for models in which one caustic or two superimposed caustics form. These calculations yield constraints on variations in the amplitude and phase of the wave. Rayleigh wave fields are also calculated for a model of the real Earth. It is shown that, at some points, the Rayleigh wave spectrum can be strongly distorted because caustics corresponding to different periods differ in shape.     

位场各阶垂向导数换算的新正则化方法

位场垂向导数大量应用于位场数据处理与解释中.当前广泛采用的位场各阶垂向导数换算方法为基于Laplace方程并结合波数域和空间域方法的具有递推特性的ISVD(integrated second vertical derivative)算法.本文在位场垂向导数换算的正则化方法和径向平均功率谱的基础上,提出一种位场各阶垂向导数换算的新正则化方法.新正则化方法仅需通过分析位场径向平均功率谱来确定一个截止波数,即可稳定换算位场各阶垂向导数.理论模型和实测数据实验结果表明:(1)新正则化方法物理意义明确、计算简单,且各阶垂向导数换算的稳定性和精度明显优于ISVD算法;(2)在用新正则化方法求得各阶垂向导数的基础上,利用泰勒级数法可以获得大深度、高精度的位场向下延拓结果.     

A method of calculating the non‐linear seismic response of a building braced with viscoelastic dampers

Buildings are continually subject to dynamic loads, such as wind load, seismic ground motion, and even the load from internal utility machines. The recent trend of constructing more flexible high‐rise buildings underscores the importance of including viscoelastic dampers in building designs. Viscoelastic dampers are used to control the dynamic response of a building. If the seismic design is based only on the linear response spectrum, considerable error may occur when calculating the seismic response of a building; rubber viscoelastic dampers show non‐linear hysteretic damping that is quite different from viscous damping. This study generated a non‐linear response spectrum using a non‐linear oscillator model to simulate a building with viscoelastic dampers installed. The parameters used in the non‐linear damper model were obtained experimentally from dynamic loading tests. The results show that viscoelastic dampers effectively reduce the seismic displacement response of a structure, but transmit more seismic force to the structure, which essentially increases its seismic acceleration response. Copyright © 2003 John Wiley & Sons, Ltd.     

Double parameterized regularization inversion method for migration velocity analysis in transversely isotropic media with a vertical symmetry axis

Simultaneous estimation of velocity gradients and anisotropic parameters from seismic reflection data is one of the main challenges in transversely isotropic media with a vertical symmetry axis migration velocity analysis. In migration velocity analysis, we usually construct the objective function using the l₂ norm along with a linear conjugate gradient scheme to solve the inversion problem. Nevertheless, for seismic data this inversion scheme is not stable and may not converge in finite time. In order to ensure the uniform convergence of parameter inversion and improve the efficiency of migration velocity analysis, this paper develops a double parameterized regularization model and gives the corresponding algorithms. The model is based on the combination of the l₂ norm and the non‐smooth l₁ norm. For solving such an inversion problem, the quasi‐Newton method is utilized to make the iterative process stable, which can ensure the positive definiteness of the Hessian matrix. Numerical simulation indicates that this method allows fast convergence to the true model and simultaneously generates inversion results with a higher accuracy. Therefore, our proposed method is very promising for practical migration velocity analysis in anisotropic media.     

初始震源深度对双差定位结果的影响分析

选取芦山M7.0地震余震中初始震源深度在10~15 km范围内的地震,通过将震源深度减小5 km、增加5 km和直接固定震源深度的方法,获得不同的震源深度值来作为初始震源深度,采用双差定位法分别对不同初始震源深度地震进行重新定位,并对定位结果的震源位置进行对比分析。通过计算,认为初始震源深度误差对双差定位结果的震中位置影响比较小,但对震源深度结果却存在一定的影响。     

利用Tilt-depth求取埋藏深度及其与边界位置的关系研究

对斜导数方法理论进行了研究,编写了利用斜导数方法来提取异常体边界和利用Tilt-depth方法来确定异常体顶面埋深的MATLAB程序,并实现了MATLAB与C#的混合编程.另外对深度点的三维可视化显示进行了研究,显示效果理想.理论模型试算结果表明,斜导数方法能够有效圈定异常体的边界,对异常体的顶面埋深计算较准确.实际资料的试算也取得了理想的结果,表明该方法具有良好的应用前景.