Interpretation of marine magnetic anomalies. Part II. Analysis of the new method and algorithm based on the least squares method

In this work, the problem of interpreting linear marine magnetic anomalies in the context of the spreading model is considered. Based on the least squares method, a new algorithm for determining the position of direct and reverse polarity blocks is proposed. The global minimum of the residual is found by a combination of the multistart and Monte Carlo methods. Using an example of a field of three blocks perturbed by a normal noise, it is shown that the method yields an error close to the minimum possible. Using a model constructed by the inversion scale, it is revealed that the proposed algorithm allows one to find positions of block boundaries of the field without noise with a higher accuracy determined in fact by the computation time.     

长应力波对于深部隧道衬砌的作用

应力波与隧道衬砌的相互作用问题为岩石力学的一个十分复杂的问题,到目前为止还没有得到圆满的解决。对于考虑介质与结构弹塑性性质的课题,解析解更难以求得。研究表明长波与深地下硐室的作用问题可以用拟静法解答。本文用拟静法研究了考虑岩体塑性性质时长纵波与地下硐室的相互作用问题。并获得了确定长应力波对于隧道支护作用的解析解。     

Problem on the vibrations of plates

Summary In this paper, the problem on the vibrations of rectangular, elliptical and circular plates of non-isotropic material have been solved by using Galerkin's method. With the help of this method, the same problem for an isotropic circular plate has also been considered at the end.     

基于非均匀Fourier变换的地震数据重建方法研究

不规则采样地震数据会对地震数据的多道处理造成严重影响,将非均匀Fourier变换和贝叶斯参数反演方法相结合,对不规则空间带限地震数据进行反演重建.对每一个频率依据最小视速度确定出重建数据的带宽,然后从不规则地震数据中估计出重建数据的空间Fourier系数.将不规则地震数据重建视为信息重建的地球物理反演问题,运用贝叶斯参数反演理论来估计Fourier系数.在反演求解时,使用共轭梯度算法,以保证求解的稳定性,加快解的收敛速度.理论模型和实际资料处理验证了本方法的有效性和实用性.     

Artificial refraction of radiowaves in the ionosphere

A method to control the propagation of a frequency-modulated wave packet in the ionosphere with the use of the dispersive refraction effect is considered. The problem is solved in the spectral domain on the basis of the superposition principle. In this spectral approach, the dispersive refraction is considered as space–time focusing of the spectral components of the wave packet. Numerical results demonstrate the possibility to use the dispersive properties of the ionosphere for the creation of controlled radio channels.     

水平地震激发的具有非线性阻尼的动水压力对斜面水坝的作用

采用非线性Rayeigh阻尼于问题的控制方程中。首先用小参数摄动法，把非线性偏微分方程的控制方法线性化，得出小参数的各阶渐近控制方程，得出头两阶渐近控制方程的解析解。再直接求解非线性控制方程，也得出头两次的渐近解。不但讨论了直形面重力水坝问题，还讨论了圆弧形拱坝问题。     

Radon变换的抽样取值与小波

Radon变换在实际应用中必须考虑抽样取值的问题,通信理论中常用的Shannon取样定理在地球物理学等领域中并不适用,因为它要求函数是频谱有限的.本义介绍利用小波理论建立新的取样定理的方法,这一方法的优点在于可以根据具体问题的要求选取适当的基本空间V_0,从而获得较佳的抽样插值效果.     

Spatio-temporal filtering using wavelets

 In this paper, a class of spatio-temporal processes with first-order autoregressive temporal structure and functional spatio-temporal interaction is introduced. The spatial second-order regularity is allowed to change over time and is characterized in terms of fractional Sobolev spaces. The associated filtering problem is considered, assuming that observations are defined by spatial linear functionals of the process of interest, being affected by additive noise. Conditions under which a stable solution to this problem is obtained are studied. A functional least-squares linear estimate fusion method is derived to calculate this solution A multiscale finite-dimensional approximation to the problem is obtained from the wavelet-based orthogonal expansions of the time cross-section spatial processes, which allows the numerical inversion of the linear operator involved.     

利用流固耦合模型模拟地震和海啸全过程

海底地震引起的海啸过程在力学上是一个流固耦合问题。地震引起的海底变形会影响流体的运动,流体运动会影响地震引起的海底变形。海啸的数值模拟,通常采用浅水波控制方程,把地震引起的海底变形作为海啸波动的边界条件或初始条件,不考虑它们之间的相互作用。本文采用势流体的流固耦合有限元方法模拟了地震和海啸的全过程。地震过程的模拟与地震位错模型不同,在位错模型中,断层的位错是事先指定的;而在本文中,首先形成自重作用下的初始应力场,然后通过断层材料的突然软化引起的错动,模拟地震震源的动力学过程。模拟结果显示,在海面除了可以看到大振幅的海啸波外,还可以发现体波震相和面波震相。在600 km的海面震中距上,它们要比海啸波早到48分钟,在此处面波的最大平均振幅可达0.55 m,是相同震中距海底面波最大平均振幅的2倍。因此,海啸预警信息在海面可以比在地表更早地得到。海啸波的传播速度在水深3 km的开阔海面是175.8 m/s,它要比理想长波理论预测的大,其平均振幅为2 m,波长可达32 km. 到达大陆架后其速度、波长都减小,在岸边可以激起10 m高的巨浪,水平方向深入陆地达53 m。震中附近海面和地震断层上的最大垂直加速度分别为5.9 m/s2和16.3 m/s2,后者是前者的2.8倍。由此看来,海水是很好的减震器。海啸波的加速度到达岸边会衰减10倍。与加速度不同,海面震中处的振动速度为3.2 m/s, 是海底震源处的1.4倍。震源处的最大位移小于震中海面的最大位移, 其差就是海啸波源的振幅。值得注意的是,海底地震的最大位错在震后23 s达到,不是发生在断层滑动的开始。      

Analysis of biodegradation in a 3-D heterogeneous porous medium using nonlinear stochastic finite element method

Probabilistic analysis by Monte Carlo Simulation method (MCSM) is a computationally prohibitive task for a reactive solute transport involving coupled PDEs with nonlinear source/sink terms in 3-D heterogeneous porous media. The perturbation based stochastic finite element method (SFEM) is an attractive alternative method to MCSM as it is computationally efficient and accurate. In the present study SFEM is developed for solving nonlinear reactive solute transport problem in a 3-D heterogeneous medium. Here the solution of the biodegradation problem involving a single solute by a single class of microorganisms coupled with dynamic microbial growth is attempted using this method. The SFEM here produces a second-order accurate solution for the mean and a first-order accurate solution for the standard deviation of concentrations. In this study both the physical parameters (hydraulic conductivity, porosity, dispersivity and diffusion coefficient) and the biological parameters (maximum substrate utilization rate and the coefficient of cell decay) are considered as spatially varying random fields. A comparison between the MCSM and SFEM for the mean and standard deviation of concentration is made for 1-D and 3-D problem. The effects of heterogeneity on the degradation of substrate and growth of biomass concentrations for a range of variances of input parameters are discussed for both 1-D and 3-D problems.     

A novel spherical polar finite element for the solution of the steady-state scalar wave equation in three-dimensions

A novel method has been proposed for the finite element solution of the steady-state scalar wave equation in three-dimensions. In this the governing equation and the prescribed boundary conditions in the physical space are transformed into a spherical polar space in which the radial direction is logarithmically condensed; the physical problem domain is also mapped into the new space. The transformed equation is then solved in the mapped domain using conventional finite elements. Because physical dimensions of the problem are logarithmically condensed in the proposed spherical polar space, the method is particularly suitable for solving truly three-dimensional problems in which the aspect ratio(s) is large or very large. A number of illustrative examples considered show that the proposed method is capable of a high degree of accuracy, achieved efficiently and economically. A hybrid scheme has also been proposed for dealing with awkward-shaped domains.     

Dynamic responses of a sediment-filled valley with a fluid layer subject to incident waves

The diffraction of elastic waves by a sedimentary valley in a homogeneous elastic half-space is studied in this paper. The sediment-filled valley is composed of a fluid layer over a soft soil deposit whose characteristics may be significant and should be carefully considered when designing long span bridges with high piers. The method of analysis adopted in the paper is to decompose the problem into an interior region and an exterior region. In the exterior region, the scattered wave fields are constructed with the linear combinations of two independent sets of Lamb’s singular solutions, i.e., the integralsolutions for two concentrated surface loads in two directions; and their derivatives are used to represent the scattered wave fields. A technique is proposed to calculate the integrals in the wave-number domain based on the method of steepest descent. For the interior region, the wave fields for the fluid layer and soft soil deposit are expressed in terms of wave functions which satisfy the equation of motion. The continuity condition at the interface of the media is satisfied in the least square sense. The effects of geometric topography, soil amplification and fluid layer subject to different types of incident harmonic plane waves are analyzed and discussed..     

极坐标系有限差分中起伏地表边界条件处理

有限差分算法是地震学中重要的算法,在直角坐标系下同位网格有限差分中使用牵引力镜像方法,可以高效准确地处理起伏地表边界条件.当研究区域-全球尺度问题时需要考虑地球曲率影响,此时选择极坐标系更加直观方便,但已有方法无法在极坐标系下准确计算起伏地表影响.本文在极坐标系有限差分中引入贴体网格和牵引力镜像方法处理起伏地表边界条件,并在多个算例中验证算法正确性和适用范围,证明牵引力镜像法在极坐标系有限差分中有效.     

局部倾角约束最小二乘偏移方法研究

随着石油勘探难度的进一步加大,地震数据往往存在采样不规则、地震道缺失等现象,如果不对其进行处理,会对后续的地震成像产生影响,引入成像噪音.针对这一问题,一般是通过地震道插值或数据规则化对叠前数据进行处理,然后采用常规的偏移方法进行成像,本文则是将地震成像看作最小二乘反演问题,在共成像点道集引入平滑算子,在共偏移距/角度道集引入平面波构造算子(PWC)进行约束,通过预条件共轭梯度法使得反偏移后数据与输入数据之间的误差达到最小,最终得到信噪比更高、振幅属性更为可靠的成像结果.理论模型和实际资料处理表明,本文方法不仅可以有效压制数据不规则对成像产生的噪音,而且具有更高的成像精度.     

框架结构的串联多自由度简化体系等效刚度参数的识别法

地框架结构和高耸建筑物进行地震反应分析时它常常被简化为串联多自由度体系。本文对此体系的刚度参数提出了一般的计算方法－参数识别法。     

A family of explicit algorithms for general pseudodynamic testing

A new family of explicit pseudodynamic algorithms is proposed for general pseudodynamic testing. One particular subfamily seems very promising for use in general pseudodynamic testing since the stability problem for a structure does not need to be considered. This is because this subfamily is unconditionally stable for any instantaneous stiffness softening system, linear elastic system and instantaneous stiffness hardening system that might occur in the pseudodynamic testing of a real structure. In addition, it also offers good accuracy when compared to a general second-order accurate method for both linear elastic and nonlinear systems.     

REPORTS ON MEETINGS

Abstract

The problem of stratified groundwater flow (salt water intrusion) is considered in the general case where the hydrological boundaries can have any shape and the impervious bed can have any configuration. The recharge and discharge can also be considered according to any given function of time. The fluid density is assumed to be constant throughout each layer. The effect at the boundaries is considered, whether these are a river or a continuation of the aquifer with different parameters.

The systems of equations are taken in alternative matrix forms. The three time level implicit scheme is used and the multi sweep method is applied for the computation. The numerical procedure of the mathematical model is linearly unconditionally stable. In this procedure, no iteration routines are introduced, therefore it is considered exceptionally economical in memory and in computing time.     

Far-Zone Contribution in Ellipsoidal Stokes Boundary-Value Problem

In the first attempt to solve the Stokes boundary-value problem in ellipsoidal coordinates numerically (Ardestani and Martinec, 2000), we focused on the near-zone contribution since the effect of the ellipsoidal Stokes function in the far-zone contribution is not considered. We present a method for solving the ellipsoidal Stokes integral in far-zone contribution. The numerical results of computing the magnitude of this term for an area in north of Canada are presented.     

贴井壁声波测井仪的有限差分模拟研究

贴井壁声波测井仪在石油勘探开发中具有广泛的应用.它能够避开泥浆的影响而直接检测井壁附近的地层性质.但目前对此进行的数值模拟研究还仅局限于比较简单的模型.有限差分法可以模拟比较复杂的井眼模型,然而贴井壁声源的频率较高（80kHz左右）,使有限差分法计算量过大.本文应用局部加密交错网格有限差分方法解决了这类数值模拟中计算精度和计算量之间的矛盾.用这种算法模拟了井中有仪器时贴井壁声源激发的声场,并将其与无仪器时的声场作了比较.对模拟结果的验证和分析显示,该有限差分方法能够正确模拟贴井壁声源激发的声场.通过考察井中仪器本体对贴井壁声源激发声场的影响发现,测井仪器本体能够对直达波进行衰减而对环绕井壁传播的面波影响不大.     

具有地震抑制功能的结构主动控制算法与仿真分析

提出了一种具有地震抑制功能的结构抗震主动控制算法。其特点是设计一组状态反馈控制律，使得闭环结构系统在具有希望极点的同时，还能够减小结构地震输人的影响。首先，在特征结构配置参数化方法的基础上，将该控制问题转化为一个含有约束条件的优化问题；其次，给出了求解该问题的算法及实施步骤，该方法直接基于结构系统原始矩阵，不涉及系统的增广或变换，便于工程应用；最后，对地震作用下三层剪切型Benchmark结构模型进行了仿真分析，结果表明本文所提具有地震干扰抑制功能算法的有效性。