Computer-aided geometric design of geologic surfaces and bodies

Bivariate quadratic simplicial B-splines are employed to obtain aC ¹-smooth surface from scattered positional or directional geological data given over a two-dimensional domain. Vertices are generated according to the areal distribution of data sites, and polylines are defined along real geological features. The vertices and the polylines provide a constrained Delaunay triangulation of the domain. Note that the vertices do not generally coincide with the data sites. Six linearly independent simplex B-splines are associated with each triangle. Their defining knots and finite supports are automatically deduced from the vertices. Specific knot configurations result in discontinuities of the surface or its directional derivatives. Coefficients of a simplex spline representation are visualized as geometric points controlling the shape of the surface. This approach calls for geologic modeling and interaction of the geologist up front to define vertices and polylines, and to move control points initially given by an algorithm. Thus, simplex splines associated with irregular triangles seem to be well-suited to approximate and allow further geometrically modeling of geologic surfaces, including discontinuities, from scattered data. Applications to mathematical test as well as to real geological data are given as examples.     

大尺度环境场和CISK与西南低涡发展的动力学分析

本文根据文献1)提出的用CISK理论研究西南低涡发展的设想,采用早期最简单的积云参数化模式,把积云对流同低层次天气尺度扰动联系起来,用描述大尺度环境场和积云对流对次天气尺度扰动作用的方程组,在简单两层模式中求解,分析了影响西南涡发展的各个因子,讨论了发展型西南涡在模式中的简单结构。     

INFLUENCES OF NONUNIFORM STRATIFICATION ON WAVE RAYS OF INTERNAL GRAVITY WAVE*

In this paper the influences of nonuniform stratification on the propagating paths of internal inertial-gravity and pure gravity wave energy are discussed by using the WKB approximation method.The conditions for conservation of wave energy,generalized wave action and wave enstrophy are obtained.The necessary condition of instability for internal gravity waves and the equation governing the refraction of wave rays are derived.Two types of critical levels are given.Finally,the wave rays for different distributions of stratification are calculated by using the fourth-order Runge-Kutta method.     

3D wavefield extrapolation with optimal separable approximation

An accurate and wide-angle one-way propagator for wavefield extrapolation is an important topic for research on wave-equation prestack depth migration in the presence of large and rapid velocity variations. Based on the optimal separable approximation presented in this paper, the mixed domain algorithm with forward and inverse Fourier transforms is used to construct the 3D one-way wavefield extrapolation operator. This operator separates variables in the wavenumber and spatial domains. The phase shift operation is implemented in the wavenumber domain while the time delay for lateral velocity variation is corrected in the spatial domain. The impulse responses of the one-way wave operator show that the numeric computation is consistent with the theoretical value for each velocity, revealing that the operator constructed with the optimal separable approximation can be applied to lateral velocity variations for the case of small steps. Imaging results of the SEG/EAGE model and field data indicate that the new method can be used to image complex structure.     

一种时间分数阶扩散方程初边值问题的隐式有限差分格式

通过Caputo型与G runwald型的分数阶导数的转化关系以及利用G runwald型的标准数值近似公式对Caputo型分数阶导数进行离散,可构建时间分数阶扩散方程初边值问题的隐式有限差分格式。此差分格式是无条件稳定和无条件收敛的。     

A MATHEMATICAL QUASI-2D OVERLAND FLOW MODEL

1 INTRODUCTIONThe prediction of future impacts on terrestrial ecosystems by atmospheric, climatic and land-usechanges is the aim of watershed management. Meeting these requirements scientists, managers and policymakers try to achieve the sustainable management of the vitally important resources of watersheds due toan integrated ecosystem approach at the catchment scale. As composite landscapes often have a highdegree of contingency between its elements, the transport over these landscape s…     

Analysis and comparison of mixed finite element and multipoint flux approximation methods for homogeneous media

We consider discretization on quadrilateral grids of an elliptic operator occurring, for example, in the pressure equation for porous-media flow. In a realistic setting – with non-orthogonal grid, and anisotropic, heterogeneous permeability – special discretization techniques are required. Mixed finite element (MFE) and multipoint flux approximation (MPFA) are two methods that can handle such situations. Previously, a framework for analytical comparison of MFE and MPFA in special cases has been suggested. A comparison of MFE and MPFA-O (one of two main variants of MPFA) for isotropic, homogeneous permeability on a uniformly distorted grid was also performed. In the current paper, we utilize the suggested framework in a slightly different manner to analyze and compare MFE, MPFA-O and MPFA-U (the second main variant of MPFA). We reconsider the case previously analyzed. We also consider the case of generally anisotropic, homogeneous permeability on an orthogonal grid.     

基于余弦函数的自适应单频干扰消除

在野外地震数据采集过程中,如果地震测线上空有高压输电线通过时,在地震记录中就存在一个50HZ左右强单频干扰.这种干扰在地震记录的整个时间段上具有很强的能量,并且从浅层到深层频率、相位和振幅可能不相同,但是它们的变化不太大,可以认为基本保持不变.采用频率域压制方法很难完全消除这种干扰,仅仅是噪声和信号同时压制一定的倍数,因此并没有改善单频分量频率附近的信噪比.我们提出了基于余弦函数的自适应单频干扰消除方法,以有效消除地震数据单频干扰.在时间域内采用频率、时延和振幅的余弦函数来逼近这种单频干扰并从地震记录中减去,以实现消除这种单频干扰的目的.单频干扰余弦函数的振幅使用公式直接计算,单频干扰频率和时延采用自适应方法估算.本方法的最大优点就是能够有效消除干扰,而并不伤害干扰附近有效信号,因此在单频干扰频率分量附近数据信噪比提高了.通过实际数据的试算,说明了本方法的有效性和可行性.     

广义WKB法在波场模拟中的应用研究

针对地震勘探中的波场模拟和反演困难等问题,本文从二维波动方程出发,采用Fourier变换得到了赫姆霍兹方程,并创造性地提出了一种全新的近似解法－广义WKB法;该法可以更加近似赫姆霍兹方程,且它的解中包含WKB的近似值.数值模拟显示了WKB法与广义WKB求解的异同.结果表明：广义WKB法是WKB法的一种推广,在求解非线性波数问题时具有更好的优势.