一种新的波浪变形三维数值模式──0-1混合型边界元

为提高边界元法模拟三维波场波浪变形的数值计算精度,借鉴常数元和线性元剖分方式、波势函数及波势函数法向导数对单元节点设定的各自适应性,提出了一种新的单元剖分模式──0-1混合型边界元,以控制和减缓由于计算误差累计而造成的波浪数值计算上的“横向振动”,借此结合边界元法的分区模式可实现较大范围的波场线性波浪变形计算,并为时域内的波浪非线性变形计算提供时间步长的数值保证.     

The Mid-atlantic Ridge (31°S–34°30′S): Temporal and spatial variations of accretionary processes

The ridge located between 31° S and 34°30′S is spreading at a rate of 35 mm yr⁻¹, a transitional velocity between the very slow (≤20 mm yr⁻¹) opening rates of the North Atlantic and Southwest Indian Oceans, and the intermediate rates (60 mm yr⁻¹) of the northern limb of the East Pacific Rise, and the Galapagos and Juan de Fuca Ridges. A synthesis of multi-narrow beam, magnetics and gravity data document that in this area the ridge represents a dynamically evolving system. Here the ridge is partitioned into an ensemble of six distinct segments of variable lengths (12 to 100 km) by two transform faults (first-order discontinuities) and three small offset (< 30 km) discontinuities (second-order discontinuities) that behave non-rigidly creating complex and heterogeneous morphotectonic patterns that are not parallel to flow lines. The offset magnitudes of both the first and second-order discontinuities change in response to differential asymmetric spreading. In addition, along the fossil trace of second-order discontinuities, the lengths of abyssal hills located to either side of a discordant zone are observed to lengthen and shorten creating a saw-toothed pattern. Although the spreading rate remains the same along the length of the ridge studied, the morphology of the spreading segments varies from a deep median valley with characteristics analogous to the rift segments of the North Atlantic to a gently rifted axial bulge that is indistinguishable from the shape and relief of the intermediate rate spreading centers of the East Pacific Rise (i.e., 21°N). Like other carefully surveyed ridge segments at slow and fast rates of accretion, the along-axis profiles of each ridge segment are distinctly convex upwards, and exhibit along-strike changes in relief of 500m to 1500 between the shallowest portion of the segment (approximate center) and the segment ends. Such spatial variations create marked along-axis changes in the morphology and relief of each segment. A relatively low mantle Bouguer anomaly is known to be associated with the ridge segment characterized by a gently rifted axial bulge and is interpreted to indicate the presence of focused mantle upwelling (Kuo and Forsyth, 1988). Moreover, the terrain at the ends of each segment are known to be highly magnetized compared to the centers of each segment (Carbotte et al, 1990). Taken together, these data clearly establish that these profound spatial variations in ridge segment properties between adjoining segments, and along and across each segment, indicate that the upper mantle processes responsible for the formation of this contrasting architecture are not solely related to passive upwelling of the asthenosphere beneath the ridge axis. Rather, there must be differences in the thermal and mechanical structure of the crust and upper mantle between and along the ridge segments to explain these spatial variations in axial topography, crustal structure and magnetization. These results are consistent with the results of investigations from other parts of the ridge and suggest that the emplacement of magma is highly focused along segments and positioned beneath the depth minimum of a given segment. The profound differences between segments indicate that the processes governing the behavior of upwelling mantle are decoupled and the variations in the patterns of axis flanking morphology and rate of accretion indicate that processes controlling upwelling and melt production vary markedly in time as well. At this spreading rate and in this area, the accretionary processes are clearly three-dimensional. In addition, the morphology of a ridge segment is not governed so much by opening rate as by the thermal structure of the mantle which underlies the segment.     

任意曲线曲面上重磁位场转换的B样条函数法

提出用B样条函数求解曲线、曲面上重磁位场的向上延拓,水平、垂向导数计算,磁异常分量互换的方法。该方法的特点是:原理简明,程序通用性强,计算精度高。     

地下水非稳定流的LTFAM算法

渗流域内应用拉普拉斯变换(LT)建立相应的有限分析(FAM)方程,顾及渗流域内地下水流的初始条件和边界条件,可在LT空间构成一个封闭的以水头像函数为变量的线性方程组。将此方程组所得的解,通过Stehfest数值反演公式,可归化为时间域的解(水头)。由于时间t被隐含在数值方程内,从而克服了传统数值法按时段(△t)逐步迭代的缺陷,提高了计算效率,也为用嵌入法建立地下水流管理模型提供了一条捷径。     

Comparison of methods to model the gravitational gradients from topographic data bases

A number of methods have been developed over the last few decades to model the gravitational gradients using digital elevation data. All methods are based on second-order derivatives of the Newtonian mass integral for the gravitational potential. Foremost are algorithms that divide the topographic masses into prisms or more general polyhedra and sum the corresponding gradient contributions. Other methods are designed for computational speed and make use of the fast Fourier transform (FFT), require a regular rectangular grid of data, and yield gradients on the entire grid, but only at constant altitude. We add to these the ordinary numerical integration (in horizontal coordinates) of the gradient integrals. In total we compare two prism, two FFT and two ordinary numerical integration methods using 1" elevation data in two topographic regimes (rough and moderate terrain). Prism methods depend on the type of finite elements that are generated with the elevation data; in particular, alternative triangulations can yield significant differences in the gradients (up to tens of Eötvös). The FFT methods depend on a series development of the topographic heights, requiring terms up to 14th order in rough terrain; and, one popular method has significant bias errors (e.g. 13 Eötvös in the vertical–vertical gradient) embedded in its practical realization. The straightforward numerical integrations, whether on a rectangular or triangulated grid, yield sub-Eötvös differences in the gradients when compared to the other methods (except near the edges of the integration area) and they are as efficient computationally as the finite element methods.     

Laplace-transform analytic element solution of transient flow in porous media

A Laplace-transform analytic element method (LT-AEM) is described for the solution of transient flow problems in porous media. Following Laplace transformation of the original flow problem, the analytic element method (AEM) is used to solve the resultant time-independent modified Helmholtz equation, and the solution is inverted numerically back into the time domain. The solution is entirely general, retaining the mathematical elegance and computational efficiency of the AEM while being amenable to parallel computation. It is especially well suited for problems in which a solution is required at a limited number of points in space–time, and for problems involving materials with sharply contrasting hydraulic properties. We illustrate the LT-AEM on transient flow through a uniform confined aquifer with a circular inclusion of contrasting hydraulic conductivity and specific storage. Our results compare well with published analytical solutions in the special case of radial flow.     

裂隙岩体中的对流扩散研究

揭示一个基于代数拓扑理论的裂隙网络中物质弥散模型，还给出了应用于网络中的对流扩散的对应性原理的证明。应用拓扑理论给出的框架，使其起了一个数据结构的组织者的作用，由此得到网络中每一个分支上的浓度的解。这个解是在拉普拉斯空间上的解析解。网络中任意点在任何时刻的浓度可以很方便地用数值拉氏反变换求出。     

半空间埋置动点源荷载问题的传递矩阵法

引用了流体饱和两相多孔介质的动力控制方程分析半空间埋置动点源荷载问题的位移和变形。经过Laplace Hankel变换 ,控制方程化成常微分方程组。利用数学软件mathmatic对上述方程组求解 ,可以得到单层砂土的传递矩阵。分析过程中 ,假设在两层面上 ,位移与应力相互连续 ,可以借鉴有限元的思想进行耦合计算。这样就获得了在饱和砂土中施加竖向动荷载问题的Laplace Hankel变换解 ,其最终的解还需要通过Laplace Hankel逆变换得到     

SH Wave Propagation in Viscoelastic Media

When comparing solutions for the propagation of SH waves in plane parallel layered elastic and viscoelastic (anelastic) media, one of the first things that becomes apparent is that in the elastic case the location of the saddle points required to obtain a high frequency approximation are located on the real p axis. This is true of the branch points also. In a viscoelastic medium this is not typical. The saddle point corresponding to an arrival lies in the first quadrant of the complex p-plane as do the branch points. Additionally, in the elastic case the saddle point and branch points lie on a straight line drawn through the origin (the positive real axis in the complex p-plane), while in the viscoelastic case this is generally not the case and the saddle point and branch points lie in such a manner as to indicate the degree of their complex values.In this paper simple SH reflected and transmitted particle displacement arrivals due to a point torque source at the surface in a viscoelastic medium composed of a layer over a half space will be considered. The path of steepest descent defining the saddle point in the first quadrant will be parameterized in terms of a real variable and the high frequency solutions and intermediate analytic results obtained will be used to formulate more specific constraints and observations regarding saddle point location relative to branch point locations in the complex p-plane.As saddle point determination for an arrival is, in general, the solution of a non-linear equation in two unknowns (the real and imaginary parts of the complex saddle point p ₀), which must be solved numerically, the use of analytical methods for investigating this problem type is somewhat limited.Numerical experimentation using well documented solution methods, such as Newton's method, was undertaken and some observations were made. Although fairly basic, they did provide for the design of algorithms for the computation of synthetic traces that displayed more efficient convergence and accuracy than those previously employed. This was the primary motivation for this work and the results from the SH problem may be used with minimal modifications to address the more complicated subject of coupled P-SV wave propagation in viscoelastic media.Another reason for revisiting a problem that has received some attention in the literature was to approach it in a fairly comprehensive manner so that a number of specific observations may be made regarding the location of the saddle point in the complex p-plane and to incorporate these into computer software. These have been found to result in more efficient algorithms for the SH wave propagation and a significant enhancement of the comparable software in the P-SV problem.