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181.
对有限频率层析成像线性理论的波恩近似问题进行梳理, 用数值方法统计分析其适用范围, 结果表明波恩近似要求最大速度扰动不超过1%; 然后对相关走时一阶近似进行统计分析, 结果表明它也只适用于最大速度扰动在1%以内的情形. 然而, 结合波恩近似和相关走时一阶近似而得到的有限频率线性理论, 其适用的速度扰动范围最大可达10%. 这个表面上的逻辑悖论, 称为“波恩近似佯谬”. 此佯谬是由于不恰当地使用波恩近似造成的. 本文摒弃波恩近似, 使用泛函的Fréchet微分和隐函数定理推导得到有限频率线性理论, 圆满解释了波恩近似佯谬. 由于有限频率非线性理论早已摒弃了波恩近似, 因此波恩近似概念在有限频率层析成像理论中完全没有必要. 相似文献
182.
Multifractal measures,especially for the geophysicist 总被引:9,自引:0,他引:9
Benoît B. Mandelbrot 《Pure and Applied Geophysics》1989,131(1-2):5-42
This text is addressed to both the beginner and the seasoned professional, geology being used as the main but not the sole illustration. The goal is to present an alternative approach to multifractals, extending and streamlining the original approach inMandelbrot (1974). The generalization from fractalsets to multifractalmeasures involves the passage from geometric objects that are characterized primarily by one number, namely a fractal dimension, to geometric objects that are characterized primarily by a function. The best is to choose the function (), which is a limit probability distribution that has been plotted suitably, on double logarithmic scales. The quantity is called Hölder exponent. In terms of the alternative functionf() used in the approach of Frisch-Parisi and of Halseyet al., one has ()=f()–E for measures supported by the Euclidean space of dimensionE. Whenf()0,f() is a fractal dimension. However, one may havef()<0, in which case is called latent. One may even have <0, in which case is called virtual. These anomalies' implications are explored, and experiments are suggested. Of central concern in this paper is the study of low-dimensional cuts through high-dimensional multifractals. This introduces a quantityD
q, which is shown forq>1 to be a critical dimension for the cuts. An enhanced multifractal diagram is drawn, includingf(), a function called (q) andD
q.This text incorporatesand supersedes
Mandelbrot (1988). A more detailed treatment, in preparation, will incorporateMandelbrot (1989). 相似文献
183.
基于极限分析上限定理,考虑堆石料内摩擦角较大以及抗剪强度具有非线性的特性,提出一个用于求解土石坝极限抗震能力的有限元计算方法。该方法通过功能平衡条件、位移协调条件、边界条件、屈服条件以及所求极限荷载,形成标准的二阶锥规划数学模型,并用内点法进行优化迭代求解,得到土石坝坡极限抗震能力的上限值。运用该方法对一个典型面板堆石坝进行抗震极限分析。结果表明:按规范设计的土石坝具有较强的抗震能力,且竖向地震力对大坝的极限抗震能力存在一定影响;此外上限有限元法具有较高的计算精度及工程实用价值。 相似文献
184.
考虑了一类具p-Laplacian算子型带积分边界条件的三点奇异方程组边值问题正解的存在性.通过使用锥上的不动点定理,在适当的条件下,建立了这类方程组边值问题存在一个或多个正解的充分条件,并给出两个例子来验证主要结果. 相似文献
185.
Positive definiteness is not enough 总被引:2,自引:0,他引:2
M. Armstrong 《Mathematical Geology》1992,24(1):135-143
Geostatisticians know that the mathematical functions chosen to represent spatial covariances and variograms must have the appropriate type of positive definiteness, but they may not realize that there are restrictions on the types of covariances and variograms that are compatible with particular distributions. This paper gives some examples showing that (1) the spherical model is not compatible with the multivariate lognormal distribution if the coefficient of variation is 2.0 or more (even in 1-D), and (2) the Gaussian covariance and several other models are not compatible with indicator random functions. As these examples concern quite different types of random functions, it is clear that there is a general problem of compatibility between spatial covariance models (or variograms) and a specified multivariate distribution. The problem arises with all distributions except the multivariate normal, and not just the two cited here. The need for a general theorem giving the necessary and sufficient conditions for a covariance or a variogram to be compatible with a particular distribution is stressed. 相似文献
186.
187.
A. P. S. Selvadurai 《国际地质力学数值与分析法杂志》2004,28(2):191-208
This paper examines the problem of the advective transport of a contaminant from sources in the shape of either a penny-shaped crack or an elongated needle-shaped cavity located in a porous medium of infinite extent. The advective transport is induced by Darcy flow in the porous medium, where the internal boundary is maintained at a constant potential. The paper presents an approximate analytical solution to this problem, which is deduced from a formulation that models a cavity in the shape of either an oblate or a prolate spheroid. The results also represent one of the few spatially three-dimensional exact analytical solutions for the, albeit linear, hyperbolic problem governing the contaminant transport problem. The paper also presents a canonical proof of uniqueness for advective contaminant transport problems associated with media of infinite extent. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
188.
Michael Bevis 《Mathematical Geology》1987,19(6):561-569
Standard models of present-day plate motions are framed in terms of rates and poles of rotation, in accordance with the well-known theorem due to Euler. This article shows how computation of relative plate velocities from such models can be viewed as a simple problem in spherical trigonometry. A FORTRAN subroutine is provided to perform the necessary computations.EDITOR'S NOTE: Teaching geomathematics and geostatistics is a particularly difficult task. It requires a good knowledge of the mathematical theory and of its applications in the earth sciences. Good textbooks are relatively rare. So finding suitable examples and easy-to-follow proofs is time-consuming.This Teacher's Aide Column has been initiated to help get teaching material into circulation, and to act as a forum for exchanging questions and answers. Readers' suggestions are most welcome.Margaret ArmstrongAssociate Editor 相似文献
189.
190.
基于上限定理的边坡潜在破裂面确定方法与稳定性判识研究 总被引:1,自引:0,他引:1
边坡潜在破裂面的确定与稳定性判识一直是岩土工程界研究的热点问题。将边坡潜在破裂面看成是由若干段组合而成的复合破裂面,并沿各段将边坡垂直条分为多块体,在假设边坡岩土体服从摩尔-库仑屈服准则条件下,根据极限分析上限定理,分别计算各块体外功率与内能耗散,并建立边坡稳定系数的多元函数。利用数学优化方法给出边坡稳定系数的最优解,可以方便地给出边坡潜在破裂面形状及其对应的边坡稳定系数。通过算例分析并与前人研究成果比较,结果表明:理论方法是合理有效的,可以用于边坡潜在破裂面的确定与稳定性判识。 相似文献