Determination and interpretation of preferred orientation with texture goniometry: An application of indicators to maximum entropy pole- to orientation-density inversion

The probability density function of orientations of crystals generally cannot be measured directly without destruction of the specimen. Therefore it is usual practice to sample pole density functions of several crystal forms in diffraction experiments with a texture goniometer. Determining a reasonable orientation density function from experimental pole density functions is then the crucial prerequisite of quantitative texture analysis. This mathematical problem may be addressed as a tomographic inversion problem specified by the crystal and statistical specimen symmetries and the properties of the diffraction experiment. Its solution with maximum entropy preferred orientation portion and maximum uniform portion is proposed because it yields the most conservative orientation density function with systematically reduced correlation effects, thus avoiding artificial texture ghost≓ components caused by the specific properties of the diffraction experiment.     

Comparison between two types of multifractal modeling

The interrelationships between two previously developed multifractal models are discussed. These are the Evertsz-Mandelbrot model developed on the basis of the multifractal spectrum f(), and the Schertzer-Lovejoy model based on the codimension function C() where and represent Hölder exponent and field order, respectively. It is shown how these two models are interrelated: they are identical for values of within the range D–(0)D–_min. where D is the Euclidean dimension. For D–_maxD–(0), however, f() remains a continuous function of whereas C() assumes constant value. In this respect, the fractal spectrum f() can provide more information about the multifractal measure than the codimension function C(). The properties of the two models are illustrated by application to the binomial multiplicative cascade model.     

Interpretation of magnetic anomalies of dikes using correlation factors

The magnetic anomaly due to a buried dike consists of the sum of two easily separated elementary functions. These functions, which have simple symmetry, are called even and odd functions. The correlation factors (r _0,1 for the even andr _0,2 for the odd function) between least-squares residual anomalies from even and odd functions are computed. Correlation values are used to determine the depth to the top and the half-width of the dike. The method also includes the determination of the index parameter and the amplitude coefficient. The validity of the method is tested against a theoretical and a field example where the parameters of the latter were determined by other investigators in comparing the results.     

周期基数插值尺度函数和小波函数的对称性

设 g(x1,x2 )是一个 Fourier系数为正的周期函数 ,研究了二维周期基数插值小波函数。得到了关于 g(x1,x2 )的二维周期基数插值的尺度函数和小波函数的对称性     

Fractal and chaotic phenomena of seismic dissipated energy in an energy system of engineering structures

Fractal and chaotic phenomena in engineering structure are discussed in this paper, it means that the characters of fractal and chaos on dynamic system of seismic dissipated energy activity intensity E _d and activity intensity of seismic dissipated energy moment I _e are analyzed carefully. Based on the conceptions of the energy system of engineering structures Θ, seismic dissipated energy activity intensity E _d and activity intensity of seismic dissipated energy moment I _e, the chaotic phenomena of dynamic systems E _d and I _e are discovered by theoretic derivation, then the fractal characters of them are also discovered from theoretical inferring and numerical computation. Attractor of relative dimension d ₂, Renyi entropy of the second order k ₂, mean predictable time scale 1/k ₂ and other parameters of the dynamic system which were constructed in light of a large number of actual measuring seismic data have been achieved in the end. These parameters are exactly what the fractal and chaotic phenomena have represented in practical dynamic system, which may be valuable for earthquake-resistant theory and analytical method in practical engineering structures.     

Fractal analysis applied to faults and earthquakes—A case study of China

The characteristics and correlation of faults and earthquakes are discussed based on fractal and statistical analysis of the earthquakes in the last 500 years and the active faults in China. It is found that fractal relationship exists between the frequency and the length of the active faults, and the fractal dimension is 1.70 in the continental region of China, and 1.40 in the northwest China. The fractal relationship also exists between the frequency and the scales of earthquakes during the last five centuries and the fractal dimension is 1.30 for the whole continental region of China and 1.08 for the northwest China. The differences of the fractal dimensions between the active faults and the earthquakes indicate that some of the active faults have not caused earthquakes during the last 500 years. The differences of fractal dimensions of the active faults and earthquakes between the northwest China and the whole continental region of China suggest that the frequency of strong earthquakes is greater in northwest China than that of the average level of China, because the number of longer active faults is larger in northwest China than that of the average in whole China. Thus, the fractal analysis is an effective method for studies of faults and earthquakes.     

Verification and refinement of spectral magnitude calibrating functions for P-waves

Calibrating functions for determination of P-wave spectral magnitudes calculated by Duda and Yanovskaya (1994) on the basis of the IASP91 velocity model and the PREM Q-model are verified empirically. For this purpose IRIS broadband records for 120 earthquakes are used, each earthquake having been recorded at about 100 stations. The discrepancies indicate that anelastic absorption assumed in PREM is too high. New calibrating functions are calculated on the basis of the AK135 velocity and anelasticity models (Kennet et al., 1995; Montagner and Kennet, 1996), in which Q in the mantle is higher than in PREM. The verification of the new calibrating functions based on the same observations yields magnitude figures less depending on the epicentral distance. In addition the parameter ₂in the Liu-Anderson Q(T) model is estimated, proceeding from the assumption that on the average the radiated spectra comply with the ²-model. The value of ₂ was assumed to be 0.1 s in the analysis and its use resulted in the verification of the ²-model for the source spectrum.     

Saltmarsh deposition and its relationship to coastal forcing over the last century on the north-west coast of Ireland

The mesoscale (time) control of annual storm-surge activity on quasi-annual saltmarsh (tidal marsh) deposition is studied from two estuarine saltmarshes on the high-energy NW coast of Ireland. Both saltmarshes exhibit a cliffed edge where maximum sedimentary variation is expressed in the form of lamination. Sections were logged and characterised by lithofacies based on grain-size determinations. Sections dated using Cs and Pb determinations indicated deposition records of decadal to century scale (c. 0.5 cm a^-1). Linear multiple regression explains (p< 0.05) half the variation of the deposition rate by annual coastal forcing (surge frequency and magnitude) and sediment modes (coarse silt to clay). Further variability in deposition rate is partially reflected in the non-linear response between forcing and deposition that is affected by mesoscale (30, 11 and 5-year) periodicities in forcing. Increased annual surge activity appears to be associated with a coarsening of, and reduction in annual deposition. A relationship between annual deposition rate and fractal dimension of surge timing (i.e. the clustering of surge events) is identified.     

江西德兴铜厂斑岩体铜品位的分形结构

铜厂斑岩体铜品位空间分布的分形研究表明,７个钻孔的铜品分布具有统计自相似性。铜吕位分维值由斑岩体南东侧向北西侧逐次增大,并在上盘表现为双重分维结构,表明铜厂玉岩体铜主要来自岩浆。     

江西德兴斑岩铜矿田断裂分形研究

本文将分形几何学的原理和方法应用于江西德兴斑岩铜矿田三组断裂系统的二维平面分布特征研究,发现在研究的标度范围不人有统计自相似性,而且不同矿区了区域具有孙现的分维数Ｄ值,矿化岩体产出部位分维明显高于整个矿山分维值,ＮＥ向断裂体系分维值略高于ＷＮＷ向体系分维值,结合断裂产状,时代,穿切关系与岩体侵入部位对比可知,分维值越高,越有利于矿床形成,矿床规模也越大,其中ＮＥ向和ＷＮＷ向断裂体系起主控矿作用。