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71.
Arthur Frankel 《Pure and Applied Geophysics》1989,131(4):639-685
This paper reviews applications of the finite-difference and finite-element methods to the study of seismic wave scattering in both simple and complex velocity models. These numerical simulations have improved our understanding of seismic scattering in portions of the earth where there is significant lateral heterogeneity, such as the crust. The methods propagate complete seismic wavefields through highly complex media and include multiply scattered waves and converted phases (e.g.,P toSV, SV toP, body wave to surface wave). The numerical methods have been especially useful in cases of moderate and strong scattering in complex media where multiple scattering becomes important. Progress has been made with numerical methods in understanding how near-surface, low-velocity basin structures scatter surface waves and vertically-incident body waves. The numerical methods have proven useful in evaluating scattering of surface waves and body waves from topography of both the free surface and interfaces buried at depth. Numerical studies have demonstrated the importance of conversions from body waves to surface waves (andvice versa) when lateral heterogeneities and topographic relief are present in the uppermost crust. Recently, several investigations have applied numerical methods to study seismic wave propagation in velocity models which vary randomly in space. This stochastic approach seeks to understand the effects of small-scale complexity in the earth which cannot be resolved deterministically. These experiments have quantified the relationships between the statistical properties of the random heterogeneity and the measurable properties of high-frequency (1 Hz) seismograms. These simulations have been applied to the study of many features observed in actual high-frequency seismic waves, including: the amplitude and time decay of seismic coda, the apparent attenuation from scattering, the dispersion of waveforms, and the travel time and waveform variations across arrays of receivers. 相似文献
72.
Dimension and entropy in the soil-covered landscape 总被引:2,自引:0,他引:2
W. E. H. Culling 《地球表面变化过程与地形》1988,13(7):619-648
Both the Hausdorff dimension and the K-entropy supply a measure of the irregularity of the landspace surface. The relationship between the two measures is investigated over a variety of terrains in Britain and a method of calculating the entropy is checked against an independent estimate of the dimension with reasonable agreement. The calculation of the K-entropy requires that the landscape surface be represented by an homogenous ergodic random field. This condition is satisfied by the tendency of soil-covered terrains to progressively approximate to a form well represented by a Gaussian field. Gaussian random fields can either be very smooth, possessing derivatives of all orders at every point or they are highly irregular and non-differentiable everywhere. Within the regular conceptualization the Rice-Kac theory is used to predict the numbers of crossing points and the extent of excursion sets. These predictions are tested against an example terrain from the High Weald of East Sussex with very good agreement, apart from predictions of local maxima. A worked example of the calculation of the K-entropy is given as an appendix. The potential role of information theory in geomorphology extends beyond the use made of entropy in this investigation. In particular ergodic theory has important practical and theoretical implications. 相似文献
73.
随机误差传递与合成的蒙特卡罗模拟 总被引:2,自引:0,他引:2
对分析测试过程中随机误差的传递与合成进行了蒙卡罗模拟,并偏制了BASIC程序。该方法解决了当被合成误差不相互独立时泰勒级数公式所遇到的困难,当被合成误差相互独立时,与泰勒公式计算结果一致。 相似文献
74.
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76.
77.
Robert A. Langel 《Journal of Earth System Science》1990,99(4):581-618
Among the first measurements made from near-Earth orbiting satellites were measurements of the magnetic field. The sources
of that field lie both within the Earth, in its core and crust, and in the surrounding ionosphere and magnetosphere. This
article summarizes some of the methodology and results for studies of the Earth’s mantle and crust. Mantle conductivity studies
can be made either by studying signals impressed on the Earth from outside, e.g., the ionosphere or magnetosphere, or by studying
signals originating in the core and transmitted through the mantle. Crustal field studies begin with a careful selection of
the data and subsequent removal of core and external fields by some sort of filtering. Average maps from different local times
sometimes differ, presumably due to the remaining presence of fields of external origin. Several techniques for further filtering
are discussed. Where large-area aeromagnetic maps are available, crustal maps derived from satellite data can be compared
with upward continued data. In general, the comparisons show agreement, with some differences, particularly in and near the
auroral belts. The satellite data are further reduced by various methods of inverse and forward modelling, sometimes including
reduction to the pole (RTP). These techniques are generally unstable at the equator. Common methods of stabilizing the inversions
include principle components analysis and ridge regression. Because of the presence of the core field, the entire crustal
contribution from the field is not known. Also, there is a basic nonuniqueness to the inverse solutions. Nevertheless, magnetizations
that are interpretable can be derived. 相似文献
78.
This paper presents an analysis of Hagen-Poiseulle flow through plane random anisotropic networks of interconnected channels. Macroscopic permeability tensor of the network is expressed in terms of statistico-geometrical characteristics like the degree of anisotropy in channel orientations, average co-ordination number of the network and first two moments of channel length distribution. Analytical results are illustrated and verified using numerical analysis of flow in a simulated random network. The emphasis of the paper is on the effects of anisotropy on distributions of flow rates in channels. It is shown that, due to anisotropy the maximum flow rate generally occurs in channels that are not aligned along the direction of the macroscopic pressure gradient. 相似文献
79.
N. C. Lind H. P. Hong 《Stochastic Environmental Research and Risk Assessment (SERRA)》1991,5(1):77-87
The method of Relative Entropy with Fractile constraints (REF method) is explained and applied to model extreme compound hydrological phenomena, such as extreme sea levels under storm conditions. Also presented is a simple method of Tail Entropy Approximation (TEA), which amounts to a correction of traditional statistical estimates for extreme observations.Distribution assumptions are necessary but downplayed in the REF method, relegating the prior distribution to the role of an extrapolation function. The estimates are objective in an information-theoretical sense. They also satisfy a strict requirement of self-consistency that is generally not satisfied by standard statistical methods: invariance under monotonic transformations of the random variable.Historical records of storm surge levels in the Netherlands and annual maximum tidal heights for Sheerness, UK, are used as examples. Comparison is made with distributions obtained using other methods.It is concluded that the tail entropy approximation provides simple, objective estimates of extremes in the tail beyond the range of observations. 相似文献
80.
A model of a multivariate covariance function with an ellipsoidal directional correlation scale has been developed. The axes of the ellipsoidal scale are related to the eigenvalues and eigenvectors of a matrix B which characterizes the ellipsoid of the range of influence. The matrix B is found to be related to a matrix T which can be estimated directly from sparse sampling data and can be used to determine estimates of the matrix B. The method has been applied to both two-dimensional and three-dimensional cases. The numerical results show that the satisfactory accuracy is obtained with sparse sampling data from an anisotropic random function. 相似文献