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1.
The soil-covered landscape surface can be idealized from two viewpoints. The intuitive view is of a smooth, absolutely continuous surface with continuous contour lines and measurable in integral dimensions. The alternative view emphasizes the roughness, a surface of little regularity and at the limit of no contours, the appropriate measure being that of fractional Hausdorff dimension. Regularity is a local property and both idealizations need to stop far short of the limit to avoid awkward consequences. The dichotomy of viewpoint can be matched in the theory of Gaussian random fields. These, if they are smooth, are very smooth but if they are irregular they are highly irregular (erratic); there is no middle ground. This Belayev dichotomy is defined and both modes applied to the soil-covered landscape. On the one hand, if the landscape is subject to a general diffusive type degradation or more generally a Davisian downwasting regime then the curvature of the landscape surface is progressively straightened and the distribution of gradient (increments) along a typical traverse will eventually adopt a Gaussian form. Then from the irregular viewpoint the surface is ultimately well represented by a fractional Brownian surface of low Hausdorff dimension (2·0 < dim < 2·3). The Hausdorff dimension is directly related to the entropy of the landscape and as degradation proceeds both quantities decrease in value. On the other hand, if the surface is regarded as smooth and well represented by an absolutely continuous Gaussian field then the mean value of the number of upcrossings of a level or the extent of an excursion set will also be Gaussian. This analysis is restricted to one dimension; the number of times a profile curve crosses or the amount of time it spends above any given level. Predictions from both viewpoints are substantially corroborated in a map analysis of 15 sites on varied terrains in Southern England and the map analysis checked against one based upon digital tape data for one of the sites. 相似文献
2.
Xavier Emery 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(2):211-219
The multi-Gaussian model is used in geostatistical applications to predict functions of a regionalized variable and to assess
uncertainty by determining local (conditional to neighboring data) distributions. The model relies on the assumption that
the regionalized variable can be represented by a transform of a Gaussian random field with a known mean value, which is often
a strong requirement. This article presents two variations of the model to account for an uncertain mean value. In the first
one, the mean of the Gaussian random field is regarded as an unknown non-random parameter. In the second model, the mean of
the Gaussian field is regarded as a random variable with a very large prior variance. The properties of the proposed models
are compared in the context of non-linear spatial prediction and uncertainty assessment problems. Algorithms for the conditional
simulation of Gaussian random fields with an uncertain mean are also examined, and problems associated with the selection
of data in a moving neighborhood are discussed. 相似文献
3.
地表起伏地形在野外矿产资源勘察中不可避免,其对直流电阻率法勘探影响巨大.近年来,电阻率三维正演取得诸多进展,特别是应用非结构网格我们能够进行任意复杂地形和几何模型的电阻率三维数值模拟,但面向实际应用的起伏地形下电阻率三维反演依然困难.本文基于非结构化四面体网格,并考虑到应用GPS/GNSS时,区域地球物理调查中可非规则布设测网的实际特点,实现了任意地形(平坦或起伏)条件下、任意布设的偶极-偶极视电阻率数据的不完全Gauss-Newton三维反演.合成数据的反演结果表明了方法的有效性,可应用于复杂野外环境下的三维电法勘探. 相似文献
4.
N. Ardjmandpour C. Pain J. Singer J. Saunders E. Aristodemou J. Carter 《Geophysical Prospecting》2011,59(4):721-748
An artificial neural network method is proposed as a computationally economic alternative to numerical simulation by the Biot theory for predicting borehole seismoelectric measurements given a set of formation properties. Borehole seismoelectric measurements are simulated using a finite element forward model, which solves the Biot equations together with an equation for the streaming potential. The results show that the neural network method successfully predicts the streaming potentials at each detector, even when the input pressures are contaminated with 10% Gaussian noise. A fast inversion methodology is subsequently developed in order to predict subsurface material properties such as porosity and permeability from streaming potential measurements. The predicted permeability and porosity results indicate that the method predictions are more accurate for the permeability predictions, with the inverted permeabilities being in excellent agreement with the actual permeabilities. This approach was finally verified by using data from a field experiment. The predicted permeability results seem to predict the basic trends in permeabilities from a packer test. As expected from synthetic results, the predicted porosity is less accurate. Investigations are also carried out to predict the zeta potential. The predicted zeta potentials are in agreement with values obtained through experimental self potential measurements. 相似文献
5.
本文详细地分析了用数字化仪和激光扫描仪对模拟加速度记录进行数字化时所产生的误差及消除这些误差的方法，并开发了相关处理软件。数字化误差由数字化设备的系统误差和读数员在操作过程中的随机误差迭加而成，随机数字化误差是具有各态历经性质的、其振幅按高斯规律分布的平稳随机过程。利用激光扫描仪做强震记录数字化，工作效率很高。本文给出了激光扫描仪分析处理软件和消除数字化噪声实例。 相似文献
6.
Fractal generation of surface area of porous media 总被引：2，自引：0，他引：2
Hongbing Sun Manfred Koch 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(2):83-96
Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they
are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify
a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure
with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating
a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is
presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic
porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a
nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which
is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity,
the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical
fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation
structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean,
variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately
2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous
medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82.
The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy
assumed. 相似文献
7.
Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they
are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify
a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure
with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating
a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is
presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic
porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a
nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which
is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity,
the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical
fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation
structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean,
variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately
2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous
medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82.
The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy
assumed. 相似文献
8.
Sergio G. Ferraes 《Earth and Planetary Science Letters》1991,106(1-4)
The determination of the probability distribution of recurrence times is the most important problem in the calculation of long-term conditional probabilities for the recurrence of large and great earthquakes.The principle of maximum entropy in conjunction with a goodness-of-fit test (chi-square or Kolmogorov-Smirnov test) may be employed to obtain estimates of these densities using recurrence data for some seismic regions.Four different distributions are characterized by the property of maximum entropy, as possible laws for recurrence times of the largest earthquakes: uniform, exponential, Gaussian and log-normal. To discriminate among these different probability distributions we use the probability theory and the chi-square test to check the goodness-of-fit to the distribution of recurrence time of shocks of magnitude 6.5 and largest occurred in the west-northwestern zone of the Hellenic arc from 1791 to 1983.It is found that the recurrence times data for the west-northwestern zone of the Hellenic arc cannot be represented by the uniform and the Gaussian probability densities. The recurrence times data for the west-northwestern zone of the Hellenic arc can be described accurately by the exponential and log-normal probability densities, which were predicted from the principle of maximum entropy. In other words, the principle of maximum entropy does not necessarily lead to a unique solution. In turn, the mathematical properties of these distributions could be used to derive different physical properties of the earthquake process in the west-northwestern zone of the Hellenic arc. 相似文献
9.
Aspasia Zerva 《地震工程与结构动力学》1992,21(4):351-361
An improved version of the spectral representation method (References 12–14) for the generation of simulations of random processes and random fields by means of the Fast Fourier Transform algorithm is developed. The new formulation produces simulations that are ergodic in the mean without any restricting assumptions at the origin of the spectra and leads to a faster convergence rate of the stochastic characteristics of the simulations to those of the random field. As an example of the methodology, simulations in space and time based on a spatial variability model for the seismic ground motions are generated. 相似文献
10.
In this work, the concept of entropy based on probability is applied in modeling the vertical distribution of velocity in open channel turbulent flow. Using the principle of maximum entropy, one-dimensional velocity distribution is derived by maximizing the Renyi entropy subject to some constraints by assuming dimensionless velocity as a random variable. The Renyi entropy-based equation is capable of modeling the velocity distribution from the channel bed to the water surface. The derived velocity distribution is tested with field and laboratory observations and is also compared with existing entropy-based velocity distributions. The present model has shown good agreement with observed data and its prediction accuracy is superior than the other existing models. 相似文献
11.
The geologic architecture in aquifer systems affects the behavior of fluid flow and the dispersion of mass. The spatial distribution and connectivity of higher-permeability facies play an important role. Models that represent this geologic structure have reduced entropy in the spatial distribution of permeability relative to models without structure. The literature shows that the stochastic model with the greatest variance in the distribution of predictions (i.e., the most conservative model) will not simply be the model representing maximum disorder in the permeability field. This principle is further explored using the Shannon entropy as a single metric to quantify and compare model parametric spatial disorder to the temporal distribution of mass residence times in model predictions. The principle is most pronounced when geologic structure manifests as preferential-flow pathways through the system via connected high-permeability sediments. As per percolation theory, at certain volume fractions the full connectivity of the high-permeability sediments will not be represented unless the model is three-dimensional. At these volume fractions, two-dimensional models can profoundly underrepresent the entropy in the real, three-dimensional, aquifer system. Thus to be conservative, stochastic models must be three-dimensional and include geologic structure. 相似文献
12.
13.
This paper deals with the generation of seismic accelerograms which are compatible with a given response spectrum and other design specifications. The time sampling of the stochastic accelerogram yields a time series represented by a random vector in high dimension. The probability density function of this random vector is constructed using the maximum entropy (MaxEnt) principle under constraints defined by the available information (design specifications). In this paper, an adapted algorithm is proposed to identify the Lagrange multipliers introduced in the MaxEnt principle to take into account the constraints. This algorithm is based on (1) the minimization of an appropriate convex functional and (2) the construction of the probability distribution defined as the invariant measure of an Itô stochastic differential equation in order to estimate the integrals in high dimension of the problem. The constraints related to a seismic accelerogram are developed explicitly. This methodology is validated through an application for which the available information is related to the variance of each component of the random vector representing the accelerogram, statistics on the response spectrum, on the peak ground acceleration, on the cumulative absolute velocity and on the end-values for the velocity and for the displacement. 相似文献
14.
Jalal Ferahtia Kamel Baddari Nouredine Djarfour Abdel Kader Kassouri 《Pure and Applied Geophysics》2010,167(11):1389-1404
Seismic noise is a fundamental part of seismic data which cannot be avoided when conducting any seismic survey. It consists
of coherent and random noise. Noise removal or filtering is one of the major concerns in the field of seismic processing.
In this paper, we introduce an image filtering technique based on a detection-estimation algorithm for Gaussian and random
noise removal in seismic data, namely the trilateral filter, based on a statistic called rank-ordered absolute differences.
The non-linear and adaptive behaviour of this filter makes it very robust in the presence of random and coherent noise, in
addition to its computational simplicity and its ability to automatically identify noise in data. We have modified the strategy
of trilateral filtering by adapting the rank-ordered absolute differences formula in order to extract the signal component.
We have successfully used this filter for the removal of surface waves and random spiky noise from synthetic and field data.
Results are very encouraging and show the superiority of this filter compared with other filters, particularly when used recursively. 相似文献
15.
The objective of this study was to calibrate the Everglades Wetland Hydrodynamic Model (EWHM) to the Everglades Nutrient Removal (ENR) Project, from April 1995 through July of 1996. Model predictions were evaluated graphically and statistically against field observations to quantify the accuracy of model predictions and evaluate the success of model calibration. Comparisons between model predictions and field observations of water surface elevations at interior stations indicated that the model was successfully calibrated and model predictions were highly correlated with observed water surface elevations (r2 ranged from 0.79 to 0.84). Model-predicted chloride (Cl) concentrations fell within the observed range of field observations, further confirming the success of model calibration. Good agreement found in these comparisons between observed and predicted results warrants the use of the model in a predictive mode. This is further supported by noting that the model contains no adjustable constants and requires no computational fitting of parameters to experimental data as is necessary in many previous obstructed flow studies. 相似文献
16.
Comparison of different mass transport calculation methods for wind erosion quantification purposes 总被引：2，自引：0，他引：2
Quantitative estimation of the material transported by the wind under field conditions is essential for the study and control of wind erosion. A critical step of this calculation is the integration of the curve that relates the variation of the amount of the material carried by the wind with height. Several mathematical procedures have been proposed for this calculation, but results are scarce and controversial. One objective of this study was to assess the efficiency of three mathematical models (a rational, an exponential, and a simplified Gaussian function) for the calculation of the mass transport, as compared to the linear spline interpolation. Another objective of this study was to compare the mass transport calculated from field measurements obtained from a minimum of three discrete sampling heights with measurements of nine sampling heights. With this purpose, wind erosion was measured under low surface roughness conditions on an Entic Haplustoll during 25 events. The rational function was found to be mathematically limited for the estimation of wind eroded sediment mass flux. The simplified Gaussian model did not fit to the vertical mass flux profile data. Linear spline interpolation generally produced higher mass transport estimates than the exponential equation, and it proved to be a very flexible and robust method. Using different sampling arrangements and different mass flux models can produce differences of more than 45% in mass transport estimates, even under similar field conditions. Under the conditions of this study, at least three points between the soil surface and 1·5 m high, including one point as closest as possible to the surface, should be sampled in order to obtain accurate mass transport estimates. Additionally, the linear spline interpolation and the non‐linear regression using an exponential model, proved to be mathematically reliable methods for calculating the mass transport. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
17.
18.
从声波波场理论出发,首先在不考虑自由表面反射的情况下研究了有效波波场传播及反射规律,继而考虑自由表面反射的情况,并详尽推导了压制自由表面多次波的正演和反演数学模型。从物理本质上对自由表面多次波的产生、预测及压制做了深入的剖析,讨论了基于数据一致性时空域褶积的多次波预测方法原理,实现了自由表面相关多次波自适应压制的迭代方法过程。复杂起伏海底的理论模型试算实例表明：在多次波产生系统非常复杂的情况下,本方法仍能非常有效地压制各种与自由表面相关的多次波,同时还能很好地保持有效波的能量,取得了很好的压制多次波效果。 相似文献
19.
复杂度理论为研究地磁变化场提供了新思路和新途径.地磁变化场从物理起源上可以看作是一种复杂系统,因此,本文从军事工程应用需求出发,基于复杂度理论,提出运用样本熵、多尺度熵及滑动窗样本熵方法对不同磁扰程度下的地磁变化场时间序列进行复杂度特征分析,结果表明：（1）样本熵和多尺度熵能够很好地表征地磁扰动强度及演化特征,启发我们可设计一种新的“熵指数”来衡量地磁扰动大小;（2）滑动窗样本熵能够准确定位地磁扰动时间段,对于磁暴识别与预测、空间灾害性天气预警等有一定的参考价值;（3）Mackey-Glass时滞混沌方程随时间的演化呈现出与地磁场日变曲线非常相似的形态,因此,地磁变化场或许可用时滞混沌方程来表示,对于我们更好地认识地磁变化场物理机理、建模预测与地磁寻的等军事工程应用都有一定的意义. 相似文献
20.
Random field characteristics of earthquake occurrence and test of earthquake occurrence rate 总被引：1，自引：0，他引：1
高孟潭 《地震学报(英文版)》1994,(Z1)
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