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1.
S-S. Xu A. F. Nieto-Samaniego S. A. Alaniz-Álvarez L. G. Velasquillo-Martínez 《International Journal of Earth Sciences》2006,95(5):841-853
The power-law exponent (n) in the equation: D=cL
n
, with D = maximum displacement and L = fault length, would be affected by deviations of fault trace length. (1) Assuming n=1, numerical simulations on the effect of sampling and linkage on fault length and length–displacement relationship are done in this paper. The results show that: (a) uniform relative deviations, which means all faults within a dataset have the same relative deviation, do not affect the value of n; (b) deviations of the fault length due to unresolved fault tip decrease the values of n and the deviations of n increase with the increasing length deviations; (c) fault linkage and observed dimensions either increase or decrease the value of n depending on the distribution of deviations within a dataset; (d) mixed deviations of the fault lengths are either negative or positive and cause the values of n to either decrease or increase; (e) a dataset combined from two or more datasets with different values of c and orders of magnitude also cause the values of n to deviate. (2) Data including 19 datasets and spanning more than eight orders of fault length magnitudes (10−2–105 m) collected from the published literature indicate that the values of n range from 0.55 to 1.5, the average value being 1.0813, and the peak value of n
d (double regression) is 1.0–1.1. Based on above results from the simulations and published data, we propose that the relationship between the maximum displacement and fault length in a single tectonic environment with uniform mechanical properties is linear, and the value of n deviated from 1 is mainly caused by the sampling and linkage effects. 相似文献
2.
徐琼 《成都信息工程学院学报》2006,21(1):110-112
证明了由任意a尺度正交单尺度函数和任意一组正交滤波器生成a尺度r重正交多尺度函数的一个充分必要条件,并给出了a尺度r重正交多小波的一种构造方法. 相似文献
3.
Trond Reitan Asgeir Petersen-Øverleir 《Stochastic Environmental Research and Risk Assessment (SERRA)》2008,22(3):351-365
This paper presents a Bayesian approach for fitting the standard power-law rating curve model to a set of stage-discharge
measurements. Methods for eliciting both regional and at-site prior information, and issues concerning the determination of
prior forms, are discussed. An efficient MCMC algorithm for the specific problem is derived. The appropriateness of the proposed
method is demonstrated by applying the model to both simulated and real-life data. However, some problems came to light in
the applications, and these are discussed. 相似文献
4.
In a recent work [Valiani A, Caleffi V. Depth–energy and depth–force relationships in open channel flows: analytical findings. Adv Water Resour 2008;31(3):447–54], the authors analytically inverted the depth–specific energy and depth–total force relationships for flows in open channels with wide rectangular cross-sections. 相似文献
5.
Trond Reitan Asgeir Petersen-Øverleir 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(5):627-642
This study explores Bayesian methods for handling compound stage–discharge relationships, a problem which arises in many natural
rivers. It is assumed: (1) the stage–discharge relationship in each rating curve segment is a power-law with a location parameter,
or zero-plane displacement; (2) the segment transitions are abrupt and continuous; and (3) multiplicative measurement errors
are of equal variance. The rating curve fitting procedure is then formulated as a piecewise regression problem where the number
of segments and the associated changepoints are assumed unknown. Procedures are developed for describing both global and site-specific
prior distributions for all rating curve parameters, including the changepoints. Estimation and uncertainty analysis is evaluated
using Markov chain Monte Carlo simulation (MCMC) techniques. The first model explored accounts for parameter and model uncertainties
in the interpolated area, i.e. within the range of available stage–discharge measurements. A second model is constructed in
an attempt to include the uncertainty in extrapolation, which is necessary when the rating curve is used to estimate discharges
beyond the highest or lowest measurement. This is done by assuming that the rate of changepoints both inside and outside the
measured area follows a Poisson process. The theory is applied to actual data from Norwegian gauging stations. The MCMC solutions
give results that appear sensible and useful for inferential purposes, though the latter model needs further efforts in order
to obtain a more efficient simulation scheme. 相似文献
6.
Fast error analysis of continuous GPS observations 总被引：4，自引：1，他引：3
It has been generally accepted that the noise in continuous GPS observations can be well described by a power-law plus white
noise model. Using maximum likelihood estimation (MLE) the numerical values of the noise model can be estimated. Current methods
require calculating the data covariance matrix and inverting it, which is a significant computational burden. Analysing 10 years
of daily GPS solutions of a single station can take around 2 h on a regular computer such as a PC with an AMD AthlonTM 64 X2 dual core processor. When one analyses large networks with hundreds of stations or when one analyses hourly instead
of daily solutions, the long computation times becomes a problem. In case the signal only contains power-law noise, the MLE
computations can be simplified to a process where N is the number of observations. For the general case of power-law plus white noise, we present a modification of the MLE equations
that allows us to reduce the number of computations within the algorithm from a cubic to a quadratic function of the number
of observations when there are no data gaps. For time-series of three and eight years, this means in practise a reduction
factor of around 35 and 84 in computation time without loss of accuracy. In addition, this modification removes the implicit
assumption that there is no environment noise before the first observation. Finally, we present an analytical expression for
the uncertainty of the estimated trend if the data only contains power-law noise.
Electronic supplementary material The online version of this article (doi: ) contains supplementary material, which is available to authorized users. 相似文献
7.
A system consisting of an elastic matrix with randomly distributed pores of uniform shapes but with sizes governed by a power-law
distribution is investigated in a theoretical way. The velocities of elastic waves propagating through such a system are calculated.
The obtained results are that the velocities decrease with increasing total porosity and for a given porosity velocities moderately
decrease with increasing absolute value of the exponent D in a power-law distribution of pore sizes.
Received: 3 July 1995 / Accepted: 2 August 1996 相似文献
8.
Du Jiulin 《Astrophysics and Space Science》2007,312(1-2):47-55
By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating
long-range interactions. It is shown that the power-law distributions describe the long-range nature of the interactions and
the non-local correlations within the self-gravitating system with the inhomogeneous velocity dispersion. A relation is established
between the nonextensive parameter q≠1 and the measurable quantities of the self-gravitating system: the velocity dispersion and the mass density. Correspondingly,
the nonextensive parameter q can be uniquely determined from the microscopic dynamical equation and thus the physical interpretation of q different from unity can be clearly presented. We derive a nonlinear differential equation for the radial density dependence
of the self-gravitating system with the inhomogeneous velocity dispersion, which can correctly describe the density distribution
for the dark matter in the above physical situation. We also apply this q-kinetic approach to analyze the nonextensivity of self-gravitating collisionless systems and self-gravitating gaseous dynamical
systems, giving the power-law distributions the clear physical meaning.
相似文献
9.
Non-Darcian flow towards a well which fully penetrates a confined single vertical fracture is presented in this paper on the basis of the Izbash equation. We have obtained semi-analytical solutions for non-Darcian flow by using the Boltzmann transform and developed the non-Darcian flow well functions for cases with and without the effect of wellbore storage. The results show that the non-Darcian flow type curves are more or less deviated from the Darcian flow type curve. The non-linear effect is mainly attributable to the turbulent factor, v, a dimensionless parameter related to the pumping rate, the fracture aperture, the fracture thickness, and two constants k′ and n used in the Izbash power-law. The non-linear effect appears to be less sensitive to the power-law index, n. When excluding wellbore storage, the well function at early times is proportional to v−1/(n−1)u−n/(n−1), where u is a dimensionless term inversely proportional to time; whereas the well function at late times is approximated as , where A0(n) is a finite term depending on n. When considering wellbore storage, drawdowns inside the well with different v values approach the same asymptotic value at small times, and the effect of wellbore storage is only found at the early stage of pumping. 相似文献
10.
Application of fractal models to characterization of vertical distribution of geochemical element concentration 总被引：1，自引：0，他引：1
Characterization of the vertical distribution of geochemical element concentration is essential for economic planning in the mining industry. 10 mineralized boreholes and 1 non-mineralized borehole from the Qulong copper deposit, Tibet, western China, were collected to identify the vertical distribution properties of Cu values using fractal models. The vertical distribution of Cu values in mineralized and non-mineralized boreholes shows a positive skewed distribution in the former and multimodal distribution in the latter. The results obtained by the box counting method show that the vertical distributions of Cu values in mineralized and non-mineralized boreholes exhibit self-similarity with box dimensions ranging from 1.28 to 1.37. The box dimensions of mineralized boreholes are greater than that of Cu values in the non-mineralized borehole, indicating that the mineralization makes the distribution of Cu values more irregular. The power-law frequency analysis reveals that Cu values in mineralized boreholes are bifractal. The two portions of the plot define a crossover point at 0.33%, for Cu values less than and greater than 0.33, fractal dimensions range from 0.1 to 0.65, in non-mineralized rocks, and range from 2.71 to 5.79, in the mineralized rocks. Hurst exponents for mineralized boreholes occur at 0.8, which are greater than 0.5, indicating that Qulong copper deposit has a good continuity of mineralization. 相似文献