共查询到20条相似文献，搜索用时 652 毫秒
1.
J. Rydén 《Stochastic Environmental Research and Risk Assessment (SERRA)》2006,20(4):238-242
The distribution of maxima during a given time interval is of interest in many applications in risk analysis. Within the framework of stationary Gaussian processes, several theoretical results considering asymptotics from different aspects have been derived for this distribution. In this note, we review results from the theory and study the accuracy of these approximations by exemplifying with a model for wave heights from oceanography. It turns out that for high values and the time periods normally encountered for buoy measurements, care should be taken in use of approximation based on the Gumbel distribution. 相似文献
2.
L. Telesca V. Cuomo V. Lapenna M. Macchiato C. Serio 《Pure and Applied Geophysics》1999,156(3):487-501
—We use advanced methods to extract quantitative time dynamics from geomagnetic signals. In particular we analyse daily geomagnetic time series measured at three stations in Norway. The dynamics of geomagnetic measurements has been investigated using autoregressive models. The procedure is based on two forecasting approaches: the global autoregressive approximation and the local autoregressive approximation. The first technique views the data as a realisation of a linear stochastic process, whereas the second considers them as a realisation of a deterministic process, supposedly non-linear. The comparison of the predictive skill of the two techniques is a strong test to discriminate between low-dimensional chaos and stochastic dynamics. Our findings suggest that the physical system governing the phenomena is characterised by a stochastic dynamics, and the process could be described by numerous degrees of freedom. We also investigated the kind of stochasticity of the geomagnetic signals, analysing the power spectrum density. We identify a power law P(?)∝?-α, with the scaling exponent α which is a typical fingerprint of irregular processes. In this analysis we use the Higuchi method, which presents an interesting relationship between the fractal dimension D and the spectral power law scaling index α. 相似文献
3.
Based on the fact that the Hankel matrix representing clean seismic data is low rank, low-rank approximation methods have been widely utilized for removing noise from seismic data. A common strategy for real seismic data is to perform the low-rank approximations for small local windows where the events can be approximately viewed as linear. This raises a fundamental question of selecting an optimal rank that best captures the number of events for each local window. Gavish and Donoho proposed a method to select the rank when the noise is independent and identically distributed. Gaussian matrix by analysing the statistical performance of the singular values of the Gaussian matrices. However, such statistical performance is not available for noisy Hankel matrices. In this paper, we adopt the same strategy and propose a rule that computes the number of singular values exceed the median singular value by a multiplicative factor. We suggest a multiplicative factor of 3 based on simulations which mimic the theories underlying Gavish and Donoho in the independent and identically distributed Gaussian setting. The proposed optimal rank selection rule can be incorporated into the classical low-rank approximation method and many other recently developed methods such as those by shrinking the singular values. The low-rank approximation methods with optimally selected rank rule can automatically suppress most of the noise while preserving the main features of the seismic data in each window. Experiments on both synthetic and field seismic data demonstrate the superior performance of the proposed rank selection rule for seismic data denoising. 相似文献
4.
John H. Cushman Moongyu Park Monica Moroni Natalie Kleinfelter-Domelle Daniel O��Malley 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(1):1-10
When formulated properly, most geophysical transport-type process involving passive scalars or motile particles may be described
by the same space–time nonlocal field equation which consists of a classical mass balance coupled with a space–time nonlocal
convective/dispersive flux. Specific examples employed here include stretched and compressed Brownian motion, diffusion in
slit-nanopores, subdiffusive continuous-time random walks (CTRW), super diffusion in the turbulent atmosphere and dispersion
of motile and passive particles in fractal porous media. Stretched and compressed Brownian motion, which may be thought of
as Brownian motions run with nonlinear clocks, are defined as the limit processes of a special class of random walks possessing
nonstationary increments. The limit process has a mean square displacement that increases as tα+1 where α > −1 is a constant. If α = 0 the process is classical Brownian, if α < 0 we say the process is compressed Brownian while
if α > 0 it is stretched. The Fokker–Planck equations for these processes are classical ade’s with dispersion coefficient
proportional to tα. The Brownian-type walks have fixed time step, but nonstationary spatial increments that are Gaussian with power law variance.
With the CTRW, both the time increment and the spatial increment are random. The subdiffusive Fokker–Planck equation is fractional
in time for the CTRW’s considered in this article. The second moments for a Levy spatial trajectory are infinite while the
Fokker–Planck equation is an advective–dispersive equation, ade, with constant diffusion coefficient and fractional spatial
derivatives. If the Lagrangian velocity is assumed Levy rather than the position, then a similar Fokker–Planck equation is
obtained, but the diffusion coefficient is a power law in time. All these Fokker–Planck equations are special cases of the
general non-local balance law. 相似文献
5.
T. N. Kaseke M. E. Thompson 《Stochastic Environmental Research and Risk Assessment (SERRA)》1997,11(1):1-16
Abstract: Linear continuous time stochastic Nash cascade conceptual models for runoff are developed. The runoff is modeled
as a simple system of linear stochastic differential equations driven by white Gaussian and marked point process noises. In
the case of d reservoirs, the outputs of these reservoirs form a d dimensional vector Markov process, of which only the dth
coordinate process is observed, usually at a discrete sample of time points. The dth coordinate process is not Markovian.
Thus runoff is a partially observed Markov process if it is modeled using the stochastic Nash cascade model. We consider how
to estimate the parameters in such models. In principle, maximum likelihood estimation for the complete process parameters
can be carried out directly or through some form of the EM (estimation and maximization) algorithm or variation thereof, applied
to the observed process data. In this research we consider a direct approximate likelihood approach and a filtering approach
to an algorithm of EM type, as developed in Thompson and Kaseke (1994). These two methods are applied to some real life runoff
data from a catchment in Wales, England. We also consider a special case of the martingale estimating function approach on
the runoff model in the presence of rainfall. Finally, some simulations of the runoff process are given based on the estimated
parameters. 相似文献
6.
给出了计算多层垂直对称轴横向各向同性（VTI）介质精确射线路径和走时的方法,所用的体波相速度公式、群速度公式和Snell定律都是严格的显式解析公式. 任意基本波的射线路径和走时计算问题都可以转化成一个等效的透射问题,再用文中的公式来计算,具体实现方法用一个多次波和一个首波的实例给出. 最后分别用精确公式和Thomsen近似公式计算了相同模型相同基本波的走时曲线. 比较两者计算结果可发现, 近似公式反复使用会使误差积累,同时揭示了近似公式适用范围的局限性,强调了使用近似公式需要注意其适用范围的重要性. 相似文献
7.
L. Klimeš 《Studia Geophysica et Geodaetica》2006,50(3):417-430
Explicit equations for the spatial derivatives and perturbation derivatives of amplitude in both isotropic and anisotropic
media are derived. The spatial and perturbation derivatives of the logarithm of amplitude can be calculated by numerical quadratures
along the rays.
The spatial derivatives of amplitude may be useful in calculating the higher-order terms in the ray series, in calculating
the higher-order amplitude coefficients of Gaussian beams, in estimating the accuracy of zero-order approximations of both
the ray method and Gaussian beams, in estimating the accuracy of the paraxial approximation of individual Gaussian beams,
or in estimating the accuracy of the asymptotic summation of paraxial Gaussian beams. The perturbation derivatives of amplitude
may be useful in perturbation expansions from elastic to viscoelastic media and in estimating the accuracy of the common-ray
approximations of the amplitude in the coupling ray theory. 相似文献
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10.
Spatial models for probabilistic prediction of wind power with application to annual-average and high temporal resolution data 总被引：1，自引：1，他引：0
Producing accurate spatial predictions for wind power generation together with a quantification of uncertainties is required to plan and design optimal networks of wind farms. Toward this aim, we propose spatial models for predicting wind power generation at two different time scales: for annual average wind power generation, and for a high temporal resolution (typically wind power averages over 15-min time steps). In both cases, we use a spatial hierarchical statistical model in which spatial correlation is captured by a latent Gaussian field. We explore how such models can be handled with stochastic partial differential approximations of Matérn Gaussian fields together with Integrated Nested Laplace Approximations. We demonstrate the proposed methods on wind farm data from Western Denmark, and compare the results to those obtained with standard geostatistical methods. The results show that our method makes it possible to obtain fast and accurate predictions from posterior marginals for wind power generation. The proposed method is applicable in scientific areas as diverse as climatology, environmental sciences, earth sciences and epidemiology. 相似文献
11.
Natrocarbonatitic magmas are characterized by their extremely low viscosities and fast elemental diffusion, and as a consequence
of this, their chemistry and crystallinity can change significantly during residence in shallow reservoirs or even due to
cooling during lava flow emplacement. Here, we present the results of a series of crystallization experiments conducted at
1-atm confining pressure and in a temperature range between 630°C and 300°C. The experiments were set up to characterize the
chemistry and growth processes of the phenocryst phases present in natrocarbonatites. The results are applicable to (1) processes
occurring during residence in shallow magma reservoirs and/or (2) during lava flow emplacement. We show that during crystallization
of natrocarbonatites at atmospheric pressure, gregoryite is the first mineral to crystallize at 630°C, followed by nyerereite
at 595°C. Crystal size distributions of the gregoryites show that the crystals grow rapidly by textural coarsening (i.e.,
Ostwald ripening). As the crystallization is a continuous process at this pressure, the composition of the residual melt changes
in response to the crystallization. However, the experiments also show that individual crystals completely reequilibrate with
the changes in melt composition in as little time as <11 min. We therefore conclude that crystallization and diffusion are
extremely fast processes in the natrocarbonatitic system and that the measured chemical variations in phenocrysts from Oldoinyo
Lengai can be explained by different cooling histories. Finally, we model the rheological control on the emplacement of highly
crystallized natrocarbonatitic lavas at Oldoinyo Lengai. 相似文献
12.
Martin Schrinner Karl-Heinz Rädler Matthias Rheinhardt Ulrich R. Christensen 《地球物理与天体物理流体动力学》2013,107(2):81-116
Mean-field theory describes magnetohydrodynamic processes leading to large-scale magnetic fields in various cosmic objects. In this study magnetoconvection and dynamo processes in a rotating spherical shell are considered. Mean fields are defined by azimuthal averaging. In the framework of mean-field theory, the coefficients which determine the traditional representation of the mean electromotive force, including derivatives of the mean magnetic field up to the first order, are crucial for analyzing and simulating dynamo action. Two methods are developed to extract mean-field coefficients from direct numerical simulations of the mentioned processes. While the first method does not use intrinsic approximations, the second one is based on the second-order correlation approximation. There is satisfying agreement of the results of both methods for sufficiently slow fluid motions. Both methods are applied to simulations of rotating magnetoconvection and a quasi-stationary geodynamo. The mean-field induction effects described by these coefficients, e.g., the α-effect, are highly anisotropic in both examples. An α2-mechanism is suggested along with a strong γ-effect operating outside the inner core tangent cylinder. The turbulent diffusivity exceeds the molecular one by at least one order of magnitude in the geodynamo example. With the aim to compare mean-field simulations with corresponding direct numerical simulations, a two-dimensional mean-field model involving all previously determined mean-field coefficients was constructed. Various tests with different sets of mean-field coefficients reveal their action and significance. In the magnetoconvection and geodynamo examples considered here, the match between direct numerical simulations and mean-field simulations is only satisfying if a large number of mean-field coefficients are involved. In the magnetoconvection example, the azimuthally averaged magnetic field resulting from the numerical simulation is in good agreement with its counterpart in the mean-field model. However, this match is not completely satisfactory in the geodynamo case anymore. Here the traditional representation of the mean electromotive force ignoring higher than first-order spatial derivatives of the mean magnetic field is no longer a good approximation. 相似文献
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The linear and nonlinear stabilities of the single degree of freedom spring-slider system which accords to the revised rate- and state-dependent friction law (RSF) (Nagata et al. J Geophys Res 117 (B2):B2314, 2012) are analyzed. The revised ageing law obtained by Nagata et al. (J Geophys Res 117 (B2):B2314, 2012) incorporates the effects of changes in shear stress. Numerical simulations on the cyclic stick–slip motions of the system are developed and compared with the results of the systems according to the original ageing law or the slip law. From the insight of the stability analyses and numerical simulations, it is found that the revised ageing law integrates the “healing effect” feature of the original ageing law and the dynamic slip features of the slip law. In the stick–slip cycles, the velocity decreases with non-constant states during the dynamic overshoot for the revised ageing law, which is different from both the original ageing law and the slip law. Although the revised ageing law concluded from the low velocity friction experiments cannot account for the earthquake-like high velocity friction experiments, it can be used in earthquake nucleation with low velocity. The stability analyses and the results of numerical simulations are helpful to understanding the implications of the revised ageing law. 相似文献
16.
Z. T. Yucel R. H. Shumway 《Stochastic Environmental Research and Risk Assessment (SERRA)》1996,10(2):107-126
This paper is concerned with developing computational methods and approximations for maximum likelihood estimation and minimum mean square error smoothing of irregularly observed two-dimensional stationary spatial processes. The approximations are based on various Fourier expansions of the covariance function of the spatial process, expressed in terms of the inverse discrete Fourier transform of the spectral density function of the underlying spatial process. We assume that the underlying spatial process is governed by elliptic stochastic partial differential equations (SPDE's) driven by a Gaussian white noise process. SPDE's have often been used to model the underlying physical phenomenon and the elliptic SPDE's are generally associated with steady-state problems.A central problem in estimation of underlying model parameters is to identify the covariance function of the process. The cumbersome exact analytical calculation of the covariance function by inverting the spectral density function of the process, has commonly been used in the literature. The present work develops various Fourier approximations for the covariance function of the underlying process which are in easily computable form and allow easy application of Newton-type algorithms for maximum likelihood estimation of the model parameters. This work also develops an iterative search algorithm which combines the Gauss-Newton algorithm and a type of generalized expectation-maximization (EM) algorithm, namely expectation-conditional maximization (ECM) algorithm, for maximum likelihood estimation of the parameters.We analyze the accuracy of the covariance function approximations for the spatial autoregressive-moving average (ARMA) models analyzed in Vecchia (1988) and illustrate the performance of our iterative search algorithm in obtaining the maximum likelihood estimation of the model parameters on simulated and actual data. 相似文献
17.
An approach to calculate the accurate ray paths and traveltimes in multi-layered VTI media (transversely isotropic media with a vertical symmetry axis) is proposed. The expressions of phase velocity, group velocity and Snell’s law used for computation are all explicit and exact. The calculation of ray paths and traveltimes for a given ele-mentary wave is equivalent to that of a transmission problem which is much easier to be treated with the formulae proposed. In the section of numerical examples, the proce... 相似文献
18.
Heavy tailed random variables (rvs) have proven to be an essential element in modeling a wide variety of natural and human-induced processes, and the sums of heavy tailed rvs represent a particularly important construction in such models. Oriented toward both geophysical and statistical audiences, this paper discusses the appearance of the Pareto law in seismology and addresses the problem of the statistical approximation for the sums of independent rvs with common Pareto distribution F(x)=1 – x– for 1/2 < < 2. Such variables have infinite second moment which prevents one from using the Central Limit Theorem to solve the problem. This paper presents five approximation techniques for the Pareto sums and discusses their respective accuracy. The main focus is on the median and the upper and lower quantiles of the sums distribution. Two of the proposed approximations are based on the Generalized Central Limit Theorem, which establishes the general limit for the sums of independent identically distributed rvs in terms of stable distributions; these approximations work well for large numbers of summands. Another approximation, which replaces the sum with its maximal summand, has less than 10% relative error for the upper quantiles when < 1. A more elaborate approach considers the two largest observations separately from the rest of the observations, and yields a relative error under 1% for the upper quantiles and less than 5% for the median. The last approximation is specially tailored for the lower quantiles, and involves reducing the non-Gaussian problem to its Gaussian equivalent; it too yields errors less than 1%. Approximation of the observed cumulative seismic moment in California illustrates developed methods. 相似文献
19.
We investigate numerically apparent multi‐fractal behavior of samples from synthetically generated processes subordinated to truncated fractional Brownian motion (tfBm) on finite domains. We are motivated by the recognition that many earth and environmental (including hydrological) variables appear to be self‐affine (monofractal) or multifractal with Gaussian or heavy‐tailed distributions. The literature considers self‐affine and multifractal types of scaling to be fundamentally different, the first arising from additive and the second from multiplicative random fields or processes. It has been demonstrated theoretically by one of us that square or absolute increments of samples from Gaussian/Lévy processes subordinated to tfBm exhibit apparent/spurious multifractality at intermediate ranges of separation lags, with breakdown in power‐law scaling at small and large lags as is commonly exhibited by real data. A preliminary numerical demonstration of apparent multifractality by the same author was limited to Gaussian fields having nearest neighbor autocorrelations and led to rather noisy results. Here, we adopt a new generation scheme that allows us to investigate apparent multifractal behaviors of samples taken from a broad range of processes including Gaussian with and without symmetric Lévy and log‐normal (as well as potentially other) subordinators. Our results shed new light on the nature of apparent multifractality, which has wide implications vis‐a‐vis the scaling of many hydrological as well as other earth and environmental variables. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
20.
The simplest form of input required for step-by-step simulation of response of a structure to a gusty wind is a stochastic process having Gaussian distribution and a specified power spectrum. Methods for generating such a process are described in detail, and the extension outlined for generating a number of partially correlated input processes having specified power spectra and cross-spectra. 相似文献