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Fractals are famous for their self‐similar nature at different spatial scales. Similar to fractals, solutions of scale invariant processes are self‐similar at different space–time scales. This unique property of scale‐invariant processes can be utilized to translate the solution of the processes at a much larger or smaller space–time scale (domain) based on the solution calculated on the original space–time scale. This study investigates scale invariance conditions of kinematic wave overland flow process in one‐parameter Lie group of point transformations framework. Scaling (stretching) transformation is one of the one‐parameter Lie group of point transformations and it has a unique importance among the other transformations, as it leads to the scale invariance or scale dependence of a process. Scale invariance of a process yields a self‐similar solution at different space–time scales. However, the conditions for the process to be scale invariant usually dictate various relationships between the scaling coefficients of the dependent and independent variables of the process. Therefore, the scale invariance of a process does not assure a self‐similar solution at any arbitrary space and time scale. The kinematic wave overland flow process is modelled mathematically as initial‐boundary value problem. The conditions to be satisfied by the system of governing equations as well as the initial and boundary conditions of the kinematic wave overland flow process are established in order for the process to be scale invariant. Also, self‐similarity of the solution of the kinematic wave overland flow under the established invariance conditions is demonstrated by various numerical example problems. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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深层地震勘探为地震波传播理论研究提出了新的挑战和机遇。深层地震勘探的主要难点是上覆层的影响甚大,使后续的处理有隔靴挠痒之感,必须应用波场延拓消除上覆层影响。深层波速的高速性和横向不均匀性决定了大角散射和弹性波处理方法的重要性。本文具体评述了深层地震勘探的主要方法对策,深入探讨了波场延拓的李群方法和弹性反演的某些问题,目的在于为深化深层地震提供新的研究手段和方法。 相似文献
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波动方程地震偏移成像方法的现状与进展 总被引:15,自引:19,他引:15
综述了波动方程地震偏移成像方法研究的现状,指出了各种算法的问题和解决方案;给出了相空间小波分析步进算法偏移成像以及保幅保结构李群算法偏移成像的最新进展;对波动方程偏移成像发展趋势进行展望。 相似文献
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For successful snowdrift modelling, measured drift shapes should be geometrically similar to full-scale shapes and develop at rates that scale in a known manner. Consensus exists on most modelling methods and the similitude requirements needed to meet these objectives. A notable exception is the manner to scale drift development rates. A rationale is presented for rate scaling based on an independent model and prototype mass transport measurements. This approach is validated by comparing the rate of drift development for a model Wyoming snow fence with corresponding field data. This method yields excellent agreement, whereas the alternatives differ substantially. 相似文献
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地震活动的随机标度和非线性标度律 总被引:1,自引:0,他引:1
把地震作为一个复杂系统,研究了地震活动的随机性质.当不考虑震级范围时,全球地震活动、人震的余震和区域震群均有以幂次律为特征的长尾现象.地震的强度由震级确定,具有一特定震级的地震可形成一个地震活动系列,很多这样的地震活动系列就形成具有各种震级的地震的集合.不同地震系列间的统计特征由随机标度来表征,随机标度表明了由地震震级分类的不同地震系列间统计时刻的标度关系.为了统一地方、区域和全球地震活动性的统计特性,引入了非线性标度率. 相似文献
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In this paper, we propose a nearly analytic exponential time difference (NETD) method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations (ODEs). Then, the converted ODE system is solved by the exponential time difference (ETD) method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in multilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Marmousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods. 相似文献
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Effectively managing groundwater relies heavily on estimating the amount of precipitation that may infiltrate the subsurface and supply groundwater. In this study, we present a novel estimation method based on a stochastic approach to evaluate the quantity of precipitation that may recharge groundwater. The precipitation recharge coefficient is also investigated based on an unconfined aquifer with an unbound, infinitely extended boundary condition. Moreover, a spectrum's relationship to the precipitation and groundwater level variation is also derived. The precipitation recharge coefficient can be obtained from the solution of the spectrum equation. Furthermore, sensitivity analysis is performed in order to determine the key variable on the precipitation recharge coefficient. Analysis results indicate that the location of an observation well affects the estimated precipitation recharge coefficient. If the precipitation recharge area is large enough, the precipitation recharge coefficient becomes insensitive to the location of the observation well. The spectrum's relationship between the precipitation recharge and groundwater level variation is also applied when estimating the precipitation recharge coefficient upstream of the Cho‐Shui River alluvial fan. According to those results, the precipitation recharge coefficient is 0·03 and the amount of groundwater recharge from precipitation is 35 million tons of water annually upstream of the Cho‐Shui River alluvial fan. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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Gradient-based similarity in the atmospheric boundary layer 总被引:2,自引:0,他引:2
Zbigniew Sorbjan 《Acta Geophysica》2008,56(1):220-233
The “flux-based” and “gradient-based” similarity in the stable boundary layer and also in the interfacial part of the convective
boundary layer is discussed. The stable case is examined on the basis of data collected during the CASES-99 experiment. Its
interfacial counterpart is considered in both the quasi-steady (mid-day) and non-steady states, utilizing the results of large-eddy
simulations.
In the stable regime, the “gradient-based” approach is not unique and can be based on various master length scales. Three
local master length scales are considered: the local Monin-Obukhov scale, the buoyancy scale, and the Ellison scale. In the
convective “quasi-steady” (mid-day) case, the “mixed layer” scaling is shown to be valid in the mixed layer and invalid in
the interfacial layer. The temperature variance profile in non-steady conditions can be expressed in terms of the convective
temperature scale in the mixed layer. The analogous prediction for velocity variances is not valid under non-steady conditions. 相似文献
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Abstract Unconfined aquifer parameters, viz. transmissivity, storage coefficient, specific yield and delay index from a pumping test are estimated using the genetic algorithm optimization (GA) technique. The parameter estimation problem is formulated as a least-squares optimization, in which the parameters are optimized by minimizing the deviations between the field-observed and the model-predicted time–drawdown data. Boulton's convolution integral for the determination of drawdown is coupled with the GA optimization technique. The bias induced by three different objective functions: (a) the sum of squares of absolute deviations between the observed and computed drawdown; (b) the sum of squares of normalized deviations with respect to the observed drawdown; and (c) the sum of squares of normalized deviations with respect to the computed drawdown, is statistically analysed. It is observed that, when the time–drawdown data contain no errors, the objective functions do not induce any bias in the parameter estimates and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the case considered, defining the objective function as the sum of the squares of absolute deviations between the observed and simulated drawdowns resulted in the best possible estimates. A comparison of the GA technique with the curve-matching procedure and a conventional optimization technique, such as the sequential unconstrained minimization technique (SUMT), is made in estimating the aquifer parameters from a reported field pumping test in an unconfined aquifer. For the case considered, the GA technique performed better than the other two techniques in parameter estimation, with the sum-of-squares errors obtained from the GA about one fourth of those obtained by the curve matching procedure, and about half of those obtained by SUMT. Citation Rajesh, M., Kashyap, D. & Hari Prasad, K. S. (2010) Estimation of unconfined aquifer parameters by genetic algorithms. Hydrol. Sci. J. 55(3), 403–413. 相似文献
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K. B. Broberg 《Pure and Applied Geophysics》2006,163(9):1867-1879
Although mode I and mode II crack propagation show many similarities, in particular when analysed by linear elastic fracture
mechanics, they differ significantly in the micro-structural behaviour. These differences, which are clearly noticeable in
the fracture surface morphology, lead to fundamental differences in the macroscopic behaviour. Thus, mode II crack expansion
under remote loading, appears to obey micro-structural scaling laws, implying that the dimensions of the process region stay
essentially constant during crack expansion, rather than increasing with crack length. Therefore, expanding mode II cracks
can almost reach the Rayleigh velocity, and actually also intersonic velocities. An expanding mode I crack, on the other hand,
seems to obey continuum scaling laws, implying that the dimensions of the process region increase in proportion to crack length,
leading to self-similar crack expansion at a velocity significantly below the Rayleigh speed and dependent on the remote load. 相似文献
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Five tracer experiments have been performed in a coarse‐textured soil near the new main airport at Gardermoen, Norway. In two lysimeter walls, 30 and 40 measuring points form the basis for spatial moment calculations. Although experiments were performed under different meteorological conditions (autumn and snowmelt) and at two different sites, the ratios of centres of vertical mass over cumulative infiltration were of the same order of magnitude, indicating a gravity‐dominated flow. Two‐dimensional transport simulations with SUTRA (Voss, 1984), with a priori estimated input parameters and random fields of soil hydraulic properties revealed a relatively good agreement with the experimental results. Three possible sources of heterogeneity affecting the vertical displacement of solute during snowmelt were identified: variability of soil physical properties, soil surface elevations and variability of ground frost during the melting period. To obtain accurate predictions, soil heterogeneity was the most important factor to characterize for the coarse‐textured soil under consideration. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
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A space-time envelope of minor seismicity related to major shallow earthquakes is identified from observations of the long-term Precursory Scale Increase () phenomenon, which quantifies the three-stage faulting model of seismogenesis. The envelope, which includes the source area of the major earthquake, is here demarcated for 47 earthquakes from four regions, with tectonic regimes ranging from subduction to continental collision and continental transform. The earthquakes range in magnitude from 5.8 to 8.2, and include the 24 most recent mainshocks of magnitude 6.4 and larger in the San Andreas system of California, the Hellenic Arc region of Greece, and the New Zealand region, together with the six most recent mainshocks of magnitude 7.4 and larger in the Pacific Arc region of Japan. Also included are the destructive earthquakes that occurred at Kobe, Japan (1995, magnitude 7.2), Izmit, Turkey (1999, magnitude 7.4), and W.Tottori, Japan (2000, magnitude 7.3). The space (A
P
) in the space-time envelope is optimised with respect to the scale increase, while the time (T
P
) is the interval between the onset of the scale increase and the occurrence of the earthquake. A strong correlation is found between the envelope A
P
T
P
and the magnitude of the earthquake; hence the conclusion that the set of precursory earthquakes contained in the envelope is intrinsic to the seismogenic process. Yet A
P
and T
P
are correlated only weakly with each other, suggesting that A
P
is affected by differences in statical conditions, such as geological structure and lithology, and T
P
by differences in dynamical conditions, such as plate velocity. Among other scaling relations, predictive regressions are found between, on the one hand, the magnitude level of the precursory seismicity, and on the other hand, both T
P
and the major earthquake magnitude. Hence the method, as here applied to retrospective analysis, is potentially adaptable to long-range forecasting of the place, time and magnitude of major earthquakes. 相似文献
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A method has been developed to simulate the long‐term migration of radionuclides in the near‐surface of a river catchment, following their release from a deep underground repository for radioactive waste. Previous (30‐year) simulations, conducted using the SHETRAN physically based modelling system, showed that long‐term (many decades) simulations are required to allow the system to reach steady state. Physically based, distributed models, such as SHETRAN, tend to be too computationally expensive for this task. Traditional lumped catchment‐scale models, on the other hand, do not give sufficiently detailed spatially distributed results. An intermediate approach to modelling has therefore been developed which allows flow and transport processes to be simulated with the spatial resolution normally associated with distributed models, whilst being computationally efficient.The approach involves constructing a lumped model in which the catchment is represented by a number of conceptual water storage compartments. The flow rates to and from these compartments are prescribed by functions that summarize the results from physically based distributed models run for a range of characteristic flow regimes. The physically based models used were, SHETRAN for the subsurface compartments, a particle tracking model for overland flow and an analytical model for channel routing. One important advantage of the method used in constructing the lumped model is that it makes down scaling possible, in the sense that fine‐scale information on the distributed hydrological regime, as simulated by the physically based distributed models, can be inferred from the variables in the lumped model that describe the hydrology at the catchment scale. A 250‐year flow simulation has been run and the down scaling process used to infer a 250‐year time‐series of three‐dimensional velocity fields for the subsurface of the catchment. This series was then used to drive a particle tracking simulation of contaminant migration. The concentration and spatial distribution of contaminants simulated by this model for the first 30 years were in close agreement with SHETRAN results. The remaining 220 years highlighted the fact that some of the most important transport pathways to the surface carry contaminants only very slowly so both the magnitude and spatial distribution of concentration in surface soils are not apparent over the shorter SHETRAN simulations. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
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Although for many years it was thought that amplitude scaling of acceleration time series to reach a target intensity did not introduce any bias in the results of nonlinear response history analyses, recent studies have showed that scaling can lead to an overestimation of deformation demands with increasing scale factors. Some studies have suggested that the bias can be explained by differences in spectral shape between the response spectra of unscaled and scaled records. On the basis of these studies, some record selection procedures assume that if records are selected using spectral-shape-matching procedures, amplitude scaling does not induce any bias on the structural response. This study evaluates if bias is introduced on lateral displacement demands and seismic collapse risk estimates even when spectral shape is carefully taken into consideration when selecting ground motions. Several single-degree-of-freedom and multiple-degree-of-freedom systems are analyzed when subjected to unscaled and scaled ground motions selected to approximately match the mean and the variance of the conditional spectrum at the target level of intensity. Results show that an explicit consideration of spectral shape is not enough to avoid a systematic overestimation of lateral displacement demands and collapse probabilities as the scale factor increases. Moreover, the bias is observed in practically all cases for systems with strength degradation and it increases with decreasing period and decreasing lateral strength relative to the strength required to remain elastic. Key reasons behind the bias are presented by evaluating input energy, causal parameters, and damaging pulse distributions in unscaled and scaled ground motion sets. 相似文献
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四川芦山7.0级强烈地震影响区域内有大量的砌体结构房屋,既有未采取任何抗震构造措施的非约束砌体结构,也有设置了圈梁和构造柱的约束砌体结构.文中首先简要讨论了本次地震强震动特性,表明其高频成分丰富,反应谱中低频部分衰减较快,是刚性结构和柔性结构地震破坏表现差别较大的原因之一;继而论文重点以现场震害调查资料为基础,总结了不同烈度区、不同类型砌体结构的震害特征;高烈度区不同类型砌体结构的震害程度和破坏比对比表明,约束砌体结构的抗震性能明显优于非约束砌体结构. 相似文献