Indicators of critical point behavior prior to rock failure inferred from pre-failure damage   总被引：4，自引：0，他引：4  

Xinglin Lei  Takashi Satoh   《Tectonophysics》2007,431(1-4):97

To investigate possible indicators of critical point behavior prior to rock failure, the statistical properties of pre-failure damage were analyzed based on acoustic emission events (AE) recorded during the catastrophic fracture of typical rock samples under differential compression. AEs were monitored using a high-speed 32-channel waveform recording system. Time-dependent statistics, including the energy release rate, b-value of the magnitude–frequency distribution, fractal dimension and spatial correlation length (SCL) of the AE hypocenters were calculated for each data set. Each parameter is a function of the time-to-failure and thus can be treated as an indicator of the critical point. It is clear that the pre-failure damage evolution prior to catastrophic failures in several common rock-types is generally characterized by: 1) accelerated energy release, 2) a decrease in fractal dimension and SCL with a subsequent precursory increase, and 3) a decrease in b-value from  1.5 to  0.5 for hard rocks, and from  1.1 to  0.8 for soft rocks such S–C cataclasite. However, each parameter also reveals more complicated temporal evolution due to either the heterogeneity of the rock mass or the micro-mechanics of shear fracturing. This confirms the potential importance of integrated analysis of two or more parameters for successfully predicting the critical point. The decreasing b-value and increasing energy release may prove meaningful for intermediate-term prediction, while the precursory increase in fractal dimension and SCL may facilitate short-term prediction.  相似文献   

水系结构的分形和分维——Horton水系定律的模型重建及其参数分析   总被引：26，自引：3，他引：26  

陈彦光  刘继生 《地球科学进展》2001,16(2):178-183

基于标准分形水系等级序列的镜象对称性，重建水系构成定律：从Horton第一，第二定律出发，导出关于河流长度与位序关系的三参数Zipf模型，从Horton第二，第三定律出发，导出广义的Hack定律；从Horton第一，第三定律出发，导出关于河流长度一流域面积关系的异速生长方程，根据上述数学变换结果建立了水系分维方程式，澄清了不同空间，不同类型的各种维数之间的数理关系。  相似文献   

The hurst effect and its implications for extrapolating process rates     

M. J. Kirkby 《地球表面变化过程与地形》1987,12(1):57-67

In long-term records of climatic or hydrological events, persistent periods of high and low values are measured by the ‘rescaled range’, which is defined for a sequence of n consecutive values. As n increases the rescaled range for historic sequences increases as n^H for 0·5 < H < = 1. This is the Hurst effect. Sequences of independent random events give H = 0·5, while sequences in which the values are successive positions of a random walk (i.e. the sum of independent events) give H = 1. Intermediate values of H may be obtained from fractal sequences, from sequences with a steadily changing mean, or through a storage model. In all but the fractal case H exceeds 0·5 for a time related to the duration of the changing mean or the response time of the store. An exponential storage model has been explored in some detail. Storage models have the advantage of offering a plausible physical mechanism for persistence. Analysis of simulated sequences shows that the Hurst effect is evident for about 30 x the response time of the store, so that relatively modest store sizes are enough to explain observed Hurst effects over available periods of record. Comparison with empirical values shows that high H values seem to be associated with large physical stores. Whether the Hurst effect is due to storage effects or climatic or other change imposed from outside, the effect on longterm process rates is strong. Short-term measurements of process rates show compressed variances and simple extrapolation is likely to produce large errors. If it is assumed that long-term rates are strongly influenced by climatic variables, then measurements may be used to obtain parameters of a climatic model for differences in process rates. Errors in extrapolation will be least where the model has a sound physical basis. A first implication for magnitude and frequency distributions is that the sequence of events may be as important as their distribution over time in determining process impact. A second conclusion is that the geomorphic history of an area is inevitably dominated by a sequence of larger and larger events receding into the past, and that the Hurst exponent over geologic time-spans measures the extent of that domination.  相似文献   

The privilege as the cause of power distributions in geophysics     

Zbigniew Czechowski 《Geophysical Journal International》2003,154(3):754-766

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Fractal behavior in space and time in a simplified model of fluvial landform evolution     

Jon D. Pelletier   《Geomorphology》2007,91(3-4):291

Two general approaches have been applied to understanding the fractal structure of fluvial topography: (1) deterministic, process-based models, and (2) stochastic partial differential equations (PDE). Deterministic models reproduce the fractal behavior of fluvial topography but have two limitations: they often underestimate the amount of lateral valley and ridge migration that occurs in nature, and the complexity has made it difficult to identify the precise origin of fractal behavior in fluvial landscapes. The simplicity of stochastic PDE models has made them useful for investigating fractal behavior, but they incorrectly suggest that fractal behavior is only possible with stochastic forcing. In this paper I investigate whether simplified, deterministic PDE models of landform evolution also exhibit fractal behavior and other features of complexity (i.e. deterministic chaos). These models are based on the KPZ equation, well known in the physics literature. This equation combines diffusion (i.e. hillslope processes) and nonlinear advection (i.e. bedrock or alluvial channel incision). Two models are considered: (1) a deterministic model with uniform erodibility and random initial topography, and (2) a deterministic model with random erodibility and uniform initial topography. Results illustrate that both of these deterministic models exhibit fractal behavior and deterministic chaos. In this context, chaotic behavior means that valley and ridge migration and nonlinear amplification of small perturbations in these models prevent an ideal steady state landscape from ever developing in the large-system limit. These results suggest that fractal structure and deterministic chaos are intrinsic features of the evolution of fluvial landforms, and that these features result from an inverse cascade of energy from small to large wavelengths in drainage basins. This inverse cascade differs from the direct cascade of three-dimensional turbulence in which energy flows from large to small wavelengths.  相似文献   

Fractal approach in modelling of earthquakes     

V. V. Silberschmidt 《International Journal of Earth Sciences》1996,85(1):116-123

A model for an earthquake simulation is proposed with the use of a fractal approach. Multiple generation and coalescence of shear faults in stochastic brittle media (modelled as a 2d lattice) are considered to be a source of seismicity. Dynamics of local failure events are governed by accumulation of shear defects, described in terms of continuum damage mechanics. Fractal tree structure is used as an analogue for a stress redistribution process. Energy release, caused by the non-uniform failure, is studied for a non-conservative case. Effect of various types of rocks' properties stochasticity on energy release dynamics is analysed with a utilization of multifractal formalism. The latter is shown to be an additional method for seismicity characterization.  相似文献   

海城地震前后地震活动的广义分维变化     

王海涛  朱令人 《内陆地震》1991,5(3):202-205

应用广义分维的概念于地震活动时间分形的研究可避免确定无标度区的困难。海城地震前后地震活动的广义分维D_o(ε)的变化表明,时间标度区间为2—16天时,D_o(ε)的变化可以反映大震酝育过程中地震时间分布的不均匀性,并表现出震前降维的前兆变化特征。  相似文献   

Geomorphic application of the hausdorff-besicovich dimension     

Samuel I. Outcalt  Mark A. Melton 《地球表面变化过程与地形》1992,17(8):775-787

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Space–time correlation of earthquakes     

Patrizia Tosi  Valerio De Rubeis  Vittorio Loreto  Luciano Pietronero 《Geophysical Journal International》2008,173(3):932-941

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Simulating geophysical models through fractal algorithms          下载免费PDF全文

Michele De Stefano 《Geophysical Prospecting》2018,66(1):26-33

I present an algorithm, borrowed from the computer graphics industry, that is able to efficiently and effectively simulate pseudo‐realistic topographies and three‐dimensional geophysical models. It has been widely exploited in the movie industry for generating artificial landscapes and for simulating the surface of planets. The geophysical applications are manifold: simulation for testing inversion algorithms, interpolation, and upscaling are only some of the possibilities.  相似文献