Modeling aggregate size distribution of eroded sediment resulting from rain-splash and raindrop impacted flow processes

Soil susceptibility to detachment and transport sub-processes of erosion is generally controled by the aggregate breakdown mechanism. Measuring particle size and aggregation to the estimate erodibility potential of soils is important under erosive rainfall conditions. The Aggregate Size Distribution (ASD) is one of the most important determinants of soil structure along with soil organic matter content for describing the efficiency of applied, sustainable management strategies. This study aimed to compare the performances of three different aggregate size distribution models to predict the characteristic aggregate size parameter (median diameter, D50) for eroded sediment from interrill erosion processes of Rain- Splash Transport (RST) and Raindrop Impacted Flow Transport (RIFT). The ASDs of 1143 collected sediment samples from the RST and RIFT processes were measured and modeled by the Log-normal, Fractal, and Weibull approaches. The D50 value, as a characteristic parameter for aggregate size distributions, derived from the cumulative ASD curve was compared for soils from different land use types and different slope and rainfall intensity conditions. The performance of each model was evaluated using the Mean Square Error (MSE) and Coefficient of Determination (R^2). The Weibull approach was the most accurate model showing the best fit with the lowest MSE values (0.0002 ≤MSE≤ 0.0048) and having the greatest R2 values (0.936≤ R^2≤ 0.998) when compared with the Log-normal and Fractal models. Herewith, for semi-arid land use and soil, specific shape and scale parameters for the Weibull distribution, the respective ASDs were successfully re-generated for modeling the eroded sediment of the simulated RST and RIFT interill processes.     

震前自然电场的前兆及其可能机理

研究了震前自然电场的前兆及礤可能机理。主要结论：（１）５．４￣６．２级地震在１５０￣２００ｋｍ,７．０￣７．９级地震在２５０ｋｍ范围内自然电场出现前兆;（２）过滤电场、电化学电场、土体受压变密和机电转换可能是自然电场的前兆机理。     

Statistical distribution of nonlinear random wave height

1 Introduction The probability distribution of ocean wave element is one of the results of application of random process theory to the ocean wave study. A great amount of outcome has obtained in this field[1,2]. In fact, a great deal of research on linear…     

Using the Weibull distribution to improve the description of riverine wood loads

Reporting uncertainty in environmental measurements and estimates is important for cross‐comparison and inter‐comparison of sites and other spatial units. One such measure is the load of large in‐stream wood in river systems. In this paper we propose the use of the Weibull distribution to describe the central tendency and variability of wood loads along a river reach. We illustrate the link between the average wood load and the central tendency or scale parameter of the Weibull distribution. The shape of the Weibull distribution is strongly related to the ability of rivers to transport and rearrange the wood in a reach. We use six Victorian rivers to test the fit of the Weibull distribution, showing that the Weibull is a useful and flexible distribution that provides common reporting metrics useful for future studies. Using common reporting metrics provides a stronger tool for comparisons of wood loads between rivers and with reaches. Copyright © 2016 John Wiley & Sons, Ltd.     

Statistical property of candidate earthquake precursors and its apparent focal mecha- nism dependence

Introduction Increasing evidences show that the properties of candidate earthquake precursors seem to befocal mechanism dependent (Tsuruoka, et al, 1995; Reasenberg, 1999; Wan, et al, 2002). Test ofearthquake precursors without the classification of earthquakes could be misleading (Wu, 1999,Nature debates, http://helix.nature.com/debates/). In this paper we use the reported earthquakeprecursors for some earthquakes in China (ZHANG, 1988; 1990a, b; 1999; 2000; CHEN, 2002a, b;2003) to…     

Statistical property of candidate earthquake precursors and its apparent focal mechanism dependence

Statistical properties of reported earthquake precursors show apparent focal mechanism dependence. Intensity of anomaly is described by the ‘anomaly ratio’ as defined by the number of stations/items reporting anomalies before the target earthquake over the number of stations/items in operation around the target earthquake. Variation of the ‘anomaly ratio’ with the magnitude of the target earthquake was studied for dip-slip earthquakes all over China, strike-slip earthquakes in eastern China, and strike-slip earthquakes in western China, respectively. It is observed that for strike-slip earthquakes, the ‘anomaly ratio’ increases linearly with the magnitude of the target earthquake, while earthquakes in eastern China and western China have different slopes. For dip-slip earthquakes, however, the ‘anomaly ratio’ has no statistically significant change with the magnitude of the target earthquake. Limited data imply that the ‘anomaly ratio’ seems proportional to the apparent stress of the target earthquake. The result might be heuristic for the analysis of candidate earthquake precursors. Foundation item: National Natural Science Foundation of China (40274013) and MOST Project (2001BA601B02). Contribution No.04FE1020, Institute of Geophysics, China Earthquake Administration.     

中国大陆地震空间分布模型检验

本文以中国大陆地震目录为基础资料,以泊松模型为零假设模型,并将Neyman-Scott空间丛集过程的各子模型设为检验模型,采用K-function 点过程分析法和最大似然估计法计算各模型参数,并以AIC准侧判定模型的拟合优度,来检验中国大陆地震空间分布模型.检验结果表明：泊松模型的拟合优度最差,说明地震在空间的分布不是完全随机的;广义Thomas模型的拟合优度最好,说明地震的空间分布是丛集的,可用由两个高斯核组成的广义Thomas模型较好地描述.研究结果还表明,同一研究区内,采用不同时段具有不同最小完整起始震级的地震目录计算得到的地震空间分布的丛集尺度几乎不变,这意味着地震空间丛集尺度不受小地震的控制,且可能与研究区的断层规模有关.     

2008年MS6.1攀枝花地震震源区多参数结构成像及发震机制研究

通过联合反演123,053个P、Pn、Pg震相和100,176个S、Sn、Sg震相数据,获得了2008年M_S6.1攀枝花地震震源及其周边区域的高分辨率三维纵、横波速度(V_P,V_S)和泊松比(σ)图像.结合研究区域地壳应力数据综合分析发现,攀枝花地震发生在高-低纵、横波速度转换带,并且在震源下方存在一显著的低V_S和高σ异常体延伸至下地壳.本研究认为,该构造特征主要是由于西侧坚硬的川滇菱形块体对来自深部流体或熔融物质具有一定的阻挡作用,绝大部分流体或熔融物质通过断裂带向东南侧的块体内部迁移,造成断裂带两侧块体的岩石物理属性差异较大所致.研究结果表明,攀枝花地震发生在剪切应力较强的元谋—绿汁江断裂带上,震源下方的流体或部分熔融物质被挤入至震源的断层或裂隙中,增加了震源区岩石的流体应力,降低了横波速度(V_S)、增加了岩石的泊松比(σ).我们推测,流体侵入在攀枝花地震形成上扮演了重要角色,来自于青藏高原下地壳的大量的流体或部分熔融物质被挤入震源区岩体的断层或裂缝中,这一过程增加了震源区的孔隙流体压力、减弱岩石的机械强度,同时岩石的静摩擦力增加,导致容易引起岩体脆性形变,从而诱发地震.     

Statistical distribution of surface elevation for the fourth order nonlinear random sea waves

Based upon the nonlinear model of random sea waves, the statistical distribution of wave surface elevation exact to the fourth order is derived as the truncated Gram-Charlier series,by calculating directly each order moment. The phenomenon found by Huanget al. that the agreement between observed data and investigated series deteriorates much more when the series is kept to λ₈ is explained. The effect of the approximation order on the truncation of series and the determination of coefficients is investigated. For themth order approximation, the derived series is truncated atH _3m-3 with the absence of H_3m-4, and the coefficients ofH _3m-3 andH _3m-6 are connected by a simple algebraic relation. Project supported by the National Natural Science Foundation of China.     

地震带应力分布的震源机制解程序

在MapSIS里用震源机制解研究地震带的程序,只能作些剖面图和三维立体图,做震源机制解靠震相的初动符号,但是如何运用已有的震源机制解资料来画应力分布图等没有提供,不能满足我们的实际需要,为了在实际工作中更好地利用震源机制解分析地震活动性,我们编写了这个程序,利用本文程序可以做到,在任何区域、任何深度内地震带的应力分布情况及地震震源机制解的玫瑰图、地震的节面图、断层的性质。提供了行之有效的程序,对日常的地震活动性分析有很大的帮助。     

Two-phase flow properties of a horizontal fracture: The effect of aperture distribution

A systematic numerical method has been presented to investigate the constitutive relationships between two-phase flow properties of horizontal fractures and aperture distributions. Based on fractal geometry, single rough-walled fractures are generated numerically by modified successive random addition (SRA) method and then aperture distributions with truncated Gaussian distribution are formed by shear displacement between lower and upper surfaces. (The truncated Gaussian distribution is used to describe aperture evolution under different normal stresses.) According to the assumption of two-dimensional porous media and local parallel plate model, invasion percolation approach is employed to model the two-phase flow displacement (imbibition) in generated horizontal fractures, in which capillary forces are dominant over viscous and gravity forces. For truncated Gaussian distributions, constitutive relationships from numerical simulation are compared to closed-form relationships and a good agreement is obtained. The simulation results indicate strong phase interference with the sum of two phase relative permeability values being less than one in the intermediate saturations. It is found that fracture properties related to residual saturations depend on spatial correlation of aperture distributions. Based on the simulation results, we proposed an empirical relationship between the fracture residual-saturation-rated parameters and the corresponding aperture distributions.     

Statistical probability distribution of snow depth at the model sub‐grid cell spatial scale

Comprehensive snow depth data, collected using georadar and hand probing, were used for statistical analyses of snow depths inside 1 km grid cells. The sub‐grid cell spatial scale was 100 m. Statistical distribution functions were found to have varying parameters, and an attempt was made to connect these statistical parameters to different terrain variables. The results showed that the two parameters mean and standard deviation of snow depth were significantly related to the sub‐grid terrain characteristics. Linear regression models could explain up to 50% of the variation for both of the snowcover parameters mentioned. Copyright © 2004 John Wiley & Sons, Ltd.     

On the physical essence of the b value for AE of rock tests and natural earthquakes in terms of fracture mechanics

The problem of physical essence of theb value forAE of rock tests and natural earthquakes has been a controversial topic during the past two decades. In the present paper the order and energy of each microfracturing of the microcrack system existing in a rock specimen is discussed from the viewpoint of fracture mechanics, then the whole series ofAE and subsequently the value ofb are determined. The order of microfracturing depends on the parametersKei/Kci whereKei is the effective stress intensity factor of thei-th microcrack andKci is the fracture toughness in the site of thei-th crack. The energy of eachAE can be expressed asηi ∫ loili Gids whereG is the energy release rate of microcarck,loi andli are the original and final crack lengths respectively andηi is the emanating efficiency for thei-th crack. If we assume that the distribution density function of microcrack lengthl isp(l)=Bl−v whereB andγ are constants, then the expressionb=3γ/2 can be deduced. Hence, we have come to the conclusion that the value ofb mirrors essentially the “crack-system-configuration” of the material, which means the distribution of the sizes, shapes and orientations of microcracks over space as well as the distribution of the other relevant physical parameters such as fracture toughness, friction coefficient, etc. Our conclusion is somewhat similar in character to Mogi’s. He concluded thet the heterogeneity of the material plays the most important role in determining the value ofb. The term heterogeneity of course covers the idea of “crack-system-configuration, but we think that our view has a little bit deeper insight to the problem than that of Mogi. This subject is supported by Chinese Joint Seismological Science Foundation.     

Predicting return periods of hydrological droughts using the Pearson 3 distribution: a case from rivers in the Canadian prairies

Abstract

The standardized series of monthly and weekly flow sequences, referred to as standardized hydrological index (SHI) series, from five rivers in the Canadian prairies were subjected to return period (T_r) analysis of drought length (L). The SHI series were truncated at drought probability levels q ranging from 0.5 to 0.05 with the intention of deducing drought events and corresponding drought lengths. The values of L were fitted to the Pearson 3, the gamma (2-parameter), the exponential (1-parameter), the Weibull 3 and the Weibull (2-parameter) probability density functions (pdfs). A priori assignment of one week or one month for the location parameter in the Pearson 3 pdf proved logical and also facilitated the rapid estimation of other parameters using either the method of moments or the method of maximum likelihood. The Pearson 3 turns out to be the most suitable pdf to describe and to estimate return periods of drought lengths. At the monthly and weekly time scales, it was inferred that the sample size (T, months or weeks) of SHI series could be treated equivalent to the return period of the largest recorded drought length. At the annual time scale, however, the sample size (T, years) should be modified using either the Hazen or the Gringorten plotting position formula to reflect the actual return period of the largest recorded drought length in years.

Editor D. Koutsoyiannis; Associate editor E. Gargouri     

Statistical distribution of nonlinear random wave height in shallow water

Here we present a statistical model of random wave,using Stokes wave theory of water wave dynamics,as well as a new nonlinear probability distribution function of wave height in shallow water.It is more physically logical to use the wave steepness of shallow water and the factor of shallow water as the parameters in the wave height distribution.The results indicate that the two parameters not only could be parameters of the distribution function of wave height but also could reflect the degree of wave heigh...     

库仑应力变化与余震对应关系的初步探讨——以集集地震为例

本文以集集地震为例,讨论了在多个小断层的位错模型,分层地质结构这种更加接近实际的情况下的库仑应力变化,计算结果表明有必要考虑这些符合实际的模型.本文分别讨论了走滑断层上库仑应力变化与走滑地震、逆冲断层上库仑应力变化与逆冲地震空间分布的对应关系,计算结果表明集集地震所引起的库仑应力变化确实有利于本地区余震的发生.     

Spatial distribution and focal mechanism solutions of the Wenchuan earthquake series: Results and implications

We relocate the spatial distribution of the devastating 12 May 2008 Wenchuan earthquake and its aftershocks. The relocation database is obtained from 89 stations deployed by the China Earthquake Administration, including 54 525 seismograms from 1 376 local earthquakes over M_S 3.5 between 12 May 2008 and 3 August 2008. The cross-correlation technique used in this paper has greatly improved the relocation precision by giving much more accurate P-wave differential travel-time measurements than those obtained from routinely picked phase onsets. At the same time, we pick P-wave polarity observations of the Wenchuan earthquake series (hereafter referred to as WES) from 1 023 stations in China and 59 IRIS (incorporated Research Institutions of Seismology) stations. Then, employing a newly developed program CHNYTX, we obtain 83 well-determined focal mechanism solutions (hereafter referred to as FMSs). Based on spatial distribution and FMSs of the WES, we draw following conclusions: (1) The region near the main shock exhibits a buried low-angle northwest-dipping seismic zone with the main shock at its upper end and two conjugated seismic zones dipping southeast with roughly equal dip-angle; (2) The compressional directions of all kinds of FMSs of the WES are subhorizontal, which reflects the dominant stress in this area is compressional; (3) The principal compressional direction of the regional stress around Wenchuan is roughly perpendicular to the strike of Beichuan-Yingxiu fault, while around Qingchuan it is roughly parallel to the strike of Qingchuan fault. In intermediate part of the Longmenshan area, the principal compressional direction of the stress should be in-between; (4) The possibly existed molten materials in the lower crust of Songpan-Garze terrain have small contribution to the local stress state in Longmenshan area. The listric geometries of the Longmenshan faults most probably resulted from subhorizontal compression along NW-SE direction in history.     

Spatial distribution and focal mechanism solutions of the Wenchuan earthquake series:Results and implications

We relocate the spatial distribution of the devastating 12 May 2008 Wenchuan earthquake and its aftershocks.The relocation database is obtained from 89 stations deployed by the China Earthquake Administration,including 54 525 seismograms from 1 376 local earthquakes over MS3.5 between 12 May 2008 and 3 August 2008.The cross-correlation technique used in this paper has greatly improved the relocation precision by giving much more accurate P-wave differential travel-time measurements than those obtained from ...     

Field experiments constraining the probability distribution of particle travel distances during natural rainstorms on different slope gradients

Rain splash erosion is an important soil transport mechanism on steep hillslopes. The rain splash process is highly stochastic; here we seek to constrain the probability distribution of splash transport distances on natural hillslopes as a function of hillslope gradient and total precipitation depth. Field experiments were conducted under natural precipitation events to observe splash travel on varying slope gradients. The downslope fraction of splash transport on 15°, 25° and 33° gradients were 85%, 96% and 96%, respectively. Maximum splash transport (L_max) was related to the rain splash detachment of soil particles and slope gradient. An empirical relationship of L_max to the precipitation depth and gradient was obtained; it is linearly proportional to hillslope gradient and logarithmically related to precipitation depth. Measured splash distances were calibrated to the fully two‐dimensional (2D) model of splash transport of Furbish et al. (Journal of Geophysical Research 112 : F01001, 2007) that is based on the assumption that radial splash distances are exponentially distributed; calibrated values of mean splash transport distances are an order of magnitude greater than those previously determined in a controlled laboratory setting. We also compared measured data with several one‐dimensional (1D) probability distributions to asses if splash transport distances could be better explained by a heavy‐tailed probability distribution rather than an exponential probability distribution. We find that for hillslopes of 15° and 25°, although a log‐normal probability distribution best describes the data, we find its likelihood is nearly indistinguishable from an exponential distribution based on computing maximum likelihood estimators for all 1D distributions (exponential, log‐normal and Weibull). At 33°, however, we find stronger evidence that measured travel distances are heavy‐tailed. Copyright © 2011 John Wiley & Sons, Ltd.