Influence of crack distribution of rocks on P‐wave velocity anisotropy – a laboratory and field scale study‡

The purpose of this paper is the comparison of P‐wave velocity and velocity anisotropy, measured at different scales under laboratory and field conditions. A shallow seismic refraction survey with shot/receiver spacing of up to 10 m was carried out on a flat outcrop of lhertzolite in the southern part of the Balmuccia massif. Oriented rock samples were also obtained from the locality. The particular advantage of the laboratory method used is the possibility of measuring velocity in any direction under controlled conditions. Laboratory tests were made on spherical peridotite samples, 50 mm in diameter, by ultrasonic velocity measurements in 132 directions (meridian and parallel networks) under confining stress ranging from atmospheric to 400 MPa. The mean P‐wave velocity of the field and laboratory data differed by between 20–30%. In addition, P‐wave velocity anisotropy of 25% was detected in the field data. Whereas the anisotropy in the laboratory samples in the same orientation as the field surveys was less than 2%. This observed scaling factor is related to the different sampling sizes and the difference in frequencies of applied elastic waves. With an ultrasonic wavelength of 10 mm, laboratory samples represent a continuum. The field velocities and velocity anisotropy reflect the presence of cracks, which the laboratory rock samples do not contain. Three sub‐vertical fracture sets with differing strikes were observed in the field outcrop. Estimates of fracture stiffness from the velocity anisotropy data are consistent with other published values. These results highlight the difficulty of using laboratory velocity estimates to interpret field data.     

Geostatistical modelling of the Wasia aquifer in Central Saudi Arabia

Aquifers in sedimentary basins provide a regional domain for the spatial variabilities in geologic, hydrologic, geomorphologic and hydrochemical phenomena. Their study should account for this spatial variability within the study area prior to any formal modelling. A cumulative semivariogram scheme is adopted in this paper for the spatial variability, which is then incorporated with the kriging technique to provide maps of regional variation concerning variables such as storativity, transmissivity, piezometric levels, total dissolved solids and groundwater flow velocity. It is shown that the classical semivariogram models are not capable of accounting for the spatial variability of the Wasia aquifer. Comparison between the cumulative and classical semivariograms are given on the basis of hydrogeologic variables observed in the field. It is concluded, in general, that the cumulative semivariogram modelling of the spatial variability is more effective and yields realistic regional variables.     

Using geostatistics to elucidate temporal change in the spatial variation of aeolian sediment transport

Little is known about the spatial and temporal scales of variation in aeolian processes. Studies that aim to investigate surface erodibility often sample aeolian sediment transport at the nodes of a regular grid of arbitrary size. Few aeolian transport investigations have the resources to obtain sufficient samples to produce reliable models for mapping the spatial variation of transport. This study reports the use of an innovative nested strategy for sampling multiple spatial scales simultaneously using 40 sediment samplers. Reliable models of the spatial variation in aeolian sediment transport were produced and used for ordinary punctual kriging and stochastic simulated annealing to produce maps for several wind erosion events over a 25 km² playa in western Queensland, Australia. The results support the existence of a highly dynamic wind erosion system that was responding to possibly cyclic variation in the availability of material and fluctuations in wind energy. The spatial scale of transport was considerably larger than the small scale expected of the factors controlling surface erodibility. Thus, it appears that transport cannot be used as a surrogate of erodibility at the scale of this investigation. Simulation maps of transport provided considerably more information than those from kriging about the variability in aeolian sediment transport and its possible controlling factors. The proposed optimal sampling strategy involves a nested approach using ca 50 samplers. Copyright © 2003 John Wiley & Sons, Ltd.     

Evolution of crust- and core-dominated lava flows using scaling analysis

The distribution of clasts deposited around a volcano during an explosive eruption typically contoured by isopleth maps provides important insights into the associated plume height, wind speed and eruptive style. Nonetheless, a wide range of strategies exists to determine the largest clasts, which can lead to very different results with obvious implications for the characterization of eruptive behaviour of active volcanoes. The IAVCEI Commission on Tephra Hazard Modelling has carried out a dedicated exercise to assess the influence of various strategies on the determination of the largest clasts. Suggestions on the selection of sampling area, collection strategy, choice of clast typologies and clast characterization (i.e. axis measurement and averaging technique) are given, mostly based on a thorough investigation of two outcrops of a Plinian tephra deposit from Cotopaxi volcano (Ecuador) located at different distances from the vent. These include: (1) sampling on a flat paleotopography far from significant slopes to minimize remobilization effects; (2) sampling on specified-horizontal-area sections (with the statistically representative sampling area depending on the outcrop grain size and lithic content); (3) clast characterization based on the geometric mean of its three orthogonal axes with the approximation of the minimum ellipsoid (lithic fragments are better than pumice clasts when present); and (4) use of the method of the 50th percentile of a sample of 20 clasts as the best way to assess the largest clasts. It is also suggested that all data collected for the construction of isopleth maps be made available to the community through the use of a standardized data collection template, to assess the applicability of the new proposed strategy on a large number of deposits and to build a large dataset for the future development and refinement of dispersal models.     

甘肃北山花岗岩裂隙几何学特征研究及岩石质量初探

文中以甘肃北山花岗岩中发育的构造裂隙(主要指节理)为研究对象,通过野外裂隙调查,应用传统的概率统计方法与分形几何学理论,利用Mapinfo,ArcGIS平台进行裂隙几何学参数(方位、长度、密度等)的统计、计算和裂隙网络的空间结构分析,研究花岗岩岩体中裂隙的几何学特征。并以此为基础,对甘肃北山花岗岩岩体质量优劣进行初步评价。结果表明:在10～200cm范围内,裂隙网络是分形的;5个测点裂隙网络的分维值分别是1.636,1.548,1.596,1.724,1.604。分维数D不仅能刻画岩体中结构面发育的数量,而且能反映结构面在岩体中分布的均匀程度和交切方式。因此,可以表征岩体的质量优劣,对岩体质量进行分级。按照分维所划分的岩体质量分级,北山花岗岩属于裂隙较发育、岩体质量等级一般的岩体     

Modelling frequency-dependent seismic anisotropy in fluid-saturated rock with aligned fractures: implication of fracture size estimation from anisotropic measurements

Measurements of seismic anisotropy in fractured rock are used at present to deduce information about the fracture orientation and the spatial distribution of fracture intensity. Analysis of the data is based upon equivalent-medium theories that describe the elastic response of a rock containing cracks or fractures in the long-wavelength limit. Conventional models assume frequency independence and cannot distinguish between microcracks and macrofractures. The latter, however, control the fluid flow in many subsurface reservoirs. Therefore, the fracture size is essential information for reservoir engineers. In this study we apply a new equivalent-medium theory that models frequency-dependent anisotropy and is sensitive to the length scale of fractures. The model considers velocity dispersion and attenuation due to a squirt-flow mechanism at two different scales: the grain scale (microcracks and equant matrix porosity) and formation-scale fractures. The theory is first tested and calibrated against published laboratory data. Then we present the analysis and modelling of frequency-dependent shear-wave splitting in multicomponent VSP data from a tight gas reservoir. We invert for fracture density and fracture size from the frequency dependence of the time delay between split shear waves. The derived fracture length matches independent observations from borehole data.     

Tertiary strike-slip faulting in southeastern Mongolia and implications for Asian tectonics

Geologic maps have long portrayed the Late Cretaceous–Recent geologic history of southeastern Mongolia as tectonically quiescent. We present new data based on outcrop observations that indicate the northeast-trending East Gobi fault zone (EGFZ) was reactivated in the Cenozoic as a sinistral strike-slip fault system. Inversions of Cenozoic fault-slip data imply that faulting was associated with north–northwest subhorizontal shortening and east–northeast subhorizontal extension. We propose that faulting is Tertiary in age based on published interpretations of seismic reflection data which reveal that the mid-Cretaceous (∼100–95 Ma) unconformity is deformed by strike-slip faults, and based on field observation of strike-slip faults and fracture sets that cut Upper Cretaceous and Cenozoic strata but lack evidence for neotectonic activity. Published seismicity maps also appear to argue against significant Quaternary faulting within the EGFZ. These new data may lend credence to published models proposing a Middle Miocene or older kinematic linkage between the EGFZ and the Altyn Tagh fault in China. The recognition that the EGFZ has a history of left-lateral displacement in both the Early Mesozoic and Cenozoic means that currently available estimates of offset based on displaced Paleozoic rocks constrain total offset only. This reactivation history supports the notion that inherited lithospheric structures are important in controlling the location and, thus, modes of intracontinental deformation in Asia as a function of collisional far field effects and evolving boundary conditions of the Pacific margin.     

Spatial and temporal variability of Mehlich-1 extractable Fe, Mn and Zn over a rice field as a function of lime amendment

This study compares the effect of lime additions on the spatial variability of Fe, Mn and Zn extracted by Mehlich-1 during three different growth stages from an acid paddy soil, a Typic Plintacualf, in Corrientes, Argentina. Field trials were set up involving three treatments: control, without lime addition, plus two different dolomite doses of 625 and 1250 kg ha⁻¹. Soil was sampled first before sowing in aerobic conditions and then two more times in anaerobic conditions, i.e. by bunch formation and flowering. Ninety-six samples per plot were taken per lime treatment and sampling period, using a nested sampling strategy. Liming significantly increased extractable Fe and Mn, but decreased extractable Zn. The spatial variability of the studied soil properties was assessed using semivariogram analysis and examination of kriging maps. Models were fitted to experimental semivariograms for 27 data sets, i.e. three different soil properties, each of them sampled in three treatments and during three dates. Soil extractable and Fe, Mn and Zn exhibited a rather strong spatial dependence, as nugget variance was either null or a small proportion of the total variance, and this all over the three different study periods and for the three lime treatments. Geostatistical analysis provided insight into possible processes responsible of the observed spatial variability patterns within the rice soil. Kriging was useful in mapping soil micronutrient variability allowing identifying microrregions with high or low Fe, Mn and Zn concentrations, which showed the presence of small scale variability. These findings indicate the potential for applying the principles of precision agriculture to control spatiotemporal variability in rice fields.     

Upscaling of hydraulic conductivity and telescopic mesh refinement

Performance assessments of repositories for the underground disposal of nuclear fuel and waste include models of ground water flow and transport in the host rocks. Estimates of hydraulic conductivity, K, based on field measurements may require adjustment (upscaling) for use in numerical models, but the choice of upscaling approach can be complicated by the use of nested modeling, large-scale fracture zones, and a high degree of heterogeneity. Four approaches to upscaling K are examined using a reference case based on exhaustive site data and an application of nested modeling to evaluate performance assessment of a waste repository. The upscaling approaches are evaluated for their effects on the flow balance between nested modeling domains and on simple measures of repository performance. Of the upscaling approaches examined in this study, the greatest consistency of boundary flows was achieved using the observed scale dependence for the rock domains, measured values from the large-scale interference test for the conductor domain, and a semivariogram regularization based on the Moye model for packer test interpretation. Making the assumption that large fracture zones are two-dimensional media results in the greatest changes to the median of travel time and improves the flow balance between the nested models. The uncertainty of upscaling methods apparently has a small impact on median performance measures, but a significant impact on the variances and earliest arrival times.     

Groundwater Resources Potential in Hard Rock Terrain: A Multivariate Approach

Groundwater resources are limited and difficult to predict in crystalline bedrock due to heterogeneity and anisotropy in rock fracture systems. Municipal‐level governments often lack the resources for traditional hydrogeological tests when planning for sustainable use of water resources. A new methodology for assessing groundwater resources potential (GRP) based on geological and topographical factors using principal component analysis (PCA) and analysis of variance (ANOVA) was developed and tested. ANOVA results demonstrated statistically significant differences in classed variable groups as well as in classed GRP scores with regard to hydrogeological indicators, such as specific capacity (SC) and transmissivity. Results of PCA were used to govern the weight of the variables used in the prediction maps. GRP scores were able to identify 79% of wells in a verification dataset, which had SC values less than the total dataset median. GRP values showed statistically significant correlations using both parametric (using transformed datasets) and non‐parametric methods. The method shows promise for municipal or regional level planning in crystalline terrains with high levels of heterogeneity and anisotropy as a hydrogeologically and statistically based tool to assist in assessing groundwater resources. The methodology is executed in a geographic information systems environment, and uses often readily available data, such as geological maps, feature maps and topography, and thus does not require expensive and time‐consuming aquifer tests.     

广州地磁台转换函数的长期变化和季节变化

本文全面系统地研究了1960——1987年广州地磁台转换函数的变化.结果表明:(1)季节变化的特点是夏季幅度大,冬季幅度小,具有12和6个月的主要周期成份;长期变化则表现以每年0.0025的速率下降.转换函数 B 的长期变化和季节变化不明显;(2)由转换函数 A,B 求出的帕金森矢量的方向明显地受海洋的影响,反映了海洋效应;(3)转换函数 A,B 的逐月值与地磁活动相关,而年均值与地磁活动无关.A 的年均值无明显的11年或22年周期.长期变化可能主要受地球内部电性结构的影响.      

Using semivariogram parameter uncertainty in hydrogeological applications

Geostatistical estimation (kriging) and geostatistical simulation are routinely used in ground water hydrology for optimal spatial interpolation and Monte Carlo risk assessment, respectively. Both techniques are based on a model of spatial variability (semivariogram or covariance) that generally is not known but must be inferred from the experimental data. Where the number of experimental data is small (say, several tens), as is not unusual in ground water hydrology, the model fitted to the empirical semivariogram entails considerable uncertainty. If all the practical results are based on this unique fitted model, the final results will be biased. We propose that, instead of using a unique semivariogram model, the full range of models that are inside a given confidence region should be used, and the weight that each semivariogram model has on the final result should depend on its plausibility. The first task, then, is to evaluate the uncertainty of the model, which can be efficiently done by using maximum likelihood inference. The second task is to use the range of plausible models in applications and to show the effect observed on the final results. This procedure is put forth here with kriging and simulation applications, where the uncertainty in semivariogram parameters is propagated into the final results (e.g., the prediction of ground water head). A case study using log-transmissivity data from the Vega de Granada aquifer, in southern Spain, is given to illustrate the methodology.     

Probabilistic seismic hazard analysis for spatially distributed infrastructure

Two key issues distinguish probabilistic seismic risk analysis of a lifeline or portfolio of structures from that of a single structure. Regional analysis must consider the correlation among lifeline components or structures in the portfolio, and the larger scope makes it much more computationally demanding. In this paper, we systematically identify and compare alternative methods for regional hazard analysis that can be used as the first part of a computationally efficient regional probabilistic seismic risk analysis that properly considers spatial correlation. Specifically, each method results in a set of probabilistic ground motion maps with associated hazard‐consistent annual occurrence probabilities that together represent the regional hazard. The methods are compared according to how replicable and computationally tractable they are and the extent to which the resulting maps are physically realistic, consistent with the regional hazard and regional spatial correlation, and few in number. On the basis of a conceptual comparison and an empirical comparison for Los Angeles, we recommend a combination of simulation and optimization approaches: (i) Monte Carlo simulation with importance sampling of the earthquake magnitudes to generate a set of probabilistic earthquake scenarios (defined by source and magnitude); (ii) the optimization‐based probabilistic scenario method, a mixed‐integer linear program, to reduce the size of that set; (iii) Monte Carlo simulation to generate a set of probabilistic ground motion maps, varying the number of maps sampled from each earthquake scenario so as to minimize the sampling variance; and (iv) the optimization‐based probabilistic scenario again to reduce the set of probabilistic ground motion maps. Copyright © 2012 John Wiley & Sons, Ltd.     

A constitutive model for water flow in unsaturated fractured rocks

A conceptual model for describing effective saturation in fractured hard rock is presented. The fracture network and the rock matrix are considered as an equivalent continuum medium where each fracture is conceptualized as a porous medium of granular structure and the rock matrix is assumed to be impermeable. The proposed model is based on the representation of a rough‐walled fracture by an equivalent porous medium, which is described using classical constitutive models. A simple closed‐form equation for the effective saturation is obtained when the van Genuchten model is used to describe saturation inside fractures and fractal laws are assumed for both aperture and number of fractures. The relative hydraulic conductivity for the fractured rock is predicted from a simple relation derived by Liu and Bodvarsson. The proposed constitutive model contains three independent parameters, which may be obtained by fitting the proposed effective saturation curve to experimental data. Two of the model parameters have physical meaning and can be identified with the reciprocal of the air entry pressure values in the fractures of minimum and maximum apertures. Effective saturation and relative hydraulic conductivity curves match fairly well the simulated constitutive relations obtained by Liu and Bodvarsson. Copyright © 2008 John Wiley & Sons, Ltd.     

Flow and fracture maps for basaltic rock deformation at high temperatures

Understanding how the strength of basaltic rock varies with the extrinsic conditions of stress state, pressure and temperature, and the intrinsic rock physical properties is fundamental to understanding the dynamics of volcanic systems. In particular it is essential to understand how rock strength at high temperatures is limited by fracture. We have collated and analysed laboratory data for basaltic rocks from over 500 rock deformation experiments and plotted these on principal stress failure maps. We have fitted an empirical flow law (Norton’s law) and a theoretical fracture criterion to these data. The principal stress failure map is a graphical representation of ductile and brittle experimental data together with flow and fracture envelopes under varying strain rate, temperature and pressure. We have used these maps to re-interpret the ductile–brittle transition in basaltic rocks at high temperatures and show, conceptually, how these failure maps can be applied to volcanic systems, using lava flows as an example.     

Modelling failure mechanisms to explain rock slope change along the Isle of Purbeck coast,UK

Results are presented of distinct element computer modelling used to examine rates and mechanisms of change in rock slopes and cliffs, where material intact properties determine process and form but the most significant controls are the joint pattern and cross-joint properties. The modelling approach does not appear to have been used before in a geomorphological context and provides an alternative approach for examining cliff development. Field and laboratory data have been collected for the Portland Limestone outcrop of the Isle of Purbeck, central southern England. The Portland Limestome is a hard, shelly, crystalline sediment of the Upper Jurassic. It has a regular discontinuity pattern throughout the outcrop in Purbeck. While joint orientation remains relatively constant, bedding changes from horizontal to vertical, a consequence of the Purbeck Monocline. There are resulting implications for spatial variations in rock slope evolution. The modelling exercise enhances previous knowledge on rock failure mechanisms and slope development along the Purbeck coast and demonstrates its potential in research where landforms are developed in lithified, jointed rock masses. © 1998 John Wiley & Sons, Ltd.     

Seismic stability of jointed rock slopes under obliquely incident earthquake waves

Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves. However, for rock slopes, the earthquake waves might approach the outcrop still with a evidently oblique direction. To investigate the impact of obliquely incident earthquake excitations, the input method for SV and P waves with arbitrary incident angles is conducted, respectively, by adopting the equivalent nodal force method together with a viscous-spring boundary. Then, the input method is introduced within the framework of ABAQUS software and verified by a numerical example. Both SV and P waves input are considered herein for a 2D jointed rock slope. For the jointed rock mass, the jointed material model in ABAQUS software is employed to simulate its behavior as a continuum. Results of the study show that the earthquake incident angles have significance on the seismic stability of jointed rock slopes. The larger the incident angle, the greater the risk of slope instability. Furthermore, the stability of the jointed rock slopes also is affected by wave types of earthquakes heavily. P waves induce weaker responses and SV waves are shown to be more critical.     

Understanding of hydraulic properties from configurations of stochastically distributed fracture networks

A systematic investigation of the effect of configurations of stochastically distributed fracture networks on hydraulic behaviour for fractured rock masses could provide either quantitative or qualitative correlation between the structural configuration of the fracture network and its corresponding hydraulic behaviour, and enhance our understanding of appropriate application of groundwater flow and contaminant transport modelling in fractured rock masses. In this study, the effect of block sizes, intersection angles of fracture sets, standard deviations of fracture orientation, and fracture densities on directional block hydraulic conductivity and representative elementary volume is systematically investigated in two dimensions by implementing a numerical discrete fracture fluid flow model and incorporating stochastically distributed fracture configurations. It is shown from this investigation that the configuration of a stochastically distributed fracture network has a significant quantitative or qualitative effect on the hydraulic behaviour of fractured rock masses. Compared with the deterministic fracture configurations that have been extensively dealt with in a previous study, this investigation is expected to be more practical and adequate, since fracture geometry parameters are inherently stochastically distributed in the field. Moreover, the methodology and approach presented in this study may be generally applied to any fracture system in investigating the hydraulic behaviours from configurations of the fracture system while establishing a ‘bridge’ from the discrete fracture network flow modelling to equivalent continuum modelling in fractured rock masses. Copyright © 2007 John Wiley & Sons, Ltd.     

Velocity dispersion in fractured rocks in a wide frequency range

Experimental measurements of fracture-induced seismic waves velocity variations at frequencies ~ 1 kHz, ~ 40 kHz and ~ 1 MHz were performed directly in the field at the rocky outcrop and in the laboratory on specific rock samples collected from the outcrops. The peridotite–lherzolite outcrop appeared macroscopically uniform and contained three systems of visible parallel sub-vertical fractures. This rock has substantial bulk density and higher than average value of seismic wave velocity. The presence of fracture systems gives rise to its velocity anisotropy. The seismic waves passing through the rock fractures are subject to velocity dispersion and frequency dependent attenuation. Our data, obtained from field and laboratory measurements, were compared with theoretical model predictions. In this model we successfully used displacement discontinuity approach. For the velocity dispersion evaluation we used multi-frequency measurements. The a priori observation of orientations and densities of fracture sets allowed evaluation of their stiffness. Our approach revealed that the first arrivals of seismic waves can be used for evaluation of P-wave group velocities, the specific case, in which we expect anomalous velocity dispersion. Our observations contribute to the issue of up-scaling of well-log derived velocities in fractured rock to the scale of standard seismic exploration frequencies.