Limitations of dimension and displacement data from single faults and the consequences for data analysis and interpretation

The relationship between the maximum cumulative displacement on a fault (D) and the maximum linear dimension of the fault surface (W) is given by the expression D = cWⁿ, where the value of c is determined by rock properties; proposed values for n range from 1.0 to 2.0. Published datasets of D vs W measurements, together with new data, are presented in a common format. Most datasets are derived from maps and so the measurements of displacement and length do not represent maximum values for each fault. This factor, together with more than an order of magnitude range of c, causes regression on D vs W plots to be unsafe unless the range of W values plotted is ca 5 orders of magnitude. This restriction means that individual datasets must be combined to achieve the required range of fault size. Data analysis shows that the value of n must exceed 1.0 but discrimination between values of 1.5 and 2.0 cannot be made on the basis of data analysis alone. A modified fault growth model in which the increase in dimension of a fault with each slip event is proportional to W^0.5 gives rise to a value for n of 1.5. As this model has a sound mechanical basis 1.5 is the preferred value for n. The value of n influences other aspects of fault geometry, including the displacement profile on a fault surface, the spacing of depth contours on faulted horizons and the displacement populations of single fault surfaces.     

Within-taxon morphological diversity in late-Quaternary Neotoma as a paleoenvironmental indicator, Bonneville Basin, Northwestern Utah, USA

Ecological data indicate that as the amount of precipitation in an arid areas increases, so too does mammalian taxonomic richness. This correspondence has been found in two late-Quaternary mammalian faunas from Utah, one from Homestead Cave in the Bonneville Basin. We use the remains of two species of woodrat (Neotoma cinerea and Neotoma lepida) from Homestead Cave to test the hypothesis that as the amount of precipitation in an arid area increases, so too does morphological diversity within individual mammalian taxa. Morphological diversity is measured as corrected coefficients of variation and as richness of size classes of mandibular alveolar lengths. Coefficients of variation for N. cinerea are few and coincide with moisture history if temporally successive small samples are lumped together. More abundant coefficients of variation for N. lepida coincide only loosely with moisture history, likely because such coefficients measure dispersion but not necessarily other aspects of variation. Richness of size classes of N. lepida is high during the early and late Holocene when moisture was high, and lowest during the middle Holocene when climate was most arid.     

Resampling methods for evaluating the uncertainty of the nonparametric magnitude distribution estimation in the Probabilistic Seismic Hazard Analysis

The cumulative distribution function (CDF) of magnitude of seismic events is one of the most important probabilistic characteristics in Probabilistic Seismic Hazard Analysis (PSHA). The magnitude distribution of mining induced seismicity is complex. Therefore, it is estimated using kernel nonparametric estimators. Because of its model-free character the nonparametric approach cannot, however, provide confidence interval estimates for CDF using the classical methods of mathematical statistics.To assess errors in the seismic events magnitude estimation, and thereby in the seismic hazard parameters evaluation in the nonparametric approach, we propose the use of the resampling methods. Resampling techniques applied to a one dataset provide many replicas of this sample, which preserve its probabilistic properties. In order to estimate the confidence intervals for the CDF of magnitude, we have developed an algorithm based on the bias corrected and accelerated method (BC_a method). This procedure uses the smoothed bootstrap and second-order bootstrap samples. We refer to this algorithm as the iterated BC_a method. The algorithm performance is illustrated through the analysis of Monte Carlo simulated seismic event catalogues and actual data from an underground copper mine in the Legnica–Głogów Copper District in Poland.The studies show that the iterated BC_a technique provides satisfactory results regardless of the sample size and actual shape of the magnitude distribution.     

Determination of fracture intensity

Fracture intensity expressed in terms of fracture surface area per volume is rapidly estimated using a stereological equation S_v = 2P_L developed in studies of biological and metallurgic systems. Modifications are available for the case of fully oriented, partially oriented and conjugate fractures.     

Avalanche fatalities in the western United States: a comparison of three databases

Reported avalanche fatalities in the United States increased markedly through the latter half of the twentieth century, a result of the increasing popularity of winter sports. Despite this increase, the literature concerning US avalanche fatalities is sparse. This paper presents a comparison of three US databases containing avalanche fatality information: Storm Data, the West Wide Avalanche Network (WWAN) dataset, and the National Avalanche Database (NAD). The frequency of avalanche fatalities, their temporal trends, spatial distributions, and the demographic characteristics of the victims were analyzed in each database for the years 1998–2009 for the US mountainous west. The data were then pooled to arrive at an estimate of avalanche fatality frequency in the United States for the study period. While the results indicate a considerable amount of overlap between the datasets, Storm Data reports fewer avalanche fatalities than both the WWAN and NAD datasets. All three datasets report a maximum of fatalities in January and display three spatial maxima: the Rocky Mountains of west-central Colorado, the intermountain region from central Utah through Idaho to west-central Montana, and the northern Cascade Ranges of Washington; however, a large void appears in the Storm Data records in the vicinity of the Montana maximum. These maxima result from a juxtaposition of avalanche hazard in these mountainous environments with a high concentration of winter sports activities.     

Crystal structure of columbite under high pressure

The structural evolution of two columbites under pressure, one ferrocolumbite from Raode (Africa) and one manganocolumbite from Kragero (Norway), has been determined by single-crystal X-ray diffraction. Structural investigations at high pressure have been carried out on samples which were preliminarily annealed to attain the complete cation-ordered state. For each crystal, five complete datasets have been collected from room pressure up to ca. 7 GPa. Structure refinements converged to final discrepancy factors R ranging between 5.2 and 5.8% for both the crystals. Structure refinements of X-ray diffraction data at different pressures allowed characterisation of the mechanisms by which the columbite structure accommodates variations in pressure. A and B octahedral volumes in both samples decrease linearly as pressure increases, with a larger compression of the larger A site. The difference in polyhedral bulk moduli of the A sites for the two samples does not appear to relate directly to the octahedral sizes, the A site being more compressible in the Fe-rich sample than in the Mn-rich one. By far the most compressible direction in both the analysed samples is along b. The cations are in fact free to move along this direction, thus allowing the octahedral chains to slide over each other; this effect is particularly evident in the manganocolumbite sample which shows a steep shortening of interchain A–B distances along b.     

Dynamic recrystallization and fabric development during the simple shear deformation of ice

In situ observations of polycrystalline ice deformed in simple shear between −10 and −1°C are presented. This study illustrates the processes responsible for the deformation, the development of a preferred crystallographic orientation and the formation of a preferred dimensional orientation. Intracrystalline glide on the basal plane, accompanying grain rotations and dynamic recrystallization, helps to accommodate the large intragranular strains. These are the most important mechanisms for crystallographic reorientation and produce a stable fabric that favours glide on the basal plane. Localized kinks, developed in grains unfavourably oriented for easy glide, are unstable and are overprinted by dynamic recrystallization. Dynamic recrystallization is a strain softening process with nucleation occurring in the form of equiaxed grains that grow subparallel to pre-existing grain anisotropies and become elongate during deformation. Plots of grain axial ratio against orientation ( ) indicate a weak shape fabric which does not correspond to the theoretical foliation and elongation for the appropriate increment of shear strain. We argue that estimates of the strain magnitude made from orientation of elongate grains are unreliable in high temperature shear zones. These results are applicable to both geological and glacial shear environments.     

CBM and CO2-ECBM related sorption processes in coal: A review

This article reviews the state of research on sorption of gases (CO₂, CH₄) and water on coal for primary recovery of coalbed methane (CBM), secondary recovery by an enhancement with carbon dioxide injection (CO₂-ECBM), and for permanent storage of CO₂ in coal seams.Especially in the last decade a large amount of data has been published characterizing coals from various coal basins world-wide for their gas sorption capacity. This research was either related to commercial CBM production or to the usage of coal seams as a permanent sink for anthropogenic CO₂ emissions. Presently, producing methane from coal beds is an attractive option and operations are under way or planned in many coal basins around the globe. Gas-in-place determinations using canister desorption tests and CH₄ isotherms are performed routinely and have provided large datasets for correlating gas transport and sorption properties with coal characteristic parameters.Publicly funded research projects have produced large datasets on the interaction of CO₂ with coals. The determination of sorption isotherms, sorption capacities and rates has meanwhile become a standard approach.In this study we discuss and compare the manometric, volumetric and gravimetric methods for recording sorption isotherms and provide an uncertainty analysis. Using published datasets and theoretical considerations, water sorption is discussed in detail as an important mechanisms controlling gas sorption on coal. Most sorption isotherms are still recorded for dry coals, which usually do not represent in-seam conditions, and water present in the coal has a significant control on CBM gas contents and CO₂ storage potential. This section is followed by considerations of the interdependence of sorption capacity and coal properties like coal rank, maceral composition or ash content. For assessment of the most suitable coal rank for CO₂ storage data on the CO₂/CH₄ sorption ratio data have been collected and compared with coal rank.Finally, we discuss sorption rates and gas diffusion in the coal matrix as well as the different unipore or bidisperse models used for describing these processes.This review does not include information on low-pressure sorption measurements (BET approach) to characterize pore sizes or pore volume since this would be a review of its own. We also do not consider sorption of gas mixtures since the data base is still limited and measurement techniques are associated with large uncertainties.     

Estimation of statistical parameters for censored lognormal hydraulic conductivity measurements

Field tests of hydraulic conductivity (e.g., injection test, pumping test, etc.) in low permeability formations are subject to censoring due to the detection limit of the instruments used. An iterative method of estimating the mean and variance of hydraulic conductivity data with a presumed log-normal distribution function is presented. This method accounts for the data that are actually below the lower detection limit (called truncated data) and thus gives distribution parameters that are more representative for the underlying distribution. The proposed method is then tested on two simulated normally distributed random datasets having different variances. The results show that the means and variances estimated by the proposed method are very accurate. Finally, the method is used to estimate the mean and variance of hydraulic conductivity data from single hole water injection tests in a fractured geological formation.     

Graph theory and digitization of geological maps

A method is presented which describes rational digitization and efficient treatment of a geologic map. An oriented graph, S,the arcs of which are associated with stratigraphic boundaries and imply a difference in the topological nature of the map if it includes faults, is used. From S,we deduce other graphs: a dendrogram which is used to structure the data and a graph which summarizes the geologic properties of the map. This structure is useful for graphic reconstitutions on a plotter or screen, and for quantitative correlation and calculation of dips, surfaces, and volumes.     

A stepwise method for determining the number of component distributions in a mixture

This paper considers the problem of estimatingm, the number of components in a finite mixture of distributions from a parametric family. A step-up procedure using the bootstrap method is proposed. Some properties of the procedure are illustrated with simulation studies. An example of the method, applied to orientation of beach clasts, is given.     

Approximate up-scaling of geo-spatial variables applied to deep foundation design

We present a series of simple approximate methods for up-scaling the cumulative distribution function of spatially correlated variables by using an effective number n _e of independent variables. Methods are based on the property of distribution permanence of the gamma and inverse Gaussian distributions under averaging, bootstrap sampling and expansions about the normal and gamma distributions. A stochastic simulation study is used to validate each method, and simple parameters are defined to identify respective ranges of applicability. A practical example is presented where core sample rock strength data are up-scaled to shaft size for probabilistic (risk-based) deep foundation design. Supplemental material is available online.     

Multi‐proxy constraints on the significance of covariant δ13C values in carbonate and organic carbon during the early Mississippian

This study investigates the covariation between carbonate and organic δ¹³C values in a proximal to distal transect of four outcrops in the Madison Limestone in the Western United States Rockies, combined with δ³⁴S values of carbonate associated sulphate, the concentration of acid‐insoluble material and measurements of total organic carbon. These new geochemical datasets not only allow for an evaluation of carbon isotope covariance during one of the largest perturbations to the global carbon cycle over the past 550 Myr, but also constrain the cause of the excursion in carbonate δ¹³C values. The results support the hypothesis that a period of anoxia did not play a role in generating the positive carbonate δ¹³C values, but rather favour interpretations by previous workers that the proliferation of land plants destabilized the Carboniferous carbon cycle, setting the stage for a significant change in the carbonate δ¹³C values of contemporaneous marine carbonates. These results also demonstrate that one of the largest perturbations to the global carbon cycle did not produce synchronous variations in carbonate and organic δ¹³C values, emphasizing the importance of local depositional controls on carbon isotope covariance in the geological record in both modern and ancient environments.     

Application of SAXS and SANS in evaluation of porosity, pore size distribution and surface area of coal

This paper discusses the applicability of small angle X-ray scattering (SAXS) and small angle neutron scattering (SANS) techniques for determining the porosity, pore size distribution and internal specific surface area in coals. The method is noninvasive, fast, inexpensive and does not require complex sample preparation. It uses coal grains of about 0.8 mm size mounted in standard pellets as used for petrographic studies.Assuming spherical pore geometry, the scattering data are converted into the pore size distribution in the size range 1 nm (10 Å) to 20 μm (200,000 Å) in diameter, accounting for both open and closed pores. FTIR as well as SAXS and SANS data for seven samples of oriented whole coals and corresponding pellets with vitrinite reflectance (R_o) values in the range 0.55% to 5.15% are presented and analyzed. Our results demonstrate that pellets adequately represent the average microstructure of coal samples.The scattering data have been used to calculate the maximum surface area available for methane adsorption. Total porosity as percentage of sample volume is calculated and compared with worldwide trends. By demonstrating the applicability of SAXS and SANS techniques to determine the porosity, pore size distribution and surface area in coals, we provide a new and efficient tool, which can be used for any type of coal sample, from a thin slice to a representative sample of a thick seam.     

Infrared investigation of CO2-bearing cordierites

CO₂ molecules were introduced experimentally into the structural channels of synthetic well ordered Mgcordierite (Mg₂ ^[VI][(Al₄Si₅)^[IV]O₁₈]) at temperatures of 600 and 800° C, and pressures of 7, 8, 10, 12, and 25 kbar. Powder infrared spectra of the run products show five absorption bands in the region of the asymmetric stretching mode of CO₂. Two of them, strong and sharp, occurring at 2353 cm^–1 {2} and 2348 cm^–1 {3}, are related to two different types of CO₂ molecules. The relative intensity of the band {2} (type I) increases with the cell parameter c_o whereas the relative intensity of the band {3} (type II) increases with the parameter a₀ of the crystal. It is concluded that CO₂ molecules of type I may be oriented with their elongation parallel to the c-axis of the crystal, while CO₂ molecules of type II lie with their O-C-O vector parallel to the a-axis. Analytical data indicate that the intensity ratio Z of these two bands ({2}/{3}) is a linear function of the CO₂ content of cordierite. This ratio depends also on the temperature and, to a less extent, on the pressure under which cordierite entrapped CO₂ molecules. It is proposed to combine this infrared parameter Z together with an estimate of the P-T conditions of the incorporation of CO₂ into the channels, in order to determine the CO₂ content of natural cordierites. The samples do not need to be of high purity and only small amounts (<5 mg) are necessary. This semi-empirical analytical method, which does not require complicated data treatments, is suitable for CO₂-rich cordierites of granulite facies rocks.     

Ck-Reconstruction of Surfaces from Partial Data

In this paper, we study the problem of constructing a smooth approximant of a surface defined by the equation z = f(x ₁, x ₂), the data being a finite set of patches on this surface. This problem occurs, for example, after geophysical processing such as migration of time-maps or depth-maps. The usual algorithms to solve this problem are picking points on the patches to get Lagrange's data or trying to get local junctions on patches. But the first method does not use the continuous aspect of the data and the second one does not perform well to get a global regular approximant (C ¹ or more). As an approximant of f, a discrete smoothing spline belonging to a suitable piecewise polynomial space is proposed. The originality of the method consists in the fidelity criterion used to fit the data, which takes into account their particular aspect (surface's patches): the idea is to define a function that minimizes the volume located between the data patches and the function, and which is globally C ^k. We first demonstrate the new method on a theoretical aspect and numerical results on real data are given.     

Assessment of using borehole-closure data to determine the constitutive behavior of salt

Borehole closure data have often been used to determine the constitutive behaviour of rock salt. This is an inverse problem and analysis of the data is confused by the fact that borehole closure is a structural response that does not uniquely determine constitutive behaviour since both the stress and deformation depend on the constitutive behaviour. This application brief assesses the conclusion of a recent study that the transient power law, ? = K τ^mtⁿ, which includes no term to account for steady-state deformation, is a better constitutive model for salt than are models that account for steady-state straining, and that an empirical model developed from the borehole closure data could be extrapolated to give conservative predictions of long-term closure of single or widely spaced openings.     

Late Tertiary–Quaternary tectonics of the Southern Apennines (Italy): New evidences from the Tyrrhenian slope

This paper summarises the results of combined structural and geomorphological investigations we carried out in two key areas, in order to obtain new data on the structure and evolution of the Tyrrhenian slope of the southern Apennines. Analysis by a stress inversion method [Angelier, J., 1994. Fault slip analysis and paleostress reconstruction. In: Continental Deformation. P.L. Hancock Ed., Pergamon Press, Oxford, 53–100] of fault slip data from Mesozoic to Quaternary formations allowed the reconstruction of states of stress at different time intervals. By integrating these data with those deriving from the stratigraphic and morphotectonic records, chronology and timing of the sequence of the deformation events was obtained.The tectonic history of the region can be related to four deformation events. Structures related to the first event, that was dominated by a strike-slip regime with a NW–SE oriented σ1 and was active since Mid–Late Miocene, do not significantly affect the present day landscape, as they were strongly displaced and overprinted by subsequent deformation events and/or deleted by erosion. The second and third events, that may be considered as the main responsible for the morphostructural signature of the region, are comparable with the stretching phases recognised offshore and considered to be responsible for the opening and widening of the Tyrrhenian basin. In particular, the second event (with an E–W oriented σ3), took place in the Late Miocene/earliest Pliocene and was first dominated by a strike-slip regime, that was also responsible for thrusting and folding. Since Late Pliocene, it was dominated by an extensional regime that created large vertical offsets along N–S to NW–SE trending faults. The third event, that was dominated by extension with a NW–SE oriented σ3, started in the Early Pleistocene and was responsible for formation of the horst-and-graben structure with NE–SW trend that characterises the Tyrrhenian margin of the southern Apennines. The fourth deformation event, which is characterised by an extensional regime with a NE–SW trending σ3, started in the late Middle Pleistocene and is currently active.     

More accurate,calibrated bootstrap confidence intervals for estimating the correlation between two time series

Estimation of Pearson’s correlation coefficient between two time series, in the evaluation of the influences of one time-dependent variable on another, is an often used statistical method in climate sciences. Data properties common to climate time series, namely non-normal distributional shape, serial correlation, and small data sizes, call for advanced, robust methods to estimate accurate confidence intervals to support the correlation point estimate. Bootstrap confidence intervals are estimated in the Fortran 90 program PearsonT (Mudelsee, Math Geol 35(6):651–665, 2003), where the main intention is to obtain accurate confidence intervals for correlation coefficients between two time series by taking the serial dependence of the data-generating process into account. However, Monte Carlo experiments show that the coverage accuracy of the confidence intervals for smaller data sizes can be substantially improved. In the present paper, the existing program is adapted into a new version, called PearsonT3, by calibrating the confidence interval to increase the coverage accuracy. Calibration is a bootstrap resampling technique that performs a second bootstrap loop (it resamples from the bootstrap resamples). It offers, like the non-calibrated bootstrap confidence intervals, robustness against the data distribution. Pairwise moving block bootstrap resampling is used to preserve the serial dependence of both time series. The calibration is applied to standard error-based bootstrap Student’s $t$ confidence intervals. The performance of the calibrated confidence interval is examined with Monte Carlo simulations and compared with the performance of confidence intervals without calibration. The coverage accuracy is evidently better for the calibrated confidence intervals where the coverage error is acceptably small already (i.e., within a few percentage points) for data sizes as small as 20.     

A workflow for exploration sampling in regolith-dominated terranes using portable X-ray fluorescence: comparison with laboratory data and a case study

This paper presents and validates a workflow that provides for the rapid collection of reliable and robust portable X-ray fluorescence (pXRF) data in a regolith-dominated exploration setting. The analysis of regolith material by pXRF is challenging because of its variable Fe content (e.g. 0 to >70 wt%) that results in large matrix effects, which can be mitigated with appropriate standards. Here, we present a dataset from the Western Mount Isa Inlier, Queensland, Australia, comprising soil, lag, rock and rotary air blast (RAB) samples. In the soil dataset, comparison of the laboratory and pXRF datasets for Cu, Pb and Zn have R² > 0.9, and Cu and Zn fall within 2% of the laboratory data, while Pb is 77% less than the corresponding laboratory analyses. Iron, Al, K and Ca by pXRF perform reasonably well when compared with the laboratory data (R² = 0.59 for Al, R² > 0.9 for Fe, K and Ca, <25% variation from the laboratory data), while Mn, Rb and Sr have very good correlations (<8% variation) with R² > 0.94. Titanium, Zr, Ni, Cr and As have poorer comparisons. Overall, the RAB dataset shows similar trends with Cu overestimated by 17%, Zn underestimated by 4% and Pb overestimated by 69%; R² for all elements is >0.92. Since no suitable standards are available, the solid rock dataset was uncorrected; despite this limitation, the dataset shows good correlations with the laboratory data for many elements, and Cu is overestimated by 9.8% with an R² = 0.87. The poor analytical performance of Pb in all datasets is associated with erroneous Bi concentrations being reported by the pXRF unit. When high Fe and Pb amounts are present in a sample, erroneous Pb and Bi concentrations are reported, owing to a pile-up of the Fe K_α peak (6.405 keV) at ～12.8 keV, which is proximal to the Pb L_β (12.614 keV) and Bi L_β (13.023 keV) peaks. Despite the care that is required in validating data, by using pXRF there is substantial opportunity for dynamic exploration campaigns in regolith-dominated terranes with rapid turnaround times, additional elements that may not otherwise be analysed for and low analytical costs. Decisions to stop, continue or infill drill holes while the drill rig is present can be made in near-real time, and not after laboratory results are available and the drill rig has left the area.