TRANSIENT EM RESPONSE OF A LARGE LOOP ON A LAYERED GROUND *

The voltage induced in a horizontal loop on a layered ground has been calculated for the case where the loop is excited by a step current and measurements are made during the off-cycle. The expressions derived for a uniform ground show that for large time t the induced voltage E(t) is approximately given by E(t)?— (Ibαμ/20t) (σμ²/t)^3/2 where σ is the conductivity of the ground, μ the permeability, b the loop radius, and I the amplitude of the current step. For small times the corresponding result is E(t)?—Ibμ/2t. When the ground is composed of a number of layers a numerical procedure for calculating the induced voltage is described. The calculated responses of various multilayered structures show that at short times the induced voltage is asymptotic to that produced in the case of a uniform ground of conductivity equal to the top layer. Interference effects in the top layer can lead to anomalous decay curves which may result in the underestimation of the conductivity of a buried layer.     

Geochronology of Precambrian rocks in the Laramie Range and implications for the tectonic framework of Precambrian southern Wyoming

From Casper Mountain; at its northern end, to the northwestern margin of the Laramie anorthosite—syenite complex, in its central parts, the Laramie Range is underlain by granite and granitic gneiss that has a minimum age of 2.54 ± 0.04 Ga (Rb/Sr whole-rock isochron) and by metasedimentary rocks, including marble and quartzite, that appear to overlie the granitic gneiss nonconformably (minimum age: 1.7 Ga based on several horn-blende K/Ar dates). Southward from the anorthosite—syenite complex into Colorado, the Range is underlain chiefly by the Sherman Granite (1.41 Ga; Peterman and Hedge, 1968) and scattered patches of gneiss that are not dated, but are tentatively correlated wit similar gneiss in the southern Medicine Bow Mountains and in the Colorado Front Range, where they are dated as ? 1.7 Ga (Peterman and Hedge, 1968).The Laramie anorthosite—syenite complex (minimum age: ? 1.42 Ga or ? 1.51 Ga if a hornblende K/Ar date is accepted) apparently intruded the suture separating the old (? 2.5 Ga) continental edge from younger (? 1.7 Ga) geosynclinal rocks. The suture, which manifests itself as the Mullen Creek—Nash Fork shear zone in the Medicine Bow Mountains, also is the boundary between ensialic and ensimatic geosynclinal deposition that occurred during the interval 1.7–2.5 Ga ago.K/Ar dates on biotite and muscovite from rocks north of the anorthosite—syenite complex grade from 2.5 Ga on Casper Mountain down to 1.38 Ga near the complex. Near its northern tip, the Laramie Range is crossed by a geochronologic front, separating 2.5 Ga old gneiss whose K/Ar dates were not lowered by subsequent metamorphism from 2.5 Ga old gneiss whose mica dates were reset between 1.4 and 1.6 Ga ago.     

Delineation of spatial redox zones using discriminant analysis and geochemical modelling in arsenic‐affected alluvial aquifers

This study characterized the redox conditions in arsenic‐affected groundwater aquifers of the Lanyang plain, Taiwan. Discriminant analysis was adopted to delineate three redox zones (oxidative, transitional and reductive zones) in different aquifers and yielded 92·3% correctness on groundwater quality data. Arsenic is mainly distributed in the reductive zone, and arsenic distribution in the shallow aquifer is mainly affected by surface activities. According to PHREEQC modelling results, possible mechanisms for arsenic release to groundwater in Lanyang plain are explored. Arsenic released to groundwater in the oxidative zone (zone 1) is primarily caused by the oxidations of arsenic‐bearing pyrite minerals, and arsenate is the predominant species. While the reductive dissolution of Fe‐oxides are responsible for the high arsenic concentration found in the transitional and reductive zones (zones 2 and 3), arsenite is the predominant species. The reduction potential of groundwater rises as the depths and zones increase. Some sulphates may be reduced to form sulphide ions, which then react with arsenic to form arseno‐sulphide deposits (such as realgar, orpiment) and then slightly lower groundwater arsenic concentrations. A conceptual diagram which summarized the possible release processes of arsenic in different redox zones along groundwater flow in Lanyang plain is postulated. Arsenic‐bearing pyrite and arsenopyrite (FeAsS) are oxidized as they are exposed to the infiltrated oxygenated rainwater, releasing soluble arsenate Fe(II) and SO₄^2? into zone 1. The dissolution of arsenic‐rich Fe‐oxides due to the onset of reducing conditions in zones 2 and 3 is responsible for the mobility of arsenic and likely to be the primary mechanism of arsenic release to groundwater in the Lanyang plain Copyright © 2007 John Wiley & Sons, Ltd.     

Nonlinear bacterial load‐streamflow response on a marine beach

Bacterial concentration (Escherichia coli) is used as the key indicator for marine beach water quality in Hong Kong. For beaches receiving streamflow from unsewered catchments, water quality is mainly affected by local nonpoint source pollution and is highly dependent on the bacterial load contributed from the catchment. As most of these catchments are ungauged, the bacterial load is generally unknown. In this study, streamflow and the associated bacterial load contributed from an unsewered catchment to a marine beach, Big Wave Bay, are simulated using a modelling approach. The physically based distributed hydrological model, MIKE‐SHE, and the empirical watershed water quality model (Hydrological Simulation Program – Fortran) are used to simulate streamflow and daily‐averaged E. coli concentration/load, respectively. The total daily derived loads predicted by the model during calibration (June–July 2007) and validation (July–October 2008) periods agree well with empirical validation data, with a percentage difference of 3 and 2%, respectively. The simulation results show a nonlinear relationship between E. coli load and rainfall/streamflow and reveal a source limiting nature of nonpoint source pollution. The derived load is further used as an independent variable in a multiple linear regression (MLR) model to predict daily beach water quality. When compared with the MLR models based solely on hydrometeorological input variables (e.g. rainfall and salinity), the new model based on bacterial load predicts much more realistic E. coli concentrations during rainstorms. Copyright © 2014 John Wiley & Sons, Ltd.     

The effects of rock fragments on hydrologic and hydraulic responses along a slope

A model describing the three‐dimensional matrix flow along a slope with rock fragments or impermeable blocks was developed. The model was combined with modified Picard's iteration to ensure mass conservation in the unsaturated flow. We found that rock fragments obstruct water flow along the slope. The groundwater table must be raised to provide a sufficient pore water pressure gradient to facilitate water flow, but higher pore water pressure may induce slope failure. We also conducted a bench‐scale laboratory flume experiment to examine the effects of impermeable blocks on downstream seepage flow. In addition, a numerical experiment was conducted to examine how different arrangements of impermeable blocks affect downstream seepage flow and pore water pressure. This research demonstrated that the hydraulic phenomena were affected when impermeable blocks were present, and pore water pressure increased as the position of impermeable blocks was lowered. Copyright © 2006 John Wiley & Sons, Ltd.     

Lie group variational integrators for the full body problem in orbital mechanics

Equations of motion, referred to as full body models, are developed to describe the dynamics of rigid bodies acting under their mutual gravitational potential. Continuous equations of motion and discrete equations of motion are derived using Hamilton’s principle. These equations are expressed in an inertial frame and in relative coordinates. The discrete equations of motion, referred to as a Lie group variational integrator, provide a geometrically exact and numerically efficient computational method for simulating full body dynamics in orbital mechanics; they are symplectic and momentum preserving, and they exhibit good energy behavior for exponentially long time periods. They are also efficient in only requiring a single evaluation of the gravity forces and moments per time step. The Lie group variational integrator also preserves the group structure without the use of local charts, reprojection, or constraints. Computational results are given for the dynamics of two rigid dumbbell bodies acting under their mutual gravity; these computational results demonstrate the superiority of the Lie group variational integrator compared with integrators that are not symplectic or do not preserve the Lie group structure.