Constructing motion primitive sets to summarize periodic orbit families and hyperbolic invariant manifolds in a multi-body system

Celestial Mechanics and Dynamical Astronomy - The equilibrium figure of an inviscid tidally deformed body is the starting point for the construction of many tidal theories such as Darwinian tidal...     

Storm-damaged saline-contaminated boreholes as a means of aquifer contamination

Saline water from a storm surge can flow down storm-damaged submerged water supply wells and contaminate boreholes and surrounding aquifers. Using data from conventional purging techniques, aquifer test response analysis, chemical analysis, and regression analysis of chloride/silica (Cl/Si) ratio, equations were derived to estimate the volume of saline water intrusion into a well and a porous media aquifer, the volume of water needed to purge a well shortly following an intrusion event, and the volume of water needed after delay of several or more months, when the saline plume has expanded. Purging time required is a function of volume of water and pumping rate. The study site well is located within a shoreline community of Lake Pontchartrain, St. Tammany Parish, in southeastern Louisiana, United States, which was impacted by two hurricane storm surges and had neither been rehabilitated nor chlorinated prior to our study. Chemical analysis of water samples in fall 2005 and purging of well and aquifer in June 6, 2006, indicated saline water had intruded the well in 2005 and the well and aquifer in 2006. The volume of water needed to purge the study well was approximately 200 casing volumes, which is significantly greater than conventionally used during collection of water samples for water quality analyses.     

Discretizing the fracture-matrix interface to simulate solute transport

This article examines the required spatial discretization perpendicular to the fracture-matrix interface (FMI) for numerical simulation of solute transport in discretely fractured porous media. The discrete-fracture, finite-element model HydroGeoSphere ( Therrien et al. 2005 ) and a discrete-fracture implementation of MT3DMS ( Zheng 1990 ) were used to model solute transport in a single fracture, and the results were compared to the analytical solution of Tang et al. (1981) . To match analytical results on the relatively short timescales simulated in this study, very fine grid spacing perpendicular to the FMI of the scale of the fracture aperture is necessary if advection and/or dispersion in the fracture is high compared to diffusion in the matrix. The requirement of such extremely fine spatial discretization has not been previously reported in the literature. In cases of high matrix diffusion, matching the analytical results is achieved with larger grid spacing at the FMI. Cases where matrix diffusion is lower can employ a larger grid multiplier moving away from the FMI. The very fine spatial discretization identified in this study for cases of low matrix diffusion may limit the applicability of numerical discrete-fracture models in such cases.     

The value of subsidence data in ground water model calibration

The accurate estimation of aquifer parameters such as transmissivity and specific storage is often an important objective during a ground water modeling investigation or aquifer resource evaluation. Parameter estimation is often accomplished with changes in hydraulic head data as the key and most abundant type of observation. The availability and accessibility of global positioning system and interferometric synthetic aperture radar data in heavily pumped alluvial basins can provide important subsidence observations that can greatly aid parameter estimation. The aim of this investigation is to evaluate the value of spatial and temporal subsidence data for automatically estimating parameters with and without observation error using UCODE-2005 and MODFLOW-2000. A synthetic conceptual model (24 separate cases) containing seven transmissivity zones and three zones each for elastic and inelastic skeletal specific storage was used to simulate subsidence and drawdown in an aquifer with variably thick interbeds with delayed drainage. Five pumping wells of variable rates were used to stress the system for up to 15 years. Calibration results indicate that (1) the inverse of the square of the observation values is a reasonable way to weight the observations, (2) spatially abundant subsidence data typically produce superior parameter estimates under constant pumping even with observation error, (3) only a small number of subsidence observations are required to achieve accurate parameter estimates, and (4) for seasonal pumping, accurate parameter estimates for elastic skeletal specific storage values are largely dependent on the quantity of temporal observational data and less on the quantity of available spatial data.     

Assessment of chemical dispersant effectiveness in a wave tank under regular non-breaking and breaking wave conditions

Current chemical dispersant effectiveness tests for product selection are commonly performed with bench-scale testing apparatus. However, for the assessment of oil dispersant effectiveness under real sea state conditions, test protocols are required to have hydrodynamic conditions closer to the natural environment, including transport and dilution effects. To achieve this goal, Fisheries and Oceans Canada and the US Environmental Protection Agency (EPA) designed and constructed a wave tank system to study chemical dispersant effectiveness under controlled mixing energy conditions (regular non-breaking, spilling breaking, and plunging breaking waves). Quantification of oil dispersant effectiveness was based on observed changes in dispersed oil concentrations and oil-droplet size distribution. The study results quantitatively demonstrated that total dispersed oil concentration and breakup kinetics of oil droplets in the water column were strongly dependent on the presence of chemical dispersants and the influence of breaking waves. These data on the effectiveness of dispersants as a function of sea state will have significant implications in the drafting of future operational guidelines for dispersant use at sea.     

Characterization of Damage in Sandstones along the Mojave Section of the San Andreas Fault: Implications for the Shallow Extent of Damage Generation

Following theoretical calculations that suggest shallow generation of rock damage during an earthquake rupture, we measure the degree of fracture damage in young sedimentary rocks from the Juniper Hills Formation (JHF) that were displaced 21 km along the Mojave section of San Andreas Fault (SAF) and were not exhumed significantly during their displacement. In exposures adjacent to the fault, the JHF typically displays original sedimentary fabrics and little evidence of bulk shear strain at the mesoscopic scale. The formation is, however, pervasively fractured at the microscopic scale over a zone that is about a 100 m wide on the southwest side of the SAF near Little Rock. The abundance of open fractures, the poor consolidation, and the shallow inferred burial depth imply that the damage was generated close to the surface of the Earth. The spatial correlation of this damage with a seismically active trace of the SAF suggests that it was generated by SAF slip events that by assumption were of a seismic nature throughout the displacement history of the JHF. Thus the JHF provides a very shallow upper bound for the generation of brittle damage in a seismic fault zone. The fracture fabric is characterized by preferred orientations of fractures that split grains between contact points and is consistent with overall deformation under directed compression. However, the available results cannot be used to distinguish between proposed off-fault damage mechanisms. Fracture orientations are compatible with a maximum compressive stress oriented at a high angle to the fault at about 10 m, and at a lower, more variable angle farther away from the fault. The fracture distribution and fabric are consistent with observations made of the microscale damage characteristics of the Hungry Valley Formation in the northwestern section of the SAF in the Mojave, and with previous observations of exhumed, ancestral strands of the SAF.     

Kinematic transformations for planar multi‐directional pseudodynamic testing

The pseudodynamic (PSD) test method imposes command displacements to a test structure for a given time step. The measured restoring forces and displaced position achieved in the test structure are then used to integrate the equations of motion to determine the command displacements for the next time step. Multi‐directional displacements of the test structure can introduce error in the measured restoring forces and displaced position. The subsequently determined command displacements will not be correct unless the effects of the multi‐directional displacements are considered. This paper presents two approaches for correcting kinematic errors in planar multi‐directional PSD testing, where the test structure is loaded through a rigid loading block. The first approach, referred to as the incremental kinematic transformation method, employs linear displacement transformations within each time step. The second method, referred to as the total kinematic transformation method, is based on accurate nonlinear displacement transformations. Using three displacement sensors and the trigonometric law of cosines, this second method enables the simultaneous nonlinear equations that express the motion of the loading block to be solved without using iteration. The formulation and example applications for each method are given. Results from numerical simulations and laboratory experiments show that the total transformation method maintains accuracy, while the incremental transformation method may accumulate error if the incremental rotation of the loading block is not small over the time step. A procedure for estimating the incremental error in the incremental kinematic transformation method is presented as a means to predict and possibly control the error. Copyright © 2009 John Wiley & Sons, Ltd.     

Time–space continuity of daily maps of fractional snow cover and albedo from MODIS

Using reflectance values from the seven MODIS “land” bands with 250 or 500 m resolution, along with a corresponding cloud product, we estimate the fraction of each 500 m pixel that snow covers, along with the albedo of that snow. The daily products have data gaps and errors because of cloud cover and sensor viewing geometry. Rather than make users interpolate and filter these patchy daily maps without completely understanding the retrieval algorithm and instrument properties, we use the daily time series to improve the estimate of the measured snow properties for a particular day. We use a combination of noise filtering, snow/cloud discrimination, and interpolation and smoothing to produce our best estimate of the daily snow cover and albedo. We consider two modes: one is the “predictive” mode, whereby we estimate the snow-covered area and albedo on that day using only the data up to that day; the other is the “retrospective” mode, whereby we reconstruct the history of the snow properties for a previous period.     

The last 40 ka tephrostratigraphic record of Lake Ohrid,Albania and Macedonia: a very distal archive for ash dispersal from Italian volcanoes

A 1075 cm long core (Lz1120) was recovered in the south-eastern part of the Lake Ohrid (Republics of Macedonia and Albania) and sampled for identification of tephra layers. Magnetic susceptibility investigations show rather high magnetic values throughout the core, with peaks unrelated to the occurrence of tephra layers but instead to the relative abundance of detrital magnetic minerals in the sediment. Naked-eye inspection of the core allowed us to identify of two tephra layers, at 896–897 cm and 1070–1075 cm. Laboratory inspection of the grain-size fraction > 125 μm allowed for the identification of a third cryptotephra at 310–315 cm. Major element analyses on glass shards of the tephra layers at 896–897 cm and 1070–1075 cm show a trachytic composition, and indicate a correlation with the regionally dispersed Y-3 and Y-5 tephra layers, dated at ca 30 and 39 cal ka BP. The cryptotephra at 310–315 cm has a mugearitic–benmoreitic composition, and was correlated with the FL eruption of Mt. Etna, dated at 3370 ± 70 cal yr BP. These ages are in agreement with five ¹⁴C AMS measurements carried out on plant remains and macrofossils from the lake sediments at different depths along the core.