Two-dimensional physical-based inversion of confined and unconfined aquifers under unknown boundary conditions

An inverse method is developed to simultaneously estimate multiple hydraulic conductivities, source/sink strengths, and boundary conditions, for two-dimensional confined and unconfined aquifers under non-pumping or pumping conditions. The method incorporates noisy observed data (hydraulic heads, groundwater fluxes, or well rates) at measurement locations. With a set of hybrid formulations, given sufficient measurement data, the method yields well-posed systems of equations that can be solved efficiently via nonlinear optimization. The solution is stable when measurement errors are increased. The method is successfully tested on problems with regular and irregular geometries, different heterogeneity patterns and variances (maximum K_max/K_min tested is 10,000), and error magnitudes. Under non-pumping conditions, when error-free observed data are used, the estimated conductivities and recharge rates are accurate within 8% of the true values. When data contain increasing errors, the estimated parameters become less accurate, as expected. For problems where the underlying parameter variation is unknown, equivalent conductivities and average recharge rates can be estimated. Under pumping (and/or injection) conditions, a hybrid formulation is developed to address these local source/sink effects, while different types of boundary conditions can also exert significant influences on drawdowns. Local grid refinement near wells is not needed to obtain accurate results, thus inversion is successful with coarse inverse grids, leading to high computation efficiency. Furthermore, flux measurements are not needed for the inversion to succeed; data requirement of the method is thus not much different from that of interpreting classic well tests. Finally, inversion accuracy is not sensitive to the degree of nonlinearity of the flow equations. Performance of the inverse method for confined and unconfined aquifer problems is similar in terms of the accuracy of the estimated parameters, the recovered head fields, and the solver speed.     

A model of the early evolution of karst aquifers in limestone in the dimensions of length and depth

A new model of the early evolution of limestone karst aquifers in the dimensions of length and depth is presented. In its initial state the aquifer consists of a rock massive with evenly spaced fractures of about 50 μm aperture widths with an hydraulic conductivity of 10⁻⁷ ms⁻¹. In addition to this a coarser network of prominent fractures with aperture widths of several 100 μm is also present. Boundary conditions of constant recharge 450 mm/year, or constant head from the input of allogenic streams are imposed. First the position of the water table in the aquifer is calculated, then dissolutional widening during a time step in all the fractures below the water table is found by use of the well-known nonlinear dissolution kinetics of limestone. This is iterated and the position of the water table as well as the fracture widths are found as a function of time. In the case of constant recharge to a karst plateau, the water table in any case drops to base level and conduits there propagate from the spring headwards. If constant head conditions are valid the position of the water table remains almost stable and conduits propagate along the water table from the input towards the spring. There is competition between conduit evolution along prominent fractures and along tight fissures close to the water table. In any case under constant head conditions one of these pathways wins, and early karst evolution is terminated by a breakthrough event with an explosive increase of the flow through the aquifer until constant head conditions break down. Depending on the boundary conditions of constant head or constant recharge or a combination of both it is possible to describe models of cave genesis, which have been derived from field evidence, such as the water table models of Swinnerton and Rhoades as well as the four-state model by Ford and Ewers (Can. J. Earth Sci., 15 (1978) 1783).     

Delineation of sulphide ore-zones by borehole radar tomography at Hellyer Mine, Australia

Velocity and absorption tomograms are the two most common forms of presentation of radar tomographic data. However, mining personnel, geophysicists included, are often unfamiliar with radar velocity and absorption. In this paper, general formulae are introduced, relating velocity and attenuation coefficient to conductivity and dielectric constant. The formulae are valid for lossy media as well as high-resistivity materials. The transformation of velocity and absorption to conductivity and dielectric constant is illustrated via application of the formulae to radar tomograms from the Hellyer zinc–lead–silver mine, Tasmania, Australia. The resulting conductivity and dielectric constant tomograms constructed at Hellyer demonstrated the potential of radar tomography to delineate sulphide ore zones.     

氧化镍、二氧化钛高压相变及电导率压力效应

采用金刚石对顶砧压腔静高压技术，对氧化镍、二氧化钛在０-３２ＧＰａ压力范围内的电导率进行了测量．结果表明，电导率－压力关系曲线上的一些特征点与同一物质的高压相交点具有一致性．     

Sq外源和内源电流体系的经度效应和UT变化

根据ＩＧＹ／ＩＧＣ期间全球地磁台网以及中国地磁台站的资料，计算出每－ＵＴ小时的Ｓ_ｑ外源和内源电流体系．对Ｓ_ｑ电流体系ＵＴ变化和经度效应的分析研究表明，Ｓ_ｑ外源电流体系的空间图案没有显著的ＵＴ变化，电流涡焦点的地理纬度与磁赤道有密切关系，其变化范围，北半球为２５°－３５°Ｎ，南半球为３０°－４２．５°Ｓ．外源电流总强度的平均值为２２９ｋＡ（北半球）和１７３ｋＡ（南半球），其变化范围为±５０ｋＡ（北半球）和±４０ｋＡ（南半球）．Ｓ_ｑ内源电流体系的图案和强度有显著的ＵＴ变化，电流体系焦点纬度有类似于外源电流系的变化．在大西洋、印度洋、北太平洋地区，内源电流体系的总强度明显小于大陆地区的内源电流强度，表明这些大洋地区上地幔电导率低于大陆地区．     

地磁1年周期变化的响应函数

用通日月均值减去夜均值计算的月均值资料和Ｓｏｍｐｉ谱分析法分析了１４个台站的北向分量１年周期变化的振幅向相位，时段为１９８４－１９８８年。分析结果显示用Ｐ＾０ｎ（ｄｎｄ＝１，…，６）复合模式的估算的Ｃ值较合理。各台的Ｃ值比较一致。     

Signatures in flowing fluid electric conductivity logs

Flowing fluid electric conductivity logging provides a means to determine hydrologic properties of fractures, fracture zones, or other permeable layers intersecting a borehole in saturated rock. The method involves analyzing the time-evolution of fluid electric conductivity (FEC) logs obtained while the well is being pumped and yields information on the location, hydraulic transmissivity, and salinity of permeable layers. The original analysis method was restricted to the case in which flows from the permeable layers or fractures were directed into the borehole (inflow). Recently, the method was adapted to permit treatment of both inflow and outflow, including analysis of natural regional flow in the permeable layer. A numerical model simulates flow and transport in the wellbore during flowing FEC logging, and fracture properties are determined by optimizing the match between simulation results and observed FEC logs. This can be a laborious trial-and-error procedure, especially when both inflow and outflow points are present. Improved analyses methods are needed. One possible tactic would be to develop an automated inverse method, but this paper takes a more elementary approach and focuses on identifying the signatures that various inflow and outflow features create in flowing FEC logs. The physical insight obtained provides a basis for more efficient analysis of these logs, both for the present trial and error approach and for a potential future automated inverse approach. Inflow points produce distinctive signatures in the FEC logs themselves, enabling the determination of location, inflow rate, and ion concentration. Identifying outflow locations and flow rates typically requires a more complicated integral method, which is also presented in this paper.     

Radially convergent groundwater flow in sloping terrain

Abstract

The groundwater flow equation governing the elevation (h) of the steady-state phreatic surface in a sloping aquifer fed by constant recharge over a bi-circular sector is rhh′ ? r ² Bh′ + Pr ² ? PR ² = 0, where r is the radial coordinate, P is a constant involving recharge and aquifer properties, and B is the slope of the aquifer—bedrock boundary. The derived flow equation describes radially convergent flow through a sloping aquifer that discharges to a water body of fixed head. One important simplification is that in which the width of the bi-circular sector is constant, and the draining land becomes a rectangular aquifer. The bi-circular sector and rectangular-strip groundwater flow problems are solved in terms of implicit equations. The solutions for the steady-state phreatic surfaces depend on the ratio of recharge to hydraulic conductivity, the slope of the aquifer-bedrock, and the downstream constant-head boundary. Computational examples illustrate the application of the solutions.     

Statistical analysis of the effects on overland flow of spatial variability in soil hydraulic conductivity / Analyse statistique des effets de la variabilité spatiale de la conductivité hydraulique du sol sur l'écoulement de surface

Abstract

The effects of spatial variation of the saturated hydraulic conductivity (K _s ) of the soil on the variation of overland flow were tested by analysing 2000 synthetic rainfall—runoff events, all generated from real, observed rainfall events but with runoff modelled by a two-dimensional distributed model using different spatially variable K _s fields in a small (12 ha) agricultural catchment. The purpose is to determine the influence of spatial variation in K _s on runoff generation. The statistical measures used to describe the variation in the generated K _s were its coefficient of variation and correlation length. Both of these had two levels of typical values obtained from field measurements in other studies. The storms were analysed at a general event level, first using simple graphical and statistical methods and then using analysis of variance (ANOVA). The observed scale of the spatial variation of K _s does cause statistically significant variation in overland flow. The graphical analysis showed that the first flow peak in a multi-event storm had the largest variation and that differences were greater in the rising part of the hydrograph than in its recession. The greatest variation in overland flow was produced by the combination of the greater coefficient of variation and the longer correlation lengths. The smallest variation in overland flow was produced by the combination of the smaller coefficient of variation and the shorter correlation lengths. ANOVA showed that the coefficient of variation and correlation length alone did not explain all the variation of the total flow. ANOVA was not very useful due to the many restrictive assumptions that were not satisfied by the nature of the data and therefore analysis methods with less restrictive assumptions need to be tested.     

A long‐term study of stable isotopes as tracers of processes governing water flow and quality in a lowland river basin: the upper Thames,UK

A long‐term study of O, H and C stable isotopes has been undertaken on river waters across the 7000‐km² upper Thames lowland river basin in the southern UK. During the period, flow conditions ranged from drought to flood. A 10‐year monthly record (2003–2012) of the main River Thames showed a maximum variation of 3‰ (δ¹⁸O) and 20‰ (δ²H), although interannual average values varied little around a mean of –6.5‰ (δ¹⁸O) and –44‰ (δ²H). A δ²H/δ¹⁸O slope of 5.3 suggested a degree of evaporative enrichment, consistent with derivation from local rainfall with a weighted mean of –7.2‰ (δ¹⁸O) and –48‰ (δ²H) for the period. A tendency towards isotopic depletion of the river with increasing flow rate was noted, but at very high flows (>100 m³/s), a reversion to the mean was interpreted as the displacement of bank storage by rising groundwater levels (corroborated by measurements of specific electrical conductivity). A shorter quarterly study (October 2011–April 2013) of isotope variations in 15 tributaries with varying geology revealed different responses to evaporation, with a well‐correlated inverse relationship between Δ¹⁸O and baseflow index for most of the rivers. A comparison with aquifer waters in the basin showed that even at low flow, rivers rarely consist solely of isotopically unmodified groundwater. Long‐term monitoring (2003–2007) of carbon stable isotopes in dissolved inorganic carbon (DIC) in the Thames revealed a complex interplay between respiration, photosynthesis and evasion, but with a mean interannual δ¹³C‐DIC value of –14.8 ± 0.5‰, exchange with atmospheric carbon could be ruled out. Quarterly monitoring of the tributaries (October 2011–April 2013) indicated that in addition to the aforementioned factors, river flow variations and catchment characteristics were likely to affect δ¹³C‐DIC. Comparison with basin groundwaters of different alkalinity and δ¹³C‐DIC values showed that the origin of river baseflow is usually obscured. The findings show that long‐term monitoring of environmental tracers can help to improve the understanding of how lowland river catchments function. Copyright © NERC 2015. Hydrological Processes © 2015 John Wiley & Sons, Ltd.