Theoretical analysis and field evidence of reciprocity gaps during interference pumping tests

We address the question of the reciprocity of drawdowns observed during a sequence of interference pumping tests performed within a porous medium, in the context of different conceptual models of subsurface flow. We provide a generalization of the work by Bruggeman (1972) [5], extending his results obtained in 1972 for Darcian flows in an unbounded, heterogeneous porous medium. We then analyze reciprocity within a dual-continuum conceptualization, where the medium is viewed as being composed of two overlapping continua, representing the porous matrix and embedded fractures, respectively. We show theoretically, and demonstrate numerically, that only drawdowns associated with the fracture continuum display reciprocity under transient flow conditions. Conversely, non-flowing matrix and fracture continua display reciprocity behavior under steady-state conditions. We then provide field evidence of the insurgence of reciprocity gaps by analyzing interference test data from the karstic limestone aquifer of the Hydrogeological Experimental Site (HES) in Poitiers, France. On the basis of our theoretical results and experimental observations, we discuss different interpretations of the observed reciprocity gaps. These include (a) non-linear dependencies of local hydraulic parameters, (b) occurrence of internal boundaries within the domain, (c) inertial effects that develop through open conduits within the rock matrix, (d) modifications of the aquifer properties between subsequent pumping tests, and (e) significant contribution of the matrix pressure in monitored wells when the behavior of the aquifer is conceptualized by a dual-continuum approach.     

Grid Refinement in Cartesian Coordinates for Groundwater Flow Models Using the Divergence Theorem and Taylor's Series

Grid refinement is introduced in a numerical groundwater model to increase the accuracy of the solution over local areas without compromising the run time of the model. Numerical methods developed for grid refinement suffered certain drawbacks, for example, deficiencies in the implemented interpolation technique; the non‐reciprocity in head calculations or flow calculations; lack of accuracy resulting from high truncation errors, and numerical problems resulting from the construction of elongated meshes. A refinement scheme based on the divergence theorem and Taylor's expansions is presented in this article. This scheme is based on the work of De Marsily (1986) but includes more terms of the Taylor's series to improve the numerical solution. In this scheme, flow reciprocity is maintained and high order of refinement was achievable. The new numerical method is applied to simulate groundwater flows in homogeneous and heterogeneous confined aquifers. It produced results with acceptable degrees of accuracy. This method shows the potential for its application to solving groundwater heads over nested meshes with irregular shapes.     

基于超级混合虚折射干涉法的阵列声波处理方法及其在套管井中的应用

在声学测井勘探时,复杂多变的测井条件(如胶结不好的套管井和随钻测井等)下的强直达干扰信号会导致地层信号的信噪比降低,使得地层有用信号的提取十分困难.本文在超级虚折射法的基础上,利用声源与接收器的互易原理,对原始波场信号进行互相关和褶积重建,并对所有可能的位形产生的信号进行叠加,将该叠加波场与超级虚折射波场进行叠加,重构出超级混合虚折射波场,使不同接收器上的折射波信噪比在超级虚折射的基础上进一步得到提高,显著提高了有用信号的信噪比,同时解决了超级虚折射近场能量不足的问题.套管井测井的理论模拟及实际处理表明,该方法可以很好地压制套管波信号、提高地层信号的信噪比.     

流动电势和电渗压力的连续测量实验研究及低矿化度下Onsager互易性的验证

连续测量岩心的流动电势效应和电渗效应,可以获得岩心的动电渗透率,并验证Onsager互易性.通常这两个实验的岩心夹持器需要使用不同的堵头,而更换堵头会导致岩心内流体的参数和边界条件发生变化.本文设计了新的岩心夹持器和激励压力源,避免了在测量过程中更换堵头,提高了两个实验的一致性.本文测量了蒸馏水、以及0.01、0.02、0.05、0.1、0.2、0.4和0.6mol/L氯化钠溶液饱和的10块岩心的流动电势效应和电渗效应,获得了动电渗透率,并验证了低矿化度下的Onsager互易性.结果表明,Onsager互易性在低矿化度下是成立的;对于高矿化度,电渗效应能够取代流动电势效应用于反演渗透率.     

井间电磁测量的2．5维层析成像方法

利用正则化最小二乘反演方法实现了井间电磁测量数据的层析成像,对井间地层电阻率进行了重建。在成像算法中,我们假设了井间电磁的激发与接收采用电磁偶极子源,井间介质仅在二维（xoz）平面内变化。在数值模拟中,通过对构造走向（y方向）的Fourier变换,将三维电磁场问题转化为一系列二维问题,用等参有限元方法在波数域求解,使实际地层模型的处理得以实现。对于波数域中每个波数对应的电磁场方程采用等参有限元求解,并用高斯积分将波数域解变换为空间域电磁场。利用源与接收器电磁场的互易原理,实现了电磁场响应对电导率分布灵敏度的快速计算。针对正演模拟中源点的奇异性,我们采用具有一定面积的伪艿函数表达源电流分布,使数值解精度得到提高。用层状介质的解析解与数值计算结果的对比,验证了模拟算法的精度。用介质扰动产生的电磁场变化检验互易性定理计算灵敏度的有效性。对简单块状模型、斜向裂缝带模型及“大”字模型的模拟数据成像结果表明,本文介绍的层析成像方法是正确有效的。     

A cloud-based synthetic seismogram generator implemented using Windows Azure

Synthetic seismograms generated by solving the seismic wave equation using numerical methods are being widely used in seismology. For fully three-dimensional seismic structure models, the generation of these synthetic seismograms may require large amount of computing resources. Conventional high-performance computer clusters may not provide a cost-effective solution to this type of applications. The newly emerging cloud-computing platform provides an alternative solution. In this paper, we describe our implementation of a synthetic seismogram generator based on the reciprocity principle using the Windows Azure cloud application framework. Our preliminary experiment shows that our cloud-based synthetic seismogram generator provides a cost-effective and numerically efficient approach for computing synthetic seismograms based on the reciprocity principle.     

Two-dimensional correlation of geophysical data applied to the heat flow and earth's crust thickness patterns in Czechoslovakia

Summary A simple method for the mutual correlation of various geophysical fields is proposed to disclose their prospective inherent correlations. Some problems connected with the statistical and physical confidence of the resulting maps of the correlation coefficient are mentioned. The correlation between the surface heat flow pattern and the crustal thickness on the territory of Czechoslovakia is presented as an example and briefly discussed in terms of crustal structure.     

Hydraulic-Head Formulation for Density-Dependent Flow and Transport

Density-dependent flow and transport solutions for coastal saltwater intrusion investigations, analyses of fluid injection into deep brines, and studies of convective fingering and instabilities of denser fluids moving through less dense fluids typically formulate the groundwater flow equation in terms of pressure or equivalent freshwater head. A formulation of the flow equation in terms of hydraulic head is presented here as an alternative. The hydraulic-head formulation can facilitate adaptation of existing constant-density groundwater flow codes to include density-driven flow by avoiding the need to convert between freshwater head and hydraulic head within the code and by incorporating density-dependent terms as a compartmentalized “correction” to constant-density calculations already performed by the code. The hydraulic-head formulation also accommodates complexities such as unconfined groundwater flow and Newton-Raphson solution schemes more readily than the freshwater-head formulation. Simulation results are presented for four example problems solved using an implementation of the hydraulic-head formulation in MODFLOW.     

地震波走时和射线的有限差分计算

以往都是采用射线追踪的方法计算地震波的走时和射线，但是当速度模型复杂时这种方法存在一些问题。本文提出另一种计算地震波走时和射线的方法。该方法从程函方程出发，利用互换原理和Ｆｅｒｍａｔ原理计算出各种波的到时和射线。解决了射线追踪方法存在的问题。为地震波走时和射线的计算以及地震波走时反演开辟了一条新途径。     

Development and evaluation of a storm surge warning system in Taiwan

An operational storm surge forecasting system aimed at providing warning information for storm surges has been developed and evaluated using four typhoon events. The warning system triggered by typhoon forecasts from Taiwan Cooperative Precipitation Ensemble Forecast Experiment (TAPEX) has been executed with two storm surge forecasting scenarios with and without tides. Three numerical experiments applying different meteorological inputs have been designed to assess the impact of typhoon forcing on storm surges. One uses synthetic wind fields, and the others use realistic wind fields with and without adjustments to the initial wind fields for the background circulation. Local observations from Central Weather Bureau (CWB) weather stations and tide gauge stations are used to evaluate the wind fields and storm surges from our numerical experiments. The comparison results show that the accuracy of the storm surge forecast is dominated by the track, the intensity, and the driving flow of a typhoon. When the structure of a typhoon is disturbed by Taiwan’s topography, using meteorological inputs from real wind fields can result in a better typhoon simulation than using inputs from synthetic wind fields. The driving flow also determines the impact of topography on typhoon movement. For quickly moving typhoons, storm forcing from TAPEX is reliable when a typhoon is strong enough to be relatively unaffected by environmental flows; otherwise, storm forcing from a sophisticated typhoon initialization scheme that better simulates the typhoon and environmental flows results in a more accurate prediction of storm surges. Therefore, when a typhoon moves slowly and interacts more with the topography and environmental flows, incorporating realistic wind fields with adjustments to the initial wind fields for the background circulation in the warning system will obtain better predictions for a typhoon and its resultant storm surges.     

Evolution mechanism of the western Pacific subtropical high

Ever since Charney et al.[1] studied the multiple equilibrium states in atmosphere with highly truncated spectral method in 1979, many Chinese researchers, such as Li Maicun et al. (1983)[2], Liu Chongjian et al. (1983)[3], Miu Jinhai et al. (1985)[4] and…     

Wind effects on the lateral structure of density-driven circulation in Chesapeake Bay

The response of the density-driven circulation in the Chesapeake Bay to wind forcing was studied with numerical experiments. A model of the bay with realistic bathymetry was first applied to produce the density-driven flow under average river discharge and tidal forcing. Subsequently, four spatially uniform wind fields (northeasterly, northwesterly, southwesterly, and southeasterly) were imposed to examine the resulting cross-estuary structure of salinity and flow fields. In general, northeasterly and northwesterly winds intensified the density-driven circulation in the upper and middle reaches of the bay, whereas southeasterly and southwesterly winds weakened it. The response was different in the lower bay, where downwind flow from the upper and middle reaches of the bay competed with onshore/offshore coastal flows. Wind remote effects were dominant, over local effects, on volume transports through the bay entrance. However, local effects were more influential in establishing the sea-level slopes that drove subtidal flows and salinity fields in most of the bay. The effect of vertical stratification on wind-induced flows was also investigated by switching it off. The absence of stratification allowed development of Ekman layers that reached depths of the same order as the water depth. Consequently, bathymetric effects became influential on the homogeneous flow structure causing the wind-induced flow inside the bay to show a marked transverse structure: downwind over the shallow areas and upwind in the channels. In the presence of stratification, Ekman layers became shallower and the wind-induced currents showed weaker transverse structure than those that developed in the absence of stratification. In essence, the wind-driven flows were horizontally sheared under weak stratification and vertically sheared under stratified conditions.     

Particle tracking in the vicinity of Helgoland,North Sea: a model comparison

Station Helgoland Roads in the south-eastern North Sea (German Bight) hosts one of the richest long-term time series of marine observations. Hydrodynamic transport simulations can help understand variability in the local data brought about by intermittent changes of water masses. The objective of our study is to estimate to which extent the outcome of such transport simulations depends on the choice of a specific hydrodynamic model. Our basic experiment consists of 3,377 Lagrangian simulations in time-reversed mode initialized every 7 h within the period Feb 2002–Oct 2004. Fifty-day backward simulations were performed based on hourly current fields from four different hydrodynamic models that are all well established but differ with regard to spatial resolution, dimensionality (2D or 3D), the origin of atmospheric forcing data, treatment of boundary conditions, presence or absence of baroclinic terms, and the numerical scheme. The particle-tracking algorithm is 2D; fields from 3D models were averaged vertically. Drift simulations were evaluated quantitatively in terms of the fraction of released particles that crossed each cell of a network of receptor regions centred at the island of Helgoland. We found substantial systematic differences between drift simulations based on each of the four hydrodynamic models. Sensitivity studies with regard to spatial resolution and the effects of baroclinic processes suggest that differences in model output cannot unambiguously be assigned to certain model properties or restrictions. Therefore, multi-model simulations are needed for a proper identification of uncertainties in long-term Lagrangian drift simulations.     

Coupled Process Models of Fluid Flow and Heat Transfer in Hydrothermal Systems in Three Dimensions

Geothermal fields and hydrothermal mineral deposits are manifestations of the interaction between heat transfer and fluid flow in the Earth’s crust. Understanding the factors that drive fluid flow is essential for managing geothermal energy production and for understanding the genesis of hydrothermal mineral systems. We provide an overview of fluid flow drivers with a focus on flow driven by heat and hydraulic head. We show how numerical simulations can be used to compare the effect of different flow drivers on hydrothermal mineralisation. We explore the concepts of laminar flow in porous media (Darcy’s law) and the non-dimensional Rayleigh number (Ra) for free thermal convection in the context of fluid flow in hydrothermal systems in three dimensions. We compare models of free thermal convection to hydraulic head driven flow in relation to hydrothermal copper mineralisation at Mount Isa, Australia. Free thermal convection occurs if the permeability of the fault system results in Ra above the critical threshold, whereas a vertical head gradient results in an upward flow field.     

Joint conditional simulations and the spectral approach for flow modeling

The use of data to condition single random fields has a well-established history. However, the joint use of data from several cross-correlated random fields is not as well developed. For example, the use of both transmissivity and head data in a steady state 2-d stochastic flow problem is essentially an inverse problem that is very important for both flow and transport predictions. This problem is addressed here by using a combination of numerical simulation and analytical methods and its application illustrated. The type of information conveyed by the different data categories is explored. The results presented are especially interesting in that head and transmissivity each give different information: Head values would appear to constrain the geometry of the paths while transmissivity data yields information about travel times. The linearized model is expanded to an iterative procedure and the true conditional distribution at several locations is compared with the iterative solution.The problem mentioned above is one with a special transfer function specified by the flow equation. In the second part of the paper a Fast Fourier Transform method for generation and conditioning of two or more random fields is introduced. This procedure is simple to implement, fast and very flexible.     

Joint conditional simulations and the spectral approach for flow modeling

The use of data to condition single random fields has a well-established history. However, the joint use of data from several cross-correlated random fields is not as well developed. For example, the use of both transmissivity and head data in a steady state 2-d stochastic flow problem is essentially an inverse problem that is very important for both flow and transport predictions. This problem is addressed here by using a combination of numerical simulation and analytical methods and its application illustrated. The type of information conveyed by the different data categories is explored. The results presented are especially interesting in that head and transmissivity each give different information: Head values would appear to constrain the geometry of the paths while transmissivity data yields information about travel times. The linearized model is expanded to an iterative procedure and the true conditional distribution at several locations is compared with the iterative solution.The problem mentioned above is one with a special transfer function specified by the flow equation. In the second part of the paper a Fast Fourier Transform method for generation and conditioning of two or more random fields is introduced. This procedure is simple to implement, fast and very flexible.     

Stochastically conditioned flow paths and travel time distribution in highly heterogeneous synthesized aquifers / Chemins d’écoulement et distribution des temps de parcours au sein d’aquifères synthétiques hautement hétérogènes sous conditions stochastiques

Abstract

Abstract Characterization of heterogeneity at the field scale generally requires detailed aquifer properties such as transmissivity and hydraulic head. An accurate delineation of these properties is expensive and time consuming, and for many if not most groundwater systems, is not practical. As an alternative approach, stochastic representation of random fields is used and presented in this paper. Specifically, an iterative stochastic conditional simulation approach was applied to a hypothetical and highly heterogeneous pre-designed aquifer system. The approach is similar to the classical co-kriging technique; it uses a linear estimator that depends on the covariance functions of transmissivity (T), and hydraulic head (h), as well as their cross-covariances. A linearized flow equation along with a conditional random field generator constitutes the iterative process of the conditional simulation. One hundred equally likely realizations of transmissivity fields with pre-specified geostatistical parameters were generated, and conditioned to both limited transmissivity and head data. The successful implementation of the approach resulted in conditioned flow paths and travel-time distribution under different degrees of aquifer heterogeneity. This approach worked well for fields exhibiting small variances. However, for random fields exhibiting large variances (greater than 1.0), an iterative procedure was used. The results show that, as the variance of the ln[T] increases, the flow paths tend to diverge, resulting in a wide spectrum of flow conditions, with no direct discernable relationship between the degree of heterogeneity and travel time. The applied approach indicates that high errors may result when estimation of particle travel times in a heterogeneous medium is approximated by an equivalent homogeneous medium.     

Importance of cross-channel bathymetry and eddy viscosity parameterisation in modelling estuarine flow

For a proper understanding of flow patterns in curved tidal channels, quantification of contributions from individual physical mechanisms is essential. We study quantitatively how such contributions are affected by cross-channel bathymetry and three alternative eddy viscosity parameterisations. Two models are presented for this purpose, both describing flow in curved but otherwise prismatic channels with an (almost) arbitrary transverse bathymetry. One is a numerical model based on the full three-dimensional shallow water equations. Special feature of this diagnostic model is that assumptions regarding the relative importance of particular physical mechanisms can be incorporated in the computations by switching corresponding terms in the model equations on or off. We also present an idealized model that provides semi-analytical approximate solutions of the shallow water equations for all three considered alternative eddy viscosity parameterisations. It forms an aid in explaining and theorising about results obtained with the numerical model. Observations regarding Chesapeake Bay serve as a reference case for the present study. We find that the relative importance of both along-channel advective forcing and transverse diffusive forcing depends on local characteristics of the cross-sectional bottom profile rather than global ones. In our reference case, tide-residual along-channel flow induced by these forcings is not small compared to the total tidal residual. Building on this observation, we present an indicative test to judge whether advective processes should be included in leading order in modelling tide-dominated estuarine flow. Furthermore, depending on the applied eddy viscosity parameterisation (uniformly or parabolically distributed over the vertical), we find qualitatively different spatial patterns for the along-channel advective forcing.     

Numerical approximation of head and flux covariances in three dimensions using mixed finite elements

A numerical method is developed for accurately approximating head and flux covariances and cross-covariances in finite two- and three-dimensional domains using the mixed finite element method. The method is useful for determining head and flux covariances for non-stationary flow fields, for example those induced by injection or extraction wells, impermeable subsurface barriers, or non-stationary hydraulic conductivity fields. Because the numerical approximations to the flux covariances are obtained directly from the solution to the coupled problem rather than having to differentiate head covariances, the approximations are in general more accurate than those obtained from conventional finite difference or finite element methods. Results for uniform flow example problems are consistent with results from previously published finite domain analyses and demonstrate that head variances and covariances are quite sensitive to boundary conditions and the size of the bounded domain. Flux variances and covariances are less sensitive to boundary conditions and domain size. Results comparing approximations from lower-order Raviart–Thomas–Nedelec and higher order Brezzi–Douglas–Marini[9] finite element spaces indicate that higher order element space improve the estimate of the flux covariances, but do not significantly affect the estimate of the head covariances.     

Discrete stability of the Differential System Method evaluated with geostatistical techniques

The Differential System Method (DSM) permits identification of the physical parameters of finite-difference groundwater flow models in a confined aquifer when piezometric head and source terms are known at each point of the finite-difference lattice for at least two independent flow situations for which the hydraulic gradients are not parallel. Since piezometric head data are usually few and sparse, interpolation of the measured data onto a regular grid can be performed with geostatistical techniques. We apply kriging to the sparse data of a synthetic aquifer to evaluate the stability of the DSM with respect to uncorrelated measurement errors and interpolation errors. The numerical results show that the DSM is stable.