Determination of hydraulic diffusivity of aquifers by spectral analysis

This study uses the cyclical frequency to develop the mathematical relationship between hydraulic diffusivity and spectral density functions calculated from groundwater level variation. Such relationship can be applied to (1) unsteady state, one-dimensional confined aquifer with time-dependent water level on both end boundaries, and (2) linearized unconfined aquifer with or without vertical recharge. The spectral density functions of groundwater fluctuations are largely affected by the spectral density functions obtained from time-dependent end boundaries and their cross-spectral density functions. Hydraulic diffusivity of an aquifer can be solved by type-curve matching technique at a specified frequency band under the conditions of (1) confined aquifer having equal time-dependent boundaries on both ends, (2) unconfined aquifer having equal time-dependent boundaries on both ends with surface recharge, and (3) unconfined aquifer subjected to surface recharge but neglecting the water table fluctuations on both end boundaries.     

Application of spectral analysis to determine hydraulic diffusivity of a sandy aquifer (Pingtung County,Taiwan)

The study demonstrates spectral relationships in the time–frequency domain for one‐dimensional groundwater flow in aquifers bounded by fluctuating boundaries. By nature, the solutions of spectral equations are non‐linear complex functions. To determine hydraulic diffusivity in the governing equations, it is required that the data are collected from the spectra of water levels at the fluctuating boundaries and observation wells. Hydraulic diffusivity thus can be obtained by an iterative inverse approach. This paper presents an application in Pingtung County of Taiwan to determine the hydraulic diffusivity of a sandy aquifer under confined conditions. Spectral density function of water level obtained from tidal boundaries and observation wells are used to approximate hydraulic diffusivity, which yields an averaged value of 1·26 × 10⁶ m²/h. Copyright © 2004 John Wiley & Sons, Ltd.     

Hydraulic diffusivity and macrodispersivity calculations embedded in a geographic information system

Abstract

A numerical technique is presented whereby aquifer hydraulic diffusivities (D) and macrodispersivities (α) are calculated by linear equations rewritten from flow and solute transport differential equations. The approach requires a GIS to calculate spatial and temporal hydraulic head (h) and solute concentration gradients. The model is tested in Portugal, in a semi-confined aquifer periodically monitored for h and chloride/sulphate concentrations. Average D (0.46 m²/s) and α (1975 m) compare favourably with literature results. The relationship between α and scale (L) is also investigated. In this context, two aquifer groups could be identified: the first group is heterogeneous at the “macroscopic” scale (solute travelled distances <1 km), but homogeneous at the “megascopic” scale. The overall scale dependency in this case is given by an equation of logarithmic type. The second group is heterogeneous at the macroscopic and megascopic scales, with a scale dependency of linear type.

Citation Pacheco, F.A.L., 2013. Hydraulic diffusivity and macrodispersivity calculations embedded in a geographic information system. Hydrological Sciences Journal, 58 (4), 930–944.     

Estimation of in-situ hydraulic diffusivity of rock masses

A method of estimating in-situ hydraulic diffusivity of rock masses by means of well-injection history and frequency of induced seismicity is presented. The method is based on the diffusion of injected fluid from a spherical cavity in a poroelastic half-space and the effective stress theory, as proposed byTerzaghi (1925, 1936) andHubbert andRubey (1959). Application of the method to two different regions, one in western New York and the other in Japan, resulted in estimated diffusivities of the order 10³ and 10⁴ cm²/sec, respectively. These values lie within the range of published estimates of in-situ diffusivity by other means, a summary of which is presented in tabular form. The calculated diffusivities suggest that the characteristic time of fluid diffusion is close to 0.1, rather than unity, as is sometimes assumed in the literature.     

An innovative method to estimate regional-scale hydraulic diffusivity using GRACE data

ABSTRACT

Estimation of hydraulic properties in the field is usually small-scale and not cost-effective. This paper proposes an innovative method for estimating hydraulic diffusivity at regional scale. Monthly groundwater storage change over the period from 2003 to 2013 is first estimated from GRACE-derived terrestrial water storage (TWS). Assuming that the aquifer system is unconfined and the hydraulic properties are uniform in a geographical cell, the water balance principle and Darcy’s law are used to establish a relation between groundwater storage and hydraulic diffusivity. The value of hydraulic diffusivity is then adjusted using the generalized least squares and linear correlation method. This GRACE-derived hydraulic diffusivity estimation method, or GHDE method for short, is first verified with a hypothetical case and then applied in the Beishan area with available field-measured hydraulic conductivity data. The hypothetical case study demonstrates that the method works perfectly if the TWS data are error free. The Beishan case study illustrates that the estimated hydraulic diffusivities using the GHDE method correlate reasonably well with field test results, suggesting that this method is applicable. The accuracy of this method is constrained by the resolution of the GRACE-derived TWS data and is most suitable for very large scale groundwater problems due to the current accuracy of the GRACE data.

EDITOR A. Castellarin ASSOCIATE EDITOR N. Verhoest     

Quantification of the hydraulic diffusivity of a bentonite-sand mixture using the water head decrease measured upon sudden flow interruption

This paper presents a new modelling approach to quantify the hydraulic diffusivity of low-permeability unconsolidated porous media under confined saturated-flow conditions in the laboratory. The derived analytical solution for the transient variation of the hydraulic head after flow interruption was applied to experimental data obtained from continuous measurements of the water pressure at two locations in the soil column. Three soil samples made of a mixture of natural bentonite (at different mass fractions) and medium sand were studied during a series of stepwise constant flow rates of water. The numerical results well fit the experimentally measured decrease of the dimensionless hydraulic head. The study shows that the increase of the mass fraction of bentonite in the soil sample from 10 to 30% is accompanied by a strong decrease of the hydraulic diffusivity from 2.4 × 10⁻² to 1.1 × 10⁻³ m² s⁻¹, which is clearly due to the decrease of the hydraulic conductivity of the soil sample. The specific storages obtained for each of the three samples are in the same order of magnitude and seem to decrease with the increase of mass fraction of bentonite. However, they clearly reflect the predominant portion of the compressibility of the porous medium compared with that of water. Compared with reported literature values for clayey soils, the specific storage values in this study are slightly higher, varying within the range of 2 × 10⁻³ to 8.1 × 10⁻³ m⁻¹._. The experimental results also give insight into the limitations of the modelling approach. In the case of low-permeability soils (K < 2 × 10⁻⁶ ms⁻¹) and steady-flow conditions with low Reynolds numbers, for example, Re < 0.003, it is recommended to choose a time duration for flow interruption between subsequent flow rate steps of longer than 5 s. For high-permeability porous media, to increase the precision of the quantified hydraulic diffusivity, it might be useful to select a measuring frequency significantly higher than 1 Hz.     

Research on the diffusion of pore fluid and in-situ hydraulic diffusivity in the epicentral region of Xinfengjiang reservoir earthquakes

According to the fact that the Xinfengjiang reservoir earthquakes are caused mainly by water seepage, this paper using the data ofM _s⩾2. 0 earthquakes, studies the hydraulic diffusivity of the mainshock zone by the expansion of the distribution area of epicenters. It is indicated thatin-situ hydraulic diffusivity during the preshock activity of the Xinfengjiang reservoir region was about 6. 2 m²/s. However, after the main shock, thein-situ hydraulic diffusivity in the main shock region increased by fifty percent, that is to say, to 9. 7 m²/s. During the long period after main shock occurrence thein-situ hydraulic diffusivity was affected by significant anisotropy of the medium and fluctuation of water level. No regularity can be found. In addition, we compare the diffusivity found by experiment with rock samples collected with thein-situ hydraulic diffusivity estimated. It is shown that the diffusivity of rock samples with fractures is about the same as the diffusivity estimatedin-situ. However, the diffusivity of whole rock samples is 3 orders of magnitudes smaller than that estimatedin-situ. Finally, we discuss the limits on the method by the expansion of distribution area of epicenters in the study of reservoir induced seismicity. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 364–371, 1991. This subject is sponsored by the Chinese Joint Seismological Science Foundation.     

谱分析在识别初至P波中的应用

由于台站周围环境噪声干扰的增强,台站人员无法识别被背景噪声淹没的初至P波。我们利用DIMAS分析软件包中的谱分析方法,寻找初至P波的卓越周期,改善台站人员识别地震波的能力。     

频谱分析方法在气氡周期分析中的应用

利用数字信号处理的相关理论与方法,对聊古1井两年的气氡逐时值数据进行适当的滤波处理,用频谱分析的方法提取潜在周期信息。结果表明：聊古I井气氡数据除明显的年周期外,还存在12小时、24小时的短周期效应和1～2个月的中长周期波动。说明数字信号处理技术对地震前兆数据处理有很好效果和应用前景。     

Storage in confined aquifer: Spectral analysis of groundwater in responses to Earth tides and barometric effect

Dilatation of aquifer and associated water level fluctuation in groundwater well is known to be driven periodically from lunar, solar, or other tidal forces. Time‐dependent variables in groundwater system, such as water level, can be converted to power spectra in the frequency domain using Fourier transform to evaluate significant fluctuation. The major innovation of this research is to develop spectral representation in frequency domain for the groundwater system that the storage in confined aquifer can be determined considering dilatation affected by Earth tides and barometric effect. In order to verify applicability of the evolved method, time series of Earth tides and barograph are collected; aquifer storage is then determined inversely by selecting significant semidiurnal and diurnal components in spectra computation. It suggests that to discover groundwater storage using groundwater level with barograph and tidal potential of Earth in frequency domain becomes accessible and feasible.     

重力位场谱分析方法研究综述

利用Fourier变换将空间域位场数据变换到频率域进行谱分析是重力位场数据处理中的一种重要方法．这种方法在位场的延拓及转换、场分离、物性界面的正反演和位场的曲化平处理等方面已得到广泛的应用．本文详细介绍了位场谱分析的基本理论和方法,总结了国内外最近几十年来在这方面取得的主要成果,并提出了未来值得深入研究的方向．     

S-wave spectral analysis of the 1995 Kozani-Grevena (NW Greece) aftershock sequence

S-wave spectral analysis is applied to 174 strong motion accelerationrecords to obtain the source parameters of 27 aftershocks(3.1 M_L 4.3) of the May 13, 1995, M_w 6.6,Kozani-Grevena (NW Greece) earthquake. The data are derived from atemporary network, of three-component digital accelerographs, deployedwithin the strongly affected area some days after the mainshock occurrence.Site effects were evident in the strong motion records at 3 out of the 4stations used, and a correction was applied to account for theoverestimation of seismic moment due to amplification of thelow-frequency part of the spectrum. The data from this analysis arecomplimented with previously obtained source parameters for earthquakesin Greece, in order to study the applicability of the empirical scalingrelations used so far, towards smaller magnitudes. In general, a goodcorrelation was observed in most cases, validating the use of empiricalrelations that are applicable to the Aegean area. Empirical relations aredetermined between seismic moment and seismic slip, as well as, betweenseismic moment and stress drop, applicable to small magnitude earthquakes(M_L < 4.3). Stress drop values were found to be relatively small,ranging from 2 to 41 bars, indicative of inter-plate environments. Thevalues of f_c and of f_max were found in good agreement withrelations based on observations from larger worldwide earthquakes.     

Raman spectral analysis and genetic mechanism of pseudotachylyte in Xiaoqinling detachment fault

Veins and clasts of pseudotachylyte developed in the microbreccias of the detachment fault along the boundary of the Xiaoqinling metamorphic core complex. The Raman spectral analysis shows that there are three kinds of textures in the matrices of the pseudotachylyte, i.e. ultracataclastic fine-grained texture, cryptocrystalline texture and both of them with minute quantity of glass. The three different textures are the results of different degrees of ultracataclasis. This demonstrates that ultracataclasis-comminution-melting is the genetic mechanism of the pseudotachylytes in the Xiaoqinling detachment fault and the ultracataclasis-comminution dominates in their formation. Project supported by the National Natural Science Foundation of China (Grant No. 49472142).     

Effective hydraulic conductivity of nonstationary aquifers

Assuming that the ln hydraulic conductivity in an aquifer is mathematically approximated by a spatial deterministic surface, or trend, plus a stationary random noise, we treat the problem of finding what the effective hydraulic conductivity of that aquifer is. This problem is tackled by spectral methods applied to a type of diffusion equation of groundwater flow, together with suitable coordinate transformations. Analytical (exact) solutions in terms of elementary functions are presented for one- and three-dimensional finite and infinite domains. Stability criteria are obtained for the solutions, in terms of a critical parameter, that turns out to involve the product of correlation scale and trend gradient. For the case of finite and symmetrical domains, additional provisions to insure the stability of numerical calculations of effective hydraulic conductivity are provided. Effective hydraulic conductivity is an important property, with potential applications in the calibrations of groundwater and transport numerical models.     

Effective hydraulic conductivity of nonstationary aquifers

Assuming that the ln hydraulic conductivity in an aquifer is mathematically approximated by a spatial deterministic surface, or trend, plus a stationary random noise, we treat the problem of finding what the effective hydraulic conductivity of that aquifer is. This problem is tackled by spectral methods applied to a type of diffusion equation of groundwater flow, together with suitable coordinate transformations. Analytical (exact) solutions in terms of elementary functions are presented for one- and three-dimensional finite and infinite domains. Stability criteria are obtained for the solutions, in terms of a critical parameter, that turns out to involve the product of correlation scale and trend gradient. For the case of finite and symmetrical domains, additional provisions to insure the stability of numerical calculations of effective hydraulic conductivity are provided. Effective hydraulic conductivity is an important property, with potential applications in the calibrations of groundwater and transport numerical models.     

Applicability of the H/V spectral ratio of microtremors in assessing site effects on seismic motion

The authors examine the reliability of site response estimations obtained by the horizontal to vertical (H/V) spectral ratios of microtremors by means of cross‐validation with the ratio of the horizontal spectra of earthquake motion with respect to reference sites. The data comprise microtremor and ground motion records recorded at 150 sites of Yokohama strong motion array. The use of non‐supervised pattern recognition techniques aims to group the sites with more objectivity. Attributes defining the overall shape of the amplification spectra serve as input in the computation of Euclidean distance similarity coefficients amongst sites. The implementation of the Ward clustering scheme leads to the attainment of a meaningful tree diagram. Its analysis shows the possibility of summarizing the results into six general patterns. A good coincidence of site effects estimates at 80 per cent of the sites becomes apparent. However, this coincidence appears poor for sites characterized by H/V amplification ratios around 2 or smaller and predominant periods longer than 0.5 s. In such cases, the presence of stiff, sandy sediments in the soil profile proves common. To proscribe H/V estimations, relying solely on the small spectral ratios criterion seems inadequate. Copyright © 2001 John Wiley & Sons, Ltd.     

Exploratory spectral analysis of hydrological times series

Current methods of estimation of the univariate spectral density are reviewed and some improvements are made. It is suggested that spectral analysis may perhaps be best thought of as another exploratory data analysis (EDA) tool which complements, rather than competes with, the popular ARMA model building approach. A new diagnostic check for ARMA model adequacy based on the nonparametric spectral density is introduced. Additionally, two new algorithms for fast computation of the autoregressive spectral density function are presented. For improving interpretation of results, a new style of plotting the spectral density function is suggested. Exploratory spectral analyses of a number of hydrological time series are performed and some interesting periodicities are suggested for further investigation. The application of spectral analysis to determine the possible existence of long memory in natural time series is discussed with respect to long riverflow, treering and mud varve series. Moreover, a comparison of the estimated spectral densities suggests the ARMA models fitted previously to these datasets adequately describe the low frequency component. Finally, the software and data used in this paper are available by anonymous ftp from fisher.stats.uwo.ca.     

Dynamic corner frequency in source spectral model for stochastic synthesis of ground motion

The static corner frequency and dynamic corner frequency in stochastic synthesis of ground motion from finite-fault modeling are introduced, and conceptual disadvantages of the two are discussed in this paper. Furthermore, the non-uniform radiation of seismic wave on the fault plane, as well as the trend of the larger rupture area, the lower corner frequency, can be described by the source spectral model developed by the authors. A new dynamic corner frequency can be developed directly from the model. The d...     

Hydraulic diffusivity in a coastal aquifer: spectral analysis of groundwater level in responses to marine system

The hydraulic diffusivity gives a measure of diffusion speed of pressure disturbances in groundwater system; large values of hydraulic diffusivity lead to fast propagation of signals in aquifer. This research provides a novel design and derives spectral representation to determine hydraulic diffusivity using spectral analysis of groundwater levels coupled with time-dependent boundary adjacent to marine system and no flow boundary in aquifer system. To validate the proposed method, water levels of fluctuated boundary and groundwater well in a sandy confined aquifer were collected. The hydraulic diffusivity is then obtained by an inverse process in the non-linear complex form of spectral relationship. The method essentially is constructed on the conceptual design of natural forcing transmitted in large aquifer. It is unlike the conventional field pumping test which is only used to determine hydraulic properties of groundwater in small range around the well. Hydraulic diffusivity of the confined aquifer is determined using real observation and then checked by comparing to the published range. It suggests that without local aquifer test to estimate hydraulic diffusivity in a coastal aquifer using spectral representation with its relevant flow system and boundary has become feasible.     

Application of harmonic analysis of water levels to determine vertical hydraulic conductivities in clay-rich aquitards

A harmonic analysis method was used to determine vertical hydraulic conductivities (Kv) in geologic media between vertically separated piezometers using water level measurements. In this method, each water level time series was filtered and then decomposed using harmonic analysis into a sum of trigonometric components. The phase and amplitude of each harmonic function were calculated. These data were used to estimate Kv values between vertically separated data sets assuming one-dimensional transient flow. The method was applied to water level data collected from nested piezometers at two thick clay-rich till aquitards in Saskatchewan, Canada. At one site, routine water levels were measured in 12 piezometers (installed between 1 and 29 m below ground surface) since installation (1995). At the other site, water levels were measured in seven piezometers (installed between 4 and 53 m below ground surface) since installation (1998-1999). The Kv calculated using harmonic analysis decreased with depth below the water table at both sites, approaching matrix estimates of hydraulic conductivity between 10 and 11 m and between 21 and 43 m below ground surface. These depths reflected the depth of extensive vertical fracturing at the sites and showed that the depth of fracturing may be site specific.