148: aquifer characterization by geophysical …aquifer characterization by geophysical methods 2267...

148: Aquifer Characterization by GeophysicalMethods

HARRY VEREECKEN, ANDREAS KEMNA, HANS-MARTIN MUNCH, AXEL TILLMANN

AND ARRE VERWEERD

Agrosphere Institute (ICG-IV), Forschungszentrum Julich GmbH, Julich, Germany

Geophysical methods are increasingly being used to characterize the subsurface. They offer the potential to derivebasic characteristics, state variables, and properties of geological formations. In this article, we focus on theapplication of geophysical methods to derive properties and state variables of aquifer systems. Special attentionis given to the assessment of hydraulic conductivity, porosity, and water saturation. Three different groupsof methods (seismics, electrical techniques, and electromagnetics) and their combined use are discussed. Foreach method, relationships between geophysical and hydrogeological quantities are outlined and applicationsare presented. A separate section is devoted to the development and application of combined approaches inhydrogeophysics.

INTRODUCTION

The shallow subsurface is an extremely important zonethat yields much of our water resources (see Chapter 145,Groundwater as an Element in the Hydrological Cycle,Volume 4). It also serves as the repository for municipaland industrial waste. As sustainable and effective use of thesubsurface environment is a major challenge facing modernsocieties, there is a great need to improve our understandingof the shallow subsurface and, in particular, groundwatersystems. In this respect, geophysical methods can contributein a significant manner.

In the past, application of geophysical methods ingroundwater hydrology has focused on mapping geologicalstructures (e.g. clay/sand layers, bedrock valleys), delin-eation of aquifer boundaries, mapping of fracture zones andchemical pollution plumes, delineation of water-saturatedzones, and seepage flow in landslide bodies. For these pur-poses, standard methods are presently available and welldocumented in the geophysical literature (e.g. Parasnis,1997; Reynolds, 1997).

In recent years, increased attention has been givento the use of geophysical methods to derive parametersand state variables characterizing especially near-surface

groundwater systems and soils. Research in this direc-tion is mainly driven by the fact that geophysical methodsallow continuous mapping of geophysical properties, whichcan be transferred to parameters or variables characteriz-ing the aquifer system (e.g. water content, porosity, flowvelocity, and their changes in time). Classical approacheslike drilling, coring, and well testing (see Chapter 151,Hydraulics of Wells and Well Testing, Volume 4) haveshown their limitations in constraining spatial and temporalvariabilities of these quantities. Characterizing such vari-abilities is however of utmost importance for, for example,determining the success of water management strategies orpredicting pollution risks for water supply systems.

In this article, we will present the application of geo-physical methods to derive parameters (e.g. hydraulic con-ductivity, porosity, dispersivity) and state variables (e.g.water saturation) of aquifer systems relevant for waterflow and solute transport (see Chapter 149, Hydrodynam-ics of Groundwater, Volume 4). This area of research istoday referred to as hydrogeophysics (e.g. Vereecken et al.,2002; Rubin and Hubbard, 2005). Hydrogeophysics is arapidly evolving discipline aiming at integrating hydrolog-ical, hydrogeological, and geophysical methods and con-cepts to characterize the subsurface. Rather than coveringthe whole range of available geophysical methods, we

Encyclopedia of Hydrological Sciences. Edited by M G Anderson. 2005 John Wiley & Sons, Ltd.

2266 GROUNDWATER

focus on selected methods that are promising in terms ofsite-specific hydrogeophysical characterization of aquifersystems. Three groups of methods will be discussed: seis-mics, electrical techniques, and electromagnetics, the latterincluding ground-penetrating radar. In the last section, wewill address the combined use of geophysical and hydro-geological data to characterize aquifer properties.

SEISMIC AQUIFER CHARACTERIZATION

Seismic characterization of the subsurface is based upon thepropagation of elastic waves generated through a seismicsource at the surface or in boreholes. Owing to the nature ofelastic media, there exist different wave types propagatingwith different velocities. The primary information derivedfrom seismic methods comprises the wave velocities andwave attenuation. From these quantities information canbe derived about material properties of the subsurfacelike porosity, hydraulic conductivity, elastic moduli, andwater saturation.

Seismic-Hydrogeological Relationships

Seismic velocities are dependent on aquifer properties (e.g.grain material, texture, and porosity) and state variables(e.g. water saturation). The fast compressional wave (alsoknown as primary wave or P-wave) is related to the bulkand shear moduli of a medium, and its propagation velocity,vp [m s−1], is

vp =√

K + 43G

ρb(1)

where K [Pa] and G [Pa] are the bulk and shear moduli,respectively, and ρb [kg m−3] is the bulk density. P-waves occur in solids, fluids, and gases. The slower shearwave (secondary or S-wave) does not depend on the bulkmodulus; its velocity, vs [m s−1], is given by

vs =√

G

ρb(2)

Shear waves do not exist in fluids and gases since theirshear moduli are zero.

The elastic moduli of sediments depend on the charac-teristics of the solid matrix, the porosity, and the propertiesof the pore space. The effect of water saturation on theseismic velocities is well-known and subject of many theo-retical (Gassmann, 1951; Biot, 1956a,b; Kuster and Toksoz,1974a) and experimental (Wyllie et al., 1956; Kuster andToksoz, 1974b) investigations. Under the constraint thatmineral composition and porosity are the primary factorscontrolling the dry-frame elastic moduli, Nolen–Hoeksema(1993) derived a first-order approximation of the relation

between porosity and the dry-frame bulk and shear moduli,Kdry [Pa] and Gdry [Pa], respectively:

Kdry = Ksolid

(1 − n

n0

), Gdry = Gsolid

(1 − n

n0

)(3)

Here, Ksolid [Pa] and Gsolid [Pa] are the bulk and shearmoduli of the solid matrix material, n [−] is the porosity,and n0 [−] denotes the precompaction porosity, whichdefines the transition from unconsolidated (n > n0) toconsolidated (n < n0) sediments. For media consisting ofspheroidal grains, n0 is in the range of 0.35 to 0.40. Atypical rock contains a mixture of grain/pore sizes andshapes, leading to a more complicated relationship betweenelastic moduli and porosity (see e.g. Toksoz et al., 1976).

For sediments with a homogeneous and isotropic porespace, Gassmann’s equation (Gassmann, 1951) describesthe influence of fluids on the bulk modulus for low-frequency elastic waves:

K = KsolidnKdry + Q

nKsolid + Q(4)

with

Q = Kfluid,effKsolid − Kdry

Ksolid − Kgas(5)

where Kgas [Pa] denotes the bulk modulus of the gasphase, and Kfluid,eff [Pa] is the effective bulk modulusof the fluid–gas mixture. Equations (4) and (5) are validfor consolidated materials, that is, n < n0, and therefore,from equation (3), Kdry > 0. For a homogeneous fluid–gasmixture in the pore space, Kfluid,eff is given by

Kfluid,eff =(

S

Kfluid+ 1 − S

Kgas

)−1

(6)

where S [−] is the fluid (water) saturation and Kfluid

[Pa] the bulk modulus of the fluid phase. According toequations (4) to (6), an increase of water saturation givesrise to an increase of the bulk modulus of sediments,while water does not contribute to the shear modulus.Therefore, the P-wave velocity (equation (1)) shows astronger variation caused by saturation changes than theS-wave velocity (equation (2)), which is only influencedthrough changes in bulk density

ρb = (1 − n)ρsolid + nSρfluid (7)

where ρsolid [kg m−3] is the mass density of the solid matrixand ρfluid [kg m−3] the water density. Accordingly, the vp/vs

ratio is suitable to distinguish dry from saturated sedimentsand detect phreatic surfaces, that is, water tables.

For illustration, Figure 1 shows the P-wave and S-wavevelocities modeled for a porous medium consisting of

AQUIFER CHARACTERIZATION BY GEOPHYSICAL METHODS 2267

0 0.2 0.4 0.6 0.8 1

S

2600

2400

2200

2000

1800

1600

1400

v [m

s−1

]

P-wave

S-wave

Figure 1 Seismic P- and S-wave velocities as function ofwater saturation modeled for a porous medium consistingof quartz grains (see Tillmann, 2001)

quartz grains with n = 0.3 (for more details, see Tillmann,2001) as a function of water saturation. The slight decreaseof the velocities with increasing saturation at lower tomedium saturation degrees is due to the dominant effect ofthe increase of bulk density with increasing water saturationin the pore space. Near full saturation, the complete fillingof pores with water causes a rapid increase of the bulkmodulus and the P-wave velocity. Equations (3) to (6) leadto the conclusion that this P-wave velocity increase islarger for high porosities and negligible for low porositiescompared to velocity perturbations owing to changes in soilmaterial. The vp/vs ratio of the quartz grain model at fullsaturation as a function of porosity is shown in Figure 2.For n approaching the precompaction porosity, here n0 =0.4, the ratio becomes infinite since the dry matrix shearmodulus becomes zero. Figures 1 and 2 illustrate thepotential of seismic methods to detect the transition zonesto full saturation and to estimate porosity using a combinedinterpretation of P-wave and S-wave data.

Empirical relationships between P-wave velocity, poros-ity, permeability, clay content, bulk density, and water sat-uration for sandstones and carbonate rocks were derived forexample by Koesoemadinata and McMechan (2003) usingcorrelation analyses between the different quantities. Mar-ion et al. (1992) obtained velocity-porosity relationships forsediments on the basis of a simple geometric-mechanicalmodel for sand–clay mixtures. From porosity, in turn,permeability can be estimated using the Kozeny–Carmanrelation (Kozeny, 1927; Carman, 1937).

Seismic Methods

Seismic methods are based on the propagation of elasticwaves in the earth. From the experimental setup, different

0 0.1 0.2 0.3 0.4

8

7

6

5

4

3

2

1

v p v

s−1

n

Figure 2 Seismic P-wave to S-wave velocity ratio asfunction of porosity modeled for a porous mediumconsisting of quartz grains (see Tillmann, 2001)

methods can be distinguished (for an overview, see e.g.Telford et al., 1990). In the seismic refraction method, thefirst arrival times of the seismic waves are measured. Thederivation of seismic velocities from measured travel times(inversion) is based on Snell’s law from ray theory, whichimplies the assumption of a layered earth. The method issensitive to velocity changes between two layers as longas critically refracted waves are generated at the layerboundaries. Therefore the method requires an increase inseismic velocity with depth, which is a severe constraintfor many shallow applications where low-velocity layersmay be encountered.

In contrast to seismic refraction, seismic reflections occurowing to changes in the elastic impedance of the medium,that is, the product of velocity and density in a layer.Therefore, low-velocity layers and density changes can bedetected too, as long as the wavelength of the seismicsignal is small compared to the layered structure. From thisit follows that measurements in shallow sediments haveto be performed using signals in the kHz range, whichunfortunately are affected by high attenuation.

In seismic crosshole tomography, travel time measure-ments for a large number of ray paths are collected provid-ing information on the seismic velocity distribution. Whilethe application of this technique in the field involves P-wave travel time measurements between boreholes, in thevertical seismic profiling (VSP) method it is common touse surface-to-borehole shot-receiver configurations. Seis-mic crosshole tomography gives a relatively detailed veloc-ity model between the boreholes, and does not require theassumption of a layered earth.

Surface wave analysis exploits the fact that a particularwave type is formed owing to the free boundary condition

2268 GROUNDWATER

at the Earth’s surface, the amplitude of which dropsexponentially with depth. Surface wave interpretation isnormally based on the assumption of a horizontally layeredearth (Haskell, 1953). Surface waves are dispersive, thatis, the propagation velocity as well as the penetrationdepth depends not only on material parameters but also onfrequency. The analysis of this dispersive behavior leads toinformation about all elastic parameters and the depths ofshallow layer boundaries.

Hydrogeological Applications

As pointed out in Section “Seismic-hydrogeological rela-tionships”, the typically wide range of elastic propertiesof sediments normally exceeds any perturbations causedby the presence of water, which makes near-surface waterdetection by means of seismic methods difficult. Nev-ertheless, seismic methods have been successfully usedfor mapping water table depths in aquifers (e.g. Birkeloet al., 1987; Bacharach and Nur, 1998; Baker et al., 2000;Bradford and Sawyer, 2002). However, the water table isnot a trivial boundary in seismic terms. Generally, it isdefined through the pore fluid properties (such as com-pressibility, density, and viscosity) and the degree of watersaturation (depending on pore pressure and pore-size dis-tribution). Therefore, its location may vary over a rel-atively short distance in both space and time. Seismic

methods can be used to monitor temporal groundwatervariations by detecting associated changes in seismic veloc-ity. For instance, Bacharach and Nur (1998) followedthis approach for monitoring the water table at a beachunder tidal influence. On a longer time scale, Baker et al.(2000) monitored seasonal water table changes over oneyear. Tillmann and Stocker (2001) presented a joint inver-sion approach for seismic and electrical data (see Section“Electrical aquifer characterization”) taking lithologicaland hydrological parameters into account. In contrast toconventional joint inversion methods (e.g. Hering et al.,1995), their approach can handle the presence of a watertable.

As a field demonstration we present the results of aseismic crosshole tomography survey performed to resolvethe porosity distribution in a near-surface aquifer. Thesurvey was conducted at the Krauthausen test site, whichis located close to Julich in the western part of Germany.More details about the site can be found in Vereecken et al.(2000). In 1997, a series of tomographic measurementswas made to characterize the spatial variability of porosity.Figure 3(a) shows the reconstructed P-wave velocity imagealong a cross section containing several boreholes. Detailson the used tomographic reconstruction technique andfurther results are reported in Dietrich and Fechner (1997).Taking into account additional information from borehole

96

94

92

90

88

96

94

92

90

88

0 5 10 15 20 25 30 35 40

B58 B14 B6 B22

B58 B14 B6 B22

x [m]

0 5 10 15 20 25 30 35 40

x [m]

2200

2100

2000

1900

1800

0.22

0.2

0.18

0.14

0.16

0.12

0.1

0.08

nv p

[m s

−1]

(a)

(b)

z [m

]z

[m]

Figure 3 Results of a crosshole seismic tomography survey conducted at the Krauthausen test site along a transectcontaining four boreholes (B58, B14, B6, B22) to characterize a near-surface aquifer: (a) P-wave velocity distribution,(b) estimated porosity distribution


measurements, the porosity was derived from the P-wavevelocity using the approach of Yamamoto et al. (1994).The resultant porosity distribution is shown in Figure 3(b).The porosities derived from the seismic data showed goodcorrelation with those determined on cores from the welllocations.

ELECTRICAL AQUIFER CHARACTERIZATION

It has been recognized for a long time that measurementsof subsurface electrical properties can be used for theinvestigation of the underground, in particular concerninggroundwater resources (e.g. Vacquier et al., 1957). Sincesolid and aqueous phases of a porous soil/rock systemelectrically act in a different way, electrical propertiesof soils and rocks are closely related to the underlyingstructure. Importantly, in predominantly ion-conductivesystems electrical and hydraulic conduction follow similarpathways through the interconnected saturated pores – acircumstance that makes electrical methods particularlyattractive for hydrogeological aquifer characterization.

Electrical-Hydrogeological Relationships

In addition to electrolytic conduction in the saturated pores,described by an electrolytic conductivity contribution σel

[S m−1], electrical surface conduction can exist along theinterfaces between solid and aqueous phases owing to thepresence of electric surface charges and the involved for-mation of electrical double layers, leading to a surfaceconductivity contribution σs [S m−1]. Following the concep-tual model that both conduction mechanisms act in parallel(e.g. Waxman and Smits, 1968; Rink and Schopper, 1974),the bulk electrical conductivity, σ [S m−1], of sediments isgiven by

σ = σel + σs (8)

For clay free, saturated formations, the bulk electricalconductivity may be expressed as

σsat∼= σel,sat = σw

F= nm

effσw (9)

(Archie, 1942; Sen et al., 1981), where σw [S m−1]denotes the water electrical conductivity, and F [−] is aformation factor depending on the pore space geometry(porosity, tortuosity, effective pore/grain size), usuallywritten in dependence on effective porosity, neff [−], and aso-called cementation exponent m [−] (for unconsolidatedsands, typically m ≈ 1.3, see e.g. Schon, 1996). Thesurface conductivity contribution in equation (8) may beexpressed as

σs,sat = 2µsQs

F�(10)

(Johnson et al., 1986), where � [m] is an intrinsicmeasure of interconnected pore size, Qs [C m−2] is thesurface ionic charge density, and µs [m2 V−1 s−1] is theeffective ionic mobility in the electrical double layer aroundthe charged surface. In general, ionic charge density andmobility depend on water chemistry, that is, on σw. Thepore-size parameter � accounts for different surface andbulk tortuosity factors; its inverse is closely related to thesurface area to pore volume ratio.

In general, σ may also describe induced electricalpolarization (IP) phenomena attributed to ion-selectivemembrane effects in the pore space, in particular, associatedwith present clay minerals (e.g. Marshall and Madden,1959; Vinegar and Waxman, 1984; Lesmes and Frye,2001). Then, σ becomes a complex-valued quantity, σ ∗,comprising real (σ ′) and imaginary (σ ′′) parts (or magnitudeand phase). In the frequency range relevant for practicalapplications (typically <100 Hz), however, virtually onlyσs contributes to the imaginary part and, hence, σ ′′ allowsdirect access to internal surface characteristics. Importantly,σs generally depends on the applied measurement angularfrequency ω [s−1]. The relaxation times of transient IPprocesses directly correspond to the respective spatial scalesat which these processes take place in the pore space. Thisleads to a dispersive behavior σs(ω) that contains importantadditional information for textural characterization (e.g.Kemna et al., 2000; Lesmes and Morgan, 2001; Scott andBarker, 2003).

The dependence of real and imaginary conductivitieson water saturation S is normally expressed as a simplepower-law relation. For clay free formations, where onlythe electrolytic conductivity contributes to the real conduc-tivity, it is

σ ′ ∼= σel = σel,satSp (11a)

(e.g. Archie, 1942). Here p [−] is the so-called satura-tion exponent with typically p ≈ 2 (see e.g. Schon, 1996).For the imaginary conductivity, the corresponding relation-ship is

σ ′′ = σ ′′satS

q (11b)

(e.g. Vinegar and Waxman, 1984), but recent studies (e.g.Ulrich and Slater, 2004) indicate that the saturation expo-nent of the imaginary conductivity, q [−], is significantlysmaller than the saturation exponent of the real part (p).However, the saturation dependency of induced polarizationis still an issue of current research (e.g. Titov et al., 2004).

The relationships between structural, in particular textu-ral, aquifer properties and the bulk electrical conductivityhave motivated the attempt to assess hydraulic conductiv-ity, Kh [m s−1], or permeability, k [m2], from geoelectricalmeasurements. Early approaches were based on the lin-ear regression analysis of logσ –logKh correlations, whichprovides calibration functions valid for a particular set of

2270 GROUNDWATER

samples or field site (e.g. Mazac et al., 1985; Huntley,1986). For instance, Heigold et al. (1979) found the field-scale empirical relation

log Kh ≈ −1.28 + 0.93 log σ (12)

(Kh in [m s−1], σ in [S m−1]) for the Niantic-Illiopolisaquifer in Illinois, USA. However, generally both a directand an inverse relation between logσ and logKh can beobserved, depending on lithology type. In relatively cleansands, σ increases with increasing Kh since both propertiesare similarly controlled by porosity (dominance of σel). Inclayey material, clay content takes over the governing roleand, accordingly, an opposite σ -Kh relationship is found:σ increases but Kh decreases with increasing clay content(dominance of σs).

Recently, different empirical to semiempirical modelswere proposed for electrical k estimation (e.g. Borner et al.,1996; de Lima and Niwas, 2000; Purvance and Andricevic,2000; Slater and Lesmes, 2002). One approach (Borneret al., 1996) is based on an observed direct relation betweenthe surface area to pore volume ratio, Ap [m−1], and σ ′′ (seeBorner and Schon, 1991) in conjunction with a modifiedKozeny–Carman model,

k ∝ 1

FAup

(13)

where the formation factor F is estimated from measure-ments of σw. The exponent u [−] can be related to thefractal dimension of the pore surface (Pape et al., 1987),that is, to soil/rock type. In contrast, the controlling influ-ence on k might be attributed to a characteristic grain size,rgr [m], rather than a characteristic pore size (such as Ap

or �), by adopting a Hazen type model,

k ∝ rwgr (14)

with generalized exponent w [−], in conjunction withan empirically found inverse relation between rgr and σ ′′(Slater and Lesmes, 2002).

Geoelectrical Methods

With geoelectrical methods the subsurface bulk electricalconductivity σ , or resistivity ρ = σ−1 [�m], is measured.Measurements are usually accomplished by injecting aDC, or quasi DC (low-frequency), electric current intothe ground using a pair of electrodes and measuring theresultant voltage drop between another pair of electrodes(Figure 4). This defines a transfer resistance (or impedance,if also IP effects are considered) measurement, which con-tains information about a characteristic region of the under-ground, primarily depending on the measurement geometry(Figure 5). Accordingly, from a set of measurements withdifferent geometry a model of the subsurface electrical con-ductivity distribution can be derived.

−1

−0

1C

urre

nt[A

]

Time t [s]

−2

−0

2

Vol

tage

[mV

]

(a)

(b)0 2 4 6 8

Figure 4 Typical signal waveforms in geoelectrical sur-veying: (a) injected square-wave current, and (b) observedvoltage response after application of a low-pass filter toreduce power line noise

−6 −4 −2 0 2 4 6x [m]

−6 −4 −2 0 2 4 6x [m]

−10

−8

−6

−4

−2

0

z [m

]

−10

−8

−6

−4

−2

0High

sensitivity

Lowsensitivity

(a) (b)

Figure 5 Sensitivity patterns for typical geoelectrical measurements using two separated electrode pairs for currentinjection and voltage measurement (so-called dipole–dipole configuration) assuming a homogeneous ground: (a) bothelectrode pairs placed at the surface, (b) electrode pairs placed at the surface and in a borehole, respectively. Grey circlesindicate position of electrodes (Reproduced from Kemna, 1996, by permission of Landesamt fur Natur & Umwelt derLander Schlesing-Holstain)


Early approaches were restricted in terms of thegeometric parameterization of the underground as well aselectrode placement. For example, in classic geoelectricalsoundings (see e.g. Telford et al., 1990) a multilayerearth model is assumed and only surface electrodes areused. However, with the advances in instrumentationand computational capabilities more flexible electricalimaging methods were developed, yielding high-resolutionimages of the subsurface electrical conductivity distributionbased on surface and/or borehole measurements (for anoverview, see Binley and Kemna, 2005). Following theterminology in medical imaging, this approach is nowadaysusually referred to as electrical resistance (or resistivity)tomography (ERT).

ERT theory is based on the Poisson equation, whichrelates the electric potential, φ(r) [V], owing to anycurrent sources to the underlying electrical conductivitydistribution, σ (r). For a point source (electrode) at theorigin, with current strength I [A], it is

∇ · (σ∇φ) = −Iδ(r) (15)

where δ denotes the Dirac delta function. For arbitrary2D and 3D electrical conductivity models, usually finiteelement or finite difference methods are used to numer-ically solve the modeling (forward) problem defined byequation (15) subject to given boundary conditions (for anoverview, see Hohmann, 1988). The ERT imaging (inverse)problem is inherently nonlinear, nonunique, and stronglyill-posed. However, in most imaging algorithms (e.g. Lokeand Barker, 1995; LaBrecque et al., 1996) nonunique-ness and ill-posedness are overcome by applying somesort of regularization, that is, imposing some constraints(such as smoothing) on the model. More recently, theseapproaches have been extended to also include IP effectsin the interpretation (Oldenburg and Li, 1994; Kemna et al.,2000).


Geoelectrical methods have been extensively used forhydrogeological purposes. Early applications focused onthe characterization of aquifers by means of geoelectricalsoundings and subsequent hydrogeological interpretationof the derived electrical 1D models (e.g. Kosinski andKelly, 1981), usually by taking hydraulic (borehole) datainto account. Although correlations between, for example,electrical conductivity and hydraulic conductivity providedsome calibration capability, these early applications weregenerally only of qualitative nature. However, with theimproved understanding of soil/rock electrical signatures,today electrical-structural models are available that bearthe potential for an improved quantitative aquifer char-acterization, in particular if applied in conjunction with

high-resolution electrical imaging methods (Kemna et al.,2004). With further development of these approaches, itmay become possible to obtain, for example, images ofin-situ hydraulic conductivity (for inverse modeling seeChapter 156, Inverse Methods for Parameter Estima-tions, Volume 4) with relatively high spatial resolution(see Figure 6), which obviously is of extreme practi-cal relevance.

In addition to direct structure characterization, geoelec-trical methods have been likewise proven to be efficientfor the monitoring of subsurface flow and transport pro-cesses (see Chapter 78, Models of Water Flow andSolute Transport in the Unsaturated Zone, Volume 2 andChapter 155, Numerical Models of Groundwater Flowand Transport, Volume 4) when applied in a time-lapsemode. Earlier studies include the monitoring of groundwa-ter flow by profiling or mapping the electrical response toan injected saline tracer, either from the surface (e.g. White,1994; Morris et al., 1996) or with the help of borehole elec-trodes (e.g. Bevc and Morrison, 1991). From the electricalresponse, for example, the effective groundwater flow direc-tion and velocity can be determined. Using modern ERTmethodology, the imaging of subsurface water or solute

Loess

Sand,gravel

Clayey sand,gravel

Clayey silt

0

0 2 4 6

10−2 10−1 100 101

−2

−4

−6

−8

−10

−12

z (m

)

x (m)

K (darcies)

Figure 6 In-situ estimate of hydraulic permeability ina typical Quaternary environment (lithological settingshown on the left) as derived from cross-borehole electricalimaging results in conjunction with the application ofa semiempirical electrical-hydraulic model according toequation (13) (Reproduced from Kemna et al., 2004, bypermission of Society of Exploration Geophysicists)

2272 GROUNDWATER

−5 0 5−5 0 5x [m]x [m]

z [m

]

−10

−5

(a) (b)

0

0.2

0.4

0.6

0.8

1

Rel

ativ

e ch

ange

of

elec

tric

al c

ondu

ctiv

ity

Figure 7 (a) ERT derived map of temporal electrical conductivity changes in the course of a tracer experiment conductedin a heterogeneous aquifer at the Krauthausen test site, Germany. (b) Corresponding result of an equivalent 3Dadvection-dispersion model fit, assuming a linear relation between relative electrical conductivity change and tracerconcentration (Reprinted from Kemna et al., 2002. Copyright 2002, with permission from Elsevier)

plume movement is possible with high spatial resolution(e.g. Daily et al., 1992; Slater et al., 2000; Yeh et al.,2002). Recently, it was demonstrated how cross-boreholeERT results in the course of a field tracer experiment canbe used to quantify the variability of parameters relevantto flow and transport in heterogeneous aquifers (Kemnaet al., 2002) (for flow and transport parameters and modelssee Chapter 152, Modeling Solute Transport Phenom-ena, Volume 4 and Chapter 155, Numerical Models ofGroundwater Flow and Transport, Volume 4). By inter-preting images of temporal electrical conductivity changesby means of equivalent transport models (Figure 7), lon-gitudinal and lateral spreading of a tracer plume, as wellas the degree of mixing and the heterogeneity of trans-port within the plume, can be quantified in terms of fittedequivalent dispersivities (Kemna et al., 2002). The spatialvariability of equivalent transport parameters contains infor-mation about the spatial structure of the flow field, whichin turn can be used to infer information about the struc-ture of the hydraulic conductivity field (e.g. Rubin andEzzedine, 1997; Vanderborght and Vereecken, 2001) (seeChapter 154, Stochastic Modeling of Flow and Trans-port in Porous and Fractured Media, Volume 4).

ELECTROMAGNETIC AQUIFERCHARACTERIZATION

In electromagnetic (EM) methods, electromagnetic fieldsof various sources (e.g. controlled transmitter coils, radiotransmitters, telluric currents) are used to investigate theelectromagnetic properties of the subsurface. Numerousdifferent approaches exist depending on the employedsource type, the measurement principle (e.g. time domainvs. frequency domain), and the analyzed time/frequencyrange (see e.g. Telford et al., 1990).

In this section, we will distinguish between low-frequency EM methods (typically 1–100 kHz), includ-ing frequency-domain and time-domain approaches,

and the high-frequency ground-penetrating radar (GPR)method (typically 10–1000 MHz). Both methodologicalfundamentals as well as hydrogeological applications willbe addressed. Since low-frequency EM methods primar-ily characterize the subsurface in terms of electricalconductivity, it is here again referred to Section “Electrical-hydrogeological relationships” where the basis of its hydro-geological interpretation is provided. In the GPR method,however, primarily the dielectric permittivity is analyzedand therefore in the corresponding section dielectric-hydrogeological relationships are likewise reviewed.

Low-Frequency Electromagnetic Methods

Frequency-domain Methods

A typical frequency-domain (FD) EM system consistsof two coils (loops), a transmitter and a receiver coil(Figure 8). In the transmitter coil an alternating current(frequency typically ranging from 1 to 100 kHz) generatesa magnetic field, the so-called primary field, H ∗

p [A m−1](where ∗ denotes a complex quantity comprising real andimaginary parts). According to Faraday’s induction law, thetime-varying primary magnetic field induces a time-varyingelectric field in the earth. Owing to the conductive nature ofthe earth, this electric field is associated with time-varyingelectric currents, the so-called eddy currents, accordingto Ohm’s law. These eddy currents in turn generate amagnetic field, the so-called secondary field, H ∗

s [A m−1],which is picked up by the receiver coil together withthe primary field. In typical FD-EM methods the mutualcoupling of such a two-coil system is measured, whichcan be described as the ratio of the secondary to primarymagnetic fields. From this, information on the electricalconductivity distribution in the subsurface can be derived.

Maxwell’s equations form the theoretical basis of thegeneral EM problem. For the considered case of a two-coilsystem, however, an apparent electrical conductivity (i.e.the conductivity of an equivalent homogeneous half-space),


Eddy currents

Secondary field

Primary field

Transmitter coil Receiver coil

Figure 8 Measurement principle of a typical two-coil (loop–loop) frequency-domain EM system

σa [S m−1], can be simply computed from the mutualcoupling ratio H ∗

s /H ∗p according to (McNeill, 1980a)

σa = 4

ωµ0r2

(H ∗

s

H ∗p

)′′(16)

if µ ≈ µ0 is assumed and

Q ≡ r

√ωµ0σ

2� 1 (17)

where ′′ denotes the imaginary (quadrature) component,ω [s−1] is the measurement angular frequency, µ0 = 4π ·10−7Vs A−1m−1 the magnetic permeability of free space,µ [Vs A−1m−1] the subsurface magnetic permeability, r

[m] the spacing between transmitter and receiver coils,Q [−] is the so-called induction number, and σ [S m−1]an estimated maximum value for the subsurface electricalconductivity. The assumption of low induction numbers(equation (17)) is valid for most sediments and frequenciesof commercially available EM systems operating in the low-frequency range.

While the interpretation of “apparent” electrical conduc-tivities may be sufficient in certain situations, generallyknowledge of the “true” electrical conductivity distributionin the subsurface is desired. This can be derived, however,by the application of inversion schemes similar to thoseused in geoelectrics, as outlined in Section “Geoelectricalmethods”, in conjunction with appropriate electromagneticforward modeling routines (for an overview, see Oristaglioand Spies, 1999).

The induction number Q is closely related to anotherimportant parameter used in FD-EM methods, particularlyfor survey design, that is, the skin depth (e.g. Telfordet al., 1990)

δ =√

2

ωµ0σ(18)

[m]. The skin depth corresponds to the depth where thetransmitted EM signal is reduced to e−1 of its originalvalue at the surface; it is directly related to the explorationdepth of a FD-EM survey. For a homogeneous earth,obviously δ = r/Q. Equation (18) clearly shows the effectof both subsurface electrical conductivity and measurementfrequency on the attenuation of EM fields. The more

2274 GROUNDWATER

VCP HCP

T RT R

Figure 9 Vertical coplanar (VCP) and horizontal coplanar(HCP) orientations of a loop–loop EM system consistingof transmitter (T) and receiver (R) coils

conductive the earth, the stronger are the EM fieldsattenuated by Ohmic loss, and vice versa.

Besides the skin depth, also coil spacing and orientationare connected with the exploration depth. With increas-ing coil spacing, secondary field responses from greaterdepths are measured owing to the penetration charac-teristics of EM fields. For rigidly connected transmitterand receiver coils, two different system orientations arecommonly used: horizontal coplanar (HCP) and verticalcoplanar (VCP) (Figure 9). In the HCP orientation, thevertical component of the secondary field is measured; inthe VCP orientation its horizontal component is measured.The horizontal component is more sensitive to the shal-low subsurface than the vertical component. Approximatemaximum exploration depths are 1.5 and 0.75 times thecoil spacing for, respectively, HCP and VCP orientations(McNeill, 1980a).

Since the exploration depth of a FD two-coil systemdepends on measurement frequency as well as coil spac-ing and orientation, different surveying modes are possible.Many commercial systems operate in a wide frequencyband in order to enable vertical soundings of the subsurfaceelectrical conductivity via systematic frequency variationfor a fixed measurement position at the surface. Alterna-tively, in order to map the electrical conductivity laterallythe method is typically applied in a profiling mode by mov-ing the system with fixed coil spacing along a transect whileusing a single measurement frequency. Via combination ofboth sounding and profiling modes, and also in conjunctionwith varying coil spacing, multidimensional imaging canbe realized.

Besides the two-coil (loop–loop) configuration outlinedabove, there exist other FD-EM measurement approachesthat utilize external (or far-field), either artificial or nat-ural, sources as the primary field. In magnetotellurics(MT), for instance, natural ionospheric currents are usedas external sources. Far-field artificial sources are primar-ily represented by radio transmitters originally operated formilitary communication or marine/aerial navigation pur-poses; they are used in the very-low-frequency (VLF),or radio-magnetotellurics (RMT), method. At the receiverside, in addition to coils picking up magnetic field com-ponents, also electrodes may be placed in the ground tomeasure electric field responses. Depending on the sourcetype and which field components are measured, specific

data processing techniques have been developed for thedifferent approaches to infer information on the electricalconductivity distribution in the subsurface (for an overview,see Nabighian, 1991).

Importantly, EM methods solely based on magnetic fieldmeasurements do not require galvanic contact with theground and thus bear inherent advantages over geoelectricalmethods (see Section “Geoelectrical methods”). Accord-ingly, EM methods are widely used as an airborne recon-naissance method to enable a swift and relatively cheapmapping of the electrical conductivity distribution. Coilscan be located either on a plane or helicopter, or on arigid boom towed by the aircraft. Similarly, marine sur-veys are possible, where the coils are typically locatedon a cable suspended in the water or dragged along theseafloor. EM methods may also be superior to electricalmethods in highly resistive environments (provided thatinduction effects are still significant), where high contactresistances at the electrodes often impede a deeper penetra-tion of injected direct currents. In conductive environments,on the other hand, the attenuation of EM fields is relativelylarge and hence the use of electrical methods may be moreadvantageous.

Time-domain MethodsTime-domain electromagnetic (TD-EM) methods also use atransmitter and a receiver coil (Figure 10). A static primarymagnetic field is generated by a steady current in thetransmitter coil. When the current is sharply turned off,the associated abrupt change in the magnetic field inducesan electromotive force in the ground, which gives rise todecaying eddy currents (“smoke rings”) flowing in subsur-face conductors. These currents in turn generate a secondarymagnetic field, which is measured at the receiver coil andfrom which an “apparent” electrical conductivity can becalculated (McNeill, 1980b). By means of application ofappropriate modeling and inversion routines, the “true”

Receiver coil Transmitter coil

Eddy currents(“smoke rings )

“

Figure 10 Layout of a typical time-domain EM surveyshowing induced electric currents in the subsurface


electrical conductivity distribution in the subsurface canalso be obtained (Oristaglio and Spies, 1999).

Time-domain EM transmitter coils have relatively largedimensions (coils with an area of several 100 m2 arenot uncommon), whereas the receiver coils have smallerdimensions. Especially in urban areas, the signal-to-noiseratio is significantly improved by using small receiver coils.The receiver coil can be located inside the transmitter coil,at a certain distance, or the transmitter coil itself can beused as receiver. After the transmitter current is turnedoff, measurements may take several seconds. They are thenrepeated several times to increase the signal-to-noise ratio,each time with a different current polarity. This reduces theinfluence of polarization effects in the subsurface on themeasured signal. TD-EM methods are typically used as asounding tool by interpreting early and late-time responses,analogous to the spectral analysis in FD approaches.

Hydrogeological ApplicationsSince all EM methods aim to map the subsurface electri-cal conductivity distribution, they represent, in principle, analternative to geoelectrical methods for all identified hydro-geological applications (see Section “Electrical aquifercharacterization”). EM methods are typically preferred forinvestigations at a larger (e.g. aquifer) scale (e.g. Edet,1991; Puranen et al., 1999; Danielsen et al., 2003). Underfavorable conditions (little anthropogenic interference, pres-ence of high-conductive dissolved solids in the ground-water, or presence of conductive contaminants/tracers), forinstance, an image of the groundwater body or a contami-nant plume can be obtained (e.g. Wynn, 2002).

Ground-Penetrating Radar

Ground-penetrating radar (GPR) is an EM pulse reflectionmethod that is based on similar principles as reflection seis-mics (see Section “Seismic methods”). With GPR the traveltime, like in conventional sonar and radar, and amplitudeof high-frequency (10–1000 MHz) EM waves propagat-ing from a transmitter antenna through the subsurface to areceiver antenna are measured. GPR is sensitive to changesin the dielectric permittivity and electrical conductivity,which cause reflection, refraction, and diffraction, as well asattenuation of the EM waves. Variations in these propertiesinfluence the measured travel times and amplitudes. Permit-tivity and electrical conductivity strongly depend on watercontent, salinity, porosity, grain size, and clay content ofsediments, and therefore many subsurface structural char-acteristics can be detected by GPR. A benefit of GPR is itsrelatively high spatial resolution, as well as the possibilityof on-line visualization of the measuring results.

Dielectric-Hydrogeological RelationshipsExisting dielectric-hydrogeological relationships are basedon either empirical, phenomenological, or some sort of mix-ing models (e.g. Shen et al., 1985; Knoll, 1996; Hagrey

and Muller, 2000). Empirical models mostly relate thevolumetric water content, θv [−], to the relative dielectricpermittivity (dielectric constant), εr [−], which is definedas εr = ε/ε0, where ε [As V−1m−1] is the dielectric permit-tivity and ε0 = 8.854 · 10−12As V−1m−1 its value in freespace. For instance, the relation of Topp et al. (1980) isoften applied:

θv = −5.3 · 10−2 + 2.9 · 10−2 εr

− 5.5 · 10−4 ε2r + 4.3 · 10−6 ε3

r (19)

Volumetric mixing formulas relate the bulk permittivityof a multiphase mixture to the permittivities and volumetricfractions of its constituents. A general form is that ofLichtenecker and Rother (1931) (see e.g. Birchak et al.,1974):

εχ

b =∑

i

Vi εχ

i (20)

where εb is the bulk relative permittivity, Vi [−] andεi are the volumetric fraction and relative permittivity,respectively, of the i-th constituent, and χ is an empiricalconstant accounting for the geometric shape of the solidmatrix (grains). For χ = 0.5, one obtains for a three-component mixture of matrix, water, and air a formulasimilar to the complex refractive index method (CRIM)(e.g. Shen et al., 1985):

√εb = (1 − S)n

√εair + Sn

√εw + (1 − n)

√εm (21)

with porosity n, saturation S = θv/n, and εair, εw, andεm denoting the relative permittivities of air, water, andmatrix, respectively. For εw ≈ 80 and for example, εm = 4(possible value for dry soil) and S = 1 (full saturation),equation (21) yields εb ≈ 4 + 28n + 48n2.

In general, the dielectric properties can be describedby a frequency-dependent, complex dielectric permittivity,ε∗(ω), comprising real (ε′) and imaginary (ε′′) parts. Thefrequency dependence is taken into account by manyphenomenological models such as the Cole–Cole model(Cole and Cole, 1941)

ε∗(ω) = ε∞ + ε0 − ε∞1 + (iωτ)c

(22)

Here, ε0 and ε∞ represent the (real-valued) low andhigh-frequency asymptotes of ε∗, respectively, i denotesthe imaginary unit (i = √−1), c [−] is the so-calledCole–Cole-exponent and τ [s] a characteristic relax-ation time.

Measurement PrinciplesGPR utilizes short EM pulses of broadband dipole antennasthat are emitted into the ground. The propagation velocity,

2276 GROUNDWATER

v [m s−1], of the EM waves is directly related to the realpart of the relative dielectric permittivity, ε′

r, via

v ≈ c0√ε′

r

(23)

where c0 ≈ 3 · 108ms−1 is the vacuum propagation velocityof EM waves and it is assumed that σ � ωε0ε

′r (with σ

[S m−1] being the DC electrical conductivity). Typically,dominant frequencies between 10 and 1000 MHz are used,corresponding to wavelengths, λ = 2πv/ω [m], in therange 0.1 to 10 m. The wavelength defines the maximumspatial resolution of GPR; layers smaller than λ/4 cannotbe resolved (Jol, 1995). Obviously, a higher frequencyprovides a higher resolution.

Solving Maxwell’s equations for the electric fieldstrength, E∗ [V m−1], in case of an isotropic, homoge-neous medium and sinusoidal time dependence exp (iωt)yields for the transversal plane wave traveling in vertical(z [m]) direction E∗(t) = E∗

0 exp (iωt − γ ∗z), where thecomplex propagation constant γ ∗ ≡ α + iβ [m−1] consistsof an attenuation constant

α = ω

c0

√√√√ε′r

2

(√1 +

( σ

ωε′)2 − 1

)(24)

and a phase constant

β = ω

c0

√√√√ε′r

2

(√1 +

( σ

ωε′)2 + 1

)(25)

(see e.g. Hagrey and Muller, 2000).

Equations (23) to (25) exhibit the dependence of thepropagation behavior of the EM waves on material proper-ties. Water is critical for the propagation in rocks becauseits dielectric constant (ε′

r ≈ 80) is much higher than that ofair (ε′

r = 1) and the solid matrix (ε′r ≈ 4 . . . 10) (for typi-

cal values of different materials see e.g. Reynolds, 1997).The electrical conductivity is decisive for the attenuationand thus the exploration depth (skin depth), δ [m], definedas δ = 1/α (cf. equation (18)). In high-conductive envi-ronments, the use of GPR is strongly limited (e.g. vanOvermeeren, 1994).

The EM waves emitted by the GPR transmitter antennainto the ground are reflected and refracted at boundariesbetween regions (layers) with different complex impedance,Z∗ = √

µ0/ε∗ [�], leading to multiple waves associated

with different subsurface raypaths that are recorded with thereceiver antenna. Figure 11 shows the different wavepathsthat can be identified for a typical GPR survey geometrywith two antennas over a layered underground. The corre-sponding travel time curves are plotted in Figure 12.

The air wave propagates with the speed of light abovethe Earth’s surface; it can be used as a reference to markthe beginning of the measurement. Directly at the surface,the ground wave propagates with the velocity v of theuppermost layer. The corresponding travel times for air andground waves are, respectively, tair = x/c0 and tg = x/v,where x [m] denotes the distance in horizontal direction.From simple ray theory, the travel time of the reflectedwave is given as

tr =√(x

v

)2 +(

2d

v

)2

(26)

y

j

jc

e2

s2

e1

s1

s3

d

Groundwater table

Layer boundary

Refraction

Ground wave

Wide-anglereflection

Ref

lect

ion

Soil surface v = c

Ano

ther

rece

iver

posi

tion

Lateral waveAir wave

Rec

eive

r

Offset xTra

nsm

itter

xc

Figure 11 Typical GPR survey geometry showing the different waves that can be observed


0 4 8 12 16 20

Offset [m]

200

150

100

50

0

Tra

vel t

ime

[10−9

s]

Ground wave

Air wave

Lateral wave

Reflection

Wide angle reflectionUpper layer thickness d = 5mUpper layer velocity v = 108 m s−1

Figure 12 Travel time curves for the different wavesshown in Figure 11 for a two-layer model with exemplaryparameter values

where d [m] is the thickness of the uppermost layer. Whena reflected, up-traveling wave encounters the surface at anangle ϕ ≥ ϕcritical = arcsin(v/c0), the so-called lateral wave(see e.g. Huisman et al., 2003) with travel time

tl = x

c0+ 2d

v

√1 −

(v

c0

)2

(27)

can be observed, analogous to the head wave in refrac-tion seismics.

The depth of discontinuities can be directly calculatedfrom the corresponding reflection travel times (equation(26)) for given velocity values, which can be obtainedfrom common midpoint (CMP) measurements (i.e. con-stant midpoint between transmitter and receiver antennas;see e.g. Reynolds, 1997). Another measurement modeis the constant-offset gather, where both antennas aremoved with fixed separation. Because of the high pulsesuccession, quasi-continuous profiling is possible with mov-ing antennas. Borehole surveys may include borehole-to-surface and/or borehole-to-borehole measurements (e.g.Binley et al., 2002). Here, data may be collected in a zero-offset profiling mode (transmitter and receiver in differentboreholes at equal depths) or in a multiple-offset gather(transmitter and receiver in different boreholes at differ-ent depths).

The general conversion of travel times into depths(migration) is equivalent to conversion procedures usedin seismics. Prior to time-to-depth migration, however,the recorded signals must be corrected for possibleerrors caused by incorrect station geometry and zero

time, geometric spreading, transmitter radiation pattern,transmitter amplitude, and high-angle raypaths (Peter-son, 2001).


One of the main applications of GPR is the estima-tion of water content in the unsaturated zone (e.g. Bin-ley et al., 2001, 2002; Alumbaugh et al., 2002; Huis-man et al., 2002, 2003; Schmalz et al., 2002; Schmalholzet al., 2004) using proven petrophysical relationships. Vari-ations in porosity and grain size likewise influence thepropagation velocity of EM waves. Therefore, GPR canprovide indications of changes in properties connectedwith textural or hydraulic parameters. Moreover, lithol-ogy information can be inferred; typically high-velocityzones correlate to sand and gravel layers, while low-velocity regions correlate to clay and silt layers. Peter-son et al. (1999) derived 2D high-resolution images ofporosity and electrical conductivity from radar tomographydata at the Boise hydrogeophysical research site using theCRIM approach (equation (21)). Estimates showed a goodagreement with corresponding data from neutron probemeasurements.

The large contrast in dielectric permittivity betweenunsaturated and saturated zones also makes the ground-water table a common target in GPR surveys; it canbe mapped quasi-continuously with high spatial resolu-tion. Although structures below the groundwater table canbe resolved (Figure 13), information from the saturatedzone may be limited owing to the relatively high atten-uation of EM waves in this region. However, GPR canbe used to investigate various subsurface structures rel-evant to hydrogeology, such as sedimentary sequences,fractured or karstic zones, faults, and cavities (e.g. Ben-son, 1995).

The detection of subsurface contamination has also beenobjective of numerous GPR studies (e.g. Brewster andAnnan, 1994; Greenhouse et al., 1993). Contaminants havebeen found to be indicated by zones where radar reflectionsare weak or absent (Davis and Annan, 1989) or whereadditional reflections occur (Francisca and Rinaldi, 2001).Sauck et al. (1998) noted that owing to biogeochemicalprocesses the electrical conductivity of hydrocarbon spillschanges with time from resistive to conductive; thesechanges can be mapped with GPR.

Using GPR in a time-lapse manner, dynamic processessuch as infiltration of surface water (see Chapter 66, SoilWater Flow at Different Spatial Scales, Volume 2 andChapter 150, Unsaturated Zone Flow Processes, Vol-ume 4) or spreading of a contaminant plume can be studiedby mapping the associated changes in dielectric permittiv-ity over time. Recent developments aim at combining GPRwith other geophysical methods such as electrical resistivitytomography (Binley et al., 2002).

2278 GROUNDWATER

Distance in m

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Mutiple reflection Groundwater tableSurface

0

100

200

300

400

500

600

700

48444038363432302826242220

Sand

Internal reflections

ClayTw

o w

ay tr

avel

time

in 1

0−9 s

Alti

tude

in m

Figure 13 GPR profile measured over aqueoglacial sediments, revealing groundwater table, aquiclude, and reflectionsfrom the saturated zone (Reproduced from Bahloul, 2000, by permission of Shaker Verlag)

COMBINED HYDROGEOPHYSICALAPPROACHES

Combined hydrogeophysical approaches aim at the impro-ved characterization of subsurface structures or processesby using geophysical methods in conjunction with hydro-geological and/or hydrological data. These data are usuallyobtained from well bore measurements (see Chapter 151,Hydraulics of Wells and Well Testing, Volume 4) andtherefore carry only limited spatial information. Most of thecombined hydrogeophysical approaches require relation-ships between hydrogeological and geophysical properties.In this part, we will focus on aquifer systems althoughconsiderable work on combining geophysical with hydro-geological data is presently available in the vadose zoneliterature (e.g. Binley et al., 2001; Alumbaugh et al., 2002;Huisman et al., 2002).

Earlier work in hydrogeophysics has focused on syn-thetic case studies showing the potential of using geophys-ical data for aquifer characterization. Rubin et al. (1992)for example presented a method to identify the perme-ability distribution in near-surface aquifers based on ahydrogeophysical inversion technique. They incorporated,in addition to sparsely sampled pressure and hydraulicconductivity data, densely sampled seismic data, derivedfrom a reflection or tomography survey in combinationwith empirical relationships between seismic and hydraulicproperties. The feasibility of their procedure is illustratedusing a few synthetic case studies. Copty et al. (1993)showed that seismic information improved the hydraulicconductivity estimates even in cases where a random errorwas added to the seismic velocities. They proposed aBayesian updating of the hydraulic conductivity field usingseismic velocity-hydraulic conductivity-pressure relation-ships, thereby accounting for estimation uncertainty. Basedon these findings, further studies were conducted on thejoint use of geophysical and well bore data to charac-terize hydraulic properties of aquifers. Copty and Rubin(1995) used a stochastic procedure to incorporate seismic

surface reflection data and well data into the identificationof the log hydraulic conductivity field and the spatial dis-tribution of lithofacies. This procedure was tested on asynthetic case made up of a geological section consisting ofa series of sandy aquifers separated by clay layers. Hynd-man et al. (1994) used a combination of seismic and tracerdata to estimate spatial patterns of aquifer properties such ashydraulic conductivity and dispersivity (see Chapter 155,Numerical Models of Groundwater Flow and Transport,Volume 4) for two synthetic aquifers with the same seismicprofile but with different hydraulic conductivity profiles ina hypothetical lithological cross section with two differentimages. Their proposed split inversion method (SIM) doesnot require knowledge on the relationship between seis-mic velocity and hydraulic conductivity but it assumes theexistence of some relationship for large-scale lithologicalzones. This method was then used to estimate the litholog-ical zonation of the Kesterson aquifer (San Joaquin Valley,California), the hydraulic conductivity of each zone, andits dispersivity (Hyndman and Gorelick, 1996). Hyndmanand Gorelick (1996) showed that combining seismic andtracer data has the potential to provide high-resolution esti-mates of aquifer zonation and hydraulic properties. Hubbardet al. (1999) performed numerical analyses of synthetic casestudies where the scale of the geophysical measurements(tomographic radar and seismics) was varied relative to thescale of hydraulic conductivity. Site-specific petrophysicalmodels were used to relate hydraulic conductivity to eitherseismic or radar velocities. The study suggested that col-lection of a few tomographic profiles and interpretation ofthese profiles together with limited well bore data can pro-vide information on the correlation structure of hydraulicconductivity.

In the last years, a few studies appeared that deal with realcase studies. McKenna and Poeter (1995) used geological,geophysical, and hydrological data to identify hydrofa-cies and to define their spatial distribution for a field sitelocated in Golden, Colorado. Hydrofacies are defined ashomogeneous possibly anisotropic geological units being


hydrogeologically meaningful. They allow the constructionof subsurface models with sharp interfaces in hydraulicconductivities. McKenna and Poeter (1995) used multiple-indicator, stochastic simulation conditioned on hard and softinformation to produce realizations of hydrofacies geome-tries. Hard data are those data obtained in the verticaldirection from wells whereas soft data are available betweenwells (e.g. geophysical data derived from surface or cross-borehole surveys). Each of these geometries then servesas zonation pattern for inverse flow modeling in order todiscard implausible realizations and to characterize eachzonation by a specific hydraulic conductivity value. Hynd-man and Gorelick (1996) applied SIM to estimate theeffective hydraulic conductivity of the observed litholo-gies at the Kesterson aquifer and the dispersivity valuefor the entire domain, as already outlined above. In theirapproach, they combined seismic, hydraulic, and tracer datausing SIM. For the Kesterson aquifer, SIM adjusts in totalsix parameters (two seismic velocity parameters identify-ing three lithological classes with specific velocity, threehydraulic conductivities, and a regional value for the dis-persivity) to best fit tracer data. A first step in the approachwas to estimate seismic slowness (inverse seismic veloc-ity) from available seismic cross sections obtained fromwell bore measurements. From these data, vertical and hor-izontal variograms for the region were derived. SequentialGaussian simulation was used to develop multiple 3D con-ditional seismic slowness realizations. The SIM was thenused to identify three lithological classes within each real-ization, each with a specific slowness value. The effectivehydraulic conductivity was then estimated for each litho-logical zone such that observed tracer concentrations wereoptimally matched, and a value of dispersivity for the wholeregion was derived. The obtained results demonstrate thatcombining seismic and tracer data has the potential to derivestructural information and hydraulic properties of aquifers.

Another interesting study was presented by Chen et al.(2001), who explored the possibility of using ground-penetrating radar and seismic tomography to estimate thehydraulic conductivity at the South Oyster site using aBayesian approach. Their approach uses a-priori informa-tion on the hydraulic conductivity measured at selectedwells using flowmeter technique. Geophysical data wereonly used at those wells where hydraulic conductivity wasavailable. Correlation analysis showed positive correlationsbetween GPR velocity and natural log conductivity of 0.68and between seismic velocity and natural conductivity of0.67. GPR attenuation and log conductivity appeared tobe uncorrelated. To estimate log conductivity, a stochasticframework in which log conductivity, GPR velocity, GPRattenuation, and seismic velocity are considered as spatialrandom functions was adopted. Normal linear regressionmodels are used to update conditional probability distribu-tion functions (pdf) of seismic velocity, attenuation, and

GPR velocity needed in the Bayesian likelihood approachusing collocated hydrological (in this case hydraulic con-ductivity) and geophysical data. Chen et al. (2001) showedthat especially velocity data hold potential in improvingestimation of hydraulic conductivity even in cases whereboth hydraulic conductivity and geophysical tomographydata vary in narrow ranges. Important for this approach is,however, the presence of correlations between the variousproperties. Hubbard et al. (2001) used a suite of methodssuch as surface GPR and seismic crosshole tomography,cone penetrometer, and borehole flowmeter to interpret sub-regional and local stratigraphy, to provide high-resolutionhydraulic conductivity estimates and log conductivity spa-tial correlation functions. They derived horizontal and verti-cal intregal scales for hydraulic properties using a Bayesianapproach (see e.g. Chen et al., 2001) including tomographicdata (e.g. seismic and radar velocity) and a-priori knowl-edge of the hydraulic conductivity pdf. Using first-orderlinear stochastic theory, the longitudinal dispersion coeffi-cient of an inert solute plume in an aquifer with propertiesderived from the Oyster site was calculated. From thisvalue, the longitudinal plume length was estimated andcompared with visual evaluation of the plume length ofa bromide plume observed at the Oyster site. Both lengthscales were found to be in reasonable agreement.

Gloaguen et al. (2001) estimated the water content ofan unconfined sandy aquifer underlain by a 20 m thickclay layer using GPR. The 2D distribution of the satu-rated/unsaturated thickness was derived from a combina-tion of GPR reflection, piezometric, and stratigraphic datausing co-kriging. Once the piezometric levels and the claylayer depth were determined, travel times were used tocompute the velocity field, which was then transferred towater content using the CRIM relation (equation (21)).From observed GPR attenuations and electrical conductivi-ties observed in piezometer wells, porosity was determinedusing Archie’s law (equation (9)).

OUTLOOK

Noninvasive characterization of aquifer properties andhydrological processes using geophysical methods willbecome more and more important in the next years. Geo-physical methods in combination with hydrogeological andhydrological models and concepts may help to overcomesome of the unresolved problems in subsurface researchsuch as, for example, upscaling issues and characteriza-tion of space-time structures of subsurface properties andprocesses. This requires a better integration of hydrolog-ical, hydrogeological, and geophysical knowledge. In thisarticle, research activities in the area of combined hydro-geophysical approaches were outlined, which represent afirst step in tackling these unresolved problems. Furthersteps involve the development of data fusion techniques to

2280 GROUNDWATER

effectively integrate available information from the varioussources, but also the development of novel technologiesand methodologies with improved imaging and character-ization capabilities. More recent methodological advancesinclude, for instance, the surface nuclear magnetic reso-nance (SNMR) method – enabling direct access to subsur-face water – and the magneto-electrical resistivity imag-ing technique (MERIT) – utilizing also magnetic fields ofimpressed electric currents (for an overview, see Yaramanciet al., 2005). The establishment of hydrogeological test sitesproviding detailed information on geophysical, hydrologi-cal, and hydrogeological quantities is essential to developand validate novel approaches.

Acknowledgments

We are grateful to an anonymous reviewer whose commentshelped to improve this article.

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