estimation of aquifer hydraulic parameters from surficial geophysical methods: a case study of...
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Journal of Hydrology (2007) 338, 122–131
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Estimation of aquifer hydraulic parametersfrom surficial geophysical methods: A case studyof Keritis Basin in Chania (Crete – Greece)
Pantelis M. Soupios a,*, Maria Kouli a, Filippos Vallianatos a,Antonis Vafidis c, George Stavroulakis b
a Technological Educational Institute of Crete, Department of Natural Resources and Environment,Laboratory of Geophysics & Seismology, 3 Romanou, Chalepa, 73133, Chania, Crete, Greeceb Technological Educational Institute of Crete, Department of Natural Resources and Environment,Laboratory of Water and Soil Quality Control, 3 Romanou, Chalepa, 73133, Chania, Crete, Greecec Technical University of Crete, Department of Mineral Resources Engineering, Laboratory of Applied Geophysics,Campus University, Kounoupidiana, Akrotiri, Chania, Crete, Greece
Received 28 February 2006; received in revised form 13 February 2007; accepted 22 February 2007
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28
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KEYWORDSGeophysical methods;Groundwater manage-ment;Hydraulic properties;Hydraulic testing;Formation factor
22-1694/$ - see front mattei:10.1016/j.jhydrol.2007.02
* Corresponding author.21023003.E-mail addresses: soupios
[email protected] (M. Vallianatos), [email protected] (G. Stavroulakis).
r ª 200.028
Tel.: +3
@chania. Kouli),d.tuc.gr
Summary Knowledge of aquifer parameters is essential for the management of ground-water resources. Conventionally, these parameters are estimated through pumping testscarried out on water wells. Few boreholes may be available and carrying out pumping testsat a number of sites may be costly and time consuming. The application of geophysicalmethods in combination with pumping tests provides a cost-effective and efficient alter-native to estimate aquifer parameters. A geophysical method is used to obtain aquifercharacteristics that are estimated through the pumping tests. A correlation is establishedbetween these parameters at other sites where pumping has not been carried out. In thisway, the entire investigation area could be covered to characterize an aquifer system.This study has been carried out in the Keritis basin in Chania, Crete – Greece, wherethe aquifer characteristics are required for the management of groundwater in the region.ª 2007 Elsevier B.V. All rights reserved.
7 Elsevier B.V. All rights reserved
0 2821023037; fax: +30
.teicrete.gr (P.M. Soupios),[email protected](A. Vafidis), gstav@chania.
Introduction
During the last decades, the incremental need of accurateglobal groundwater resource assessment has led to a rapidlygrowing awareness in the field of groundwater manage-ment. Therefore, quantitative description of aquifers has
.
Estimation of aquifer hydraulic parameters from surficial geophysical methods: A case study 123
become vital in order to address several hydrological andhydrogeological problems. Fluid transmissivity, transverseresistance, longitudinal conductance, hydraulic conductiv-ity and aquifer depth are fundamental properties describingsubsurface hydrology. As a result, many investigation tech-niques are commonly employed with the aim of the estima-tion of spatial distribution of the above mentioned hydraulicparameters. Field estimations of the above parameters arenot always available. Hydraulic conductivity appears to bethe most problematic to obtain because of either the greatrange of observed values or the unsatisfactory laboratorymeasurements (Zecharias and Brutsaert, 1988; Mendosaet al., 2003).
Traditionally, one of the most effective ways of hydraulicconductivity calculation are the pumping tests that are car-ried out on certain boreholes sites. Nevertheless, a probablesparse spatial distribution of the available boreholes givesrise to significant problems in modeling the hydrogeologicalsystems. In such cases, drilling new boreholes has proved tobe rather expensive as well as time consuming.
Geophysicists have realised that the integration of aqui-fer parameters calculated from the existed boreholes loca-tions and surface resistivity parameters extracted fromsurface resistivity measurements can be highly effective,since a correlation between hydraulic and electrical aquiferproperties can be possible, as both properties are relatedto the pore space structure and heterogeneity (Kelly,1977; Mazac et al., 1985; Huntley, 1986; Mazac et al.,1988; Boerner et al., 1996; Christensen and Sorensen,1998; Rubin and Hubbard, 2005; De Lima et al., 2005; Niwaset al., 2006).
Specifically, resistivity techniques are well-establishedand widely used to solve a variety of geotechnical, geolog-ical and environmental subsurface detection problems(Ward, 1990). The primary purpose of the resistivity meth-od is to measure the potential differences on the surfacedue to the current flow within the ground. Since the mech-anisms which control the fluid flow and electric currentand conduction are generally governed by the same physi-cal parameters and lithological attributes, the hydraulicand electric conductivities are dependent on each other.Of course, we should note that the factors which governthe current flow and conduction into the soil (lithology,size, shape, mineralogy, packing and orientation of grains,shape and geometry of pores and pore channels, magni-tudes of porosity, tortuosity and permeability, compac-tion, consolidation and cementation and depth and waterdistribution) (Salem, 1999) are extremely variable. Thus,it should be born in mind that the measured resistivity val-ues are not absolute but relative, and therefore only rela-tive conclusions about the area’s hydraulic parameterscould be made.
For this purpose, surface geophysical methods have beenused for aquifer zone delineation and evaluation of the geo-physical character of the aquifer zone in several locations(Ungemach et al., 1969; Kelly, 1977; Heigold et al., 1979;Kosinki and Kelly, 1981; Niwas and Singhal, 1981, 1985;Frohlich and Kelly, 1985; Huntley, 1986; Shakeel et al.,1988; Worthington, 1993; Frohlich et al., 1996; Yadav andAbolfazli, 1998; De Lima and Niwas, 2000; Salem, 1999,2001a,b; Hubbard and Rubin, 2002; Niwas and de Lima,2003; Dhakate and Singh, 2005; Khalil, 2006).
The aim of our study is to demonstrate the use of aquiferparameters in the assessment and management of the shal-low (sedimentary) groundwater resources of Keritis Basin,which is located in the eastern part of Chania Municipality,Crete Island, Greece. Keritis Basin is the main source of irri-gation water for the whole plain land of Chania Basin, one ofthe most developed agricultural areas in Crete. The inade-quate number of boreholes has been overcome using thecorrelation between geophysical parameters extracted fromsurface electrical measurements interpretation and aquiferhydraulic parameters extracted from pumping tests carriedout on the existed boreholes. This approach has been uti-lized in order to estimate aquifer parameters in numerouslocations providing effective and inexpensive characteriza-tion of the study area aquifer system. The calculated aqui-fer parameters have been interpolated using the radial basisfunction (RBF) interpolator. Compared with the rest ofinterpolation methods, RBF gives the best cross-validationresults and root-mean-squared (RMS) errors for the avail-able data.
Study area
Crete is considered to be a semi-arid region. The averageannual precipitation is estimated to be 900 mm, the poten-tial renewable water resources 2650 m3/yr and the realwater used about 485 million m3/yr (Chartzoulakis et al.,2001). The major water use in Crete is in irrigation for agri-culture (84.5% of the total consumption), while domesticuse is 12% and other uses 3.5% (Chartzoulakis et al., 2001;Tsagarakis et al., 2004).
The study area is situated from 35�2450N to 35�3000N,and 23�4950E to 23�5800E (Fig. 1). The total county areais 137 km2 and is located in the central part of Keritis riverdrainage basin, 3.5 km west of the city of Chania. The cen-tral study area is characterized by a rather gentle topogra-phy. It is bordered by the villages Vryses and Galatas to thenorth, Skines and Fournes to the south, Psathogiannos to thewest and Varypetron to the east (Fig. 1). The area is drainedby the Keritis river which is considered to be the main riverof the area.
The climate of the study area is sub-humid Mediterra-nean with humid and relatively cold winters and dry andwarm summers. During winter that starts in November,the weather is unstable due to frequent changes from lowto high pressures.
The annual rainfall for the broader Chania area has beenestimated to be 665 mm (Chartzoulakis et al., 2001). About65% of the annual precipitation is lost to evapotranspiration,21% as runoff to sea and only 14% recharges the groundwater(Chartzoulakis et al., 2001). The rainfall is mainly concen-trated in the winter months while the drought period ex-tends to more than 6 months (May–October). The monthlyevaporation ranges from 140 mm to more than 310 mm inthe peak month. As a result, the water resources availabilityis limited due to the spatio-temporal variations of precipita-tion (Tsagarakis et al., 2004). The demand for irrigationwater is high, while at the same time only 31.0% of theavailable agricultural land is irrigated (Tsagarakis et al.,2004). The growing water demands make the water re-sources management extremely important for sustainabledevelopment.
Figure 1 Location map of the Keritis Basin, Chania, Crete Island, Greece.
124 P.M. Soupios et al.
Geo-tectonic and hydrolithological context
The surficial geology is composed of Quaternary depositsthat form depositional plains oriented from north to southat an elevation of 20–200 m above msl. Miocene to Pliocene
Figure 2 Hydrolithological map of the study area withtectonic faults overlain. The locations of boreholes as well asvertical electrical sounding (VES) are shown.
sediments crop out in the central and the northwestern partof the study area and Late Triasic carbonates (Tripolisnappe) in the northeastern part. Dissected hills of phyllitesand quartzites, a Late Carboniferous to Late Triassic pack-age of sedimentary rocks composed mostly of quartz-richsiliciclastic sediments, with minor limestone, gypsum, andvolcanic rocks (Krahl et al., 1983) are observed mainly inthe southwestern and southeastern part of the study areaat an elevation ranging from 200 to 580 m above msl. TheTriassic to Early Cretaceous carbonates of the Trypalionnappe are exposed in the central-eastern part of the studyarea.
In the present work the geological units have been clas-sified in the sense of permeability into four hydrolithologicalunits (Fig. 2): high permeability rocks which comprise thekarstic Triassic limestones of Tripolis and Trypalion nappes,medium permeability rocks which consist of the Quaternarydeposits as well as the Miocene to Pliocene conglomeratesand marly limestones, low permeability rocks which consistsof the Pliocene to Miocene marles and impervious rockswhich mainly consist of the phyllites–quartzites unit.
The local tectonic regime of the study area is character-ized by faults of NW-SE and E-W directions, which define theboundaries between the existing hydrolithological units(Fig. 2) as well as the groundwater flow direction. Thus,these tectonic structures probably act as underground damsbounding the underground water movement.
Geoelectrical investigation
During the current work, twenty-one (21) of the total fifty-four (54) geoelectrical soundings (CH# and V#) (Fig. 2) witha maximum half current electrode separation of 500 m havebeen used. All the data (54 VES measurements) were col-lected in four phases of field work. The first data set was ac-quired by CGG Company (HydroGaia, 1972), the second data
Estimation of aquifer hydraulic parameters from surficial geophysical methods: A case study 125
set was collected by Technical University of Crete (Vafidiset al., 1991), the third data set was gathered by Apostolop-oulos et al. (2001), and the last one was collected by theTechnological Educational Institute of Crete in 2004.Twenty-one of the total 54 available VES measurementswere selected as the most appropriate for the final model-ing since they combine the low RMS error (best in quality)with the good coverage of the area of interest. The Schlum-berger electrode array was selected because is the mosttime effective in terms of field work.
The measurements were planned with the intention ofcovering the whole area while at the same time we wantedto be as close to the existing boreholes as possible in orderto use them for calibration.
All resistivity soundings were inverted using the IPI2Winsoftware. This package performs an automated approxima-tion of initial resistivity model using the observed data(Bobachev, 2002). It works in an iterative mode by calculat-ing at the end of each step: (a) an updated model of layerthickness and resistivity and (b) the misfit function betweenobserved and calculated data. All resulting models produceda low RMS relative error of the order of 3%.
The starting model used during the inversion for each ofthe measured VES locations, consisted of four layers over ahalf-space and all depths were constrained again accordingto the nearest borehole information.
Table 1 Estimation of formation factor and other hydraulic para#, V#, L5 and BA-ND
Location Bulkresistivity(X-m)
Aquiferresistivity(X-m)
Aquiferthickness(m)
Formationfactor (Fa)
1/Fa
CH-1 122 30 50.2 4.0667 0.245CH-3 74 8.5 48 8.7059 0.114CH-4 60.4 7.9 27.6 7.6458 0.130CH-5 60 7.4 115.6 8.1081 0.123CH-6 72.2 7.6 79.8 9.5000 0.105CH-7 75 15.35 48.3 4.8860 0.204CH-8 82.4 18.3 88.2 4.5027 0.222CH-9 185 22.72 61.3 8.1426 0.122CH-10 131 17.15 113 7.6385 0.130CH-11 240 26.31 111.2 9.1220 0.109CH-12 126 28.38 90 4.4397 0.225
a m Low boundporosity
Porosity Upper boporosity
1.04 2.3 0.406 0.368 0.3460.5 2.31 0.287 0.269 0.2531.1 1.61 0.286 0.248 0.2271 1.3 0.197 0.165 0.1481 1.5 0.245 0.210 0.1911 1.7 0.289 0.252 0.2321 1.9 0.329 0.292 0.2711 2.1 0.366 0.328 0.3071 2.3 0.399 0.361 0.3401 2.5 0.430 0.392 0.371
diameter d2 0.01 (0.0001) 0.324 0.289 0.269
Sensitivity analysis on porosity and hydraulic conductivity estimates u
Valuable information such as, in situ water conductivitymeasurements (derived from the existing boreholes) andknowledge of the aquifer thickness, were collected for ele-ven (11) of the total twenty-one (21) VES measurements, inorder to have an accurate estimation of the formation fac-tor as well as for the extraction of all the hydraulic param-eters as is shown in Table 1.
Although a good fit to the data was obtained, the resistiv-ities of several layers and of the half-space were not re-solved. It is important to note that in isolatedSchlumberger soundings only 1D inversion is possible whilethe distortions introduced by treating a 3D problem applying1D or 2D modeling procedures can be quite significant andmay produce a bias towards the high resistivity values. Itis therefore not surprising that the model parameters can-not be resolved satisfactory.
Determination of aquifer properties
It is essential to estimate the hydraulic properties of any gi-ven aquifer system, in order to obtain quantitative informa-tion in groundwater flow and contaminant transportmodeling. The most common way to obtain such aquiferhydraulic properties (hydraulic conductivity and transmis-sivity) is either from pumping tests or laboratory experi-ments, when core samples are available.
meters from the geophysical data obtained from locations CH-
Longitudinal unitconductance (S)
Transverseresistance (TR)
Transmissivity (m2/s)
9 1.673 1506 1.34E�029 5.647 408 1.28E�028 3.494 218.04 7.37E�023 15.622 855.44 3.09E�023 10.500 606.48 2.13E�027 3.147 741.405 1.29E�021 4.820 1614.06 2.35E�028 2.698 1392.736 1.64E�029 6.589 1937.95 3.02E�026 4.227 2925.672 2.97E�022 3.171 2554.2 2.40E�02und Average
porosityHydraulicconductivity (m/s)
Hydraulic conductivity(m/day)
0.373 5.15E�04 4.45E+010.273 1.50E�04 1.29E+010.254 1.14E�04 9.84E+000.170 2.78E�05 2.40E+000.215 6.31E�05 5.45E+000.258 1.21E�04 1.05E+010.297 2.07E�04 1.79E+010.333 3.25E�04 2.81E+010.367 4.79E�04 4.14E+010.397 6.73E�04 5.81E+01
2.67E�04 2.31E+01
sing different Archie’s coefficients (grain size = 0.01 m).
Figure 3 Determination of the intrinsic formation factor, Fi,plotting 1/Fa versus fluid resistivity, qw.
126 P.M. Soupios et al.
Concerning our work, since bulk and water resistivitieswere available at several locations, it was desirable toexamine the possibility to obtain hydraulic conductivity val-ues using the Kozeny–Carman–Bear equation (Domenicoand Schwartz, 1990). The porosity (/) required in this equa-tion was estimated using Archie’s law, with its empiricalnature and dependence on Archie’s parameters. Moreover,we calculated the range of hydraulic conductivities pro-duced by the plausible values of these porosities.
Archie’s law (Archie, 1942) relates the bulk resistivity ofa fully saturated granular medium to its porosity and theresistivity of the fluid within the pores according to Eq. (1):
qo ¼ a � qw � /�m ð1Þ
where qo is the bulk resistivity, qw is the fluid resistivity, / isthe porosity of the medium, m is known as the cementationfactor, although it is also interpreted as grain-shape orpore-shape factor, and the coefficient a is associated withthe medium and its value in many cases departs from thecommonly assumed value of one.
For a clay-free medium, the qo/qw ratio is known as theintrinsic formation factor, Fi. Thus, Eq. (1) could be easilyreformulated in the following form, Eq. (2),
/ ¼ e1m�lnðaÞþ1
m�ln 1F i
� �ð2Þ
The values of the coefficients a and m should, ideally, bedetermined for each site under investigation. However, dueto lack of core samples in our test area, this was not possi-ble and an alternative approach was adopted whereby awide range of values for a and m reported in the literaturewas used to obtain porosity estimations. Worthington (1993)reported three different expressions for the intrinsic forma-tion factor in relation to the porosity of samples from differ-ent locations. A fourth expression in which the coefficient ahas the value of one while m is allowed to vary from 1.3 to2.5 was suggested by Jackson et al. (1978) and De Lima andSharma (1990).
However, for field data a complication arises due to thefact that Archie’s formula (Eqs. (1) and (2)) is valid only forclay-free, clean, consolidated sediments. Any deviationsfrom these assumptions make the equation invalid as dis-cussed by Worthington (1993). In the case of unclean, clayeyand shaley sands and a mixture of sand/rubble/gravels, anadditional corrective step for clay conductivity is required.A large number of such models are currently in use and themajority of them are either shale-fraction or cation-ex-change models, derived empirically using the concept ofparallel conductor (Patnode and Wyllie, 1950; Winsauerand McCardell, 1953; Waxman and Smits, 1968; Clavieret al., 1984; Sen et al., 1988).
As our aquifer system consists of clayey/silty sand mate-rial enhanced with rubbles and gravels, a modification ofthe Archie’s equation was required. For this reason, theWaxman–Smits model was considered (Vinegar and Wax-man, 1984) as it relates the apparent and intrinsic formationfactors, Fa (the ratio of bulk resistivity to fluid resistivity)and Fi, after taking into account the shale effects. Accord-ing to Worthington (1993),
Fa ¼ F i � ð1þ BQvqwÞ�1 ð3Þ
where the BQv term is related to the effects of surface con-duction, mainly due to clay particles. In case surface con-duction effects are non-existent, the apparent formationfactor becomes equal to the intrinsic one.
Re-arranging the terms of Eq. (3), we obtained a linearrelationship between 1/Fa and qw,
1
Fa¼ 1
F iþ BQv
F i
� �qw ð4Þ
where 1/Fi is the intercept of the straight line and BQv=F i
represents the gradient (Huntley, 1986; Worthington,1993). Thus, by plotting 1/Fa versus fluid resistivity qw, weshould, in principle, obtain a value for the intrinsic forma-tion factor, which will subsequently enable us to estimateporosity using Eq. (2) as is shown in Table 1.
To follow the above approach, we used bulk resistivitiesqo, as resulted from 1D resistivity inversion coupled with themeasured fluid electrical resistivities, qw, obtained usingthe wells nearest to the VES locations. These values wereused to calculate the apparent formation factor (Fa = qo/qw) of the saturated top aquifer. From Eq. (4), it is clearthat a major source of error would be the wrong estimationof the apparent formation factor which depends on the bulkresistivity as estimated from the inversion models. Thus,assuming that the fluid resistivities were measured correctlyin situ, we considered by how much the resistivities result-ing from the inversion could vary. This uncertainty wasmainly due to the fact that some of the boreholes (samplelocations) were at some distance away from the region rep-resented in the resistivity model.
The resistivity values obtained from the inversions andthe estimated apparent formation factors are shown in Ta-ble 1.
Fig. 3 shows 1/Fa plotted versus fluid resistivity, qw. Thedata could be easily separated in two individual groups(depending on the geological complexity of the study area)with common characteristics as is shown by the two fitted
Estimation of aquifer hydraulic parameters from surficial geophysical methods: A case study 127
lines. This is obtained by applying least squares best fit ofthe individual subgroups of the data, and the range of theinverse of the intrinsic formation factor Fi is calculated.For our data set, the Fi varies between 8.27 and 11.96 asis estimated from Fig. 3. The porosities could now be deter-mined through Eq. (2) for the reported values of a and m asshown in Table 1 applying an upper and a lower bound forthe determined porosity based on the division of the datainto the groups as mentioned above.
The hydraulic conductivity estimation was achievedthrough the use of the Kozeny–Carman–Bear equation, gi-ven by Domenico and Schwartz (1990) as:
k ¼ dwg
l
� �� d2
180
!� /3
ð1� /Þ2
" #ð5Þ
where d is the grain size, dw is the fluid density (taken to be1000 kg/m3), and l is the dynamic viscosity taken to be0.0014 kg/m s (Fetter, 1994). The estimated hydraulic con-ductivity values (in m/s and in m/day) using Eq. (5) areshown in Table 1.
The average geometrical hydraulic conductivity value forthe aquifer under investigation is 2.67·10�4 m/s or 23.1 m/day.
Two of the most important parameters in electrical pros-pecting are the longitudinal unit conductance (S, layerthickness over resistivity) and the transverse unit resistance(TR, layer thickness times resistivity), which define the DarZarrouk Parameters (DZP) (Maillet, 1947). The DZP werealso calculated for interpreted sounding layer parametersafter taking into account only aquifer resistivities and itsthicknesses:
S ¼ h
rand TR ¼ r � h ð6Þ
Figure 4 Relation between transverse resistance, TR (X2-m)and transmissivity, T (m2/day). The best fit regression line ispresented and is the following, TR = 0.19 Æ (T)1.28using 11 datapoints.
where h is the thickness of the aquifer (m) and r is the resis-tivity of the aquifer (X-m).
The transmissivity (ability of the layer with permeabilityk to transmit fluids through its entire thickness h, see Eq.(7)), using the estimated hydraulic conductivity(k = 2.67 · 10�4 m/s), was also calculated using Eq. (7),
T ¼ k � h ð7Þ
where T is the transmissivity (m2/s), k is the hydraulic con-ductivity (m/s) and h is the aquifer thickness (m). The ex-tracted parameters for each VES location are shown inTable 1. The transverse resistance (X-m2) is directly corre-lated to the transmissivity (m2 day�1) as is shown in Fig. 4.The progressive increase in both parameters suggests thatthe fluid potential (indicated by transmissivity) of the aqui-fer in the study area, increases considerably as the trans-verse resistance increases. The aforementionedsimultaneous change is attributed to the influence of thehydraulic and electric anisotropies, as well as to the varia-tions in lithology, mineralogy and size of the grains and sizeand shape of the pores and pore channels (Salem, 1999).
Correlation of the observed and estimatedhydraulic parameters
The most common in situ test for the calculation of realwater supply and the indirect estimation of hydraulic con-ductivity in a borehole is the pumping test performed onwells, and involves the measurement of the rise and fallof water level with respect to time. The water level fluctu-ations with time, are then interpreted to arrive at aquiferparameters. The availability of pre-existing wells makesthe pumping test cost-effective.
More than 20 water wells were operated throughout thestudy area and one of them was selected as the most repre-sentative for the indirect estimation of the hydraulic con-ductivity through the use of pumping test (both pumpingand recovery). The available information, such as, esti-mated water supply (m3/h), pumping water level (m), andrelative lithology were collected from the registration formsof the available water wells in the study area.
Using the estimated water supply (Q = 100 m3/h), thediameter (d) of the screen, as well as the thickness (h) ofthe aquifer, the hydraulic conductivity was estimated usingthe following formula:
Qðm3=hÞ ¼ p � dðmÞ � hðmÞ � kðm=hÞ ð8Þ
Applying the above equation, the hydraulic conductivityk, is estimated equal to 6.8 · 10�4 m/s (coarse grainedsand). This indirect observed value of hydraulic conductiv-ity, is in agreement with the estimated aquifer parameter(k = 2.67 · 10�4 m/s, medium grained sand) as calculatedfrom the surficial geophysical measurements. Both valuesare within the range of 10�5–10�2 m/s which is the charac-teristic range of a pure sands and gravel aquifer (Kallergis,1999).
Results and discussion
The calculated hydraulic parameters were interpolated withgeostatistical as well as deterministic techniques. After
128 P.M. Soupios et al.
applying and testing several geospatial prediction tech-niques, the radial basis function (RBF) interpolator was cho-sen (spline with tension) for interpolating aquifer thickness,transverse resistance as well as transmissivity values. Com-pared with the rest of interpolation methods, RBF gave thebest cross-validation results and root-mean-squared (RMS)errors (28.74 m for aquifer thickness, 473.6 for transverseresistance and 325 m2/day for transmissivity). RMS is givenby the equation:
RMS ¼Xni¼1
ðDIip � DIioÞn
2
;
where DIip is the predicted value for site i, DIio is the ob-served value for site i, and n the total number of sites.
Cross-validation (CV) uses all of the data to estimate thetrend. Then it removes each data location, one at a time,and predicts the associated data value. The predicted andactual values at the location of the omitted point are com-pared. For all points, cross-validation compares the mea-sured and predicted values. Generally, the best model isthe one that has the mean nearest to zero and the smallestroot-mean-squared prediction error. If the prediction errorsare unbiased, the mean prediction error should be nearzero. However, this value depends on the scale of the data(2.254 m for the aquifer thickness, 76.97 for transverseresistance and 27.44 m2/day for transmissivity). In addition,the use of Kriging interpolators led to a great number of
Figure 5 Shaded relief of the Keritis basin area with aquiferthickness map and tectonic faults overlain. A spatial correlationbetween aquifer thickness and hydrolithological units is obvi-ous, as aquifer thickness tends to decrease with the transitionfrom permeable to impervious rocks.
artifacts, possibly because of the limited number as wellas the random distribution of the available sample sites.
The radial basis function (RBF) is commonly used forinterpolating small surfaces and has been found to be appro-priate for interpolating electrical conductivity values (Rob-inson and Metternicht, 2006). For each point, an RBF isdefined, which depends on the Euclidean distance betweenthe prediction location and each sample location. The‘‘roughness’’ of the surface is reduced by the action offorming a polynomial function through the data points.
The spline with tension method controls the stiffness ofthe surface while it creates a less-smooth surface with val-ues more closely constrained by the sample data range. Dueto the small amount of data, the produced maps (Figs. 5–7)still have significant errors. More data will lead to betterrefinement of the mapped parameters.
Using the above mentioned techniques, the aquiferthickness (m), transverse resistance and transmissivity (m2
per day) thematic maps were created as is shown in Figs.5–7, respectively. Moreover, uncertainty analysis was ap-plied to demonstrate the cross validation of the createdmaps as is shown in the Table 2.
The spatial maps that were derived from the interpola-tion of the calculated hydraulic parameters show increasedaquifer thickness as we move towards rocks of high perme-ability, which represent karstic limestone formations
Figure 6 Transverse resistance (TR) map for the Keritis Basinarea with tectonic faults overlay. The TR tends to increase fromthe northwestern (impervious rocks) to the southeastern part(rocks of high permeability, i.e. karstic limestones) of the studyarea as is shown in this figure. The topography is also shown bythe shaded relief.
Figure 7 Shaded relief of the Keritis basin area with trans-missivity (m2/day) map and tectonic faults overlain. The rangeof transmissivity values shows a pattern similar with that ofaquifer thickness (Fig. 5).
Estimation of aquifer hydraulic parameters from surficial geophysical methods: A case study 129
(Fig. 5). Aquifer transverse resistance and transmissivityalso seem to be spatially related with the high permeabilityformations mentioned above (Figs. 6 and 7). Moreover, theincreased transmissivity in the south-east part of the studyarea identifies the zones of high potential within thewater-bearing formations. Furthermore, a relation betweenthe estimated and presented hydraulic parameters as shownin Figs. 5–7 and tectonic structures seems to exist withfaults acting as boundaries even between the same hydroli-thological unit, and define the place where aquifer parame-ters varies.
Table 2 Cross-validation results of the calculated hydraulic para
Location CV aquifer thickness CV transmissiv
Measured Predicted Error Measured P
CH7 48.3 103.0 54.7 546.7 1CH5 115.6 62.9 �52.7 1308.4CH6 79.8 77.8 �2.0 903.2CH3 48.0 60.4 12.4 543.5CH4 27.6 51.7 24.1 312.4CH9 61.3 80.1 18.8 693.8CH8 88.2 101.2 13.0 998.3 1CH11 111.2 77.1 �34.2 1258.6CH1 50.2 57.6 7.4 568.2CH10 113.0 86.0 �27.0 1279.0CH12 90.0 100.2 10.2 1018.7 1
Conclusions
Since drilling of wells to determine hydraulic parameters isoften prohibitively expensive, determining the aquiferparameters from VES is a cost-effective alternative. Basedon our results, the contribution of VES coupled with theavailable pumping test data proved to be significant to thequantitative estimation of aquifer parameters.
The estimated transmissivity of the geological forma-tions in the study area shows a wide range due to the highinhomogeneity of the sedimentary formations and the com-plexity of the karstic formations.
Based on the calculated hydraulic parameters of theshallow aquifer in Keritis basin, several hydrogeologicalmaps have been created, which are very useful for furtherstudies of the groundwater regime in the study area. Themaps could also be used to derive input parameters for con-taminant migration modeling and to improve the quality ofmodel. Finally, we should mention that the calculated aqui-fer parameters are well defined within the range of ob-served aquifer parameters.
Acknowledgments
The authors are grateful to two anonymous reviewers andProfessor M. Sophocleous for their valuable comments. Weare also grateful to Dr. Vargemezis and Dr. Stampolidis forkindly commenting our work. Financial support for this pro-ject was provided from the Operational Program for Educa-tion and Initial Vocational Training of the Ministry ofEducation of Greece and the European Union in the frame-work of the projects, Archimedes I: ‘‘Support of ResearchTeams of Technological Educational Institute of Crete’’,sub-project 2.6.6 – MIS86455 entitled ‘‘Application of mod-ern techniques in landfills’’ and Archimedes II: ‘‘Support ofResearch Teams of Technological Educational Institute ofCrete’’, entitled ‘‘Multiparametric identification systemdevelopment for the origin of water resources in karstic ba-sins : Application in the Keritis river basin (Natura 2000-Chania)’’.
meters
ity CV transverse resistance
redicted Error Measured Predicted Error
177.6 630.9 741.4 1025.5 284.1713.3 �591.2 855.4 658.8 �196.6893.6 �9.6 606.5 577.6 �28.8682.5 139.2 408.0 474.7 66.7572.2 259.8 218.0 588.7 370.7895.0 210.2 1392.7 1680.2 287.5146.2 147.9 1614.1 1981.5 367.5871.8 �386.8 2925.7 1677.3 �1248.4640.3 72.1 1506.0 954.7 �551.3977.6 �301.5 1938.0 1609.5 �328.5158.5 139.8 2554.2 130.5
130 P.M. Soupios et al.
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