In 2003, the first MRS test campaign was carried out in the northern part of Denmark, with the aim of testing the applicability of the method. The survey was planned by Hydrogeophysics Group of Århus University (HGG) and Institute for Research and Development, France (IRD). A high level of artificial electromagnetic noise was observed during the survey, due to the country-specific constraints. A second MRS test campaign was conducted in May 2006 by the Danish company Rambøll in cooperation with the former County of Vejle (Denmark), Paris 6 University and IRD (both France). The MRS results obtained suggest optimal locations for water supply boreholes within subsurface structures with homogeneous electrical resistivity conditions mapped by TDEM [2]. An optimisation procedure during field measurements made it possible to obtain good quality MRS data and the method was thereby optimised to fit the Danish conditions.

Based on these results, a third campaign was planned and conducted by Rambøll in cooperation with the Environmental Centre Århus, Odense and Ringkøbing in November 2007 in different geological settings.

In total, between 2003 and 2007, 12 sites were investigated with MRS in Denmark (Fig. 1). At two sites (Kragelund and Sæby), it was impossible to measure with MRS due to the high level of ambient electromagnetic noise. A total of 47 MRS stations were measured in Denmark between 2003 and 2007. During all three campaigns, NUMIS^PLUS equipment from IRIS Instruments was used. Measurement procedures and configurations were adapted according to each site's specific constraints (ambient noise, required depth resolution) [2].

The Danish landscape was formed by glacial activity during the Weichselian ice age and the geology is composed mainly of glacial sedimentary structures. The south-western part of Jutland is dominated by glacial melt water plains with sandy sediments and sandy soil from old moraine landscapes of the Saale glaciation. The rest of Jutland and the Danish isles are generally built up of moraine landscape with sediments deposited through melting of the Weichselian ice [17,18]. The Quaternary sediments consist of moraine-clay, -sand and -gravel as well as fluvio-glacial-clay, -sand and -gravel. These Quaternary sediments overlie mica sediments, sand, clay and limestone from the Tertiary and Cretaceous.

Aquifers in Denmark are mainly found in glacial Quaternary melt water sediments, deep Tertiary sandy formations and in Cretaceous and Palaeocene limestone. Aquifers in the deep Tertiary sandy formations are often regional aquifers, but aquifers in limestone and glacial sediments can be both regional and local. The glacial aquifers in the eastern part of Jutland are often found in buried valleys eroded into the Tertiary clays and can be rather complex with a primary and several secondary aquifers, consolidated and unconsolidated.

A short description of the aquifers within the investigated areas, according to the geology and the hydrogeology of the areas [6] and available description of boreholes [5], is presented in Table 1.

The MRS method is based on the property of the nuclei of the hydrogen atoms (protons) in groundwater molecules to possess a magnetic moment. These moments are excited using a surface loop with current passing through. The magnetic resonance signal generated by the precessing nuclei is measured, with the same loop, after the current cut-off. The amplitude of the signal is proportional to the number of hydrogen nuclei of water molecules that generate the signal, and the decay of the signal is linked to the mean size of the pores that contain the water. The basics of the method are discussed in [11].

The geophysical parameters derived from the magnetic resonance signal are the MRS water content (θMRS) and the relaxation times (T2* and T₁) versus depth. θMRS is defined as the volume of water with a sufficiently long decay time constant (>30 ms) per unit volume [12]. Signals with short decay time constants are generated by bound-water, i.e. water that is attached to the rocks due to the forces of molecular attraction, which cannot be measured.

Both T₁ and T2* are linked to the mean pore size containing water but T2* is influenced by the local heterogeneities of the local magnetic field [11]. Thus, T₁ is a more reliable parameter, usually called the longitudinal relaxation time, which is linked to the mean pore size of the aquifer as [7,8]:

θMRS and T₁ are used to estimate the hydraulic conductivity (KMRS) and the transmissivity (TMRS) of aquifers [13,15] as follows:

Different schemes are known for MRS data inversion [1,3,4,16]. However, the resolution of the inversion is not defined by the inversion algorithm but by the physical basis of the method and the signal to noise ratio. For MRS data inversion in this study, the SAMOVAR software based on the Tikhonov regularization method [10] was used. This software allows processing of complex signals (amplitude and phase). It is possible to use either the “smooth” inversion or the “block” inversion schemes. The software allows automatic estimation of the uncertainty δz in MRS results based on the eigenvalues of the matrix that approximates the MRS integral equation [14].

An example is presented in Fig. 2, where automatic “smooth” and “block” inversion were used for Bredal-4 MRS station data inversion. Both schemes fit raw data equally well (0.6% fitting error for smooth inversion and 1.5% fitting error for block inversion).

Inversion results (θMRS, T₁ and KMRS) using “smooth” and “block” inversion schemes for Bredal-4 MRS station are presented in Fig. 3. For KMRS estimation, the calibration constant, Cp=3.82×10−9, previously calculated for this site [2], is used. The MRS depth resolution uncertainty δz is also shown. This graph makes it possible to estimate the uncertainty of aquifer resolution within ±δz with respect to the Signal / Noise ratio [14]. Both inversion scheme results are acceptable.

The regularization method provides the unique solution that is selected based on the signal-to-noise estimation. As noise is not necessarily constant, selection of the minimum and maximum values of the parameter of regularization provides a solution between the maximum and the minimum water content (Fig. 3a). For each depth (zi), the water content derived from the inverse model can be attributed to the depth (zi±δz).

When using the “block” inversion scheme, we stabilise the solution by defining the minimum number of blocks. For this example (Fig. 3b), we selected a one-block solution that allows fitting raw data within the noise magnitude. However, even selecting one block we obtain the minimum and maximum thickness solutions both of which fit the experimental data within the noise magnitude (Fig. 3b). Thus, for the “block” inversion, the uncertainty is given directly. Comparison of the inversion results obtained by “smooth” and “block” inversion presented in Fig. 3 shows that the “smooth” inversion is closer to the maximum thickness solution given by the “block” inversion. Even if the “block” inversion scheme provides a rectangle with well-defined thickness and water content, “block” inversion is not more accurate than “smooth” inversion because of the many other different rectangles which can fit experimental data equally well. As we have no other information about the solution (e.g. number of water-saturated layers, static water level, bottom of the aquifer), except the signal-to-noise ratio, we use the “smooth” inversion scheme.

In the present study, the “smooth” inversion of complex signal routine was used. For “smooth” inversion, T₁ corresponds to the maximum value of the θMRS inversion curve (Fig. 3a).

Within the investigated sites, aquifers can be found mainly in melt water sandy sediments and on a few rare occasions in clayey melt water and moraine sediments [5,6]. In order to compare the MRS parameters obtained with the available geological data, a qualitative classification of the aquifer grain-size was attempted, based on the geological description of boreholes (corresponding depth of the installed screen).

From the borehole descriptions [5], four main classes of aquifers can be recognised within the investigated sites: moraine clay (MCl), fine sand (FS), medium sand (MS) and coarse sand (CS). Three intermediate classes within the main classes are also considered (MCL-FS, FS-MS, MS-CS). This grain-size classification based entirely on the available borehole data is qualitative due to the absence of detailed grain-size analyses. Hence, to improve the legitimacy of the aquifer classification, an arbitrary uncertainty error (Eclass) was estimated as follows:

Freg is a factor related to the hydrogeological variability in the area of the borehole; regional aquifer: Freg=1, local aquifer: Freg=1.25.

Elog is the uncertainty related to the geological description of the borehole: good description: Elog=0%, fair description: Elog=12.5%, poor description: the borehole is not used for comparison.

Fyear is a factor related to the year of the drilling before and after the Danish guide for borehole sample description [9] published in 1995. After 1995: Fyear=1; before 1995: Fyear=2.

An upper limit of 500 m distance for comparison was chosen based on an assessment of average hydrogeological variability [6] of the specific investigated sites. Increased age of the borehole and only fair borehole description increases the uncertainty of the aquifer class, since the description of the grain-size in these cases is considered less accurate. The attributed percentage of uncertainty may be inexact because the formula is empirical and values are based on several hydrogeological assessments and evaluations.

We demonstrate this approach by using the example of MRS station Bredal-4 and DGU-borehole 116.1624 (Fig. 4). Bredal-4 MRS inversion results (θMRS and T1) are compared with TDEM sounding results. The MRS depth resolution uncertainty δz is also shown. The borehole's screen was set within sediments described as medium to coarse sand. Thus, the attributed class is MS-CS. The borehole was drilled in 2006 and the quality of the geological description is good. However, as the borehole is situated at a distance of 500 m from the MRS station and the aquifer is considered regional, the uncertainty error of 25% on the grain-size classification was prescribed.

For our study, only 23 MRS stations have a borehole with an acceptable geological description within a distance of 500 m. Comparison is made for these MRS stations with the simplified classification of the aquifer at the depth of the screen in the adjacent DGU-borehole.

6.1 MRS parameters

θMRS and T₁ for each site are plotted against the grain-size class of the aquifer (Figs. 5 and 6, respectively). The MRS values are estimated using the smooth inversion results, as shown in Figs. 3 and 4. The X-axis error bar shows the estimated uncertainty of the grain-size classification. The Y-axis error bar shows the estimated uncertainty of the MRS-obtained parameters. This uncertainty corresponds to the minimum and maximum values presented in Table 2.

6.2 MRS hydraulic conductivity estimator

In Fig. 7, KMRSn for each site is plotted against the grain-size class of the aquifer, in the corresponding borehole, given in Table 2 (total of 23 MRS stations). We can observe that MRS hydraulic conductivity is higher in aquifers with coarser sediments and lower in aquifers with decreasing grain-size or increasing fraction of clay. Consequently, the general rule for implanting water supply boreholes would be to select sites with larger KMRSn values. This rule can also be applied to aquifers in MS–CS (medium to coarse sand) grain-size class, despite a larger dispersion of KMRSn values as compared to other classes.

To summarise the MRS results in Denmark, KMRSn from 37 out of 47 MRS stations from ten successfully investigated areas are presented in Fig. 8. The excluded MRS soundings are not used due to the high uncertainty of MRS-derived parameters [2].

Using the normalised values of KMRSn, we separated the aquifers into four families characterised by 0<KMRSn<1 with an equal step of 0.25. We assumed that every family corresponds to a different range of hydraulic conductivity.

The MRS results reveal clear variations in the hydraulic conductivity within the investigated areas. In some areas, such as Søndersø, all types of different families are present. In Ærø on the other hand, mainly one family of aquifers with low hydraulic conductivity is present. Fig. 7 shows that this family corresponds mainly to clayey-fine sand aquifers.

Despite the fact that MRS transmissivity TMRS is a more robust parameter regarding equivalence problems [2], it was not used for the present study since it is also related to the aquifer thickness, Δz. The MRS hydraulic conductivity estimator KMRSn is a more appropriate parameter since it is related to the geological (grain-size) consistence of sedimentary aquifers.

Our experience shows that the MRS method is applicable in Denmark. We observed a qualitative relationship between MRS results and the grain-size class of the aquifer: larger values of MRS-derived parameters correspond to aquifers with coarser material. Thus, the MRS method seems to be able to provide a qualitative estimation of aquifer grain-size within clayey-sandy sedimentary formations.

Additionally, KMRSn results reveal variations within the investigated areas. These observed variations can suggest preferential locations for water supply boreholes. Since these variations seem to be related to the aquifer class defined by geological description of adjacent boreholes, the MRS method could be used as a tool for optimising borehole implantation. However, the generally high level of ambient electromagnetic noise around the country can often be a limiting factor for MRS application.

Our results suggest that a further study comparing MRS data to detailed grain-size analyses and pumping tests from near-by boreholes is warranted. We expect that such a study would allow the use of MRS as a quantitative tool for aquifer characterisation in Denmark.