# Innovative Hydrogeophysical Approaches as Aids to Assess Hungarian Groundwater Bodies
## 2 Materials and Methods
### The Applied Geophysical Methods
#### 2.3.2 Hydrogeophysical Logging Methods  
Wireline logging methods used in prospecting of water resources provide high-resolution in situ information about the geometrical, petrophysical and hydraulic properties of hydrogeological structures. In the investigation of groundwater formations, general electric and nuclear logging data are simultaneously processed, the aim, of which is to vertically separate the aquifers from aquitards along a borehole, estimate their effective layer-thicknesses, porosity, water (or air) saturation, amount of shale (i.e., clay and silt content, respectively), fractional volume of the rock matrix and hydraulic conductivity as accurately as possible [48]. To further improve the interpretation results, if available, magnetic resonance sounding measurement is added [49], which is able to differentiate the volume of free water from that of the bounded fluids and give a more detailed picture of the pore geometry and hence the hydraulic conductivity and fluid properties. Open-hole logging techniques are applicable to all types of water bodies dealt with in this study, even in very shallow soil formations, where direct-push tools can be used for the characterization of the unsaturated zone [50]. In this study, we focus on the possibilities of using advanced well logging methods for the investigation of Hungarian porous water bodies (Figure 2). Consider [PERSON]'s equation as basic relation used for describing the water flow through porous media:  
\[\frac{\partial\mathbf{u}}{\partial t}=-\frac{k^{*}}{\Phi\mu}\
abla p, \tag{1}\]  
where \(k^{*}\) denotes permeability, \(\Phi\) is porosity, \(\mu\) is dynamic viscosity, \(\mathbf{u}\) is the relative displacement vector of the fluid, and \(p\) is the pore pressure (\(t\) denotes time). In hydrogeological studies, the hydraulic conductivity is preferred to be used instead of permeability, which is defined as \(K=k^{*}\rho_{w}g/\mu\), including the mass density of pore water (\(\rho_{w}\)) and normal acceleration of gravity (\(g\)). Assuming a primary porosity rock as an assembly of capillary channels, one can use the following form of the Kozeny-Carman equation for the estimation of hydraulic conductivity [51]:  
\[K=\frac{\rho_{w}g}{\mu}\frac{d^{2}}{180}\frac{\Phi^{3}}{\left(1-\Phi\right)^{ 2}}, \tag{2}\]  
where \(d\) is the dominant grain diameter, which is obtained from grain-size distribution curves, e.g., by [52]:  
\[d=\frac{d_{10}+d_{60}}{2}\left(\frac{d_{10}}{d_{60}}\right)^{1/2}, \tag{3}\]  
where \(d_{10}\) and \(d_{60}\) are the characteristic grain sizes at 10% and 60% cumulative frequencies, respectively. Porosity is a key parameter in (2), which can be given either from laboratory or well logging measurements. In the assessment of groundwater formations, the bulk density tool assures good sensitivity to extract the porosity in all its domains. In sedimentary rocksfully saturated with fresh water, the porosity is calculated from the following (linear) tool response equation:  
\[\rho_{b}^{(m)}=\Phi\rho_{f}+V_{cl}\rho_{cl}+(1-\Phi-V_{cl})\rho_{ma}, \tag{4}\]  
where \(\rho_{b}^{(m)}\) is the density measured in a given depth, \(V_{cl}\) is clay volume, \(\rho_{f}\), \(\rho_{ma}\), \(\rho_{cl}\) denote the density of the fluid in the flushed zone, rock matrix and clay, respectively. In multi-mineral formations, the density of each matrix component should be taken into consideration. There are traditional methods to calculate the clay volume of the reservoirs of different ages, which are mostly based on single well log analysis [53]. The weakness of these methods that they are using the information of only one wireline log as well as highly dependent on the lithology, which should be known before the analysis. Hydraulic parameters can be derived from the resistivity log by the Csokas method [54].