## 2 Electrical and Electromagnetic Methods  
Geophysical methods such as electrical resistivity and electromagnetics are rapid and noninvasive geophysical methods for measuring groundwater properties and characterizing the spatial and temporal variability of subsurface formations [26]. These methods include electrical resistivity methods such as vertical electrical soundings (VES) and electrical resistivity tomography (ERT), and electromagnetic (EM) methods such as frequency-domain electromagnetic (FDEM) and time-domain electromagnetic (TDEM) soundings and profiling. These methods are commonly used in near-surface geophysics because the subsurface electrical properties are easily correlated to the physical and chemical properties of fluids within the pore space [27]. These methods can produce a high-resolution image of the shallow subsurface formation and have been widely used in hydrogeology and environmental studies.  
In electrical resistivity, a current is injected across a pair of electrodes, and the voltage difference between the potential electrodes is measured. The voltage difference is a function of the injected current and the resistivity beneath the electrode array. In the electrical resistivity method, commonly used electrode configurations include the Wenner, Schlumberger, and dipole\(-\)dipole arrays. In dipole\(-\)dipole arrays, the dipoles are equal in width (a) and separated by a distance n \(\times\) a, where n is an integer multiplier (Figure 2B).  
Electromagnetism uses the principles of electromagnetic induction to map variations in electrical conductivity. EM waves from a transmitting coil induce eddy currents in subsurface conductors, resulting in a secondary magnetic field detected in a receiver coil. The electrical resistivity and EM data are modeled to infer the electrical conductivity of the subsurface.  
Figure 2: Geophysical experimental set up in West Lake, Everglades National Park, FL. (**A**) EM experimental set up. (**B**) Electrical resistivity experimental set up. In the dipole\(-\)dipole array, A,B are the current electrodes. M and N are the potential electrodes.  
Different regularization optimization techniques have been developed to invert and model these data, including [PERSON]'s inversion [28], layered and laterally constrained inversion [29], and ridge regression [30, 31]. For example, [PERSON]'s inversion solution fits the measurement with the smoothest possible model, and the inverted models generally do not show sharp changes [29]. [PERSON]'s inversion trades off the roughness of the model improvement and the least-squares error predicted from the linearized forward problem, whereas the ridge regression trades off the size of the model improvement [30, 31]. In the ridge regression, for each iteration, a model correction is calculated using the best damping factor available for that iteration [30]. Equivalency analysis shows the possible range of models that can fit the data. The results obtained from the inverse model need careful interpretation.  
In porous media, currents are carried by electrolytic conduction of ions in the pore waters. The pore fluid conductivity, \(\sigma_{GW}\), and the bulk conductivity of the rock \(\sigma_{rock}\) are related by \(\sigma_{GW}=F\sigma_{rock}\), where F is the formation factor. The formation factor can be determined by coincident measurements of groundwater and formation conductivity or from empirical relationships such as Archie's Law [17]. The estimated formation factor can be used to infer the electrical conductivity of the pore fluids. Then, the salinity of the subsurface formation can be calculated using the general equation given by [32, 33, 34].