Regardless of the type of arrangement of electrodes used in geoelectric prospecting measurements, there are basically two ways of performing the electrical resistivity measurements: (i) vertical or (ii) horizontal. The choice of which method to use is related to the purpose of the study, however there is a need for both vertical and horizontal investigations to carry out the 3D mapping. To find to the distribution of the apparent electrical resistivity on the soil surface, the lateral profiling method is applied. By using Wenner’s method, the values of a (distance between two consecutive electrodes) are varied to identify soil variations in depth.
This work considers: (i) soil stratification as the process of finding the number of soil layers with their respective values of resistivity and thickness and (ii) 3D soil mapping as the presentation in the graphical form of data obtained and treated after stratification.
2.1. Determination of Apparent Electrical Resistivity of the Soil
The lateral profiling method is the geoelectrical investigation technique used to find the mapping of the apparent electrical resistivity
on the soil surface, which consists of placing the arrangement of the electrodes at the measuring spots, keeping fixed the distance between the rods. In this situation,
is determined at the center point of the arrangement, between the potential electrodes. Thus, it is possible to map the whole area, identifying the measuring spots and consequently delimiting distinct regions of resistivity [
6,
7].
Figure 1, adapted from Silva Filho et al. [
32], illustrates the lateral profiling method of soil investigation, in which the measurement process of apparent electrical resistivity
is performed for the measuring spots given by the intersection between the
Column 1 and the
Row A,
Row B,
Row C and
Row D. The Wenner’s method is applied in
Figure 1, where the current and voltage electrodes are represented by dots in the blue color while the dots in the red color are the measuring spots of
. By performing the lateral profiling method along
Column 1,
Column 2,
Column 3 and
Column 4, the mapping of the apparent electrical resistivity over the surface of the soil being studied is obtained [
33,
34].
Soil mapping is used in many areas from civil engineering to precision agriculture. Each area needs to know specific parameters of the subsoil and its dynamics. However, there are parameters that are common to all areas, such as apparent resistivity of the soil (and its inverse to apparent conductivity) and the depths of each layer, illustrated in
Figure 2, adapted from Calixto et al. [
5,
6].
Several methods are applied to determine the apparent resistivity value of the soil. In an elementary way, some methodologies use the relation given by (
1), where
l [m] is the length and
A [m
is the cross sectional volume of a parallelepiped composed of a certain material.
V [V] is the potential difference and
I [A] is the electrical current injected in the volume extremities using electrodes, which have the same cross section of the volume.
To calculate the electrical resistivity of the soil in a noninvasive way, we need an alternative formulation to (
1). This formulation is the well known geoprospecting method called Wenner’s method [
35], where the apparent electrical resistivity
may be given by:
where
a represents the distances between two consecutive electrodes, and
p is the burial depths of the electrodes, as illustrated in
Figure 2. In this figure,
,
,
and
are terrometer terminals, and
,
,
and
are electrode terminals. The electrical current
I is injected through terminals
and
, and voltage
V is measured in terminals
and
[
6].
Electrical conductivity is the intrinsic property of all conductive material of electrical current. In geoprospecting, the conductor is the soil, in which the electrical current circulates due to the presence of free salts in the soil solution (liquid phase) and also due to the exchangeable ions on the surface of the particles (solid phase). However, unlike the conductive wire, the electrical current in the ground may go through several paths, as illustrated in
Figure 3, adapted from Silva Filho et al. [
36]. In sufficiently moist soils, the conduction of current occurs due mainly to the salt content in the water of the soil that occupies some pores (pores with water). The solid phase may also contributes to electrical conductivity due mainly to interchangeable cations associated with clay minerals (dry soil). The third path to the electrical current in the soil occurs through soil particles with
in direct and continuous contact with each other (wet soil). These three paths illustrated in
Figure 3 present the current flow, which contributes to the apparent electrical conductivity of the soil [
6,
33,
34].
In
Figure 2, the variable
N which is subscript in
and
indicates the appropriate amount of layers for the stratification model to fit the studied soil. The electrical current passing through the soil from
to
is represented by red lines, which mostly goes through the shallow regions of the soil (58% at a depth of up to
). Since the remaining current sinks into deeper regions, this method is able to survey those depths as well. In (
2),
is the measured apparent resistance and if the soil is heterogeneous
. Note that in (
1) we include the electrical resistivity of the material, and in (
2) we include the apparent resistivity. Most devices map the soil electrical conductivity
by either (i) using (
1) with invasive methods (which might follow erroneous procedures, as (
1) is derived from electromagnetism equations, and it may only be used in homogeneous materials, which is not the case of the soil); (ii) using (
2) for mapping out the apparent electrical conductivity
and observing its spatial variation.
For example, two situations are presented in
Figure 4, adapted from Calixto et al. [
6], in which (
1) would not correctly identify the structure of the soil layers for depth
. The usual devices would obtain the same values of apparent electrical conductivity for both
Figure 4a,b. These results would be only accurate for depth
, whereas the different layers would be neglected for depth
. Observe that in
Figure 4b the separating surface of the second layer crosses the depth
, while in
Figure 4a this does not occur. This distinction between the soil layers may only be observed using 3D mapping, using (
2) [
6].
To calculate the soil electrical conductivity
, after collecting the values of the soil apparent electrical resistivity
, we apply a stratification method. Among the different methods for geoelectrical stratification found in the literature [
2], there is a recently proposed method that minimizes the difference between the experimental and theoretical apparent resistivity curves; one of which is obtained from experimental data collected in the field, and the other is produced analytically [
5]. The authors build an experimental curve of apparent resistivity
utilizing Wenner’s method [
37] (
Figure 2), and a theoretical curve of apparent resistivity
utilizing Sunde’s algorithm [
38], as illustrated in
Figure 5, adapted from Calixto et al. [
7].
In
Figure 5 we first collect the field data using Wenner’s method, as in (
2) and
Figure 2, to construct an experimental curve [
39]. Once the experimental curve is obtained, the soil stratification is calculated and the experimental values for the resistivities and thicknesses of each layer are found. The simulation uses Sunde’s algorithm, which takes the experimental values for the resistivities and the thicknesses of the layers as input. In the simulation, we look for the theoretical curve that is identical to the experimental curve. The theoretical curve is constructed using the values of resistivities and thicknesses of each layer and compared with the experimental curve (
Figure 5). If both curves are identical, the values of resistivities and thicknesses represent the stratified soil. Otherwise, if they are not identical, the resistivity values and thicknesses of the layers are modified by the optimization process, seeking to adjust the theoretical curve to experimental one as much as possible.