# Estimate of Secondary Porosity from Surface Crossed Square Array Resistivity Measurements

## Abstract

**:**

## 1. Introduction

## 2. Crossed Square Array of Electrodes and Secondary Porosity Estimates

_{m}“ and the non-dimensional anisotropy coefficient “λ”, so that:

_{max}and ρ

_{min}are the maximum and minimum apparent resistivity values in the area under investigation.

_{max}and ρ

_{min}will be very close and, for homogeneous ground, they should be equal. On the other hand, in these conditions, the “n” values should approach the value 1. Thus, it is possible that anomalous large values greater than 1 for the calculated secondary porosity can be produced and, in these cases, it is necessary to check the values to identify these situations, as the calculated values have no geological meaning.

_{max}becomes ρ

_{min}and ρ

_{min}becomes ρ

_{max}; then, negative secondary porosity values will be computed. This occurs at low “n” values [15,17] and, in these cases, the values must also be checked.

## 3. Secondary Porosity Computed over an Analogue Model

_{max}and square array 2 will provide the values for ρ

_{min}; therefore, the secondary porosity Equation (1) can be applied.

_{max}and ρ

_{min}is very small and these negative secondary porosity values must be seen as noise. Therefore, at low “n” values, estimates for the secondary porosity are difficult and meaningless.

_{max}and ρ

_{min}as they are recorded over the isotropic block, and thus have no meaning.

## 4. Field Survey

_{max}, whilst square array 2 will give the values for ρ

_{min}, and Equation (1) can be used.

#### 4.1. Chapel le Dale 1 (CLD1)

_{max}and square array 2 provides the values for ρ

_{min}, as mentioned before.

_{max}and ρ

_{min}.

#### 4.2. Chapel le Dale 2 (CLD2)

_{max}and ρ

_{min}or local inhomogeneities near the electrodes.

## 5. Conclusions

_{max}and ρ

_{min}are very similar; that is, when the formations’ homogeneity prevails. These data must also be checked and confirmed as they do not have geological meaning.

_{max}and ρ

_{min}to use in the secondary porosity equation.

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Relation between the calculated strike and “n” (on the left) and relation between “n” and the calculated secondary porosity (on the right).

**Figure 5.**Secondary porosity vs. “n”: square side 4 cm (top); square side 11 cm (center); square side 32 cm (bottom). (YY’ axis: fraction of the total volume occupied by voids and fractures).

**Figure 6.**Pseudo section of secondary porosity values. (Secondary porosity as the fraction of the total volume occupied by fractures and voids).

**Figure 8.**Relation between the calculated strike and “n”, on the left, and relation between “n” and the calculated secondary porosity, on the right, for CLD1 data.

**Figure 10.**Secondary porosity vs. “n” for CLD1: square side 4 m (top); square side 22.6 m (center); square side 45.2 m (bottom). (YY’ axis: fraction of the total volume occupied by voids and fractures).

**Figure 11.**Pseudo section for the secondary porosity in CLD1. (Secondary porosity as the fraction of the total volume occupied by fractures and voids).

**Figure 12.**Relation between the calculated strike and “n”, on the left, and relation between “n” and the calculated secondary porosity, on the right, for CLD2 data.

**Figure 14.**Secondary porosity vs. “n” for CLD2: square side 4 m (top); square side 32 m (center); square side 45.2 m (bottom). (YY’ axis: fraction of the total volume occupied by voids and fractures).

**Figure 15.**Pseudo section for the secondary porosity in CLD2. (Secondary porosity as the fraction of the total volume occupied by fractures and voids).

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**MDPI and ACS Style**

Matias, M.J. Estimate of Secondary Porosity from Surface Crossed Square Array Resistivity Measurements. *Geosciences* **2023**, *13*, 101.
https://doi.org/10.3390/geosciences13040101

**AMA Style**

Matias MJ. Estimate of Secondary Porosity from Surface Crossed Square Array Resistivity Measurements. *Geosciences*. 2023; 13(4):101.
https://doi.org/10.3390/geosciences13040101

**Chicago/Turabian Style**

Matias, Manuel Joao. 2023. "Estimate of Secondary Porosity from Surface Crossed Square Array Resistivity Measurements" *Geosciences* 13, no. 4: 101.
https://doi.org/10.3390/geosciences13040101