# A Different Processing of Time-Domain Induced Polarisation: Application for Investigating the Marine Intrusion in a Coastal Aquifer in the SE Iberian Peninsula

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{W}, where ρ is the resistivity of the medium and ρ

_{W}is the resistivity of the pore fluid); hence, the hydrochemical characteristics of the pore fluid strongly affect the resistivity of the medium. For example, an aquifer composed of granular lithologies can have resistivities very similar to those of clays (~10 Ω m) when the formation fluid has a conductivity of a few tenths of S/m, corresponding to that of a freshwater/seawater transition fluid (interface). However, this ambiguity can be reduced by using more than one geophysical parameter.

_{P}(primary potential) and the potential measured just after cancelling the external field V

_{S}(secondary potential) ([7]; Equation (1)):

_{S}, it is common practice to measure the decay of the voltage over time, which is typically measured in successive time windows, while obtaining the value of m using the following expression [8]:

_{S}(t) is the potential value measured over time after cancelling the primary potential, and (t

_{2}− t

_{1}) = Δt is the integration interval. Thus, the value ${\overline{V}}_{\mathrm{S}}$ obtained through this integral is attributed to the secondary potential.

_{s}(0)/e. For this reason, in this study, the term chargeability refers to the value obtained by Equation (2), and polarisability P refers to the value obtained by Equation (1), modified to consider only the part of the secondary potential that corresponds to the V

_{IP}(t = 0

^{+}) polarisation effect.

_{1}>> ω

_{2}given by Equation (3):

_{2}= 0, i.e., ρ(ω

_{2}) = ρ

_{DC}[10]. In the model defined by Cole and Cole [11], the complex resistivity for frequency ω

_{k}is given by Equation (4) [12]:

_{0}is the resistivity in direct current, m is the chargeability, τ is the time constant of the IP, and c is the frequency exponent (slope on the logarithmic scale of both sides of the phase curve) with a maximum value of 1. Regarding the relationship between the two domains, which was introduced by Cole and Cole [11], different researchers have introduced different expressions established by different researchers [13,14], including an expression accounting for the electromagnetic coupling (EM) effects [15]. Thus, several studies used the IP method in the frequency domain and its relation to the time domain, thereby determining different time constants depending on the petrochemical and hydrochemical characteristics of the subsurface. Pelton et al. [12] conducted an exhaustive study of the electrical response of metallic formations and found typical frequency-exponent values ranging from 0.1 to 0.6, with a mean value of 0.25; they also conducted an analysis of the spectral behaviour of the studied reservoirs, thereby determining different values for τ. Given the above-mentioned terminological differentiation, the logical interrelation of IP in the time and frequency domains is more closely linked to chargeability.

_{IP}(t = 0

^{+}) polarisation potential with the aim of differentiating the presence of clay levels through geoelectric soundings conducted in coastal detrital aquifers. The inclusion of such clay levels, which have higher polarizability values than those of granular strata, improves the inversion of resistivity soundings in which this presence was not considered [16] and elucidated the marine intrusion progress. The proposed methodology was applied to a case of marine intrusion and eventually provided the seasonality of the salt wedge.

## 2. Background

#### 2.1. Influence of Electromagnetic (EM) Coupling

#### 2.2. Measurements in the Time Domain

_{p}value; for these ‘noisy’ bands, specific criteria can be adopted. Overall, it is worth remembering that using filters for non-infinite signals involves limitations.

_{n}·exp(−α

_{n}·t), corresponding to the different contributions to the total polarisation of the different subsurface formations:

## 3. Materials and Methods

#### 3.1. Data Acquisition

#### 3.2. Analysis of the Decay Curves

_{0EM}value is only analyzed with regard to the decomposition of the decay curve. The reason for including a residual potential V

_{R}is the presence of a potential difference between the electrodes, which can be considered constant in conventional measurement times in IP studies. In fact, V

_{R}showed differences between successive measurement points or stations of each sounding without stratigraphic justification. Although this effect has been minimized by using non-polarisable electrodes (Figure 2), its elimination is necessary and relatively easy in the treatment of IP in the time domain.

^{+}divided by the potential just before that time, t = 0

^{−}) and the period or decay constant τ

_{IP}of the curve. In this study, we considered that the petrology of the medium mainly affects the decay period, whereas the mineralogical characteristics particularly affect the polarisability. As mentioned above, the measurements of polarisability and decay time represent a clear advantage over the measurement of chargeability within a given time window (although this is currently the most common procedure). It is easy to see that two different decay curves can have the same chargeability, measured in a single window; however, analysis of the complete decay curve shows that both the cut-off point at t = 0

^{+}and the decay period are different while representing more intrinsic values of the rock (Figure 1).

_{IP}and τ

_{EM}are intrinsically different. Typically, the polarization time varies between one and several seconds, whereas the induction time is a few tenths of a second long. In this study, the decomposition method involved performing a series of approximating iterations, which required an initial decomposition to avoid convergence problems. Thus, the steps for the decomposition of the decay curve were as follows.

_{n},t

_{n}) to a simple exponential plus a constant potential, V

_{S(t)}= V

_{0}·e

^{−(t/τ)}+ V

_{R0}, we obtained the value of the cut-off potential V

_{0T}and verified that the obtained valued coincided (i.e., ±2%) with that obtained by determining the residual potential minimizing the variance between successive point-to-point decays. Then the next steps were:

_{MED}of the successive point-to-point decays, the integral is the same as that of the original data curve (Equation (11)).

_{0EM}+ V

_{0IP}+ V

_{R}= V

_{0Σ}+ V

_{R2}, and that V

_{0EM}+ V

_{0IP}= 1.16·V

_{0M}. The difference between the cut-off potentials corresponding to the two equations, V

_{0M}and V

_{0Σ}+ V

_{R2}, were highly correlated (i.e., R

^{2}= 0.98) with the residual potential. Thus, the minimum deviation relationship providing the residual potential was given by Equation (12):

_{R}= (V

_{0Σ}+ V

_{R2}) − 1.16·V

_{0M}.

_{R}= 0).

_{R}, a V

_{IPEM}(t) curve is obtained, in which the separation between the two remaining exponentials is subtler. For this separation, after obtaining an initial potential V

_{01}by fitting to a modulated exponential ${V}_{\mathrm{IPEM}}\left(t\right)={V}_{01}\xb7{\mathrm{e}}^{-{\left(t/{\tau}_{1}\right)}^{n}}$, and a decay period τ

_{2}by approximating to a simple exponential ${V}_{\mathrm{IPEM}}\left(t\right)={V}_{02}\xb7{\mathrm{e}}^{-\left(t/{\tau}_{2}\right)}$, the cut-off potential and the polarization period were obtained by approximating the expression Equation (13):

_{0EM}= V

_{0IP}= ½V

_{01}, τ

_{IP}= τ

_{2}, and τ

_{EM}= 0.33·τ

_{2}. By considering that V

_{IPEM}(0) = V

_{0EM}+ V

_{0IP}= V

_{01}, the values of V

_{0IP}and τ

_{IP}were obtained, and thus the final polarisation curve (Equation (14)):

_{IPEM}(t) values; therefore, the similarity in the second derivative was adopted as the iteration criterion. Figure 3 shows an example of the two curves of V

_{01}and V

_{02}obtained with very low error for the data of a decay curve, which nevertheless show a clear difference in curvature, such that the ratio between the two should be centred around 1.

_{0IP}and τ

_{IP}. Figure 4a,b show two examples of the decomposition of the decay curves at one of the case-study points. In the first example, the electric field is mostly above the freshwater/saltwater interface, showing a clear positive coupling; in the second example, where a larger fraction of the electric field penetrates below the marine interface, V

_{0EM}and V

_{0IP}decrease, showing an apparent induction opposite to that of the created field.

#### 3.3. VES-IPS Inversion

_{a}(r) is the apparent resistivity for the half-space of the r electrodes, ρ

_{j}is the resistivity of layer j, P

_{j}is the polarisability of layer j.

## 4. Application for Investigating the Marine Intrusion in the Almuñécar Coastal Aquifer

#### 4.1. Overview of the Study Area and Field Survey

#### 4.2. Analysis of the VES-IPS Results

#### 4.3. Seasonal Variation of the Freshwater/Saltwater Interface

## 5. Discussion

^{+}.

_{R}, we note that although it has been attributed to the possible polarisation of the electrodes, the comparative analysis of the obtained values showed the existence of a strong correlation (correlation coefficient: 0.96) between this potential and the polarisation of the medium. Even non-polarisable potential electrodes deviate from their expected behaviour by an amount proportional to the polarisation potential exerted on them by the subsurface. However, we note that there may be a relationship between V

_{R}and ground behaviour.

_{0EM}(and its unique time constant), it is important to note that it is futile searching for a direct interpretation of the resulting values, as this has been obtained by analyzing the decay curve, whose effect is already very small and its evolution towards zero has no particular significance. Moreover, assigning only the first section of the decay curve to an induction effect in the subsurface would be problematic, as this value may include other effects, such as coupling between the cables.

#### Error Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Example of two decay curves with the same chargeability but different polarisabilities and decay times.

**Figure 2.**(

**a**) Scintrex TSQ-3 equipment and IPR-10A receiver. (

**b**) Fat non-polarisable electrodes with CuSO

_{4}.

**Figure 4.**(

**a**). Decay curve of sounding A6-O, station 9. (

**b**). Decay curve of sounding A6-F, station 9.

**Figure 5.**Location of the study area, a sketch of the locations of the soundings, and geology of the area. The coordinates of the river’s mouths are Seco River 437,720.62 m E & 4,065,188.01 m N, Verde River 438,855.70 m E & 4,065,187.01 m N.

**Figure 6.**Results of the (

**a**) A1-O VES-IPS obtained mid-autumn and (

**b**) A5-F VES-IPS obtained late winter.

**Figure 7.**Results of the (

**a**) A5-O VES-IPS obtained mid-autumn and (

**b**) of the CF2 VES-IPS conducted in another basin in the same region.

**Figure 8.**Results of the (

**a**) A4-O VES-IPS obtained before winter and (

**b**) A4-F VES-IPS obtained after winter.

**Figure 9.**Results of the (

**a**) A9-O VES-IPS and (

**b**) A8-O VES-IPS were both obtained mid-autumn, showing a clear differentiation of the geoelectric levels and an apparent uncertainty of the values of the deeper layers.

Sondeo | T (°C) | σ (μS/cm) |
---|---|---|

CDP | 16.9 | 31,504 |

Pz5 | 15.4 | 18,701 |

Pz7 | 17.4 | 4063 |

Pz14 | 17.4 | 23,551 |

VA | 18.8 | 2868 |

Pz16 | 18.7 | 6767 |

BS | 19.2 | 13,546 |

Pz17 | 19.6 | 2056 |

LB | 21.9 | 6686 |

LA | 25.5 | 1249 |

SJO | 22.3 | 1796 |

Pz21 | 19.07 | 934 |

Pz24 | 18.4 | 882 |

Pz19 | 20.2 | 5546 |

CDP | 16.9 | 31,504 |

**Table 2.**Resistivity and polarisability values in October (mid-autumn) were obtained with VES-IPS inversion.

A1 | A2 | A3 | A4 | A5 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

z | ρ | P | z | ρ | P | z | ρ | P | z | ρ | P | z | ρ | P |

3.9 | 121 | 6.9 | 9.5 | 132 | 6.4 | 15 | 156 | 6.4 | 20 | 139 | 7.4 | 8.1 | 137 | 5.1 |

36 | 35.5 | 7.9 | 41 | 47.9 | 7.0 | 39 | 41 | 6.5 | 42 | 33.0 | 6.6 | 11 | 13.8 | 18 |

59 | 1.36 | 7.6 | 60 | 0.95 | 6.5 | 54 | 9.0 | 26 | 56 | 10.9 | 26 | 26 | 192 | 5.7 |

-- | 157 | 68 | -- | 174 | 87 | 70 | 1.4 | 5.1 | 68 | 1.3 | 6.1 | 47 | 30.0 | 5.2 |

-- | 208 | 87 | -- | 173 | 85 | 64 | 1.6 | 4.9 | ||||||

215 | 74 | |||||||||||||

A6 | A7 | A8 | A9 | |||||||||||

z | ρ | P | z | ρ | P | z | ρ | P | z | ρ | P | |||

2.7 | 112 | 6.7 | 3.8 | 155 | 7.2 | 3.1 | 95.2 | 6.1 | 2.5 | 70.3 | 6.2 | |||

32 | 241 | 5.7 | 38 | 312 | 7.9 | 48 | 341 | 5.6 | 33 | 367 | 7.0 | |||

49 | 37 | 6.3 | 45 | 10.2 | 20 | 58 | 40.7 | 4.8 | 40 | 19.9 | 15 | |||

60 | 1.5 | 5.5 | 59 | 41.5 | 6.3 | -- | 172 | 61 | 47 | 79.8 | 6.4 | |||

-- | 171 | 91 | -- | 193 | 87 | -- | 217 | 89 |

**Table 3.**Resistivity and polarisability ranges used for lithological assignment and mean values when applicable.

ρ→ | 121 | 367 | Gravels/conglomerates Fresh water | 30 | 48 | Gravels/conglomerates Interface | 1.0 | 1.6 | Gravels/conglomerates Salt water | 9.0 | 14 | Clay | 157 | 217 | Schist (Substrate) |

40 | 1.2 | 10 | |||||||||||||

P→ | 5 | 10 | 5 | 10 | 5 | 10 | 15 | 25 | 60 | 90 | |||||

6 | 6 | 6 | 22 | 75 |

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## Share and Cite

**MDPI and ACS Style**

Díaz-Curiel, J.; Biosca, B.; Arévalo-Lomas, L.; Miguel, M.J.
A Different Processing of Time-Domain Induced Polarisation: Application for Investigating the Marine Intrusion in a Coastal Aquifer in the SE Iberian Peninsula. *Sensors* **2023**, *23*, 708.
https://doi.org/10.3390/s23020708

**AMA Style**

Díaz-Curiel J, Biosca B, Arévalo-Lomas L, Miguel MJ.
A Different Processing of Time-Domain Induced Polarisation: Application for Investigating the Marine Intrusion in a Coastal Aquifer in the SE Iberian Peninsula. *Sensors*. 2023; 23(2):708.
https://doi.org/10.3390/s23020708

**Chicago/Turabian Style**

Díaz-Curiel, Jesús, Bárbara Biosca, Lucía Arévalo-Lomas, and María Jesús Miguel.
2023. "A Different Processing of Time-Domain Induced Polarisation: Application for Investigating the Marine Intrusion in a Coastal Aquifer in the SE Iberian Peninsula" *Sensors* 23, no. 2: 708.
https://doi.org/10.3390/s23020708