September 28, 2023

# Resistivity Formula, Survey, and the application

The resistivity survey method is more than 100 years old and is one of the most commonly used geophysical exploration methods. It has been used to image targets from the millimeter scale to structures with dimensions of kilometers. It is widely used in environmental and engineering and mineral exploration.

Resistivity:  Resistivity is a geophysical technique for imaging sub-surface structures from electrical measurements made at the surface of resistivity.

Actually, electrical resistivity is a fundamental property of a material that measures how strongly it resists electrical current. A low resistivity indicates a material that readily allows electric current. Before going to the in-depth application we have to know the basic principle and the resistivity formula to know how to use it in the exploration of geophysical science.

## What is a resistivity survey and the resistivity formula?

A resistivity survey is a non-destructive geophysical survey method used to investigate subsurface conditions with the aid of those surface images. This method utilizes differences in electric potential to identify subsurface material.

A survey of the electrical resistivity of the ground at a different point over an area or along a

The route, typically based on measurements of the current passing between electrodes embedded in the ground at successive pairs at the point and used to locate buried structure features, is a similar survey of the internal structures of a solid object.

Electrical resistance surveys another name Earth Resistance. It is a Geophysical method, where two electrodes known as current electrodes, are used to inject an electrical current into the ground and the potential differences are measured between two distant electrodes, known as potential electrodes.

Electrical resistivity surveying methods have been widely used to determine the thickness and resistivity of layered media for the purpose of assessing groundwater potential and siting boreholes in fractured unconfined aquifers. Traditionally, this has been done using one-dimensional (1-D), two-dimensional (2-D), three dimensional ( 3-D).

## How a resistivity survey works :

During resistivity surveys, the current is injected into the earth through a pair of current electrodes, and the potential difference is measured between a pair of potential electrodes. The current and potential electrodes are generally arranged in a linear array. There are basically two types of resistance meters: Low frequency and High-frequency models.

Most soils and non-ore-bearing rocks are electrically resistive, (i.e., insulators).

Soil moisture and groundwater are often electrically conductive due to the contained dissolved minerals. Therefore the resistivity measured in the ground is predominantly controlled by the amount of moisture and water within the soil and rock (a function of the porosity and permeability), and the concentration of dissolved solids (salts) in that water.

The basic method requires at least 4 steel electrodes to be driven into the ground. An electrical current is then applied to the outer electrodes by a battery or generator. A voltage is measured between the 2 inner electrodes using a simple voltmeter. To know the

Resistivity Formula we need to go Through Ohm’s Law (V=IR) and by knowing the input current, the measured voltage, and the geometry of the electrode array, a value known as resistance can be calculated.

Resistivity measured in Ohm-meters is resistance times area divided by distance. Because the actual current flow is highly influenced by conductive layers, the value measured is known as the “apparent resistivity”.

In its simplest terms, it represents an average value encompassing all of the different materials within the volume (half-space) of materials being measured. Most modern resistivity meters calculate apparent resistivity once the geometric parameters are input.

## Resistivity Formula:

Most of the time can not remember the resistivity formula, hence we need to search online to know the details of the resistivity formula. if you forget the resistivity formula go through the below. The resistivity measurements are normally made by injecting current into the ground through two current electrodes and measuring the resulting voltage

difference at two potential electrodes. To get the Resistivity Formula we have to use a current (I) and voltage (V)

values, an apparent resistivity (pa) value is calculated. pa = k V / I where k is the geometric factor that depends on the arrangement of the four electrodes.

Resistivity meters normally give a resistance value, R = V/I so in practice the apparent resistivity value is calculated by, pa = k R

The calculated resistivity value is not the true resistivity of the subsurface, but an “apparent” value which is the resistivity of a homogeneous ground that will give the same resistance value for the same electrode arrangement.

The relationship between “apparent” resistivity and the “true” resistivity is a complex relationship. To determine the true subsurface resistivity, an inversion of the measured apparent resistivity values using a computer program must be carried out.

From the resistivity formula, we know that the resistance (R) is directly proportional to the length of the length (L), which means if we increase the (L) the resistance (R) will be higher. From the above resistivity formula, we can see that, directly proportional to area (A) and inversely proportional to length (L)

## How To Conduct An Electrical Resistivity Survey Knowing the basic resistivity formula:

2. Decide on an interval for your electrodes.
3. Lay out the tape measure.
4. Hammer in the stakes.
5. Connect the stakes, electrode cable, switch box, and Superstring.
6. Run a contact resistance test to check that all is connected right.

## There are three types of resistivity surveys.

The three main methods of electric resistivity surveys are

 Vertical electric sounding (VES)

 Electric profiling

 Electric imaging

Vertical Electrical Sounding (VES) :

Vertical Electrical Sounding or Electrical drilling retains current and potential electrodes along a straight line at the same relative spacing around a fixed central point. It presumes that current penetrates continuously deeper with increasing separation of current electrodes.

Electrical Profiling:

Electrical profiling is simply a two-dimensional resistivity method, where an image representing a slice of the earth is created and electrical property contracts are used to interpret differing geological or hydrological conditions. We use color contouring to visually identify these conditions.

Electrical imaging:

The method of measuring sub-surface resistivity involves placing four electrodes in the ground in a line at equal spacing, applying a measured AC current to the outer two electrodes, and measuring the AC voltage between the inner two electrodes.

## Scopes of usage of the Electrical Resistivity Survey:

1. It delineates 3-D structures with anomalous electrical conductivities.
2. It is useful for simultaneously detecting lateral and vertical changes in subsurface conductivities.
3. Determine the depth of the water table.
4. Detect fracture zones and faults.
5. detect contaminant plums.
6. Determine exact karst features.
7. Assist in dam stability analysis.
8. Provide data for corrosion control design.
9. Private or public re-medical investigation and feasibility studies.
10. Determine lithology and structure.
11. Water resources management.
12. Landfill closures geological mapping.
13. Interception of horizontal profiling data.

## Equipment used in the resistivity survey and their functions:

1) Electrical survey: Mapping subsurface resistivity by injecting an electrical current into the ground.

2) Resistivity meter: An instrument used to carry out resistivity surveys that usually has a current transmitter and voltage-measuring circuitry.

3) Electrode: A conductor planted into the ground through which current is passed or which is used to measure the voltage caused by the current.

4) Apparent resistivity: The apparent resistivity is the resistivity of an equivalent homogeneous earth model that will give the same potential value as the earth model for the same current and electrode arrangement.

5) Multi-core cable: A cable with a number of independent wires.

## Principles of resistivity survey:

Surface electrical resistivity surveying is based on the principle that the distribution of electrical potential in the ground around a current-carrying electrode depends on the electrical resistivity and distribution of the surrounding soils and rocks. Low ground resistivity is associated with clay soils, moist soils, buried metals, and other conductive materials. High-ground resistivity is common in sandy soils, dry soils, and other relatively non-conductive materials.

The apparent resistivity of the subsurface materials can be calculated by knowing the electrode spacing, the geometry of the electrode positions, the applied current, and the measured voltage. To know details go back to the resistivity formula and how it works. The depth of the resistivity measurement is related to the spacing of the electrodes and may vary depending on the subsurface condition.

It is capable of obtaining data to about 30 meters (100 feet) deep, using self-contained, rechargeable batteries. Two cross-selection diagrams of vertical columns of apparent surface resistivity geo-electric sections are shown below. This shows the results of a surface resistivity survey to locate the water table.

1) The resistivity method is used in the study of horizontal and vertical discontinuities in the electrical properties of the ground.

2) It utilizes direct currents or low-frequency alternating currents to investigate the electrical properties(resistivity) of the subsurface.

3) A resistivity contrast between the target and the background geology must exist.

## Applications of resistivity survey :

1) Groundwater exploration: To determine the thickness of layered media as well as to map the geological environment of existing aquifers.

2) Lithology: To detect bodies of anomalous materials or in estimating the depths of bedrock surfaces.

3) Civil engineering: To test for the presence of underground voids such as old basements or embedded pipes that can cause safety and technological problems during construction.

4) Geophysical survey: To map contrasts between the physical properties of buried archaeological remains and the surrounding soil.

5) Soil exploration: To measure and record the changes of the mean resistivity or apparent specific resistance of various soil.

## Limitations of the resistivity survey :

The resistivity test should be limited to an expansion of subsurface data obtained by borings at structure sites. Its use in tracing aquifers may be adversely affected by depths to the aquifer and its thickness. Natural ground currents can be so strong as to be very troublesome when using the equipment.

## Resolution of limitations in resistivity methods :

1) MERIT( Multi-Electrode Resistivity Implant Technique) is a novel resistivity method

that uses buried electrodes to effectively increase resolution at depth.

2) Optimized arrays are used to maximize the depth resolution using the “Compare R” method.

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