# Borehole Resistivity Survey

- Jul 29, 2019-

WHAT IS RESISTIVITY?

Resistivity is a measurement of the resistance of a “bulk volume” of material.

To measure the resistivity of materials, the geometry of the electrodes used to make the measurement is incorporated into an equation. The fundamental equation for resistance is

based on ohms law.

OHMS LAW:

Ohms law:                    E = I x R

Where:            E = Voltage in volts

I = Current in amperes

R = Resistance in ohms

GEOMETRIC FACTOR:

When a bulk measurement of earth material is made, the resistance varies according to the dimensions of the material. A constant is derived based on the geometry (volume)

of the material included within the measurement. When voltage is applied to a material, current will flow through the material proportional to the voltage applied and inversely

proportional to the resistance to the flow imposed by the material having area (A), and the length (L) between or spacing of the electrodes.

The geometry of Area/Length = meters2/meter = meters

or…

Area/Length   = feet2/feet = feet

Calculation of the geometric constant when a “whole earth” surrounds the electrodes, as in a borehole, the calculation is performed as follows:

G = 4 x pi x L

Where:

G = geometric constant (no units)

L = distance between measuring electrodes in the normal electrode configuration.

Pi = 3.14 (approximately)

Illustration: Resistivity model.

Rearranging ohms law,                       R = E/I

Where:

R = resistance (ohms)

E = voltage

I = current

Including a geometric constant (G) to calculate resistivity,

Resistivity (p) = G x E/I

Where:

p = resistivity (ohm-meters or ohm-feet)

E = voltage

I = current