Gate_2020
23)
The geometrical factor for the electrode configuration given below is
_____m
(Thanks to Chandrasekhar, ANU)
Solution:
The
apparent resistivity of the electrode array is as follows
$\rho_{a}
=( 2\pi)(\frac{\triangle
V}{I})\left\{(\frac{1}{r_{1}}-\frac{1}{r_{2}})-(\frac{1}{r_{3}}-\frac{1}{r_{4}})\right\}^{-1}$
In
this the term $ (
2\pi)\left\{(\frac{1}{r_{1}}-\frac{1}{r_{2}})-(\frac{1}{r_{3}}-\frac{1}{r_{4}})\right\}^{-1}$
I s defined as the geometric factor for the Schulumberger array.
$K
=(
2\pi)\left\{(\frac{1}{r_{1}}-\frac{1}{r_{2}})-(\frac{1}{r_{3}}-\frac{1}{r_{4}})\right\}^{-1}$
Given
that
$
r_{1} =20 m$
$
r_{2} =30 m$
$
r_{3} =30 m$
$
r_{4} =20 m$
$K
=(
2\pi)\left\{(\frac{1}{r_{1}}-\frac{1}{r_{2}})-(\frac{1}{r_{3}}-\frac{1}{r_{4}})\right\}^{-1}$
$K
=(
2\pi)\left\{(\frac{1}{20}-\frac{1}{30})-(\frac{1}{30}-\frac{1}{20})\right\}^{-1}$
$K
=( 2\pi)\left\{(\frac{2}{20}-\frac{2}{30})\right\}^{-1}$
$K
=( 2\pi)\left\{(\frac{20}{600})\right\}^{-1}$
$K
= 2\times 3.14 \times 30$
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