GATE-2016
42. A Schlumberger array with current electrode separation 50m and potential electrode separation 5m is placed over an inhomogeneous medium. If the measured potential difference is 50mV and the computed apparent resistivity is 100ohm m , then the magnitude of current passing through the subsurface is...........mA
Solution:
The
Schlumberger array consists of four collinear electrodes. The outer
two electrodes are current (source) electrodes and inner two
electrodes are potential (receiver) electordes. The potential
electrodes are installed at the center of the electrode array with a
small separation, typically lee then are one fifth of the spacing
between the current electrodes.
Apparent
resistivity (ρa)
= ( (AB/2)2
– (MN/2)2
/ MN ) * Π * (V/I) -----------------(1)
current
electrode spacing AB = 50m
potential
electrode spacing MN = 5 m
Volatage
= 50 mV
apparent
resistivity = 100 Ωm
current
= ?
from
eq (1)
current
(I) = ( (AB/2)2
– (MN/2)2
/ MN ) * Π * (V/ρa)
=
( (50/2)2
– (5/2)2
/ 5 ) * 3.14* (50/100)
=
( (625) – (6.25)2
/ 5 ) * 3.14 * (50/100)
current
passing through the subsurface (I) = 194.28 mA
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