GATE-2018 (24) :Wyllie – Time average equation

CSIR-NET 2014

112. In an electrical sounding with Wenner configuration, resistance values of 4Ω , 3Ω and 1Ω are measured for electrode spacing of 25m, 50m and 75m respectively. Which of the following inferences is likely to be correct?

1) The resistivity of the layers decreases with depth

2) A high resistivity layer is sandwiched between two relatively low resistivity layers

3) A low resistivity layer is sandwiched between two relatively high resistivity layers

4) The resistivity of the layers increases with depth

Solution:

In the Wenner configuration the current and potential electrode pairs have a common mid-point and the distance between adjacent electrodes are equal.

Apparent resistivity ρ_a= ( 2*Π*a* (V/I) ) ----------------(1)

a= electrode spacing

V / I = R, resistance

ρ_a= ( 2*Π*a*R ) -------------------(2)

Given values :

R₁= 4 Ω , a₁= 25 m

R₂= 3 Ω , a₂ =50 m

R₃ = 1 Ω , a₃ = 75 m

Apparent resistivity of the first layer (ρ_a1)= 2* 3.14* 25* 4

= 628 Ωm

Apparent resistivity of the second layer (ρ_a2 )= 2*3.14*50*3

= 942 Ωm

Apparent resistivity of the third layer (ρ_a3)= 2*3.14*75*1

=471 Ωm

Therefore, ρ_a1 < ρ_a2 > ρ_a3

A high resistivity layer is sandwitched between the two relatively low resistivity layers.