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

CSIR -NET 2015 (Dec)

98. A magneto-telluric survey over a layered structure calculates the apparent resistivity as 1 ohm-m. If the amplitude of the horizontal electric field is doubled, then the apparent resistivity will be

A) doubled

B) increased three times

C)increased four times

D)reduced to half

Solution:

The relation between the apparent resistivity, electric field, magnetic field and time period is

ρ_a = (0.2*T (|E/H|)²) ------------------(1)

From above problem we need a relation between apparent resistivity and electrical field

So,

ρ_a= E² --------------(2)

ρ₁/ ρ₂ = E₁²/ E₂² ------------------(3)

given data

ρ₁= 1 Ωm

E₁ = E

E₂= 2E

Substitute above values in eq (3)

(1/ρ₂) = (E² /4E²)

(1/ρ₂) = (1/4)

ρ₂ = 4 Ωm

Therefore apparent resistivity increases by four times.