GATE_2020

Gate_2020

3) Skin depths in homogeneous media of resistivity

$\rho_{1}$ and

$\rho_{2}$ are 100 m and 200 m respectively at 1000Hz frequency. The ration of

$\rho_{1}$ /

$\rho_{2}$ will be _________

(Thanks to Chandrasekhar, ANU)

Solution:

Skin depth

$\delta_{1}$ at

$\rho_{1}$ and f is given 100 m

Skin depth

$\delta_{2}$ at

$\rho_{2}$ and f is given 200 m

Formula

$\delta =503.8\sqrt{\frac{\rho}{f}}$

$\frac{\delta_{1}}{\delta_{1}}=\frac{503.8\sqrt{\frac{\rho_{1}}{f}}}{503.8\sqrt{\frac{\rho_{2}}{f}}}$

$\frac{100}{200}=\sqrt{\frac{\rho_{1}}{\rho_{1}}}$

$(0.5)=\sqrt{\frac{\rho_{1}}{\rho_{1}}}$

${\frac{\rho_{1}}{\rho_{1}}}= 0.25$

GEOPHYSICS