CSIR NET Dec 2015 Q98: Geophysics

In magnetotelluric (MT) sounding, the apparent resistivity is computed from the ratio of orthogonal horizontal electric (E) and magnetic (H) field components via the Cagniard formula: rho_a = (1/(omega*mu)) * |E/H|^2 = (0.2/f) * |Zxy|^2, where Zxy = Ex/Hy is the surface impedance. Because apparent resistivity depends on the square of the impedance (and hence the square of the electric field amplitude, for a fixed magnetic field), doubling the amplitude of the horizontal electric field quadruples (2^2 = 4 times) the computed apparent resistivity, since rho_a is proportional to |E|^2. Thus the apparent resistivity becomes four times its original value (chaugani / increased four times), matching option 3.

Option 1 (doubled) would apply if apparent resistivity were linearly proportional to E, but the Cagniard formula involves the square of the impedance, not a linear relationship. Option 2 (tripled) does not correspond to any consistent scaling relationship in the MT apparent resistivity formula. Option 3 is correct: since rho_a proportional to |E|^2 (for fixed H and frequency), doubling E quadruples rho_a. Option 4 (halved) would incorrectly imply an inverse relationship between apparent resistivity and electric field amplitude, the opposite of the actual direct-square dependence.