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

88(b).Magnetic anomalies in the vertical and horizontal components at a station close to the magnetic latitude 30°are found to be 150 and -173 gammas respectively. Then the anomaly in the total field would be around 

(1) 230 gammas 

(2) -75 gammas 

(3) -23 gammas 

(4) Zero

Solution:

To calculate the components of the magnetic anomaly in the direction of the Earth’s magnetic file, F, we need to determine the magnetic inclination at the point.

Formula to calculate the anomaly of the total field is

$\triangle F=\triangle H cosI +\triangle Z sinI----(1)$

Latitude is given that $\phi =30^0$

To find the inclination from latitude is

$\tan I= 2\tan\phi$

$\tan I= 2\tan30^0$

$\tan I= 2 * \frac{1}{\sqrt{3}}$

$\tan I= 1.154$

$I= \arctan(1.154)$

Inclination is $I= 49^0 ----(2)$

Vertical (Z) and horizontal (H) components are given 150 and -173 respectively.

Above values substitute in eq(1)

$\triangle F=-173*cos49^0 +150*sin49^0$

$\triangle F=-173*0.656 +150*0.754$

$\triangle F=-113 +113$

Therefore the anomaly of the total field is

$\triangle F=0$

Reference: Solved problems in geophysics-Cambridge University Press (2012) by Elisa Buforn, Carmen Pro and Agustin Udias