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

 21. Assuming Airy isostatic compensation, the depth to the Moho from a point located 2 km above the mean sea level is _________ km. (round off to 1 decimal place). 

(The depth of compensation T for the crust at mean sea level is 30 km, the density of crust and upper mantle are 2.67 gm/cc and 3.30 gm/cc,respectively).

Solution:

Crustal thickness = 30 km

mountain thickness (h)= 2 km

Density of the crust = 2.67 gm/cc

Density of the mantle = 3.30 gm/cc

From Airy isostatic compensation, 

$$root =  \frac{\rho_{c}} {\rho_{m}-\rho_{c}} * h$$


$$ root = \frac{2.67} {3.30-2.67} * 2$$


root = 8.476 km

The depth to the Moho from a point located 2 km above the mean sea level is = Mountain thickness + crustal thickness + root

                              = (2 + 30 + 8.476) km

                              = 40.476 km