Question

1. If soone predicts that Sal Lake City can be hit by a Mw»14 carthk,cn you tell whether that's poble? Assuming an earthquake cuts the entire earth into half and slips 30 km, estimate the magnitude of the earthquakc. Assuming the whole earth is homogeneous with mantle composition (Shear velocity Vs ~5 km/s; density N-4000kg/m2)

Answer 1

Two largest reported earthquakes are 1960 Chile earthquake and 1964 Alaska earthquake where Moment Magnitude Scale, Mw is 9.6 and 9.3 respectively. With reference to this, the damage that will happen with Mw > 14 is unimaginable. However, a group of scientists conducted experiments to predict the possibility of earthquake in Salt Lake City. As per thier study, there is 43% chance of 6.75 magnitude earthquake in next 50 years.

But, in recently conducted studies, it is found that there is chance of powerful erthquake due to bounding of two faults. And they predicted an earthquake of 7.5 magnitude with a 16.5% chances in next 100 years. So, based on these results, earthquake with Mw > 14 will not be predicted and not possible.

Magnitude of the earthquake can be found by unsig the formula below:

$Mw = \frac{2}{3} (\log (Mo)) - 10.7$

Where, M₀​ = Siesmic Moment in dyn-cm

Where, G = Shear Strength of the Earth = 75 GPa, considering earth as homogeneous and as mantle

             A = Area of the fault = 3.14 x 6371² = 127.5161 x 10^​6 ​km²​ (Radius of earth = 6371 km)

             D = Avg dispalcement of the fault = 30 km as given

M₀​ = 75 x 10⁶ x 127.5161 x 10⁶​ x 30 = 2.8691 x 10²⁹ Nm = 2.8691 x 10³⁶ dyn-cm

Substituting value of M₀ in M_w​ equation,

M_w​ = 13.6051