Moment Magnitude scale and energy: a) Given that an atomic bomb the size of that

Question

Moment Magnitude scale and energy: a) Given that an atomic bomb the size of that detonated at Hiroshima releases the same energy as a magnitude 6 earthquake, how many of these bombs would be required to match the energy of the M9.2, 1964 Alaska quake? a) Suppose a 70 km deep fault ruptured all the way from San Diego to Anchorage, a distance of 5000 km. Suppose it ruptured in a single earthquake and the average relative displacement across the fault was 125 m. Estimate the seismic moment, the moment magnitude, and duration of the rupture for this earthquake. Assume the average depth of the crust is 35 km and the average shear modulus of the crust is 30 GPa and the shear modulus of the mantle is 70 GPa. To estimate the duration of the rupture, assume the rupture propagates at 80% of the shear wave velocity in the upper mantle (Vrupture = 0.8*4.5 km/s). b) Suppose a fault in the earth’s crust ruptured over an area 10 m x 10 m resulting in an average slip displacement of 10 mm. Estimate the seismic moment, the moment magnitude, and duration of this earthquake if the shear modulus of the rock is 30 GPa and the density of the rock is 2800 kg/m3 .

Explanation / Answer

Answer:a

There would be require about 1.5 bombs of that size to release same energy.

Answer:a

Seismic moment can be calculated by following formula;

M=u*A*D

M= Seismic moment, u= Shear modulus, A= area along fault, D= average slip.

u= 30GPa, A= 70*5000= 350000 km2, D= 125m =0.125 km

Put the values in above equation we get,

M= 30*350000*0.125= 1312500 Nm

Answer:b

M=u*A*D

Here, u= 30Gpa, A= 10*10=100m2, D= 10mm

Put the values in above equation we get,

M= 30*100* 10= 30000Nm

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