Question

a) Give reasons why moment magnitude Mw is the most common used method to define the size of an earthquake.

Data on a major earthquake are as follows:

· Depth of fault rupture is 25 km

· Length of the surface faulting is 800 km

· Average slip along the fault is 5 m

· Shear modulus of material along the fault plane is 2x1010 N/m2

b) Calculate the seismic moment, Mo

c) Compute the moment magnitude of the earthquake (note, Mo in dyne-cm; one Newton-m = 107 dyne-cm)

Answer 1

PART (a):

Moment magnitude measures the earthquake’s magnitude quantitatively.

Moment magnitude (Mw) is the most common method to define the size of an earthquake, because of the following reasons:

• Earthquake size measurement using Mw is related to magnitude of seismic moment (Mo) than the amplitude of seismic waves (see formulas (A) and (B) below)

(Seismic moment provides a scientific scale of the size of the earthquake)

• The calculations of Moment magnitude avoid the magnitude saturation problem (since , the Mw is based on the total energy of the earthquake)
• Moment magnitude scale is capable of measuring most destructive earthquakes and is the most reliable in this case.

The seismic moment is calculated using the formula,

Mo = D x A x µ.......................................................Formula (A)

Where,

Mo = Seismic moment

D = Average fault displacement

A = Total area of fault surface

µ = Modulus of rigidity

The moment magnitude is calculated using the formula,

.......................................... Formula (B)

Where,

Mo = Seismic moment (in dyne cm)

Mw = Moment magnitude

PART (b): Calculation of seismic moment (Mo)

Mo = D x A x µ

A = Total area of fault surface

A = length x Depth of fault rupture

Length of faulting = 800 km (given)

Length of faulting = 800 x 103 m

Depth of fault rupture = 25 km (given)

Depth of fault rupture = 25 x 103 m

Thus, Area = length x Depth of fault rupture

Area = 800 x 103 x 25 x 103

Area = 2 x 1010 m2

µ = 2 x 1010 N/m2 (given)

D = 5 m (given)

Substituting the above values in the Formula (A), we get:

Mo = D x A x µ

Mo = 5 x 2 x 1010 x 2 x 1010

Mo = 2 x 1021 Nm

(1 Newton m = 107 dyne cm)

Thus, Mo = 2 x 1028 dyne cm

Thus seismic moment (Mo) = 2 x 1021 Nm or 2 x 1028 dyne cm

PART (c): Calculation of moment magnitude (Mw)

Substituting, Mo = 2 x 1028 dyne cm in the Formula (B), we get,

Mw = 8.167

Thus moment magnitude (Mw) = 8.167

Numerical Answers:

Answer (b): Seismic moment (Mo) = 2 x 1021 Nm or 2 x 1028 dyne cm

Answer (c): Moment magnitude (Mw) = 8.167