Page 136 - Introduction to Petroleum Engineering

SEISMIC WAVES 123

A
M = log = log A − log A 0 (7.3)
L
A 0
where A is the maximum amplitude measured on the seismograph and A is a
0
correction factor for a particular region like southern California. Both A, A were
0
expressed in mm. Richter assigned M = 3 to an amplitude A = 1mm on a Wood–
L
Anderson seismograph that was recorded 100 km from the source of an earthquake.
Example 7.3 Richter Scale

What is the correction factor A when M = 3 and A = 1mm on a Wood–Anderson
L
0
seismograph that was recorded 100 km from the source of an earthquake?
Answer
We rearrange Equation 7.3 to find the correction factor A :
0
−
3
⋅
.
A = A 10 − M L = 1mm ⋅ 10 = 0 001mm
0
The Richter scale tended to underestimate the size of large earthquakes. A more
fundamental measure of the magnitude of an earthquake is the seismic moment M
0
defined in terms of the movement of one fault block relative to another. If we define
G as the shear modulus (Pa) of the rock, d as the distance one fault block slips relative
to another fault block (m), and S as the estimated surface area that is ruptured at the
2
interface between the two fault blocks (m ), then seismic moment M is
0
⋅
⋅
M = Gd S (7.4)
0
The unit of seismic moment M is N·m in SI units. The seismic moment M is a mea-
0
0
sure of the strength of the motion of the earthquake that connects seismographic
measurements to the physical displacement of fault blocks. The energy E released by
the earthquake is based on the empirical relationship
M
E ≈ 0 (7.5)
20000
The SI unit of E is Joules. The physical units of seismic moment M (N·m) and
0
energy E (J) are used to denote that M and E are different physical quantities.
0
The magnitude of the earthquake is based on empirical relationships between
seismic moment M and moment magnitude M . For example, the moment–magnitude
0
w
relationship (Hanks and Kanamori, 1978)
2
M = log M ( ) − 91.   (7.6)

w 3 0
relates seismic moment M and moment magnitude M , where M is dimensionless
0
w
w
and M is in N·m.
0