There are lots of areas with major earthquakes.
They occur on or near Tectonic Plates.

In Dec, 2004, major quakes were near Indonesia:
See the circle & arrow?

Yesterday a major earthquake, magnitude 7.0, hit Haiti.

The island lies just South of an edge of the Caribbean Plate.
Worse, a fault line runs through Haiti.
Indeed, the capital, Port-au-Prince, is on that fault.

I was surprised to learn (a consequence of old age, I reckon) that they don't use the Richter scale any more ... to measure earthquake "strength".
I had written a tutorial describing good ol' Richter and figured I was SO knowledgeable.
Now I have to understand the sexy new scale.
They no longer say: "7.0 on the Richter scale".
They say: "A magnitude 7.0 earthquake".
The Richter scale is measured by the amplitude of oscillation on a seismograph.
The entire seismograph case is firmly attached to the ground and oscillates with the earthquake.
A pen, attached to a large mass, generates a chart. The large mass stays (relatively) stationary.
(Sorta like a pendulum ... with the pendulum support doing the moving.)

Going from 6.0 to 7.0 means a tenfold increase in the amplitude of ground motion.
That factor-of-ten thing is because the Richter number is based upon a logarithm to base 10.
Since log10(10A) = 1 + log10(A), adding "1" to the Richter number means an amplitude 10 times larger.


These days, seismologists are more interested in the energy released by an eathquake, not the amplitude of ground motion.
It's been found that Energy varies as the 2/3 power of the amplitude of oscillation.
If A is the amplitude, that suggests using A2/3 to measure the energy released.
That suggests the "new" measure of the energy should be: log10(A2/3) ... continuing with the logarithmic ritual
This is now called the Moment Magnitude Scale: MW.

>Why the subscript "W"?
I have no idea. In fact, I have no idea why it's called the "Moment" magnitude.

Okay. Suppose that MW is increased by 1. How much does does the energy increase?

If MW increases by 1, then:   1 + log10[A2/3] = log10[10A2/3] = log10[ (103/2A)2/3].
That is, the energy increases by 103/2 ... about 31.
Mamma mia!

>Do you really understand this stuff?
Uh ... do you want the truth?

Moment Magnitude measurements

Okay, after further reading I find the following:
  • There's something called M0, the seismic moment of the earthquake.
  • M0 measures the energy associated with the earthquake:
          M0 = μ A u, where
          μ is the shear modulus of the rocks involved in the earthquake,
          A is the area of the rupture along the geologic fault where the earthquake occurred,
          u is the (average) displacement on A.
  • Note (from the figure) that M0 = μAu = F H = Force x Length ... a torque.
  • Torque is the moment of a force ... hence the name seismic moment.
  • M0 = μ A u has the dimensions of Force x Distance ... and that's energy
  • Although M0 measures the energy generated by an earthquake, not all that energy is propagated through ground waves ... and measured by a seismograph.
  • An "estimate" of how much of that energy is transmitted through ground waves?
    That's the seismic energy:   Es = M0 x 10-4.8
  • Note that the log[M0] differs from log[Es] by a constant, namely 4.8.
  • The Moment Magnitude is given by: MW = (2/3) log10[M0] - 10.7
          The 10.7 is included to achieve consistency with the older Richter scale.
          The subscript "W" means "Work".
          Work = force x distance and the forces and displacements involved in a quake generate work
          ... and work = energy.

Definition of Shear Modulus

>Wait! Do I need to know all this stuff?
You can sleep. I'd like to understand how they measure earthquake energies.
Can you see that μ has the dimensions of Force / Area (since u / H is dimensionless)?
That means that μ has the dimentions of pressure ... measured in Pascals (Pa).
A Pa is pretty small. It takes about 8900 Pas to equal 1 pound per square inch.
The rocks that take part in an earthquake have a shear modulus between 30 and 80 GPa ... and a GPa = 109 Pa.