One of Dr. Charles F. Richter's most valuable contributions was to recognize that the seismic waves radiated by all earthquakes can provide good estimates of their magnitudes. You can read about seismic waves by clicking here. He collected the recordings of seismic waves from a large number of earthquakes, and developed a calibrated system of measuring them for magnitude.

Richter showed that, the larger the intrinsic energy of the earthquake, the larger the amplitude of ground motion at a given distance. He calibrated his scale of magnitudes using measured maximum amplitudes of shear waves on seismometers particularly sensitive to shear waves with periods of about one second. The records had to be obtained from a specific kind of instrument, called a Wood-Anderson seismograph. Although his work was originally calibrated only for these specific seismometers, and only for earthquakes in southern California, seismologists have developed scale factors to extend Richter's magnitude scale to many other types of measurements on all types of seismometers, all over the world. In fact, magnitude estimates have been made for thousands of Moon-quakes and for several quakes on Mars.

Thus after you measure the wave amplitude you have to take its logarithm, and scale it according to the distance of the seismometer from the earthquake, estimated by the S-P time difference. The S minus P time, in seconds, makes Δt.

Click here to learn more about the mathematical logarithm.

Seismologists will try to get a separate magnitude estimate from every seismograph station that records the earthquake, and then average them. This accounts for the usual spread of around 0.2 magnitude units that you see reported from different seismological labs right after an earthquake. Each lab is averaging in different stations that they have access to. It may be several days before different organizations will come to a consensus on what was the best magnitude estimate.

Seismologists have more recently developed a standard magnitude scale that is completely independent of the type of instrument. It is called the moment magnitude, and it comes from the seismic moment.

To get an idea of the seismic moment, we go back to the elementary physics concept of torque. A torque is a force that changes the angular momentum of a system. It is defined as the force times the distance from the center of rotation. Earthquakes are caused by internal torques, from the interactions of different blocks of the earth on opposite sides of faults. After some rather complicated mathematics, it can be shown that the moment of an earthquake is simply expressed by:

(Moment) = (Rock Rigidity) x (Fault Area) x (Slip Distance)

M₀ = μ A d

(dyne-cm) = (dyne)/(cm²) (cm²) (cm)

The formula above, for the moment of an earthquake, is fundamental to seismologists' understanding of how dangerous faults of a certain size can be.

Now, let's imagine a chunk of rock on a lab bench, the rigidity, or resistance to shearing, of the rock is a pressure in the neighborhood of a few hundred billion dynes per square centimeter. (Scientific notation makes this easier to write.) The pressure acts over an area to produce a force, and you can see that the cm-squared units cancel. Now if we guess that the distance the two parts grind together before they fly apart is about a centimeter, then we can calculate the moment, in dyne-cm:

M₀ = (3x10¹¹ dyne/cm²) (10 cm) (10 cm) (1 cm)

M₀ = (3x10¹¹) (10²) (dyne-cm)

M₀ = 3x10¹³ dyne-cm

Again it is helpful to use scientific notation, since a dyne-cm is really a puny amount of moment.

Now let's consider a second case, the Sept. 12, 1994 Double Spring Flat earthquake, which occurred about 25 km southeast of Gardnerville. The first thing we have to do, since we're working in centimeters, is figure out how to convert the 15 kilometer length and 10 km depth of that fault to centimeters. We know that 100 thousand centimeters equal one kilometer, so we can write that equation and divide both sides by "km" to get a factor equal to one.

1 km = 10⁵ cm 1 = 10⁵ cm/km

Of course we can multiply anything by one without changing it, so we use it to cancel the kilometer units and put in the right centimeter units:

M₀ = (3x10¹¹ dyne/cm²) (10 km) (10⁵ cm/km) (10 km) (15 km) (10⁵ cm/km) (10 km) (30 cm)

M₀ = 1.1x10²⁵ dyne-cm

Of course this result needs scientific notation even more desperately. We can see that this earthquake, in 1994 the largest in Nevada since 1954, had two times ten raised to the twelfth power, or 2 trillion, times as much moment as breaking the rock on the lab table.

There is a standard way to convert a seismic moment to a magnitude. The equation is:

M_W = (2/3) [log₁₀ M₀ (dyne-cm) - 16.0]

Now let's use this equation (meant for energies expressed in dyne-cm units) to estimate the magnitude of the tiny earthquake we can make on a lab table:

M₀ = 3x10¹³ dyne-cm

M_W = (2/3) [log₁₀ (3x10¹³ dyne-cm) - 16.0]

M_W = (2/3) (~13.5 - 16.0)

M_W ~ (2/3) (-2.5)

M_W ~ -1.7

Negative magnitudes are allowed on Richter's scale, although such earthquakes are certainly very small.

Next let's take the moment we found for the Double Spring Flat earthquake and estimate its magnitude:

M₀ = 1.4x10²⁵ dyne-cm

M_W = (2/3) [log₁₀ (1.4x10²⁵ dyne-cm) - 16.0]

M_W = (2/3) (~25.2 - 16.0)

M_W ~ (2/3) (9.2)

M_W ~ 6.1

The magnitude 6.1 value we get is about equal to the magnitude reported by the UNR Seismological Lab, and by other observers.

Both the magnitude and the seismic moment are related to the amount of energy that is radiated by an earthquake. Richter, working with Dr. Beno Gutenberg, early on developed a relationship between magnitude and energy. Their relationship is:

logE_S = 11.8 + 1.5M

giving the energy E_S in ergs from the magnitude M. Note that E_S is not the total ``intrinsic'' energy of the earthquake, transferred from sources such as gravitational energy or to sinks such as heat energy. It is only the amount radiated from the earthquake as seismic waves, which ought to be a small fraction of the total energy transferred during the earthquake process.

In the late 1900s, Dr. Hiroo Kanamori came up with a relationship between seismic moment and seismic wave energy. It gives:

Energy = (Moment)/20,000

For this moment is in units of dyne-cm, and energy is in units of ergs. dyne-cm and ergs are unit equivalents, but have different physical meaning.

Let's take a look at the seismic wave energy yielded by our two examples (italics below), in comparison to that of a number of earthquakes and other phenomena. For this we'll use a larger unit of energy, the seismic energy yield of quantities of the explosive TNT (We assume one ounce of TNT exploded below ground yields 640 million ergs of seismic wave energy):

Richter TNT for Seismic Example

Magnitude Energy Yield (approximate)

-1.5 6 ounces Breaking a rock on a lab table

1.0 30 pounds Large Blast at a Construction Site

1.5 320 pounds

2.0 1 ton Large Quarry or Mine Blast

2.5 4.6 tons

3.0 29 tons

3.5 73 tons

4.0 1,000 tons Tactical Nuclear Weapon

4.5 5,100 tons Average Tornado (total energy)

5.0 32,000 tons Project Shoal nuclear test east of Fallon, NV

5.5 80,000 tons Little Skull Mtn., NV Quake, 1992

6.0 1 million tons Double Spring Flat, NV Quake, 1994;

Wells, NV Quake, 2008

6.5 5 million tons Northridge, CA Quake, 1994;

Monte Cristo Range, NV Quake, 2020

7.0 32 million tons Hyogo-Ken Nanbu, Japan Quake, 1995;

Dixie Valley, NV Quake, 1954;

Ridgecrest, CA Quake, 2019

(First Quake to Kill a Nevadan);

Soda Lake Maar, NV Volcanophreatic Blast;

Largest Thermonuclear Weapon

7.5 160 million tons Landers, CA Quake, 1992

8.0 1 billion tons San Francisco, CA Quake, 1906

8.5 5 billion tons Anchorage, AK Quake, 1964

9.0 32 billion tons Chilean Quake, 1960; Tohoku Quake, 2011

10.0 1 trillion tons (San-Andreas type fault circling Earth)

12.0 160 trillion tons (Fault Earth in half through center,

OR Earth's daily receipt of solar energy)

160 trillion tons of dynamite is a frightening yield of energy. Consider, however, that the Earth receives that amount in sunlight every day.

Most seismologists prefer to use the seismic moment to estimate earthquake magnitudes. Finding an earthquake fault's length, depth, and its slip can take several days, weeks, or even months after a big earthquake. Geologists' mapping of the earthquake's fault breaks, or seismologists' plotting of the spatial distribution of aftershocks, can give these parameters after a substantial effort. But some large earthquakes, and most small earthquakes, show neither surface fault breaks nor enough aftershocks to estimate magnitudes the way we have above. However, seismologists have developed ways to estimate the seismic moment directly from seismograms using computer processing methods. The Centroid Moment Tensor Project has been routinely estimating moments of large earthquakes around the world by seismogram inversion since starting at Harvard University in 1982.

Seismologists use a separate method to estimate the effects of an earthquake, called its intensity. Intensity should not be confused with magnitude. Although each earthquake has a single magnitude value, its effects will vary from place to place, and there will be many different intensity estimates. The Mercalli Intensity Scale is one popular way to characterize earthquake effects.

Next: Earthquake Effects