Earthquakes are now reported as “moment magnitude”. So what happened to the Richter scale?
Charles Richter & Beno Gutenberg developed
the first magnitude scale in the 1930’s to quantify earthquakes by comparing
the size, or amplitude of seismic waves, shown on the right, plotted against distance as
calculated from S-P arrival times,. Connecting the two gives you the Richter Magnitude.
The scale is logarithmic, so a one-unit increase in magnitude corresponds to ten times larger
amplitude. The limitation was that seismologists "measured
certain frequencies which meant that the signals from large earthquakes weren't adequately
represented, like not being able to hear the bass notes on your laptop speaker.
That meant that the Richter scale underestimated large earthquakes.
Scientists have since developed far-more sensitive seismometers that, with faster computers,
have enabled them to record & interpret a broader spectrum of seismic signals, These
improvements allowed them to better determine the energy released by large earthquakes.
In 1979 they connected the seismograph recordings with the actual physical displacements. that
occur during an earthquake. The result was the moment magnitude scale.
Seismologists no longer look at only the amplitudes of seismic waves but instead use much more
information contained in the seismogram to calculate what is called the seismic moment”
The seismic moment, which defines how much force is needed to generate the recorded waves,
is defined by this equation: 133 Mo = μ * D * A.
Myu (μ) is rock rigidity. It describes the resistance of the rock to bending when force
is applied and is a constant for a given rock material.
More elastic energy is stored bending rocks of high rigidity than is stored bending rocks
of low rigidity. For example, this brick has a high rigidity and when bent or sheared would
yield a strong “earthquake”. The cake has lower myu, and shears easily. Rock rigidity
Is lower in the crust than it is in the mantle. As mentioned earlier, in most cases distance
and area can be determined by mathematical modeling of seismograms.”
D is the distance that the rock slipped along one side of the fault zone relative to the
other side. In the 1906 San Francisco earthquake, this fence line was offset more than 3 meters.
A is the estimated area of the fault zone along which the rock slipped the distance
D. A is the area that actually ruptured during the earthquake.
Let’s watch an earthquake happen. The arrows show forces building on opposing
sides of a fault. Growing stress that will be relieved in the earthquake is shown in red.
Here we see Blocks of rock move in opposite
directions across a strike-slip fault zone, such as the San Andreas fault in California.
Potential energy, in the form of elastic energy, is stored in Earths crust or mantle building
stress as the ground slowly deforms between large earthquakes.
If we could look below the ground, we would see the earthquake rupture that defines the
seismic moment and is determined by mathematical modeling of seismograms.
That equation is then plugged into the Moment Magnitude equation which is used by seismologists
to measure the size of earthquakes in terms of the energy released, not just the amplitude
of the recorded waves. The constants in the moment scale are chosen
such that at smaller magnitudes the moment mag matches the Richter scale.
To truly appreciate this, consider the changes in earthquake rupture required to increase
the moment magnitude by one unit. Either the area of rupture or the slip distance or both
must increase so that the product of slip distance times area increases by a factor
of 32. While the amplitude of shaking caused by a
magnitude 5 earthquake is ten times larger than for a magnitude 4 earthquake, the energy
released increases by about 32 times for each unit increase in magnitude.
To understand the scaling we’ll look at the effects of the rupture area by using pasta
as a model for magnitude. The cross-sectional area of a strand of spaghetti
is about uh square millimeter. when you break the noodle it makes an “earthquake” of,
let’s just say magnitude 5 for our model. Myu is constant for all strands of pasta,
and for D we’ll use 1 millimeter of displacement across the fault. So here we see the pasta
break and move laterally 1 mm. To increase it to a Moment magnitude of 6,
we multiply it times 32. The surface area is 32 times higher, yet the amplitude is just
10 times higher. To reach a magnitude 7, you have to multiply 32 times 32 and you get roughly
a 1000 strands. or about a pound of spaghetti noodles.
To get a magnitude 8 you need 32,000 pieces of spaghetti.
A magnitude 8, on the other hand, would require a million pieces of spaghetti
A magnitude 9 releases 1000 times more energy than a magnitude 7 earthquake.