Magnitudes: Moment Magnitude Explained What happened to the Richter Scale?

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 the size of large earthquakes. Seismologists have since developed far more sensitive seismometers that with faster computers, have enabled them to record and interpret a broader spectrum of seismic signals. These improvements allow them to better determine the energy released by large earthquakes. In 1979, they connected the seismographic recordings with the actual physical displacements that occurred during an earthquake. 

The result was the moment magnitude scale. Seismologists no longer look at only the amplitude of seismic waves, but instead use much more information contained in the size of gram 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. Mu times distance times area. Mu 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 many ways than high rigidity. Then a stored bending locks of low rigidity. For example, this brick has a high rigidity, and when bent, or a sheared, would yield a strong earthquake. 

The cake has lower mu and shears easily. Rock rigidity is lower in the crust, than it is in the mantle. As mentioned earlier, in most cases, distance in 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 over three meters. A is the estimated area of the fault zone, along which The Rock slipped the distance D it defines the area that actually ruptured during the earthquake.

Let's watch an earthquake happen. The arrows show forces building on opposing sides of a vault. Growing stress that will be relieved in the earthquake will be shown in red. Here we see blocks of rock move in opposite directions along a slight soaked vault zone, such as the San Andreas fault in California. Potential energy in the form of elastic energy is stored in Earth's crust or mantle, building stress as the ground slowly deforms between large earthquakes. Take a look below the ground at the earthquake rupture that defines the size of the moment. 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 magnitude scale are chosen such that at smaller magnitudes, the moment magnitude matches the Richter scale. To truly appreciate this, consider the change in the 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 four 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 one square millimeter. When you break the noodle, it makes an earthquake. Of let's just say magnitude 5 for our model. New is constant for all strands of pasta. And for D, we'll use one millimeter of displacement across the false. So here we see the pasta break and move laterally, one millimeter. 

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 ten times higher. To reach a magnitude 7, you have to multiply 32 times 32, and you get roughly 1000 strands, or about a pound of spaghetti noodles. To get a magnitude 8, you need 32,000 pieces of spaghetti. A magnitude 9, on the other hand, would require a million pieces of spaghetti. A magnitude 9 releases 1000 times more energy than a magnitude 7 earthquake.