# Basic Geophysics Earthquake Magnitudes

Author:

KIT | WEBCAST

Keywords:

Geophysics,Karlsruhe Institute of Technology,KIT,Geophysics at KIT,Study Geophysics,Geosciences,Moment magnitude,Richter-scale,Body wave magnitude,Surface wave magnitude,Seismic moment,Charles F. Richter,Benno Gutenberg

Subtitles:
Many ways to express the extent of an earthquake are used today in newspapers, on TV, and on the internet. People speak of its strength, its magnitude, or “the open- ended Richter scale”. When Charles Francis Richter published his scale in 1935, his main goal was to better understand the seismic activity in California. He wanted to introduce a measurable quantity for earthquakes that did not describe long- distance effects, but the strength of the earthquake's source itself. He called this new quantity the magnitude of the earthquake. In an interview in 1980, Richter said that he was glad that the expression “open-ended” is now used in newspapers. This is because since the introduction of earthquake magnitude, people had been confusing it with the closed-ended intensity scale, which describes the damage and other effects of earthquakes. Hello and welcome. In this video, I will be showing you how the strength of earthquakes was measured in the past and how it is determined today. I will show you what different types of earthquake magnitudes exist and how they differ from each other. During his research, Richter noticed that the earthquakes occurring in California differed greatly in the maximum ground motion they caused. In order to be able to describe these differences across multiple orders of magnitude, Richter used a logarithmic scale. According to this scale, the strength of the quake is calculated from the logarithm of the maximum amplitude A measured on a seismogram, a correction factor for the distance delta times 2.76, and an adjustment factor of -2.48. The distance factor is necessary, because the greater the distance from a quake, the smaller the ground motions experienced. For the magnitude itself, the formula means that an amplitude that is 10 times higher results in a magnitude that is greater by one - and an amplitude that is 100 times higher results in a magnitude that is greater by two. This new physical quantity was developed and measured by Richter with a historic Wood-Anderson seismometer, initially only for California. The depth of the quake was not taken into account. However, because earthquakes do not only occur in California, but worldwide, and other, more modern measuring instruments are used today, the Richter scale is no longer valid in a strict sense. Despite this, magnitudes for local earthquakes are calculated using a formula similar to the original one by Charles Richter and called the local magnitude ML. Today, it is calculated as the average of all stations that record an earthquake. Richter and his colleague Beno Gutenberg soon realized that the local magnitude was unable to assess earthquakes recorded globally. That is why they introduced the surface wave magnitude MS. Gutenberg himself established another measurement after that: the body wave magnitude mb. In both magnitudes, the dominant period T is included in the measurement. MS is - as the name says - determined from the maximum amplitude of the surface waves at periods of approximately 20 s and used for earthquakes recorded worldwide. MS is calculated from the logarithm of the maximum amplitude A divided by the period T plus 1.66 times the logarithm of the distance delta plus 3.3. Correspondingly, mb is determined from the maximum amplitude of the body waves at periods of around 1 Hz and is valid for epicenter distances of up to 100°. The formula is as follows: mb equals the logarithm of the amplitude divided by the period plus an empirically determined term Q, which is dependent on the earthquake depth h and the distance delta. The advantage of all these magnitude scales is the rapid determination using the maximum amplitude in the seismogram. All scales mentioned so far are not suitable for measuring the magnitudes of very large quakes. The reason for this is that from a certain magnitude onwards, the maximum amplitudes in the seismogram no longer increase. This means that the magnitude does not exceed a certain threshold value even for larger quakes. This practical upper limit of the scale is called saturation. We can see this clearly in this illustration of theoretical earthquake source spectra. Shown here are the frequency spectra of various quakes. Plotted on the horizontal axis is the frequency, and on the vertical one the amplitude. For each earthquake magnitude, we see a plateau range which falls after a certain frequency. We call this frequency the cutoff frequency. With the body wave magnitude as an example, we see that for magnitudes up to around five and a half, the distances between the lines are approximately equal. For surface waves, this holds true for magnitudes of up to around eight. This means that for larger amplitudes, the magnitude no longer increases. In order to solve this problem, Thomas Hanks and Hiroo Kanamori developed the moment magnitude scale which performs calculations directly from the plateau area of the source spectrum, making it frequency-independent. It is based on the seismic moment, which is calculated from the shear modulus mu, the area of the rupture plane S and the displacement D on this area, and is calculated as M0=mu*D*S. Practically speaking, M0 can be determined from the level of the plateau in the source spectrum. MW is then given by 2/3 times the logarithm of M0 in joules minus 9.1. Today, the moment magnitude MW is determined globally for earthquakes with a magnitude greater than 5 and generally corresponds to what is described as strength, magnitude, or Richter scale in the media. Hence, we see that the expression “Richter scale” has not only been retained for historical reasons. But is it really open-ended? Theoretically, yes, because the amplitude of the underlying source spectrum does not have a maximum limit. Practically speaking, however, the possible rupture planes on the earth and the displacement occurring along them limit the magnitude to values less than 10. The strongest earthquake ever measured occurred on May 22, 1960, in Chile and had a moment magnitude of 9.5. This corresponds to a rupture plane of 800 km by 200 km and a displacement of 21 m. Today, local networks are able to measure magnitudes less than zero. A magnitude -2 quake, for example, has a rupture plane measuring a good square meter, or the size of an average tabletop, which is displaced by less than one millimeter during the rupture. You have now learned about magnitudes ranging from 9 to less than 0. One order of magnitude equals to a tenfold increase in amplitude. But how does the energy released behave? In this animation, you can see the energy ratios of quakes of various magnitudes. An earthquake with a magnitude that is two values higher releases 1,000 times as much energy, which is represented in this animation by the surface of the squares. The energy difference between magnitude 2 and 6 is a factor of one million. In this video, I introduced to you the various earthquake scales. Local magnitudes are highly dependent on the location where they are recorded, making them difficult to compare with those from other regions. Magnitudes are typically measured using maximum amplitudes of certain wave types. The advantage is that they can be quickly and directly determined from the seismogram, but the disadvantage is that they become saturated for larger magnitudes. The moment magnitude, on the other hand, does not become saturated, as it is derived from the source spectrum. Today, it is used in a standardized form for earthquakes worldwide with a magnitude of 5 and greater. Magnitude scales are logarithmic and the energy released increases additionally by a factor of 1.5. This means that a magnitude 4 earthquake differs from a magnitude 2 quake by a 100-fold maximum amplitude in the seismogram and a factor of 1,000 in the amount of energy released.