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# The magnitude and intensity of the earthquake

2018-11-06  |   Editor : houguangbing

There are basically two ways to represent the size of earthquake, one is to use the magnitude of an earthquake to indicate the size of an earthquake: the other is to determine the magnitude of the earthquake based on the extent of damage.

Earthquake as a natural phenomenon, it’s huge and minor, it could be as huge as the mountains fall and the earth splits, bring down the house, minor as human body cannot feel, only sensitive instruments can record it. How do you express the size of an earthquake? Utilize the energy of the earthquake released to express the size of the earthquake, utilize the magnitude of the earthquake to express the amount of energy, which released by the earthquake, large magnitude earthquakes release more energy.

After the earthquake occurred, the first thing people care about is: what is the magnitude of the earthquake? If you go back hundreds of years ago, we cannot get a similar answer to the “X magnitude of the earthquake” certainly, it's a series of seismic damage macroscopic descriptions, as the Ming history of earthquake recorded in the Hua County Shanxi Province of China: “The ground cracked and spring gushed out, fish in the spring, or houses fell into the ground the officials, soldiers and civilians crushed and killed more than 830,000.” That is to say, at that time, we can only estimate the size based on the earthquake damage intensive, intensity is not only affected by people's subjectivity, it is also related to the geological and building conditions of the earthquake area, therefore, intensity cannot measure the magnitude of an earthquake quantificationally

Magnitude

Magnitude refers to the size of an earthquake, the huger the earthquake, the larger the magnitude, at present, the world's largest magnitude is 9.5

(1) Several different magnitudes of earthquakes

There is one magnitude that represents the size of an earthquake only, but due to the magnitude scale is inconsistent, therefore, it is common to see several magnitudes from the same earthquake.

The international seismological community publishes the magnitudes with capital M add one digit after the decimal point all, to facilitate public understanding and media release.

Something are commonly used to indicate the magnitude scale: Richter magnitude(MJ)、Surface wave magnitude(Ms)、Body wave magnitude(Mb) and Moment magnitude(Mw).

Richter magnitude was put forward by Richter in 1935. It is based on the amplitude of seismic wave recorded by seismograph. When the size of seismic origin is constant, the further distance from seismic origin, the smaller amplitude of seismic wave; when the distance from seismic origin is constant, the amplitude of seismic wave is positively correlated with the size of seismic origin.

The Richter magnitude is defined as a seismograph (named Wood-Anderson at that time) with the type of standard seismic, free period 0.8s, multiplying power 2800 times, damping constant 0.8, the logarithm of the maximum amplitude A (count) recorded at a distance of 100km from the epicenter:

ML=log(A) (2-1)

Obviously, the earthquake occurred from 100 kilometers away, the true ground motion is 1Mm as the seismograph recorded, the earthquake is a zero-magnitude earthquake. From the definition of the Richter magnitude as well, if the distance remains constant between the earthquake and the station, increase 1 magnitude of the earthquake, the amplitude of vibration resulted in the earthquake increase 10 times: increase 2 magnitude of the earthquake, the amplitude of vibration resulted in the earthquake increase 100 times: increase 3 magnitude of the earthquake, the amplitude of vibration resulted in the earthquake increase 1000 times, and so on.

But not all earthquakes occur at a distance of 100km from the station, therefore, when calculate the magnitude of the earthquake, we must consider the correction of the epicenter distance from A (The distance between the epicenter and the station, the degree for unit), formula (2-1) can be modified to be：

ML=log(A)+2.561og(A)-5.12 (2-2)

The appearance of the Richter magnitude，the size of the earthquake has been made for measurable, comparable quantities for the first time, it lays a foundation for the quantitative development of seismology. Even to this day, the Wood- Anderson seismograph had already vanished, as a museum piece. But in order to keep the contrast and continuity of seismic records, many small earthquakes are still simulated by instruments, calculate the Richter magnitude.

Wood-Anderson seismograph is a short-period seismograph (period 0.8s), it can record the short period seismic wave preferably, But seismic waves in the process of transmission, due to the attenuation velocity of high frequency seismic wave (i.e. short period wave) is much higher than that of low frequency seismic wave, when the distance of seismograph is farther than the epicenter, the recording capacity of the seismograph becomes limited. In 1945, the seismologist Gutenberg invented the surface wave magnitude MS, MS can record earthquakes from a distance, that makes up the shortfall of the Richter magnitude。Including，S stands for surface wave，It is determined by the magnitude of the earthquake, which is based on the period for the surface wave size of 20s. In 1966, The Richter magnitude was further expanded at the Zurich international seismological society, when calculate the surface wave magnitude (Ms), should be considered in addition to the maximum amplitude, the period T and the epicenter distance should also be considered:

Ms=log(A/T)+l.66log(A)+3.3 (2-3)

But when the depth of hypocenter is deeper, the excited surface waves are not significant. Therefore, Gutenberg also invented the body wave magnitude Mb, b stands for body wave, it is determined by the magnitude of the earthquake, which is based on the size of the body wave (usually is P wave) in the seismic wave. Almost all of the earthquakes, whatever the distances or the depth of hypocenter, also including nuclear explosions, P wave can be clearly identified on the seismic map advisor or adviser, so Mb has the comprehensive utilization, many of the magnitudes published by the U.S. Geological Survey (USGS) are Mb.

In 1977, the professor HirooKanamori developed the method for moment magnitude (MW) in the California Institute of Technology, that the earthquake is calculated from the seismic moment (M0), this scale marker can better describe the physical properties of earthquakes, such as the size of stratigraphic dislocation and seismic energy. Including M0=uAD. u is shear modulus , A is the area of rupture plane, D is the average dislocation of earthquake rupture). Look from the formula, the larger the rupture plane, the larger the dislocation amount, the more energy released. Just because of this, the moment magnitude is not as saturated as other magnitudes. This development is based on two reasons, firstly, the Richter magnitude is a measure of magnitude, that the moment magnitude is the physical magnitude considered by the earthquake mechanism: Secondly, the Richter magnitude is difficult to measure large earthquakes. When Mw<7.25, the measured results of the moment magnitude Mw are basically consistent with the magnitude Ms measured by Richter surface wave: But when the Mw > 7.25, surface wave magnitude Ms begins to appear "saturated", that is, the measured surface wave magnitude Ms is lower than the moment magnitude Mw, which can reflect the real size of the earthquake.

However, when Mw=8.0-8.5, Ms is fully saturated, that is, no matter how the Mw increases, the measured surface wave magnitude Ms does not increase with it. Therefore, when the magnitude of huge earthquake is measured, if other than Mw earthquake magnitude scale is adopted, the magnitude of the earthquake will be underestimated due to its saturation.

At Present, the moment magnitude has become the priority recommended earthquake scale in the world, which in the most of the world's seismic networks and seismological observation agencies. However, because of the various countries in the world has respective earthquake research history and calculation formula, the earthquake magnitude scale published by various countries has not been unified. Most of the published magnitudes in China are surface wave magnitudes, rather than moment magnitudes. Such as the March in 2011 earthquake in Japan, China published the surface wave magnitude was 8.6, the USA published the moment magnitude was 9.0.

In December 26, 2004, the earthquake magnitude of Ms8.7 at the west coast of Sumatra in Indonesia , triggered the tsunami, shocked the Indian Ocean and a dozen of its coastal countries of Indonesia, Sri Lanka, India, Thailand, Bangladesh, Maldives, Somalia, Malaysia, Myanmar, Tanzania, Seychelles, Kenya etc., the death toll exceeded 280,000. The world's media competed to report, prominent seismological institutes have commented one after another, one notable piece of news came from the U.S. geological survey: Sorted by moment magnitude Mw, this major earthquake had been ranked Chile the earthquake magnitude of 9.5 in 1960 in the 20th century, the earthquake magnitude of 9.2 at prince William sound in Alaska in 1964, after the earthquake magnitude of 9.1 on Alaska's Andreanof Island in 1957, tied for the fourth place with the earthquake magnitude of 9.0 earthquake magnitude, in Kamchatka in 1952.For example, the earthquake in Chile in 1960, measured the moment magnitude Mw=9.5, and the surface wave magnitude has been already saturated, only 8.5.

(2) Why did the magnitude revised

In theory, one earthquake, there is only one magnitude for the same earthquake magnitude scale. Actually, in addition to the frequent occurrence of different countries, institutions reported by the magnitude’s inconsistency phenomenon, (For example, the west Kunlun Mountain earthquake in China in 2001, the measurement result in China is Ms=8.2, but in United States is Ms=8.0), there are also frequent occurrences of revised magnitudes (Such as the moment magnitude measured by USGS in March 11, 2011 Japan earthquake, revised to 8.9 from 8.8, revised to9.0 in March 14).

The station data used by different countries and institutions are different, which can affect the results of the magnitude. The differences of station data mainly include；①Due to the stylobate of station、different instruments, magnitude differences are possible: ②The radiation of seismic waves has directivity which generated by the earthquake, the magnitude also has many differences in different azimuth and epicentral distance, which measured in the seismograph station. As for the March 11, earthquake in Japan in 2011, the network of seismic stations used in China, all of them are distributed on the western side of Japan, the epicentral distance was also limited: The global network of seismic stations used in USA, they were distributed all over the world, covered more reasonably and evenly, therefore, in theory, the measurement of magnitude was relatively accuracy in USA.

After the earthquake, almost everyone wants to get a quick overview of the earthquake, agencies are rushing to report to the government and the public, this rapid earthquake information report, must be timely, the number of stations utilized is often limited. With the development of researching work, more stations are added to the earthquake calculation camp, the distribution of the station has become more evenly and reasonably, researchers also have more time to pick up the good seismic waves, the magnitude of the earthquake has been revised over time. The process lasts six months, or even a year usually, until the global data collection was determined, that's the final result. For example, the meteorological agency of Japan has still explained that is the interim value, after the magnitude revised several times.

1)The energy released by the earthquake is: relationship with the magnitude M

log£=ll.8+1.5M (2-4)

The relation between the energy released by the earthquake £ and the magnitude M is as follows:

Therefore, when the magnitude enlarge one more, the energy of the earthquake will be larger by l0u(about 31.6), when the magnitude enlarge two more, the energy of the earthquake will be larger by 103(1000) times.

What is the magnitude of the earthquake energy? We can do a couple of comparisons. If the atomic bomb that the United States dropped on Hiroshima, Japan in 1945 (equivalent to 20,000 tons of standard TNT explosive) was buried 10 kilometers underground, let it explode, the magnitude is 5.5: The Tangshan earthquake was equivalent to 2,800 such atomic bombs exploded underground. As shown in table 2-1, earthquake as a natural phenomenon on the earth, earthquake has great influence on human society and the whole nature.

Table 2-1 Earthquake magnitude and energy setting
Magnitude

The amount of TNT equivalent energy(10000 tons)

The number of atomic bombs equal to 20,000 tons of standard TNT
5.5
2
1
6.0
12
6
7.0
360
180
7.8
5600
2800
8.0
11200
5600

Earthquake intensity

Earthquake intensity refers to the extent of damage by the earthquake on the ground and buildings. For the same earthquake, the intensity size varies from different regions. Near the source, the damage will be large, high intensity: far from the source, the damage will be small, low intensity. Most countries, including China, adopt the scale of intensity 12 (table 2-2).

The Wenchuan earthquake had a magnitude of 8.0, belonged to the major earthquake, the intensity of the epicenter reached 11 degrees, the extent of the destruction was devastating. The 1976 Tangshan earthquake, with a magnitude of 7.8, belonged to the major earthquake, the extent of the destruction was devastating. Affected by the Tangshan earthquake, Tianjin earthquake intensity was 8 degrees, Beijing intensity was 6 degrees, while Shijiazhuang, Taiyuan and other places were 4 to 5 degrees.

Table 2-2Earthquake intensity table
 I degree Man has no feeling, only instruments can record it N degree IE degree People feel all is quiet at dead of night IV degree Sleepers awake and chandeliers swing V degree YI degree Vessel dump and houses slightly damage W degree Houses damage, ground cracking ONE degree IX degree Houses collapse ，serious ground damage X degree XI degree Devastating damage I degree
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