Richter scale

Richter scale (Шкала Рихтера) refers to the Magnitude of an earthquake. Roughly, this magnitude is proportional to logarithm of amplitude of movement of Earth due to an earthquakes or a strong explosion.

Richter magnitude is numeric qualification of strength of earthquake, its destructive ability, characterized in that, that, in order to reduce its dependence on the place of measurement, the special functional of longitudinal and transversal acoustic waves is used.

Various methods are suggested, and they are supposed to give similar estimates of the Richter magnitude. The method, that provides the smaller dispersion of the estimates of the same event by various seismic stations, is considered as "best". In such a way, the competition of various methods takes place in estimates of the Magnitude.

Various methids give similar estimates. In such a way, in the first approximation, one may use term Magnitude of an earthquake without to specify, which functional is used to evaluate it.

Explosions

The Richter scale can be used to estimate of energy of strong explosions by the movements of the ground.

Earthquakes Wiki suggests the table that shows relation of the estimate of energy \( E \) of explosion with the Richter magnitude:

Richter Approximate Magnitude	Approximate TNT for Seismic Energy Yield	Joule equivalent	Example
0.0	1 kg (2.2 lb)	4.2 MJ
0.5	5.6 kg (12.4 lb)	23.5 MJ Large hand grenade
1.0	32 kg (70 lb)	134.4 MJ	Construction site blast
1.5	178 kg (392 lb)	747.6 MJ	WWII conventional bombs
2.0	1 metric ton	4.2 GJ	Late WWII conventional bombs
2.5	5.6 metric tons	23.5 GJ	WWII blockbuster bomb
3.0	32 metric tons	134.4 GJ	Massive Ordnance Air Blast bomb
3.5	178 metric tons	747.6 GJ	Chernobyl nuclear disaster, 1986
4.0	1 kiloton	4.2 TJ	Small atomic bomb
4.5	5.6 kilotons	23.5 TJ
5.0	32 kilotons	134.4 TJ	Nagasaki atomic bomb (actual seismic yield was negligible since it detonated in the atmosphere. The Hiroshima atomic bomb was 15 kilotons ) Lincolnshire earthquake (UK), 2008
5.4	150 kilotons	625 TJ	2008 Chino Hills CA earthquake
5.5	178 kilotons	747.6 TJ	Little Skull Mtn. earthquake (NV, USA), 1992 Alum Rock earthquake (CA, USA), 2007
6.0	1 megaton	4.2 PJ	Double Spring Flat earthquake (NV, USA), 1994
6.5	5.6 megatons	23.5 PJ	2010 Ferndale CA earthquake
6.7	16.2 megatons	67.9 PJ	Northridge earthquake (CA, USA), 1994
6.9	26.8 megatons	112.2 PJ	San Francisco Bay Area earthquake (CA, USA), 1989
7.0	32 megatons	134.4 PJ	2010 Haiti earthquake
7.1	50 megatons	210 PJ	Energy released was equivalent to that of Tsar Bomba, the largest thermonuclear weapon ever tested.
7.5	178 megatons	747.6	PJ Kashmir earthquake (Pakistan), 2005 Antofagasta earthquake (Chile), 2007
7.8	600 megatons	2.4 EJ	Tangshan earthquake (China), 1976
8.0	1 gigaton	4.2 EJ	Toba eruption 75,000 years ago; which, according to the Toba catastrophe theory, affected modern human evolution Shaanxi earthquake (China), 1556, San Francisco earthquake (CA, USA), 1906
8.5	5.6 gigatons	23.5 EJ
9.0	32 gigatons	134.4 EJ
9.2	90.7 gigatons	379.7 EJ	Anchorage earthquake (AK, USA), 1964
9.3	114 gigatons	477 EJ	Indian Ocean earthquake, 2004 (40 ZJ in this case)
9.5	178 gigatons	747.6 EJ	Valdivia earthquake (Chile), 1960 (251 ZJ in this case)
10.0	1 teraton	4.2 ZJ	Estimate for a 2 km (~1.2 mi) rocky meteorite impacting at 25 km/s (~55,000 mph)

Values in this table can be approximated with relation

\( E = \exp_{10}(6.7+1.5\, R) \) Joule

where \( E \) is part of the energy transferred to the movement of the ground, and \( R \) is the Richter magnitude.

The estimate refers to energy that part of the explosion energy, that is converted to acoustic waves of the ground. At the mixed energy of the explosion, this energy strongly depend also on the condition of explosion: for the underground explosions it is higher; for underwater explosions it is smaller, and for the atmospheric explosions it is even smaller. In such a way, the total energy, released in the explosion, can be few orders of magnitude higher, than in the estimate above.

References

1979.05.10. https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JB084iB05p02348 Thomas C. Hanks Hiroo Kanamori. A moment magnitude scale. Journal of Geophysical Research. Volume84, Issue B5, 10 May 1979, Pages 2348-2350. First published: 10 May 1979 https://doi.org/10.1029/JB084iB05p02348 .. \( \log E_s = 1.5 M_s + 11.8 \) .. \( \log M_0 = 1.5 M_s + 16.1 \) ..

1989.09.01. https://www.sciencedirect.com/science/article/pii/004019518990200X
http://w.daveboore.com/pubs_online/richter_scale_tectonophysics_1989.pdf David M.Boore. The Richter scale: its development and use for determining earthquake source parameters/ Tectonophysics, Volume 166, Issues 1–3, 1 September 1989, Pages 1-14. Received 11 January 1988, Accepted 19 January 1988, Available online 14 April 2003. The scale, introduced by Richter in 1935, is the antecedent of every magnitude scale in use today. The scale is defined such that a magnitude-3 earthquake recorded on a Wood-Anderson torsion seismometer at a distance of 100 km would write a record with a peak excursion of 1 mm. To be useful, some means are needed to correct recordings to the standard distance of 100 km. Richter provides a table of correction values, which he terms, the latest of which is contained in his 1958 textbook. A new analysis of over 9000 readings from almost 1000 earthquakes in the southern California region was recently completed to redetermine the values. Although some systematic differences were found between this analysis and Richter's values (such that using Richter's values would lead to underand overestimates of at distances less than 40 km and greater than 200 km, respectively), the accuracy of his values is remarkable in view of the small number of data used in their determination. Richter's corrections for the distance attenuation of the peak amplitudes on Wood-Anderson seismographs apply only to the southern California region, of course, and should not be used in other areas without first checking to make sure that they are applicable. Often in the past this has not been done, but recently a number of papers have been published determining the corrections for other areas. If there are significant differences in the attenuation within 100 km between regions, then the definition of the magnitude at 100 km could lead to difficulty in comparing the sizes of earthquakes in various parts of the world. To alleviate this, it is proposed that the scale be defined such that a magnitude 3 corresponds to 10 mm of motion at 17 km. This is consistent both with Richter's definition of at 100 km and with the newly determined distance corrections in the southern California region.

Keywords

[[]], Magnitude, Seismology,