Since the advancement of the conception of earthquake magnitude in the late 1920s and the early 1930s, the magnitude scale has experienced development from local magnitude to surface wave magnitude, body wave magnitude to moment magnitude and even energy magnitude. Moment magnitude is an absolute mechanical scale and it is not saturated. Whether it is for large or small earthquakes, micro-seismic earthquakes, or even extremely micro-seismic earthquakes, for shallow earthquakes or deep earthquakes, the use of far-field, near-field seismic data, geodetic surveys, or any data in geological data, the moments can be measured. Moment magnitude can be coupled with well-known magnitude scales such as surface wave magnitude M_{S}. The moment magnitude is a uniform magnitude scale and is suitable for statistics with a wide range of magnitudes. Because of the above advantages, moment magnitude has become the preferred magnitude chosen by the international seismological community, and is the priority magnitude for the seismic information department responsible for magnitude release to the public. Moment magnitude measurement has become one of the routine tasks in seismic observation practice.This paper will briefly describe the concept of seismic magnitude and its historical development, briefly introduce moment magnitude, analyze the advantages of moment magnitude, explain the calculation method of moment magnitude, and introduce the problems encountered in the calculation of moment magnitude and the solutions.
1 FROM LOCAL TO MOMENT MAGNITUDEEarthquake magnitude, referred as magnitude, is a measure of the magnitude of an earthquake itself that is, not related to the location of the observation (Richter C.F., 1935, 1958). After the seismologists understood how to locate the earthquake, the problem that followed the study was how to measure the size of the earthquake. Whether it is from a scientific point of view or from the perspective of social needs, measuring the size of an earthquake is a significant piece of work (Fu Chengyi et al., 1985; Chen Yuntai et al., 2004; Liu Ruifeng et al., 2015).
The best way to measure the size of an earthquake is to determine the overall characteristics of its seismic moment and source spectrum. In order to determine the seismic moment and source spectrum, it is necessary to simulate or invert the waveform of the seismic body wave or surface wave. From a practical point of view, there is a need for a simple and easy method of determining the size of an earthquake, such as measuring the magnitude of an earthquake by using the amplitude of a seismic wave such as a body wave (P-wave or S-wave). However, measuring the magnitude of the earthquake by using the amplitude of the body wave and the characteristics of the waveform is disadvantageous because the waveform of the far-field body wave is directly proportional to the rate of change of the seismic moment over time, namely the seismic moment rate (Aki K. et al., 1980), therefore, even for earthquakes with the same seismic moment, if the time history of the fault dislocation is different from the source time function, the waveform and amplitude of the generated far-field body waves are also different. In addition, different types of seismographs have different frequency bands, and the waveforms and amplitudes of the same seismic phases recorded by them are also different. In spite of this, it is still widely used to determine the size of the earthquake—the magnitude by measuring the amplitude. This is because: ① the method of determining the magnitude is simple and easy; ② the magnitude is used to measure the earthquake in a relatively narrow but high frequency band. For example, the local magnitudes mentioned below is measured in the frequency band around 1Hz (Hertz), and this frequency band happens to be (although not always) the band in which most buildings and structures are destroyed by earthquakes.
Magnitude is a measure of the relative magnitude of an earthquake by measuring the amplitude of a seismic phase in a seismic wave. It was proposed and developed by Charles Francis Richter (1900-1985) of the United States in the early 1930s(Richter C.F., 1935) under the suggestion by Beno Gutenberg (1889-1960). Before Richter, from the late 1920s to the early 1930s, only Kiyoo Wadati of Japan (1902-1995) used similar methods to determine the size of Japanese earthquakes (Wadati K., 1928, 1931; Richter C F., 1935). The term magnitude is used by Harry Oscar Wood (1879-1958) to suggest that Richter (Richter C.F., 1935) distinguishes it from the intensity which indicates the impact of destruction of an earthquake or the amount of destruction in different locations. In seismology, the scalar seismic moment is referred to as the seismic moment when it does not cause confusion. The scalar seismic moment is different from the seismic moment tensor. It is the physical size of an earthquake defined by the product of the area of the seismic fault, the average sliding distance of the fault (mean offset distance) and the shear modulus of the medium near the fault plane. The term earthquake moment was first proposed by Ketti Aki (1930-2005) based on his study of the 1964 Niigata earthquake in Japan (Aki K., 1966). Seismic moments can be measured either by the far-field displacement spectrum of the seismic wave, which is much larger than the source, or by near-field seismic waves, geology, and geodetic surveys. Aki K., (1966) used a variety of data to determine the seismic moments of the Niigata earthquake. The result was very consistent and is a very strong and quantitative support for the theory that the earthquake originates in the fault (fault theory). 30 years went by from the first time Rickett measured the magnitude in 1935 to 1966 when Aki proposed and measured seismic moments. Moment magnitude was proposed by Hiroo Kanamori of the United States (1936-), George Purcaru of Germany (1939-2016) and Hans Berckehemer (1926-2014) and Thomas of the United States between 1977 and 1982 (Kanamori H., 1977; Purcaru G. et al., 1978, 1982; Hanks T.C. et al., 1979). It took more than 10 years from the presentation and measurement of the concept of earthquake moments in 1966 to the presentation of the moment magnitude scale from 1977 to 1979.
2 MAGNITUDE SATURATIONWhen the magnitude of the observed seismic wave is used to determine the magnitude (e.g., local magnitude M_{L}, body wave magnitude m_{b}, long period body wave magnitude m_{b}, surface wave magnitude M_{S}, etc.), the amplitude of the seismic wave in a specific frequency band is determined due to different magnitude scales. When the magnitude is greater than a certain level, and the maximum amplitude of the measurement no longer increases, and the measured magnitude of the earthquake does not increase with the increase of the earthquake, it is called magnitude saturation. The magnitude saturation is due to the fact that the displacement spectrum of a typical seismic signal is characterized by the corner frequency. When the frequency is higher than the corner frequency, the displacement amplitude spectrum decreases rapidly. When the earthquake is larger, the corner frequency moves toward the low frequency. Thus, when the magnitude of an earthquake is measured with a certain magnitude scale, if the magnitude scale is used to determine the magnitude of an earthquake, if the magnitude is higher than the corner frequency, the magnitude scale will appear saturated. In the magnitude determination based on the seismograms recorded by short-period seismographs, the smaller the period, the smaller the corresponding saturation magnitude. For example, when the moment magnitudes M_{W} are greater than 6.0, 6.5, 7.0, and 8.0, respectively, the body-wave magnitude m_{b}, the local magnitude M_{L}, the long-period body wave magnitude, m_{B}, and the surface-wave magnitude M_{S} begin to saturate, respectively; they reach complete saturation at 6.5, 7.0, 7.5, and 8.5, respectively. Actual observations show that m_{b} > 6.5, M_{L} > 7.0, m_{B} > 7.5 and M_{S} > 8.5 are very rare.
Magnitude saturation is a reflection of magnitude scale and frequency. In order to objectively measure the size of the earthquake, a magnitude scale is needed, which does not appear to be saturated as m_{b}, M_{L}, m_{B} and M_{S} described above.
Moment magnitude is a magnitude scale that will not be saturated.
3 RATIO OF SEISMIC WAVE ENERGY TO SEISMIC ENERGY MOMENTFor the sake of narrative convenience, before introducing the moment magnitude, this section first introduces related terms such as seismic wave energy and seismic energy moment ratio and their physical concepts.
During an earthquake, due to fault slip, the energy that propagates outward in the form of seismic waves is called seismic wave energy, seismic radiated energy, radiated seismic energy, and radiated energy or radiation energy. All these are referred to as seismic energy. Let E_{P} be the total strain energy (mainly including elastic strain energy and gravitational potential energy) released by the entire earth media system before and after the earthquake. It is equal to the work W done by the entire earth media system before and after the earthquake to the outside world.
$ {E_{\rm{P}}} = W = \frac{1}{2}\left( {{\sigma ^0} + {\sigma ^1}} \right)DA $ | (1) |
In the formula, σ^{0} and σ^{1} are called the initial stress and the final stress respectively, and the latter is also called the residual stress. A is the area of the fault plane; D is the average slip of the fault. We call
$ \bar \sigma = \frac{1}{2}\left( {{\sigma ^0} + {\sigma ^1}} \right) $ | (2) |
the average stress, so the total strain energy E_{P} released by the entire earth media system before and after the earthquake is
$ {E_{\rm{P}}} = \bar \sigma DA $ | (3) |
From the sliding to the stop of the seismic fault, the earth media system must overcome the friction between the fault planes to do work. The work done by the earth media system to overcome friction E_{F} is known as friction energy. If the dynamic friction stress is expressed as σ_{f}, the friction energy E_{F} (Kanamori H., 1994) is
$ {E_{\rm{F}}} = {\sigma _{\rm{f}}}DA $ | (4) |
The energy consumed by a new fault plane during an earthquake rupture is called rupture energy, also known as surface energy. So far, the estimation of the fracture energy is still very rough; so research is still being done on it.
Let's temporarily ignore rupture energy. However, in some cases, the fracture energy may become so important that it can't be ignored (Kanamori H. et al., 2006).
Seismic wave energy E_{S} can be obtained from the law of energy conservation.
$ {E_{\rm{S}}} = {E_{\rm{P}}} - {E_{\rm{F}}} - {E_{\rm{G}}} $ | (5) |
If the breaking energy E_{G} is not considered for a moment, the seismic wave energy can be obtained from equations (1) to (5).
$ {E_{\rm{S}}} = {E_{\rm{P}}} - {E_{\rm{F}}} = \left( {\bar \sigma - {\sigma _{\rm{f}}}} \right)DA = \frac{{\left( {{\sigma ^0} + {\sigma ^1} - 2{\sigma _{\rm{f}}}} \right)}}{2}DA $ | (6) |
Seismic radiant energy E_{S} is only a part of the total potential energy E_{P} released during an earthquake and is usually related to E_{S} and E_{P} the following formula.
$ {E_{\rm{S}}} = \eta {E_{\rm{P}}} $ | (7) |
In the formula, η is called seismic efficiency, also referred to as the seismic efficiency coefficient. By definition, η≤1, substituting equation (3) and equation (6) into equation (7), we can determine the seismic efficiency without considering fracture energy.
$ \eta = \frac{{{\sigma ^0} + {\sigma ^1} - 2{\sigma _{\rm{f}}}}}{{{\sigma ^0} + {\sigma ^1}}} = 1 - \frac{{{\sigma _{\rm{f}}}}}{{\bar \sigma }} $ | (8) |
It can be seen from equation (8) that seismic efficiency is related to dynamic frictional stress σ_{f} and average stress σ. Since both σ_{f} and σ are physical quantities not easy to measure, seismic efficiency is also a physical quantity that is not easy to measure.
Substituting equation (3) into equation (7) yields
$ \eta \bar \sigma = \frac{{\mu {E_{\rm{S}}}}}{{{M_0}}} $ | (9) |
In the formula, M_{0} is a scalar seismic moment, or simply a seismic moment.
$ {M_0} = \mu DA $ | (10) |
μ is the rigidity of the medium. Definitions
$ {\sigma _{\rm{a}}} = \eta \bar \sigma $ | (11) |
σ_{a} is called apparent stress. Apparent stress can be obtained from equation (11) and equation (9) (Wyss M. and Brunce J. 1968, 1971)
$ {\sigma _{\rm{a}}} = \frac{{\mu {E_{\rm{S}}}}}{{{M_0}}} $ | (12) |
It can be known from equation (11) that since η≤1, the apparent stress is the lower limit of the average stress
$ {\sigma _{\rm{a}}} \le \bar \sigma $ | (13) |
By equation (8) the following can be obtained
$ {\sigma _{\rm{a}}} = \bar \sigma - {\sigma _{\rm{f}}} $ | (14) |
If the dynamic frictional stress σ_{f} is equal to the final stress σ^{1}, that is, σ_{f}=σ^{1}, then
$ {\sigma _{\rm{a}}} = \frac{{\Delta \sigma }}{2} $ | (15) |
In the formula, Δσ is the stress change that occurs along with the formation of a seismic fault, that is, the stress released on the fault plane during an earthquake — stress drop
$ \Delta \sigma = {\sigma ^0} - {\sigma ^1} $ | (16) |
thus the formula corresponding to equation (12) is
$ \Delta \sigma = \frac{{2\mu {E_{\rm{S}}}}}{{{M_0}}} $ | (17) |
The above analysis shows that although the average stress σ is a physical quantity that is not easy to measure, the apparent stress σ_{a} that is the lower limit of the average stress can be obtained by measuring μ, E_{S} and M_{0}. μ, E_{S} and M_{0} are the physical quantities obtained by appropriate measurement. Although it is not the average stress measured by equation (12), it is still very valuable to be able to measure the apparent stress as the lower limit of the average stress. In addition, if the dynamic frictional stress is equal to the final stress, then the apparent stress is equal to 1/2 of the stress drop.
The apparent stress has a dimension of "stress" and is often easily confused with other stresses. To avoid confusion, you can define dimensionless parameters
$ \tilde e = \frac{{{\sigma _{\rm{a}}}}}{\mu } = \frac{{{E_{\rm{S}}}}}{{{M_0}}} $ | (18) |
Equation (18) is the ratio of seismic wave energy E_{S} to seismic moment M_{0}. It is called seismic energy-moment ratio, also called scaled energy, or reduced energy.The seismic energy moment ratio has a dimension of strain and is a dimensionless quantity that represents the seismic wave energy radiated from a unit of seismic moment (Kanamori H. et al., 2000, 2006). Seismic energy moment ratio (scale energy, equivalent energy) multiplied by the rigidity coefficient μ of the medium in the source region is the apparent stress.
According to Kanamori H. et al., (1975) and Abe K., (1995), the stress drop in the crust and mantle is Δσ ≈(2—6)MPa, μ ≈ (3—6)×104 MPa; if you take Δσ=5 MPa, μ=5×104 MPa, that is
$ \frac{{\Delta \sigma }}{{2\mu }} = 5 \times {10^{ - 5}} $ | (19) |
Substituting equation (19) into equation (17), i.e. (Stein S. et al., 2003)
$ \frac{{{E_{\rm{S}}}}}{{{M_0}}} \approx 5 \times {10^{ - 5}} $ | (20) |
or
$ \lg {E_{\rm{S}}} = \lg {M_0} - 4.3 $ | (21) |
Equation (20) or its equivalent equation (21) is called Kanamori's condition. Kanamori's condition indicates that the ratio of the seismic wave energy to the seismic moment released during the earthquake is approximately 5×10^{-5}. From equation (20), we can see that the dimension of the seismic moment is the same as the dimension of the seismic wave energy. If the international system is adopted (Système International d'Unitès, SI), [E_{S}]~J, [M_{0}]~N·m, Since 1J=1N·m, so [E_{S}/M_{0}]~1. If we use the centimeter-gram-second system (CGS system), then [E_{S}]~erg, [M_{0}]~1 dyn·cm. Since 1 erg=1 dyn·cm, so [E_{S}/M_{0}]~1. Although the dimensions of E_{S} and M_{0} are the same, their physical meanings are different, and numerically, the seismic wave energy is only 5×10^{-5}=0.00005 of the seismic moment released during the earthquake. This is not surprising, because the seismic moment released during an earthquake is not the energy of the seismic wave radiated by the earthquake. It is essentially the integral of the stress change (unit: N/m^{2}) within the volume of the entire source region [(unit: m^{3}): (N·m^{2})×m^{3}, that is N·m]. Although the two units are equal, in order to clearly express that the seismic moment and the seismic wave energy are two physical quantities with different properties, we always express the seismic moment with N·m (or dyn·cm), and use J (or erg) to indicate seismic wave energy. Therefore, M_{0}/μ is the integral of the strain in the volume of all the source regions. M_{0}/μ is multiplied by the average stress Δσ/2 acting on the fault plane during the earthquake to obtain the seismic wave energy radiated during the earthquake.
4 MOMENT MAGNITUDEThe seismic energy E_{S} and surface wave magnitude M_{S} have the following semi-empirical relationship, Gutenberg-Richter seismic wave energy-magnitude relationship (Kanamori H., 1977; Purcaru G. et al., 1978, 1982).
$ \lg {E_{\rm{S}}} = 1.5{M_{\rm{S}}} + 4.8 $ | (22) |
In the formula, E_{S} is in units of N·m. Substituting equation (20) or equation (21) into equation (22) gives the relationship between the seismic moment M_{0} and the surface wave magnitude M_{S}.
$ \lg {M_0} = 1.5{M_{\rm{S}}} + 9.1 $ | (23) |
or the relationship between surface wave magnitude and seismic moment
$ {M_{\rm{S}}} = \left( {\lg {M_0} - 9.1} \right)/1.5 = \left( {2/3} \right)\left( {\lg {M_0} - 9.1} \right) $ | (24) |
Replacing the M_{S} in equation (24) with M_{W} gives the definition of a new magnitude scale M_{W} (Kanamori H., 1977; Purcaru G. et al., 1978, 1982; Hanks T.C. et al., 1979).
$ {M_{\rm{W}}} = \left( {\lg {M_0} - 9.1} \right)/1.5 = \left( {2/3} \right)\left( {\lg {M_0} - 9.1} \right) $ | (25) |
The new magnitude scale M_{W} is called the moment magnitude, which is the same as the surface wave magnitude M_{S} in the magnitude range of the surface wave magnitude M_{S} unsaturated, and it will not be saturated when the size of the earthquake exceeds this range. The moment magnitude cannot be saturated because it is calculated from the seismic moment M_{0} by the above formula.
In theory, there is no upper or lower limit for the magnitude. However, as a brittle fracture that occurs within a limited, non-uniform rock layer plateau, the maximum scale of tectonic earthquakes should naturally be smaller than the scale of rock layer plates. In fact, no earthquakes exceeding M_{W}9.5 have been recorded so far, and the largest earthquake recorded by the instrument was the Chile M_{W}=9.5 earthquake on May 22, 1960. The minimum earthquake was the M_{W}=-4.4 earthquake recorded at a depth of 3, 500m underground in the Mponeng gold mine in South Africa (Kwiatek G. et al., 2010)
5 MOMENT MAGNITUDE NUMERICAL CALCULATIONThe definition equation (25) of the moment magnitude is the standard form adopted by IASPEI(2005, 2013) formally adopted (Bormann P., 2015). If the centimeter-gram-second system (CGS system) is used, the corresponding definition of the moment magnitude definition (Hanks T.C. and Kanamori H., 1979) is
$ {M_{\rm{W}}} = \left( {\lg {M_0} - 16.1} \right)/1.5 = \frac{2}{3}\left( {\lg {M_0} - 16.1} \right) $ | (26) |
In the formula, M_{0} has a unit of dyn·cm, 1 dyn·cm=10^{-7} N·m.
The first part and the second part of the right side of equation (25) are equivalent. The first part is to calculate the factor (lgM_{0}-9.1) in parentheses before dividing by 1.5. The second equation is to multiply (2/3) by lgM_{0} and 9.1 in parentheses, and then subtract them. Finally, it is rounded down to the precision required (usually accurate to 0.1) (usually rounded to the second decimal place). Equation (26) is essentially equivalent to equation (25), except that the unit used is different. Whether it is using equation (25) or equation (26), it is the factor lgM_{0} and the constant factor 16.1 which is subtracted first and then divided by 1.5, or multiplied by (2/3) and then subtracted, the result is the same.
Equation (26) is the definition used by Kanamori H., (1977) to introduce the moment magnitude, and it is the formula he and some authors use in other articles. But in other places, some authors use another formula defined by Hanks T.C.et al., (1979).
$ {M_{\rm{W}}} = \left( {\lg {M_0}} \right)/1.5 - 10.7 $ | (27) |
At first glance, equations (26) and (27) are equivalent, and using these two formulas should yield the same results, which is not always the case. Since equation (26) is equivalent to the following equation
$ \begin{array}{l} {M_{\rm{W}}} = \frac{2}{3}\lg {M_0} - 10.73\\ {\rm{or}}\;{M_{\rm{W}}} = \frac{2}{3}\lg {M_0} - 10.7333 \cdots \end{array} $ | (28) |
We can see that equation (27) is the second term (constant term) 16.1/1.5=10.73=10.7333… on the right side of equation (26), which is obtained by rounding off the second decimal place to the nearest 0.1. So if it is also accurate to 0.1, the M_{W} (calculated as M_{W}^{HK}) from equation (28) is
$ M_{\rm{W}}^{{\rm{HK}}} = {M_{\rm{W}}} + 0.0333 \cdots $ | (29) |
If the M_{W} calculation result is expressed as
$ {M_{\rm{W}}} = {x_1}{x_2} \cdot {x_3}{x_4} \cdots $ | (30) |
Then
$ M_{\rm{W}}^{{\rm{HK}}} = {x_1}{x_2} \cdot {x_3}{x_4} \cdots + 0.0333 \cdots $ | (31) |
For the second decimal place below the decimal point in equation (30), we can get:
$ \left\{ \begin{array}{l} {M_{\rm{W}}} = {x_1}{x_2} \cdot {x_3}\;\;\;\;\;\;\;\;\;\;\;\;{x_4} \le 5\\ M_{\rm{W}}^{{\rm{HK}}} = {x_1}{x_2} \cdot \left( {{x_3} + 1} \right)\;\;\;\;{x_4} \ge 5 \end{array} \right. $ | (32) |
If we round off the second digit below the decimal point of equation (31), we can get:
$ \left\{ \begin{array}{l} M_{\rm{W}}^{{\rm{HK}}} = {x_1}{x_2} \cdot {x_3}\;\;\;\;\;\;\;\;\;\;\;\;{x_4} \le 1\\ M_{\rm{W}}^{{\rm{HK}}} = {x_1}{x_2} \cdot \left( {{x_3} + 1} \right)\;\;\;\;\;{x_4} \ge 2 \end{array} \right. $ | (33) |
That is
$ \left\{ \begin{array}{l} M_{\rm{W}}^{{\rm{HK}}} = {M_{\rm{W}}} = {x_1}{x_2} \cdot {x_3}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{x_4} \le 1\\ M_{\rm{W}}^{{\rm{HK}}} = {x_1}{x_2} \cdot \left( {{x_3} + 1} \right),{M_{\rm{W}}} = {x_1}{x_2} \cdot {x_3}\;\;\;\;\;\;2 \le {x_4} \le 2\\ M_{\rm{W}}^{{\rm{HK}}} = {M_{\rm{W}}} = {x_1}{x_2} \cdot \left( {{x_3} + 1} \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{x_4} \ge 5 \end{array} \right. $ | (34) |
When the second digit x_{4} below the decimal point is 2≤x_{4}≤4, the M_{W} calculated by equation (26) is 0.1 more than that calculated by using equation (27). As we saw earlier, this is due to equation (27) that first calculates the right constant term and rounds it off, and then subtracts it from (lgM_{0})/1.5.
6 CONCLUSIONOn May 12, 2017, the General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China and the National Standardization Administration issued the National Standards Announcement No. 11 (2017) of the People's Republic of China, and officially issued the new national earthquake magnitude rule, General Rules for Earthquake Magnitude (GB17740-2017). The new rule fully embodies the diversity and complexity of magnitude, and stipulates six magnitudes of local magnitude M_{L}, short-period body wave magnitude m_{b}, broadband body wave magnitude m_{B(BB)}, surface wave magnitude M_{S}, broadband surface wave magnitude M_{S(BB)} and moment magnitude M_{W}, establishing preliminarily the China magnitude measurement system to make the method of magnitude measurement more scientific.
The new rule stipulates that the moment magnitude M_{W} is the preferred magnitude for seismic network surveys and is the preferred magnitude for releasing seismic information to the public. In the new rule, the formula for the moment magnitude M_{W} is the definition of the moment magnitude equation (25), which is the same as that adopted by the IASPEI(2005, 2013). After General Rules for Earthquake Magnitude (GB17740-2017) is implemented, the determination and release of earthquake magnitude in China will be in line with international standards.
This paper has been published in Chinese in the journal of Seismological and Geomagnetic Observation and Research, Volume 39, Number 2, 2018.
Abe K. Magnitudes and Moments of Earthquakes[C]. In: Ahrens T.J. (Editor), Global Earth Physics: A Handbook of Physical Constants[M]. Washington, DC: AGU, 1995. 206-213. http://adsabs.harvard.edu/abs/1995geph.conf..206A |
Aki K. Generation and propagation of G waves from the Niigata earthquake of June 16, 1964. Part 2:Estimation of earthquake moment, released energy, and stress-strain drop from the G wave spectrum[J]. Bulletin of the Earthquake Research Institute of Tokyo University, 1966, 44: 73–88. |
Aki K, Richards P. G. Quantitative Seismology:Theory and Methods[M]. San Francisco: W.H. Freeman, 1980: 1-932. |
Bormann P. Are new data suggesting a revision of the current M_{W} and M_{e} scaling formulas?[J]. Journal of Seismology, 2015, 19(4): 989–1002. DOI:10.1007/s10950-015-9507-y. |
Chen Yuntai, Liu Ruifeng. Earthquake magnitude[J]. Seismological and Geomagnetic Observation and Research, 2004, 25(6): 1–12 (in Chinese with English abstract). |
Fu Chengyi, Chen Yuntai, Qi Guizhong. Basic of Geophysics[M]. Beijing: Science Press, 1985: 1-447. (in Chinese). |
Hanks T. C, Kanamori H. A moment magnitude scale[J]. Journal of Geophysical Research, 1979, 84(B5): 2348–2350. DOI:10.1029/JB084iB05p02348. |
IASPEI. Summary of magnitude working group recommendations on standard procedures for determining earthquake magnitudes from digital data, Preliminary Version October 2005[EB/OL]. (2005-10)[2018-03-09]. http://www.iaspei.org/commissions/CSOI/summary_of_WG_recommendations_2005.pdf. |
IASPEI. Summary of magnitude working group recommendations on standard procedures for determining earthquake magnitudes from digital data, Updated Version 27 March 2013[EB/OL]. (2013-03-27)[2018-03-09]. http://www.iaspei.org/commissions/CSOI/Summary_WG_recommendations_20130327.pdf. |
Kanamori H. The energy release in great earthquakes[J]. Journal of Geophysical Research, 1977, 82(20): 2981–2987. DOI:10.1029/JB082i020p02981. |
Kanamori H. Mechanics of earthquakes[J]. Annual Review of Earth and Planetary Sciences, 1994, 22(1): 207–237. DOI:10.1146/annurev.ea.22.050194.001231. |
Kanamori H, Anderson D. L. Theoretical basis of some empirical relations in seismology[J]. Bulletin of the Seismological Society of America, 1975, 65(5): 1073–1095. |
Kanamori H. and Heaton T. H. Microscopic and Macroscopic Physics of Earthquakes[C]. In: Rundle J. B., Turcotte D. L. and Klein W. (Editors), Geocomplexity and the Physics of Earthquakes[M]. Washington, DC: AGU, 2000. 147-163. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/GM120p0147 |
Kanamori H. and Rivera L. Energy Partitioning during an Earthquake[C]. In: Abercrombie R., McGarr A., Di Toro G. and Kanamori H. (Editors), Earthquakes: Radiated Energy and the Physics of Faulting[M]. Washington, DC: AGU, 2006. 3-13. http://www.mendeley.com/research/energy-partitioning-during-earthquake/ |
Kwiatek G., Plenkers K., Naketani M., Yabe Y., Dresen G, JAGUARS-group. Frequency-magnitude characteristics down to magnitude -4.4 for included seismicity recorded at Mponeng Gold Mine, South Africa[J]. Bulletin of the Seismological Society of America, 2010, 100(3): 1165–1172. DOI:10.1785/0120090277. |
Liu Ruifeng, Chen Yuntai, Ren Xiao, Xu Zhiguo, Wang Xiaoxin, Zou Liye, Zhang Liwen. Determination of the Magnitude[M]. Beijing: Seismological Press, 2015: 1-154. (in Chinese). |
Purcaru G., Berckhemer H. A magnitude scale for very large earthquakes[J]. Tectonophysics, 1978, 49(3/4): 189–198. |
Purcaru G., Berckhemer H. Quantitative relations of seismic source parameters and a classification of earthquakes[J]. Tectonophysics, 1982, 84(1): 57–128. DOI:10.1016/0040-1951(82)90154-8. |
Richter C.F. An instrumental earthquake magnitude scale[J]. Bulletin of the Seismological Society of America, 1935, 25(1): 1–32. |
Richter C.F. Elementary Seismology[M]. San Francisco: WH Freeman, 1958: 1-768. |
Stein S., Wysession M. An Introduction to Seismology, Earthquakes and Earth Structure[M]. Malden: Blackwell Publishing, 2003: 1-498. |
Udías A. Principles of Seismology[M]. Cambridge: Cambridge University Press, 1999: 1-475. |
Wadati K. Shallow and deep earthquakes[J]. Geopysical Magazine, 1928, 1: 162–202. |
Wadati K. Shallow and deep earthquakes (3rd paper)[J]. Geopysical Magazine, 1931, 4: 231–283. |
Wyss M, Brune J. N. Seismic moment, stress, and source dimensions for earthquakes in the California-Nevada region[J]. Journal of Geophysical Research, 1968, 73(14): 4681–4694. DOI:10.1029/JB073i014p04681. |
Wyss M, Brune J. N. Regional variations of source properties in Southern California estimated from the ratio of short-to long-period amplitudes[J]. Bulletin of the Seismological Society of America, 1971, 61(5): 1153–1167. |