IASPEI magnitude determination

IASPEI standard procedures for magnitude determination

These procedures address the measurement of amplitudes and periods for use in calculating the generic magnitude types: ML; Ms; mb; mB; and mb(Lg). A standard equation is also specified for Mw. For further details, please refer to the recommendations published by the IASPEI Working Group on Magnitudes (Magnitude WG).

Summary of the Magnitude WG recommendataions (pdf) - please refer to for seismometer responses referred to below and the Gutenberg and Richter (1956) attenuation function.

M_L local magnitude consistent with the magnitude of Richter (1935)

For crustal earthquakes in regions with attenuative properties similar to those of Southern California, the standard equation is

(1) ML = log₁₀(A) + 1.11 log₁₀R + 0.00189*R - 2.09

where:

A = maximum trace amplitude in nm that is measured on output from a horizontal-component instrument that is filtered so that the response of the seismograph/filter system replicates that of a Wood-Anderson standard seismograph but with a static magnification of 1;

R = hypocentral distance in km, typically less than 1000 km.

Equation (1) is an expansion of that of Hutton and Boore (1987). The constant term in equation (1), -2.09, is based on an experimentally determined static magnification of the Wood-Anderson of 2080, rather than the theoretical magnification of 2800 that was specified by the seismograph’s manufacturer. The formulation of equation (1) reflects the intent of the Magnitude WG that reported M_L amplitude data not be affected by uncertainty in the static magnification of the Wood-Anderson seismograph.

For seismographic stations containing two horizontal components, amplitudes are measured independently from each horizontal component, and each amplitude is treated as a single datum. There is no effort to measure the two observations at the same time, and there is no attempt to compute a vector average.

For crustal earthquakes in regions with attenuative properties that are different than those of coastal California, and for measuring magnitudes with vertical-component seismographs, the standard equation is of the form:

(2) ML = log₁₀(A) + C(R) + D

where A and R are as defined in equation (1), except that A may be measured from a vertical-component instrument, and where C(R) and D have been calibrated to adjust for the different regional attenuation and to adjust for any systematic differences between amplitudes measured on horizontal seismographs and those measured on vertical seismographs.

M_S(20) teleseismic surface-wave magnitudes at period of ~ 20 s.

(3) M_S(20) = log₁₀(A/T)+ 1.66 log₁₀Δ + 0.3

where:

A = vertical-component ground displacement in nm measured from the maximum trace-amplitude of a surface-wave phase having a period between 18 s and 22 s on a waveform that has been filtered so that the frequency response of the seismograph/filter system replicates that of a World-Wide Standardized Seismograph Network (WWSSN) long-period seismograph, with A being determined by dividing the maximum trace amplitude by the magnification of the simulated WWSSN-LP response at period T;

T = period in seconds (18 s ≤ T ≤ 22 s);

Δ = epicentral distance in degrees, 20° ≤ Δ ≤ 160°;

and where the earthquake has a focal-depth of less than 60 km.

Equation (3) is formally equivalent to the Ms equation proposed by Vanĕk et al. (1962), but is here applied to vertical motion measurements in a narrow range of periods.

M_S(BB) surface-wave magnitudes from broad-band instruments.

(4) M_S(BB) = log₁₀(V_max/2π) + 1.66 log₁₀Δ + 0.3

where:

V_max = ground velocity in nm/s associated with the maximum trace-amplitude in the surface-wave train, as recorded on a vertical-component seismogram that is proportional to velocity, where the period of the surface-wave, T, should satisfy the condition 3 s < T < 60 s, and where T should be preserved together with V_max in bulletin databases;

Δ = epicentral distance in degrees,2° ≤ Δ ≤ 160°, focal depth less than 60 km.

Equation (4) is based on the Ms equation proposed by Vanĕk et al. (1962), but is here applied to vertical motion measurements and is used with the log₁₀(V_max/2π) term, replacing the log₁₀(A/T)_max term of the original.

m_b short-period body-wave magnitude

(5) m_b= log₁₀(A/T) + Q(Δ, h) - 3.0

where:

A = P-wave ground displacement in nm calculated from the maximum trace-amplitude in the entire P-phase train (time spanned by P, pP, sP, and possibly PcP and their codas, and ending preferably before PP);

T = period in seconds, T < 3s; of the maximum P-wave trace amplitude.

Q(Δ, h) = attenuation function for PZ (P-waves recorded on vertical component seismographs) established by Gutenberg and Richter (1956);

Δ = epicentral distance in degrees, 20° ≤ Δ ≤ 100°;

h = focal depth in km;

and where both T and the maximum trace amplitude are measured on output from a vertical-component instrument that is filtered so that the frequency response of the seismograph/filter system replicates that of a WWSSN short-period seismograph, with A being determined by dividing the maximum trace amplitude by the magnification of the simulated WWSSN-SP response at period T.

m_B(BB) broadband body-wave magnitude

(6) m_B(BB)= log₁₀(V_max/2π) + Q(Δ,h) - 3.0

where:

V_max = ground velocity in nm/s associated with the maximum trace-amplitude in the entire P-phase train (time spanned by P, pP, sP, and possibly PcP and their codas, but ending preferably before PP) as recorded on a vertical-component seismogram that is proportional to velocity, where the period of the measured phase, T, should satisfy the condition 0.2 s < T < 30 s, and where T should be preserved together with V_max in bulletin databases;

Q(Δ, h)= attenuation function for PZ established by Gutenberg and Richter (1956), as discussed above with respect to m_b;

Δ = epicentral distance in degrees, 21° ≤ Δ ≤ 100°;

h = focal depth.

M_W moment magnitude

(7a) M_W = (2/3)·(log₁₀M₀ - 9.1)

where M₀ = scalar moment in N·m, determined from waveform modelling or from the long-period asymptote of spectra.

or its CGS equivalent (M₀ in dyne·cm),

(7b) M_W= (2/3)·(log₁₀M₀ - 16.1)

m_b(L_g) regional magnitude based on the amplitude of Lg measured in a narrow period range around 1s.

(8) m_b(L_g) = log₁₀(A) + 0.833log₁₀[r] + 0.4343γ(r - 10) - 0.87

where:

A = "sustained ground-motion amplitude" in nm, defined as the third largest amplitude in the time window corresponding to group velocities of 3.6 to 3.2 km/s, in the period (T) range 0.7 to 1.3 s;

r = epicentral distance in km.

γ = coefficient of attenuation in km^-1. γ is related to the quality factor Q through the equation γ = π/(Q·U·T), where U is group velocity and T is the wave period of the L_g wave. γ is a strong function of crustal structure and should be determined specifically for the region in which the m_b(L_g) is to be used.

A and T are measured on output from a vertical-component instrument that is filtered so that the frequency response of the seismograph/filter system replicates that of a WWSSN short-period seismograph. Arrival times with respect to the origin of the seismic disturbance are used, along with epicentral distance, to compute group velocity U.