IASPEI's  STANDARD PROCEDURES FOR MAGNITUDE DETERMINATIONS
ML -- 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. 
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 biases between amplitudes measured on horizontal seismographs and those measured on vertical seismographs.   
-------------------------------------------------------------------------------------------------------
MS(20) , teleseismic surface-wave magnitudes at period of ~ 20 sec.
 (3) MS(20) = log10(A/T) + 1.66 log10Δ + 3.3
where:
A = vertical-component ground amplitude in μm measured from the maximum trace-amplitude of a surface-wave phase having a period between 18s and 22s 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 (seismometer period 15s, galvanometer period, 90s);
T = period in seconds (18s  T   22s);
Δ = epicentral distance in degrees, 20˚     160;
and where the earthquake has a focal-depth of less than 50 km.
------------------------------------------------------------------------------------------------------
MS(BB) surface-wave magnitudes from Broad Band instruments.

 (4) MS(BB) = log10(A/T)max + 1.66 log10Δ + 3.3
where 
(A/T )max = (Vmax/2), where Vmax = ground velocity in μm/s associated with the maximum trace-amplitude in the surface-wave train as recorded on vertical-component seismogram that is proportional to velocity, and where the period T, 3s < T < 60s, should be preserved together with A or Vmax in bulletin data-bases;  
Δ = epicentral distance in degrees, 2˚     160, focal depth less than 80 km.
------------------------------------------------------------------------------------------------------
mb – short-period body-wave magnitude
 (5) mb = log10(A/T) + Q(, h) 
where,
A = P-wave ground amplitude in μm 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;
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;
Q(, h) = attenuation function for PZ (P-waves recorded on vertical component seismographs) established by Gutenberg and Richter (1956);
 = epicentral distance in degrees, 21˚     100;
h = focal depth.
--------------------------------------------------------------------------------------------------------
mB – intermediate-period/broadband body-wave magnitude
 (6) mB = log10(A/T)max + Q(, h) 
where,
(A/T )max = (Vmax/2), where Vmax = ground velocity in μm/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 in the period-range 0.2s < T < 30s, and where T should be preserved together with A or Vmax in bulletin data-bases;
Q(, h) = attenuation function for PZ established by Gutenberg and Richter (1956), as discussed above with respect to mb; 
 = epicentral distance in degrees, 21˚     100;
h = focal depth.
--------------------------------------------------------------------------------------------------------
MW – moment magnitude
 (7a) MW = (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) MW = (2/3)∙(log10M0 – 16.1),
------------------------------------------------------------------------------------------------------

mb(Lg) – regional Lg magnitude measured in a narrow period range around 1s.
 (8) mb(Lg) = 5.0 + log10[Ai(10)/110]
where,
Ai(10) = amplitude in μm of “hypothetical” Lg wave at a distance of 10 km, extrapolated from observation at station i.
The extrapolated  amplitude Ai(10) is calculated as:
(9) Ai(10) = A(ri)·(ri/10)1/3·[sin(ri/111.1)/sin(10/111.1)]1/2·exp[(ri – 10)]
where:
A(Δi) = “sustained ground-motion amplitude” in μm at ith station, 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-range 0.7 to 1.3s.  
ri = epicentral distance of ith station, in km.
 = coefficient of attenuation in km-1.    is related to the quality factor Q through the equation  = π/(Q·U·T), where U is group velocity and T is the wave period of the Lg wave.   is a strong function of crustal structure and should be determined specifically for the region in which the mb(Lg) 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.  
At the regional and near-teleseismic distances within which mb(Lg) is typically used, equations (8) and (9) may be simplified to: 
(10) mb(Lg) = 2.96 + 0.833log10[ri/10] + .4343ri + log10(Ai)