What is Mj ? 
Mj is the local magnitude defined and calculated by Japan Meteorological Agency (JMA).
It is one of the magnitude scales based on maximum amplitudes of seismograms.
There are some good points in Mj. First, Mj can be calculated faster than Mw.
Second, Mj can be calculated for small earthquakes. And there is a large amount of
earthquake magnitude data since August 1923.
Procedure to calculate Mj is as follows. (See, for details, for example, JMA(2004) ).
There are 5 magnitudes, MjJ, MjD, MjV, Mjd, and Mjv, as a candidate of Mj.
Mj is adopted according to the priority order MjJ > MjD > MjV > Mjd > Mjv.
(1) MjJ: The magnitude at the Local Meteorological Observatories
It is calculated only for large and shallow (The depth is less than 60km.) earthquakes
using acceleration data of the seismic intensitymeters at the local meteorological observatories of JMA.
MjJ is given by the average of

(1) 
using the maximum displacement amplitudes at the observatories (Tsuboi,1954).

: Maximum displacement amplitude in the horizontal components of D93 type seismometer.


The unit is micrometer: 

Δ 
: Epicenter distance (km) 
Here the acceleration data are twice integrated to obtain the displacement,
to which the highpass (6s) filter is applied to simulate the mechanical strong motion seismogram.
This method will be tentatively used while JMA can not confirm the independence of
in the next eq.(2) on the magnitude for large earthquakes, especially of Mj7 class or above.
(2) MjD, Mjd : Displacement magnitude
It is calculated as the average of

(2) 
at stations in a range of the hypocentral distance more than 30km and the
epicenter distance less than 700km,
which record the maximum amplitudes of horizontal displacement (Katsumata,2004).

: Terms showing dependence on Δ and H 

: Correction value (=0.2) used for D93 type seismometer 
H 
: Focal depth (km) 
If the number of stations involved in the average is less than 3, the stations up to
Δ=2000km are took into account.
If the number of the stations used to obtain MjD is 2, it is denoted as Mjd.
(3) MjV, Mjv: Velocity magnitude
It is calculated as the average* of

(3) 
at stations in a range of the hypocentral distance more than 5km and the epicenter distance less than 400km,
which record the maximum amplitudes of velocity in vertical component (Funasaki et al.,2004).

: Constant 1/0.85 

: Maximum velocity amplitude in the vertical components of EMT type or EMT76 type
or E93 type seismometer.


The unit is 


: Terms showing dependence on Δ and H 

: Correction value (=0.2) used for D93 type seismometer 
If the number of stations involved in the average is less than 4, the stations up to
Δ=1000km are took into account.
If the number of the stations used to obtain MjV is 2 or 3, it is denoted as Mjv.
(a) The averaging procedure in the above (1)(3) is as follows.
First JMA calculates the mean of magnitudes at all the stations.
Then JMA recalculates the mean and the standard deviation of magnitude of stations,
discarding those values deviating more than 0.5 from the initial mean.
The mean values are to be adopted as magnitudes only if the standard deviations are less than 0.35.
References:
Japan Meteorological Agency (2004),
The seismological and volcanological bulletin of Japan for January 2004,
[2]  [4].
Tsuboi,C. (1954), Determination of the GutenbergRichter's magnitude of shallow earthquakes
occurring in and near Japan (in Japanese),
Zisin, 7, 185193.
Katsumata, A. (2004), Revision of the JMA Displacement Magnitude (in Japanese),
Quart. J. Seis., 67, 110.
Funasaki, J. and Earthquake Prediction Information Division (2004),
Revision of the JMA Velocity Magnitude (in Japanese),
Quart. J. Seis., 67, 1120.

