FAQ, Acceleration to Magnitude Conversion
If I were to use an accelerometer to measure seismic events, how could I convert the acceleration data (in g's) to the magnitude numbers you folks use?
You can't convert acceleration to magnitude.
Richter magnitude is a measure of the size of the earthquake. Peak ground acceleration (pga) in percent g is a measure of the ground motion, which decreases, the further you are from the earthquake. Alternatively, if you have a %g at a given distance from magnitude M, you can get the same %g at a larger distance from a larger magnitude.
Therefore, you can't convert a g-value on an accelerometer to a magnitude without information on the distance to the earthquake. Seismologists use information from many stations at various distances from earthquakes in order to obtain a magnitude, scaling each stations recording for distance, and averaging all the estimated magnitudes.
Even if you know the distance, you can't reliably make a determination of magnitude from data from one station, because of additional problems like directivity of ground motion from the earthquake (i.e., stronger shaking in certain directions), site effect (increase or decrease in ground motion owing to geology under the site), basin effect (conversion into surface waves and reverberation experienced by sites in an alluvial basin), etc. These additional things tend to average out when using data from a wide-spread network of stations.
