Subject: Actual ground motion and the Richter scale

I have a question about the Richter scale.  I understand that the Richter scale
is a measure of horizontal ground movement during an earthquake.  It based on a
logarithmic scale and is measured by carefully calibrated seismographs at some
particular distance from the epicenter of the earthquake.  However, as with all
logarithmic scales this must be relative to some reference value.  

What I am wondering is how I can take the Richter magnitude of an earthquake and
use that to determine the actual amplitude of the horizontal motion of the
ground at the epicenter of the earthquake, or take the actual horizontal motion
of the ground at the epicenter and use that to determine the Richter magnitude.

I know it is possible other parameters are needed to do such a conversion, such
as the period of the vibrations or the length of the earthquake.  If so, what
are they?  

I am very familiar with logarithms and logarithmic scales, as well as calculus,
differential equations, and signal processing if they are required. 

Re: Actual ground motion and the Richter scale