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I have an accelerometer on a table that gives me the $x$, $y$, and $z$ axis acceleration in $m/s^2$ when I move the table. Is there a formula or method to pass this data to a earthquake grade in a Richter Rank?

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The Richter Number is a measure of total energy released in an earthquake. To calculate it, even roughly, you need to know the epicenter of the earthquake (that needs at least three measurements from three locations) and the length and intensity of the shaking to determine the energy contained in the waveform. All you seem to have with your accelerometer is the peak intensity of the shaking at a single point. So the answer is no.

verisimilidude
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    His accelerometer is multicomponent. He can get a decent estimate of the distance from the epicenter by assuming certain P- and S-wave velocity structure (or using something like Crust 1.0 [https://igppweb.ucsd.edu/~gabi/crust1.html]) and using the same concept as a Wadati diagram. Additionally, you can get a good estimate of the direction to the epicenter from the polarization of your measured waves. You may not have ideal data, but you can still do some interesting stuff with what you have. Just accept the error bars that come with it. – Antonio Aug 08 '17 at 13:01