Richter magnitude scale

Remarks

Equivalently, a magnitude $0$ earthquake produces an amplitude of $0.001$ mm at $100$ km. Example: an earthquake recorded at $100$ km with $A = 10$ mm has $M_L = \log_{10} 10 - \log_{10} 10^{-3} = 1 + 3 = 4$. Non-example: the peak amplitude of an earthquake $5000$ km away is not covered, since $A_0$ is defined only at local distances; teleseismic events use other scales. The value of $M_L$ is the average over several stations, each corrected by $A_0$. For large earthquakes the peak amplitude at the short periods of the instrument grows little with size, so $M_L$ saturates at about $7$. The logarithm is decimal, $\log_{10} x = \ln x / \ln 10$, with $\ln$ the natural logarithm.