Richter Magnitude Scale

The Math / Science

The Richter Magnitude Scale assigns a magnitude number to qualify the energy released by an earthquake. The Richter scale, developed in the 1930s, is a base-10 logarithmic scale, which defines a magnitude as the logarithm of the ratio of the amplitude of he seismic waves to an arbitrary, minor amplitude.
As measured with a seismometer, an earthquake that registers 5.0 on the Richter scale has a shaking amplitude 10 times that of an earthquake that registers 4.0, and thus corresponds to a release of energy 31.6 times that released by the lesser earthquake.

The following formula is used:

`M_L=log_(10)(A)-log_(10)(A_0)`

where:

• A = maximum excursion of the Wood-Anderson seismograph
• A₀ = empirical formula that depends on the epicentral distance

The Richter Scale was succeeded in the 1970s by the Moment Magnitude Scale.

References

Wikipedia (https://en.wikipedia.org/wiki/Richter_magnitude_scale)