### Re: Actual ground motion and the Richter scale

Date: Sun Apr 2 00:20:49 2006
Posted By: David Dunbar, Staff, Geophysics, GeoCenter, Inc.
Area of science: Earth Sciences
ID: 1142997066.Es
Message:

Todd,

Richter introduced the local magnitude scale in 1935 based on a Woods-Anderson torsion seismograph. There have been several modifications to the equation calculating the magnitude. One version is:

ML = log A – log A0 + dML

```ML is the local or Richter magnitude.
A is the maximum excursion of the seismograph trace.
A0 is the reference excursion for a magnitude 1 earthquake.
dML is a station dependent magnitude adjustment
```
The Woods-Anderson seismograph's gain is 2800. The ground motion at the seismograph is amplified by a factor of 2800.

Amplitudes are adjusted to a reference distance of 100 km. An ML of 3 has an A of 1 mm. An ML of 1 has an A of 0.001 mm.

dML is based on a statical sample of earthquakes. Typical values are fairly small, on the order of +/- 0.2.

This amplitude adjustment for distance is the first tricky part of estimating the actual ground motion at the epicenter. To first order, a 1 / (distance squared) adjustment works fairly well. In actual practice, a table of distance corrections was developed (and revised several times).

Other issues to consider include the frequency characteristics of earthquakes and the Woods-Anderson seismograph. Larger earthquakes tend to put more energy into lower frequencies. The seismograph responds better to higher frequencies. The combination causes ML to “saturate” at about 6.5. Extrapolating the seismograph amplitudes will give you the ground motion with the same frequency range.

Strictly speaking, the Richter magnitude was only good in southern California. There are several different magnitude scales in use that use different parts of the seismograph waveform. The body wave magnitude, surface wave magnitude, moment magnitude and duration magnitude are all currently used and generally disagree. The Richter magnitude is seldom used now. Woods-Anderson seismographs are fairly rare outside of museums.

David

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