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In layman's terms, how does the Richter earthquake scale translate to the amplitude of horizontal surface movement at the epicenter?

For example, given an earthquake of Richter magnitude 4, what is the horizontal amplitude (in meters) of the surface at the epicenter?

And since an earthquake with magnitude 5 is 10 times "stronger" than a 4, would that mean the horizontal amplitude of the magnitude 5 earthquake would be 10 times larger than that of the magnitude 4 one (for example, 0.1m vs 1m)?

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The Richter Scale for earthquake measurements was replaced by the Moment Magnitude Scale in 1970. People still tend to used the term Richter Scale erroneously because its what they became aware of and they do not know what has replaced it. Additionally, the Richter Scale only applied to a specific type if earthquake in southern California.

From 1935 until 1970, the earthquake magnitude scale was the Richter scale, a mathematical formula invented by Caltech seismologist Charles Richter to compare quake sizes.

The Richter Scale was replaced because it worked largely for earthquakes in Southern California, and only those occurring within about 370 miles of seismometers. In addition, the scale was calculated for only one type of earthquake wave. It was replaced with the Moment Magnitude Scale, which records all the different seismic waves from an earthquake to seismographs across the world.

Richter's equations are still used for forecasting future earthquakes and calculating earthquake hazards.

When Richter developed his scale in 1935,

Richter first applied his magnitude scale to shallow-focus earthquakes recorded within 600 km of the epicentre in the southern California region.

By way of comparison,

the great Alaska earthquake of 1964, with a Richter magnitude (ML) of 8.3, also had the values Ms = 8.4, M0 = 820 × 1027 dyne centimetres, and Mw = 9.2.

The magnitude of an earthquake is more about damaging energy released in a quake than amplitude of a wave.

Similarly, shallow earthquake tend to be more damaging than deep earthquakes. So, an earthquake of particular size that is deep will have a different effect to one of the same magnitude that is shallow.

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