Food for thought

# How far did the earth move? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

## Magnitudes

The severity of an earthquake is measured and recorded as its local magnitude, $M_L$, often referred to as its position on the Richter Scale. For instance the New Zealand earthquake of 2011 was of magnitude $6.1$ (according to USGS).

The magnitude is defined as a function of $A$, the maximum amplitude of horizontal displacement of the earth’s surface at a distance of $\quantity{100}{km}$ from the epicentre, $M_L=\log_{10}\left(\frac{A}{A_0}\right)$

where $A_0$ is a constant displacement chosen as a reference value by Charles Richter in 1935. $A_0=\quantity{1}{\mu m}=\quantity{10^{-6}}{m}$

What is the magnitude of an earthquake causing a displacement, $A$, equal to

• $\quantity{1.0}{\mu m}$?
• $\quantity{1.0}{cm}$?
• $\quantity{30}{cm}$?

What was the surface displacement for the following earthquakes? What might that have looked or felt like?

• New Zealand, 2011, $M_L=6.1$
• Lincolnshire, 2008, $M_L=5.2$
• Chile, 1960, $M_L=9.5$

What makes a logarithmic scale useful for describing phenomena like this? Do you know of any other commonly used logarithmic scales?