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

## Energy

The magnitude scale is based on horizontal displacement, $M_L=\log_{10}\left(\frac{A}{A_0}\right) \text{, where } A_0=\quantity{1}{\mu m} .$

But the destructive power of an earthquake is better indicated by the amount of energy dissipated. It has been suggested that the energy, $E$, is related to the displacement, $A$, by a simple power law, $E=E_0 \left(\frac{A}{A_0}\right)^p$ where $E_0$ and $p$ are constants.

Can you use the following data from the British Geological Survey and the US Geological Survey to verify this suggestion and find values for $E_0$ and $p$?

Earthquake Magnitude, $M_L$ Energy, $\quantity{E}{(GJ)}$
San Francisco, USA, 1906 $7.8$ $6\times10^7$
Chile, 1960 $9.5$ $1\times10^{10}$
Kobe, Japan, 1995 $6.9$ $1\times10^6$
Kent, 2007 $4.3$ $200$
Lincolnshire, 2008 $5.2$ $3000$

Estimate the energy dissipation of the 2011 New Zealand earthquake, magnitude $6.1$.