Simulation Principles and Formula

This simulation estimates the magnitude of an earthquake based on the energy released during the event. Seismologists use a logarithmic scale to describe earthquake magnitude, reflecting the exponential relationship between energy and magnitude.

The earthquake magnitude \(M\) is calculated using the formula:

$$\displaystyle M = \frac{2}{3}\,\log_{10}\!\left(\frac{E}{E_0}\right)$$

where:

• \(M\) is the earthquake magnitude (unitless, on the Richter scale),
• \(E\) is the energy released during the earthquake (in Joules), and
• \(E_0\) is the reference energy for a magnitude 0 earthquake (set as \(10^{4.8}\) Joules).

This formula indicates that an increase of one magnitude unit corresponds to roughly a 32-fold increase in energy.