The Maths of Earthquakes

As seismic waves travel through the Earth due to an earthquake, they are recorded on seismographs. Seismographs detect the varying amplitude of the oscillations of the Earth beneath the measuring instrument.

The Richter Scale

The magnitude scale for earthquakes was developed in 1935 by, and is therefore named after, Charles F. Richter. This scale allows scientists to compare the size of different earthquakes around the world.

 

The Richter Scale | Source

Initially, Richter’s idea was to measure the maximum signal amplitude recorded on the seismograph. Then, by knowing the distance from a seismograph to an earthquake, a quantitative ranking of the earthquake’s size or strength could be made.

This original magnitude scale (ML) was then extended to observations of earthquakes of any distance and focal depth ranging between 0 and 700km. Due to the fact that earthquakes effect both body waves (travel into and through the Earth) and surface waves, two magnitude scales are needed: mb and Mrespectively.

The two equations involved are:

mb = log10(A/T) + Q(D,h

  • A: amplitude of ground motion (microns)
  • T: the corresponding period (s)
  • Q(D,h): a correction factor that is a function of distance between epicentre and station, D (°), and focal depth of the earthquake, h (km).

and

MS = log10 (A/T) + 1.66 log10 (D) + 3.30 

Furthermore, the magnitude of is related to the amount of energy released in joules (J) by the following equation:

log10 E = 4.4 + 1.5M

Slightly diffrent post today, hope you still liked it! M x

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