Mathematics

Mathematics in Calculating The

Magnitude of an Earthquake

- Anju SomanRoll no. 90

A sudden violent shaking of the ground, typically causing great

destruction, as a result of movements within the earth's

crust or volcanic action.

What is Earthquake?

• Earthquake is measured using the Richter Scale• The Richter scale is a standard scale used to compare

earthquakes. • The device was developed in 1935 by Charles F. Richter

How is the magnitude of Earthquake measured?

Seismograph:• A network of geological monitoring stations,

each with instruments that measure how much the ground shakes over time

• The goal of a seismograph is to accurately record the motion of the ground during a quake

• Seismographs record a zigzag trace that shows how the ground shakes beneath

Primar

y Waves

Surface Waves

Surface Waves

Micro• Magni

tude less than-3.0

Minor• Magnitu

de in the rage of 3.0 to 3.9

Light• Magnitude

in the rage of 4.0 to 4.9

Moderate• Magnitude

in the rage of 5.0 to 5.9

Strong• Magnitude

in the rage of 6.0 to 6.9

Classification of EarthquakeMajor• Magnitude in the rage of 7.0 to 7.9

Great•Magnitude is greater than or equal to 8.0

Charles Richter's original formula was:

M= logA + 3log8t -2.92

Where: M= magnitude

A = the maximum displacement in millimeters measured on a Wood-Anderson seismograph

t = the time in seconds between the arrival of the P and S waves

Formula to calculate the magnitude of Earthquake

• If the maximum displacement is 23 millimeters and the time between the arrival of the P and S waves is 40 seconds. calculate the magnitude of earthquake.

• Sol: M= logA + 3log8t - 2.92 M= log(23) +3log(8 x 40) -2.92

M= 1.36 + 7.52 - 2.92 M= 5.96

Example: