Earth’s Normal Modes

Fundamentals and Harmonics

Remember, a guitar string can have a fundamental (lowest tone) and many harmonics (integer level multiples). They combine constructively and destructively to give the guitar its sound.

Fourier Analysis

When a guitar string is plucked, we can see its fundamental and harmonics using a Fourier Analysis shown here.

Normal Modes

Just like a guitar string, a strong earthquake can make Earth with a fundamental frequency with overtones.

Spheroidal (radial motion)

Normal Modes

Normal modes can also occur in toroidal motion

Toroidal Normal Modes

Shearer Ch.8.6Lay and Wallace, Ch. 4.6

Indexes describe spherical harmonics

Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html

Free Oscillations l=1 m=1

Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html

Free Oscillations l=1 m=2

Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html

Free Oscillations l=1 m=3

Earth’s Normal NodesDid you notice in the previous animations how some parts of the Earth moved more than other? Why is this?

Reflected waves create Constructive and Destructive Interference

Fundamentals and HarmonicsThe periods of oscillation are all greater than 10 minutes and deflect Earth’s surface only the distance of the width of a human hair

Why study normal modes???Seismologists all around the world study Earth’s normal modes to determine the internal structure of Earth and help determine how the Earth was formed!