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Seismic waves and the Earth – background notes for teachers.
Introduction:
I have put these notes together because this topic is not well covered in any of the GCSE Physics text
books. They are not, as may appear at first glance, a mere random collection of thoughts. It is true
however that they are not well
Earth: Basic structure
Mantle – solid rock
~2600 km thick
Outer core – molten iron/nickel
~ 2200 km thick
Inner Core – solid iron/sulphur
~ 600 km radius
Crust ~2050 km thick
What sort of seismic waves?
Crust: P + S + [Surface waves]
Mantle: P + S
Outer core: P only
Inner core: P*
*Note for purists (& geologists): S waves can also travel in the inner core. These can arise because a Pwave travelling through a rock can stimulate S- waves at right angles.
Speed of P & S waves in the mantle.
P-waves travel faster than S-waves.
The speed that waves travel depends upon 2 factors:
 the density of the material – the higher the density the more slowly waves travel.
 the stiffness of the material – waves travel more quickly in stiffer materials.
Both the density and stiffness increase with depth in the mantle, but the stiffness-effect wins and so the
speed of both S- and P-waves increases with depth. Because of the speed change, the waves refract – see
below.
Speed of P-waves in the core
Because the density of the iron core is very much greater than that of the mantle, their speed is much less.
As in the mantle, the speed increases with depth and the speed increases as it crosses into the stiffer solid
inner core. This is summarised in the simplified graph:
speed / km/s
15
OUTER
CORE
MANTLE
INNER
CORE
P-waves
10
S-waves
5
0
0
1000
2000
3000
4000
5000
6000
Depth / km
Evidence for the Internal Structure of the Earth
Suppose an Earthquake happens in the Earth’s
crust at A.
P-waves received
No S-waves
Seismometers all around the world detect the
waves but not all of them receive S-waves. In fact
at distances of more that 105 from the earthquake
focus, no S-waves are received.
B
What can explain this?
105
Remember that S-waves cannot travel through
liquids?
So there must be a liquid core in the Earth.
P- & S-waves
P- & S-waves
We can get an estimate of the size of the liquid
core by drawing a scale diagram:
A
How to estimate the size of the core of the Earth:
1 Draw a circle to represent the Earth: suggested scale 1 cm = 1000 km; the earth has a radius of
6400 km so make the radius of the circle 64 cm.
2 Mark a point on the surface of the Earth – label it A.
3 Draw a line from A to the centre of the Earth.
4 Draw another radius at an angle of 105 – as in the diagram above – and label point P.
5 Draw a line between A and P – this shows how the S-waves can travel from A to P.
6 Draw the biggest circle you can, with its centre at the centre of the Earth, so that that the S-waves
line just misses this circle.
7 Measure the radius of this circle – the core – and use the scale to calculate the core’s radius.
Refraction in the Earth.
The problem with the above technique for estimating the size of the Earth’s core is that it gives the wrong
answer!
Why?
Because it assumes that the S-waves travel in straight lines. This is wrong. By carefully measuring the
travel times of the waves, geo-physicists have demonstrated that they travel in curves.
Refraction in the Mantle
Over a few hundred km refraction has the following effect – ignoring the curvature of the Earth:
F = earthquake focus; S = Seismometer
S
F
increasing
speed
with
depth
Path of the Earthquake waves
The waves curve because the bottom edge travels faster than the top edge and so it overtakes the top edge.
This makes it bend upwards.
Note that both P- and S-waves curve like this. They both travel faster the deeper they go into the mantle.
Key
Path of P & S waves
A
105
Use this idea to get a better answer for the size
of the Earth’s core.
Don’t make the waves too curved.
What happens when the seismic waves pass from the mantle into the core?
Two things:
1 The S-waves get absorbed (or possible reflected – but we’ll ignore this!).
2 Looking at the graph, we see that the P-waves slow down from ~13 km/s to ~8km/s. This is
similar in proportion to when light waves go from air into glass – and the effect is the same. So
the P-waves bend towards the normal. The reason they travel more slowly in the core is that,
consisting of a nickel/iron mixture, the core is much denser than the silicate-rock mantle and there
is not much difference in the stiffness.
Remember the diagram – this is the same as a ripple-tank diagram. In the ripple tank, the lower part
of the diagram would be “shallow water” and the top would be “deep water.”
Mantle
Core
Inside the core
The waves bend at the core-mantle boundary because
they slow down. Inside the core, the waves curve
gradually, just like in the mantle, because the deeper
they get, the faster they become – because the core is
stiffer at greater depths. They don’t bend very much
though because the speed doesn’t change very much –
see the graph.
If the waves pass through the inner core, they refract
again. They also refract as they pass back into the
mantle.
A couple of drawings in case I need them again. It’s pretty obvious
what the lower one was for, but the ellipse???: