Refraction of seismic waves - Physics, Class 12 Video Lecture

I want to do a quick
primer on refraction.
And our focus here is going
to be on the seismic waves,
but the principles,
how things refract
when they go from a
fast to a slow medium
or a slow to a fast
medium, It's actually
the same as you would see when
you're studying light waves
or actually any type of wave.
So let's think about
it a little bit.
So let's say I have a slow
medium right over here.
And let's say I have a fast
medium right over here.
And let's say, just
so we can travel
through both solid and
liquids, let's think
about maybe P-waves.
And a slow medium could be
maybe some type of liquid,
and our fast medium could
be some type of solid.
So let me draw the
boundary right over here.
So if I have a P-wave.
Let's say it's going
through the water,
and it's going right
perpendicular to the boundary.
It will then just continue
to travel in the faster
medium in the same
direction if it's
going right at the boundary.
And it'll just travel
faster in the faster medium.
And that's because
that faster medium
is going to be more
dense, and the molecules
are going to bump into
each other faster.
In the same amount of time
kind of the chain reaction
is going to be
able travel further
because they are
more closely packed
and they rebound faster than
it would in the slow medium.
So that's obviously no
refraction is going on.
It has not been deflected.
And just as a bit of reminder,
in general, refraction
is when a wave gets deflected.
Reflection is when
it bounces back.
Refraction is when it gets
deflected a little bit.
Let me just make that clear.
So if I have some
type of boundary here,
and I have a wave that bounces
off, that's reflection.
But if the wave goes
through the boundary
and just gets bent a little
bit, its direction changes,
that is refraction.
That's what we're talking about.
So clearly so far this P-wave
has not been refracted.
But if this P-wave comes in
at an angle-- so let's make
this P-wave wave come in at an
angle-- what's going to happen
is, and the way you
should think about it--
and it's the easiest way to
think about which direction
will be refracted, or at least
the way I think about it,
is literally I imagine some type
of vehicle with wheels on it.
So this is the top
view of my vehicle.
So if I have some type of
vehicle, and the wheels
will be able to move
slowly in this medium.
You could kind of view
it as it's kind of on mud
so it doesn't get good
traction, and then
the fast medium maybe it's a
road so it gets good traction,
it could move faster.
So what's going to happen
when the vehicle gets
to the boundary?
Well, this bottom right wheel is
going to go on the fast medium
before any of the
other wheels do.
So it's going to get
the traction first.
These wheels on the left side
of the vehicle, these wheels
right here, these are still
going to be stuck in the mud.
So what's going to happen is
this wheel right over here
is moving faster,
so it's essentially
going to be able to
turn the vehicle.
These guys are still
stuck in the mud.
And so you fast
forward a little bit,
the direction of the
vehicle will change.
And so the vehicle will now
move in a direction something
like this.
The same thing would
happen in a wave.
If the P-wave is approaching
the boundary like this,
and something
analogous to this is
happening at the
molecular level.
You can kind of view it
as even billiard balls,
and maybe they're kind
of hitting each other.
Well, I won't go into that,
because that can kind of get
confusing depending
on the different cases
and the different boundaries.
But this is the easiest
way to think about it,
and which direction
it will refract.
And hopefully it makes a
little bit of intuitive sense.
And so when you go from a slow
to a fast medium our P-wave
its angle would accentuate
in that direction.
If you went from the fast medium
to the slow medium, once again,
you can just go through the
same thought experiment.
So let's say you have our
wave coming in like that.
Draw the car.
Visualize the car here.
Visualize the car right here.
And you'd say, well,
look, this tire's
going to get stuck in the mud,
because it was on the road.
Now, this top tire right over
here is get stuck in the mud
first.
So it's going to
be moving slower.
So these tires are going
to be able to move faster.
So the vehicle is going to turn.
So you'll be refracted in a
direction like that when you're
going from the fast
to the slow medium.
So that's just a primer
on refraction generally.
Now, let's think
about what would
happen when sound waves are
traveling through the Earth.
And this will help inform
us of, essentially,
how do we figure out what the
actual structure of the Earth
is.
So if the Earth was just made
up of some uniform material
and you had an earthquake right
here on Earth, maybe a little
bit below the surface.
So it's happening in the
crust, but a little bit
below the surface of the Earth.
If Earth was of
uniform density, if it
was all the same material, let's
just think about the P-waves.
Because P-waves can
travel in anything.
Let's think about how
those P-waves would travel.
Well, they would just
go in straight lines.
There's nothing that
would refract the P-waves.
They would just go in straight
lines radially outward
from where the
earthquake occurred.
Now, at a first
approximation, we
know that as we go deeper
and deeper into Earth
there's more and
more rock above that.
The weight of that rock is
kind of compressing the rock
below it.
So you get higher
and higher pressures
and higher and higher densities.
So this is a uniform Earth.
But let's imagine
an Earth that's
made up of uniform material,
that's all solid, a completely
solid Earth, but one where
the density is constantly
increasing as you go down.
So let's just think
about it before we
go into the continuous case.
Because we're talking about
the density as you go deeper,
it's just getting
continuously more dense,
let's think about
the discrete case,
where we have the
least dense layer.
So let me draw it
right over here.
So let's say this is the
surface of the Earth.
This is least dense.
Then let's say you have
another layer over here that
is more dense.
So this is more dense.
Let's say you have another
layer that's even more dense.
So you have another layer over
here that's even more dense.
And then let's do
one more layer.
Let's do this layer here,
this is the densest layer.
So in general, your
P-wave, your seismic wave,
is going to travel faster
in denser material.
So it's going to travel
the fastest here,
then here, then here.
It's going to travel the slowest
in this least dense material.
So if you're coming
in at an angle
let's think about
what's going to happen.
So let's say you have
your P-wave coming
in at an angle like this.
So it's going straight through
the least dense material.
Let me do a slightly
shallower angle.
So let's say it's like that.
What's going to
happen when it goes
into the more dense material?
So once again, let's
imagine our little car.
So this tire's going
to be able to go faster
before the tires
on the other side.
So the car is going to
be deflected to the left,
to the down left.
So now it's going
to travel like this.
So it's now going to
travel something like this.
Now, what's going to
happen at this boundary?
Once again, imagine the car.
This tire right here is going
to be able to travel faster
before the other tire, so
it'll be deflected even more
in that direction.
Then we go, and we go
to the densest material.
Once again, the tires on
kind of the bottom side when
we look at this
way are going to be
able to move faster
before the other tire.
So we're going to get
deflected even more.
So you see, as you go from
least dense material to more
dense material you're
kind of curving outward.
So if this was
continuous, if you
had a kind of a continuous
structure, where as you go down
it just gets more and
more dense as you go.
So this is less dense, and
then it just continuously
gets more dense.
So this is the most
dense down here.
How would the refraction look?
Well, then it would just
be a continuous curve.
It would look like this.
Your P-wave would constantly
be refracted out like that.
It would curve outwards.
So this was the simplest
example where Earth is uniform.
And that's pretty
easy to dismiss,
that obviously things will get
denser because of more pressure
down.
So let's say we
assume another thing.
We have a uniform Earth
in terms of composition,
but let's say it gets denser.
So denser at the center.
Then how would the
P-waves travel,
or how would any
seismic waves travel?
Well, then if you have your
earthquake right over here,
the ones that are
going straight down
still would go straight down.
Because we know
that we won't get
refracted if we're kind
of going perpendicular
to the change in medium, or
the change in boundaries.
But things that are
coming at a slight angle,
as they get deeper they're going
to get deflected more and more
and more, and they're
going to be refracted
outward just like we saw
in this example here.
If they go on this
angle they're going
to be refracted
outward like that.
If they go here they're going to
be refracted outward like that.
They're going to be
refracted outward like that.
If you're here you're going to
be refracted outward like that.
If you're here you're going to
be refracted outward like this.
Now, what we're going to
do in the next few videos
is use what we just
learned about refraction
in the case of seismic waves--
and hopefully we learned it
in this video-- and
how it would refract
as we're going through ever
increasing denser material.
We're going to use
that information
to essentially try to figure
out the composition of the Earth
based on what we've
actually observed.