Refraction of Seismic Waves

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Refraction of Seismic Waves

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I want to do a quick primer on refreaction
And our focus here is going to be on seismic
waves but the principal 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 your doing
When your studying ligth waves or any type of wave.
So lets think about it a little bit.
I have a slow medium rigth over here and lets say I have a fast medium over here.
lets say just for the, so that we cantravel thorugh both solid and liquid. Lets think,
about maybe P-Waves and a slow medium maybe
some type of liquid and our fasr medium could be some type of solid.
So let me draw the boundry right over here.
And lets say, so if I have something that, a P-Wave lets say it going through the water
And going right perpendicular to the boundry
We`ll then just continue to travel
in the faster medium in the same direction.
Going right if it goes right at the boundry
If it goes right at the boundry and it`l just tracel faster in the faster medium
And thats 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 more molucules kind of
a chain reaction is going to travel further because they are more closely packed and they
rebound faster than it would in the slow mediums.
So thats obviusly over is going on
It has not been deflected.
And just as a bit of a reminder.
In general refraction is when a wave gets defelcted.\
Reflection is when it bounces back refraction
is when it gets deflected a little bit.
Let me just make that clearer.
So I have some type of boundry and I have of
boundry here and I have a wave that bounces off thats reflection.
But if the way goes through the boundry.
and just gets bent a little bit its direction changes that is refraction.
And thats what we are talking about, So cleary so far this P-Wave.
Has not been refracted but if this P-Wave comes in
this angle so lets make this P-Wave
come in at a angle whats going to happen is,
the way you should think about it is, the easiest way to think about which direction
it will be refracted or atleast the way I think about it
is literally I imagine some type of vehicle
with wheels on it. 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.
Kind of viewed as kind of on mud.
So it doesn't get fraction and then the fast medium it is a,
road so it gets good fraction.
It can move faster, so whats going to happen
when the vehicle gets to the boundry.
Well this bottom rigth wheel is going to go on the fast medium.
Before any of the other wheels do. So it going,
to get the fraction first these wheels on teh left
side of the vehicle these wheels right here,
These are still going to be stuck in the mud so it going to happen is.
This wheel right over here is moving faster so its essentialy going to be able to turn the,
vehicle these guys are still stuck in the mud.
And so you fast foward a little bit,
the direction of the vehicle will change and so the vehicle will now move in a derection
something like this the same thing what happened
in a wave. If the P-Wave is approaching the boundry like this and something,
annlogus is happening at the molecular level
You can kind of view it as a even billard balls and maybe even,
they are kind of hitting each other well I,
wont go into that because that can kind of get a little confusing depending the diffrent cases and,
the diffrent boundry`s. But this is the easiest way to think about which direction it will refract.
And hopefully makes a little bit of a intuitive sence.
And so when your going from a slow to fast medium or a P-Wave,
it would kind of, its angle would excentuate in that direction if you would,
went from the fast medium too the slow medium once again you can just go to same,
thought expireeement so lets say you have our wave,
coming like that. Draw! the car visulize the.
Vizulize the car right here. And you say well,
look this tire is going to get stuck in the mud,
because it is not going from, it was on the road now from this top,
left tire is getting stuck in the mud first,
so it is 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 your going from the fast to the slow medium.
So that is just a primer on refraction generally.
Now lets think about what would happen when sound waves are travelling in,
through the earth. And this all will help,
infrom us of essentially how to 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,
You had a earthquake rigth here.
On earth maybe a little below the surface,
so like you know its in the actualy happening in the crust bit a little bit below
the surface of the earth. If earth was a,
uniform desenty is it was all the saem material how would those, lets just think,
about the P-Waves how, would cause P-Waves,
can travel in anything lets think about how,
those P-Waves would travel. Well they would just go in strait lines there is nothing,
that would refract the P-Waves. It would,
just go in straight lines radialy outward,
from where the where the earth earthquake occured.
Now at a first approximation know that as,
we go deeper and deeper in earth there is,
more and more rock above that the weight of,
that rock is kind of compressing the rock,
below. So you get higher and higher pressures,
and higher and higher densities. So how,
would, so this is a uniformer.
But lets imagine a earth that is made up of,
unifrom material that is all solid.
A completely solid earth but one where the,
density is consentantly increasing at as you go,
down. So lets just think about it in beofre,
we go into the countinous case cause we,
are talking about the density as you go,
deeper it is getting countinously more,
dense. Lets think about the discreet case,
where we have we the least dense layer.
So let me draw right over here.
So lets say this is the surface of the earth,
and this is least dense then lets say you,
have another layer over here that is more,
dense. So this is more dense. Let say you,
have another layer that is even more dense,
so you have another layer over here that is even more dense.
Then lets do one more layer lets do,
this layer here. This is the densest layer,
densest. So in general your P-Wave, your,
seismic wave is going to travel faster in,
denser material. So it is going to travel,
the fastest here than here than here.
So it is going to the slowest in the least dense material.
So if your coming in an angle.
If your coming in an angle lets think about,
whats going to happen. So lets say have your,
P-Wave coming in at a angle like this. SO
it is going straight thorugh the least dense,
material. So whats going to happen into the,
let me do a slightly shallower angle so lets,
say it is like that. What is going to happen ,
when it goes into the more dense material.
So once again lets imagine in our little car,
so this tire is going to be able to go a little,
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 is going to travel like,
this so it is now going travel like this,
now what is going to happen at this boundry.
Once again imagine the car this tire right here is,
going to be able to travel faster before,
the other tire so it will be deflected even more in that direction.
Then we go into the densest material.
Once again tires on kind of the bottom side when we look at it this way.
We are going to be able to get or move faster before the otehr tires.
So we are going to get deflected even more.
So you see as you go least dense material to more,
dense material your kind of curving outward.
So if this was continous if we had a countinous,
kind of countinous structure where as you go down it just gets more and more dense.