Download How Waves Reveal Internal Structure of the Earth.

How Waves Reveal Internal
Structure of the Earth.
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We’ll need to remember three of the wave
behaviors we have learned about:
1) refraction
2) reflection, and
3) s-waves’ inability to move through liquids.
The fourth behavior (difference in rate of
propagation) will come up in another slideshow.
Remember that we mentioned earlier that waves reflect off of density discontinuities. The various layers you’ve heard about – the
crust, mantle, and core – are made of different materials and have different densities. Their boundaries, in other words, are simply
density discontinuities.
And so it is possible to “see” these boundaries as reflections on a seismogram. Unfortunately,
as the example at right shows, seismograms are very complicated. There are numerous
reflections, refractions, aftershocks, and so on sending waves toward the seismograph.
Consequently, reflections from a discontinuity are typically much easier to spot after you
already know to expect them. Most discontinuities are first discovered in another way – by
Curious ways the waves refract.
B
seismograph
A
Crust (density ~2.5)
Mantle (density ~3.5)
R
source
C
I
Finding the Moho
The Crust/Mantle boundary
The boundary between Earth’s crust and mantle is called the Moho or M-discontinuity or Mohorovicic discontinuity after
its discoverer. There is, on any seismogram, a jiggle that records the first reflected wave from the reflection off the
Moho of seismic waves. Somewhere in the “noise”
is another first arrival – the first arrival of a
wave that refracts into the mantle. The diagram
shows how this wave moves (green arrows).
When the wave arrives at the discontinuity and
“hits” that boundary it sends waves outward
in every direction from where it “hit”. One of these, represented by the heavy green arrow in the mantle, will travel
along the discontinuity. As it goes, some of its energy is returned across the Moho at every step, radiating upward. (Do
you see some hint here of why the seismogram is so noisy?)
seismograph
Crust (density ~2.5)
Mantle (density ~3.5)
source
X
X
At some distance (X) on either side of the mid-way point between the source and seismograph the wave entering the mantle will
send out a refracted wave toward the seismograph that will be the first arrival refracted wave.
Notice that this wave travels farther than the reflected wave, and so you’d expect it to take longer.
But once in the mantle it also travels faster than the reflected wave, so the lag between them is not what you’d calculate based
on distance alone.
For stations close to the epicenter the reflected wave arrives first and there is some lag between it and the refracted wave. But
you should be able to predict that the lag time will decrease the farther from the source the station lies.
At some distance (called the critical distance) both waves arrive simultaneously, and beyond that the refracted wave actually
outruns the reflected wave and arrives first.
seismograph
Crust (density ~2.5)
Mantle (density ~3.5)
source
X
X
Mohorovicic, of course, did not know this up front. He had to reason his way through it after noticing a strange
pattern in arrival times on seismographs. For many earthquakes and many seismographs he plotted out the
distance from the epicenter to the station. The location of the station was known, of course, because they are
exactly where people put them. Locating the epicenters is something we’ll look at separately, in lab. Suffice to
say that he knew where both things were for many, many earthquakes.
The relationship between distance traveled and time traveled is generally very straightforward. It’s usually
among the first things you learn in a physics course, and the graph illustrates it. Assuming a constant speed
distance traveled = speed/time. Assume it’s about 40 miles to Albany and you can drive it at an average (or a
constant) rate of 40mph. Your travel time is 1 hour (40 miles = 40 mph/1h). If you can go 60 you’ll make it
faster in 2/3 of an hour (40 minutes) (40miles=[60mph/(2/3 hour)]. The graph is linear. The longer you drive at
a given speed, the farther you’ll go.
T
T
I
I
M
M
E
E
DISTANCE TRAVELED BY CAR
Correcting for differences in the rocks the waves went through, Mohorovicic could make a good estimate of the
average velocity of the waves through the crust, and he predicted that he could also, therefore, calculate the
arrival time at any seismograph. The same graph also applies to this – it works for cars on highways, waves in
the crust, … anything that moves.
T
TI
IM
M
E
E
DISTANCE TRAVELED BY WAVES
What he saw was different from what he predicted. His hypothesis about predicting arrival times was wrong, but
wrong in a peculiar and interesting way. This was a new observation upon which to base and test a new
hypothesis.
Dr. M’s predictions worked fine for stations within a certain distance of the seismograph – a distance he called the
Critical Distance. This is shown as segment “A” on the graph.
However, beyond the critical distance, instead of arriving at the predicted times (segment “B”) the first waves to
arrive came earlier than expected (segment “C”).
(Look at the graph and make sure you get the implication. The lower slope indicates that the first arrival wave has
travelled a greater distance (horizontal axis) in a shorter time (vertical axis). That is, it arrived faster than expected.
(Imagine Dr. M scratching his head … “How could a wave speed up?). Any ideas?
B
T
T
I
I
M
M
E
E
C
A
Critical
Distance
X
DISTANCE TRAVELED BY WAVES
Finally (or maybe quickly, I don’t know) he realized that a wave cannot speed up without moving into a denser
medium. He realized that the faster wave, arriving first beyond the critical distance, must not be the same wave as
the slower one arriving first within the critical distance! It must be an entirely different wave that had moved
through denser material.
His hypothesis has been tested and supported many times. For one thing, once the existence of the denser material
was discovered it became an easy matter to pick out its reflections on seismograms, which are always there.
Incidentally, the wave that was predicted to arrive first does, in fact, eventually arrive, but it is lost in the noise of the
seismogram.
C
B
T
T
I
I
M
M
E
E
C
A
Critical
Distance
X
DISTANCE TRAVELED BY WAVES
B?
Let’s think it through by comparing the original picture to the graph.
The red arrow to the right is always part of the path followed by “A” on
the graph. If the station is closer than the critical distance then the
red arrow on the left is a continuation of A, but it will not be the first
arrival wave beyond the critical distance. In other words it is the “B”
part of the graph beyond the critical distance.
(B)
T
IT
I
M
EM
E
A
Critical
Distance
X
DISTANCE TRAVELED BY WAVES
seismograph
source
A
(B)
Crust (density ~2.5)
Mantle (density ~3.5)
X
C
X
“C” is the complete path followed by all the green arrows.
Beyond the critical distance “B” arrives sometime after C has arrived
and we see C first. That wave has followed a longer path, but has been
able to move enough faster through the mantle to outrun “A” and “B”.
B
C
TT
II
M
M
EE
So the existence of the change in density between the crust and
mantle was discovered because of the existence of the critical
distance.
A
We can also learn something interesting from how far that critical
distance is. What?
X
DISTANCE TRAVELED BY WAVES
seismograph
source
A
(B)
Crust (density ~2.5)
Mantle (density ~3.5)
Critical
Distance
X
C
X
Remember that we are talking about observations of arrival time of wave. What controls when, say, an
automobile leaving Americus will get to some destination?
That will depend, of course, on 1) how far away the destination is, and 2) on how fast the car is driven –
distance and speed.
It’s the same with waves. Distance and speed dictate how far they travel. If the distance is known the
only variable is speed, and vice versa. Alternately the two can be entered into a set of equations and
both can be determined (2 equations with 2 unknowns in this case).
We do not know up front what the depth to the Moho is, though we can interpret it pretty easily once
we know to look for a reflected wave. The exact distances that the waves travel depend upon this and
we must either solve for it or determine it from wave reflections. The depth to the mantle is somewhat
variable, but we’ll come back to this.
That done, we can solve for something else.
We know that the refracted wave must move faster than the reflected one for that part of its course that
lies within the mantle. How much faster it can go depends on the density of the mantle. Knowing both
the critical distance and the depth to the moho it is an easy matter to solve for the density of the mantle.
(Having some idea that it is made of a rock called peridotite before you begin doesn’t hurt either.)
So Dr. M didn’t just find his discontinuity, he also figured out how deep it sits and what the density of the
mantle must be. Not surprisingly, it has the same density as peridotite!
Characterizing the Crust
We’ve mentioned that the depth to the Moho (and therefore the thickness of the crust) is variable, but that
variation is not without pattern.
In general the crust is thinner in the oceans, off the continental shelves. In most places it is about 5km thick, but
under volcanically active regions like the ocean ridges, or parts of the Pacific called “large igneous provinces” (LIPs)
it reaches 10km. Under individual highly active volcanoes it can be even thicker.
The dashed line in the diagram parallels where the land surface would be if the Earth were a perfect sphere. Its
level is not just arbitrarily chosen – it is a calculated equilibrium level for the crust. In every place in the oceans
(except under very active rapidly building volcanoes) it lies 1/7 of the way between the surface and the Moho.
The high ridges and LIPs have a depth to the Moho beneath them in proportion to how high they stand off the
surrounding ocean floor. It appears that they float in the mantle at some appropriate level, like blocks of wood of
different thicknesses floating in water. 1/7 of the crust is above the equilibrium line and 7/8 beneath it at any
point. (Again, except under especially active volcanoes.)
As we’ll see next, the continents do something similar.
The same general pattern holds under the continents but with a couple of differences in detail.
Because the continental crust is less dense the equilibrium level is not 1/8 : 7/8 but ¼ : ¾. In other words, the continental crust floats
higher than the oceanic crust – like an empty (low density) boat floats higher than a laden (high density) one. Incidentally, we can use this
difference in the equilibrium levels to compare the differences in density of the continental and oceanic crusts.
Secondly, the continental crust is several times thicker than the oceanic crust. It floats higher like two blocks of wood of different density
float at different levels. (Think of oak and balsawood.)
So the land elevation stands higher than the seafloor because it is less dense (and floats higher) and thicker (and floats higher). That’s why
the water is in the ocean – why we have oceans.
Notice that the mantle is much deeper under mountains than lowlands, and even deeper under bigger mountains than small ones. We say
they have roots. (Very active mountains like the Himalaya have roots that are not as deep as expected. They are not sinking to their
equilibrium level as fast as they are growing.
Matching the scales of the two preceding diagrams and joining them we see that the same equilibrium level applies
to both. The oceanic crust is both thinner and denser so it sinks lower – below sea level – and water naturally fills
that basin. The continental crust is both thicker and less dense so it floats too high to be covered with seawater.
This is why we have land and sea.
Sea Level
Equilibrium Level
Moho
Crust (continental)
Moho
Crust (oceanic)
Mantle
This tendency for the crust to find some equilibrium level is called isostasy. It explains several interesting places
where the crust has recently moved directly upward or downward, or, in fact, is still doing so. WE will come back to
the idea a few times over the next two terms.
The glaring question, of course, is what does the crust float in? Presumably the Mantle, but the mantle is made of
rock, right?
Let’s move on…
Characterizing the Mantle
Finding the Moho involved studying arrival times at stations fairly close to the epicenters. Stations farther
away are of progressively less use, but we do learn interesting things about the mantle from them. One is
that waves do not move according to the linear graph we used above, but according to a curve instead. They
seem to get faster with distance. This is partly an illusion and partly real.
The curve below shows the measured arrival times of the first p-wave at seismographs up to 10,000 km away.
Something weird happens past that and we’ll see what that is shortly.
Travel Time (minutes)
20
10
0
0
2000
4000
6000
8000
10000
Distance of Seismograph from Focus (km)
d
The illusory part is pretty simple to grasp. The “distance” on
the graph’s x-axis is the surface distance “d” between the
focus and the seismograph. But it isn’t surface waves we
see on a seismogram 10000 km away, its body waves. Our
first guess might be that the distance the wave actually
travels is the shortest route between the two points – the
straight-line distance (d’ in the picture).
d’
But it turns out that that distance (or the speed implied by
that distance) is not correct either. The waves arrive a bit
earlier even than that wavepath suggests.
Travel Time (minutes)
20
10
0
0
2000
4000
6000
8000
10000
Distance of Seismograph from Focus (km)
d
Once again refraction explains the discrepancy. Wavefronts that
go somewhat deeper outrun the straight path because they
cross into progressively denser material (and refract downward)
on the way in and then into less dense material (and refract
upward) on the way out of the Earth.
d’
D!
One curved path (D!) will balance distance and speed and
outrun all the other paths, including the straight-line path, and
arrive at the seismograph first. (The others will show up as
“noise”.)
This is just a reminder that we’ll be seeing curved paths, and
why.
Travel Time (minutes)
20
10
0
0
2000
4000
6000
8000
10000
Distance of Seismograph from Focus (km)
Before we leave the mantle there are a few loose ends to tie up.
1)
It’s density increases with depth. This is the best and most consistent explanation for the first
arrival times from distant earthquakes. The density is about 3.5 g/cm3 near the Moho and
increases to about 5.7g/cm3 at its lowest part, as indicated by wave arrival times.
2)
The density does not, apparently, increase perfectly consistently. There do seem to be some
minor discontinuities within the mantle. The significance of these receives a lot of attention
and debate these days, but doesn’t concern us much at this level. The best guess is that they
mark places where certain minerals can (and do) change into denser versions of themselves.
3)
The uppermost part of the mantle is very rigid and brittle – as brittle as the crust. Below a
depth of about 100km (usually) this gives way to a less rigid material that is plastic – able to
bend or even flow very slowly – like silly putty, only a lot slower. This part of the mantle is
called the asthenosphere. This is what the crust floats in. The slow rate of movement is why a
mountain chain’s “roots” don’t keep up with its “roof”. How deep the plasticity extends is a
matter of a lot of debate, largely because it is part of one hypothetical explanation for what
causes tectonic plates to move. If the asthenosphere is very thick, the mechanism works, if it is
very thin, the mechanism cannot work. This will come up again in Geology II when you talk
about plate tectonics.
Finding the Core
The Core/Mantle boundary
(G-discontinuity)
The curve we have just seen that
describes arrival times through
the mantle only works if the
seismograph is within about 103
of arc (~11461 km) of the focus.
(That’s why the graph stops at
~10,000 km).
Both p-waves and s-waves show
this odd characteristic, but what
happens beyond is different in
the two wave types.
NOTHING
Cutaway View of Earth’s Insides.
DOING
Beyond 143° (15910km) from
the focus the p-waves return,
but not at the expected arrival
times. Clearly their velocity has
not been what we’d predict for
the mantle, so they must have
moved through material of a
different density.
(The exact wave behaviors are
very complex in the real Earth. I
have simplified these drawings
to make what’s happening
apparent without tracing out
exactly how the waves behave.)
P-waves “return”
Cutaway View of Earth’s Insides.
P-waves arrive where the green
dashed arrows are, but not
where the red zones are. (There
are some but their timings are
very screwy and they are almost
unnoticeable on a seismogram.)
This region of no p-waves
(shown in red) is called the pwave shadow zone.
Make sure you realize that this
picture is an idealized picture of
Earth cut exactly in half.
Cutaway View of Earth’s Insides.
If we look at the Earth from the
outside – viewing the surface
instead of the interior – the pwave shadow zone would be
shaped like a doughnut.
The black dot is exactly 180° of
arc away from the focus. The
blue regions would receive
strong p-wave signals, the
shaded zone would not.
These observations were first explained by
a geophysicist named Gutenburg. He
realized that the waves at some depth
must cross into an even deeper layer than
the mantle with a noticeably higher
density.
Gutenburg could determine the depth to
this discontinuity (~2900km) by noticing
where the shadow zone began – 103° from
the focus. That’s where the curved
wavepaths can just graze it and keep going
to where they are expected. The next
wavepath over hits it, gets refracted, and
winds up somewhere else.
Gutenburg realized that where the waves
pick up again depends upon how much
they have been refracted – what the angle
of refraction is, in other words. That,
remember, depends on the difference in
density.
Remember that the lower mantle has an
estimated density of ~5.7 g/cm3 based on
the bending of the waves moving through
it. Given this it is a simple matter to
determine the density of the lower layer.
Again, the model you see here is very much
oversimplified, but you should be able to
dig the basic logic out of it. The wave
refracts into the inner layer, then refracts
again on returning to the mantle and so
does not go where it’s expected.
Cutaway View of Earth’s Insides.
The deeper layer is called
the core, of course. The
boundary between it and
the mantle is called the
Gutenburg discontinuity
or simply G-discontinuity
after the one who
explained its existence
and characteristics.
Cutaway View of Earth’s Insides.
Like the p-waves, the s-waves do
exactly as expected up to a
distance of 103° from the
earthquake.
Beyond that, no s-waves at all are
recorded. This is the s-wave
shadow zone.
If we look at the Earth from the
outside the s-wave shadow
zone covers nearly half the
planet!
The black dot is exactly 180° of
arc away from the focus. The
blue regions would receive
strong s-wave signals, the
shaded zone would get none.
What can explain this?
Certainly not refraction.
Characterizing the Core
Complete blockage of s-waves by
the core indicates that it is liquid
(that is, molten), at least in its
outermost part.
This also explains the odd change
in velocity of p-waves, which slow
down even though they have
moved into a denser material.
LIQUID!
Remember that the G-discontinuity lies at
about 2900km beneath the surface. The
angle of refraction of waves across the
horizon (entering the core from a mantle
of density = ~5.7 g/cm3) suggests that the
density of the outer core is about 9.9
g/cm3.
Inge Lehman first suggested that the
weak p-waves received within the
p-wave shadow zone were consistent
with reflections from horizon at a
depth of ~5200km, and this was
quickly verified and agreed upon.
The implication is that the innermost
part of the core is solid rather than
liquid.
~2900km
Outer Core
Inner
Core
Thus we infer an outer core (liquid) and
an inner core (solid).
Pressure in the core probably means that
the density at the base of the outer core is
close to 12 g/cm3.
The inner core is presumably solid
because of the extreme pressure at that
depth. Because of this the inner core
density is greater, probably reaching 13
g/cm3.
~5200km
If we sum up all the known and estimated densities of the various
layers, and if we take into account the volume of material in each
one, then the overall density of Earth can be calculated at around
5.5 g/cm3 – right where Newton put it.
Thus we see the test of our last hypothesis – the inside of Earth
must be made of denser stuff than the outside. Not only do we
learn from earthquakes that this is so, we learn what the various
internal parts are, what the depths are to them, and how dense
each one is.
This is quite a lot of information about something we cannot even
see!
This slide summarizes the important points about the internal structure of Earth. Be able to label the parts and tell their basic
characteristics – liquid or solid, composition (rock type) and general (relative) density. Don’t worry about exact density values.
Remember that there re two kinds of crust.
If we opened the Earth, took out a pieshaped piece, and enlarged it …