I will start the seismic part of this class
with some examples of my work in
earthquake hazard reduction, where I've
been generating earthquake waves in a
computer through structures, and
principally the basins that underlie
most of Nevada's cities. And I think what
this will do is tell you a little bit
about what the earthquake waves are
likely to do: how they propagate and when
they're larger and when they're smaller.
So then we'll start to see how we can
use those waves, not necessarily from
earthquakes but from artificial sources
to be able to probe the earth and figure
out actually what some of these basic
structures are, that put us at
such a risk for earthquake damage, here
in Nevada, as well as in California, in
Japan, and other places. Now the
grayscale image in front of you is a
shaded relief map of the basin that
underlies Reno, and I'm pointing up here-
UNR is about here in the northern part
of the middle of the basin. This is the
Sparks basin over here, which is about
600 meters deep. And then under West
McCarran and Mayberry
the Reno basin gets to be about to a
kilometer deep. There's also some pieces
of the basin that are down here under
South Meadows and those areas.
Four and a half years ago [2008] we
had a series of earthquakes that shook
the western neighborhoods of Reno, and
this sort of colored blob here is some
of the waves that were coming out of
that earthquake. So this is a model that
was made in computer clusters; and
then we propagate earthquake waves through
that model. Let's observe what the
what the waves do, and then we'll be able
to come back and think about how we can
use those wave propagation effects and
try to learn something about the
earth structure- not just from earthquake
waves but from waves that we can put into
the ground ourselves. So I'm going to
play this movie and you're going to see
the waves expand rapidly through the
area around Reno and there's this
curious effect that a lot of the wave
energy is left sitting within those
basins that underlie the urban areas. And
that's why places such as Mexico City,
Tokyo, and Kobe have shaken so terribly
in the earthquakes that have hit them. Now
as I go through this movie more slowly
let me rewind it back and collapse the
waves back into it the Mogul earthquake
source of April 25th, 2008.
Here the waves are just starting to hit the
surface of the earth, and if we roll this
forward now you'll see it's a very
complex wave. We try to use
simpler waves when we do seismic
exploration. But these more complicated
earthquake waves; they still obey
the many of the same features of
wave propagation that we will use in
exploration. The wave expands across
the map.
Yeah, I forgot to say this is a map view; and
you can see there's some sort of dim
waves out here that are traveling faster
than the others and there's brighter
waves
with higher amplitude that are
behind. In this class we're going to
start out by looking at these first-
arriving waves that travel faster.
Those are called P-waves. And later on
we'll take some advantage of the
slower-traveling waves, called shear
waves or surface waves or S-waves. We
can watch how even by the fourth or
fifth frame the P-waves are pretty much
propagating out of the frame of calculation
here, and what we're looking at are
principally the S-waves. It is
principally the S-waves that are getting
caught in the basins. This is an
interesting frame right here
because you can see that the basin
is somehow bending and actually delaying
the waves. Even the P-wave here
and the S-wave over here.
Those are being caught at the
edge of the basin. It's clear that
the waves don't propagate as fast within
the basin as they do outside the basin.
You can see that here- the
nice circular S-wave path outside the
basin; the S-wave "wavefront" actually,
looking down at the map view of it.
Here in Sparks where there's a basin
the nice circular path
is distorted, and the wave arrivals
delayed a little bit- maybe just
five percent or so of its overall time.
Whereas the P-waves may be even
delayed somewhat more. Little
scraps of P-wave left there in the basin.
Same thing over here too- that's in
Pleasant Valley, the southeast side of Reno.
So in addition to the waves being
stronger within the basin they're also
delayed. This speaks to a rock
property that we call "velocity," which has
a lot to do with the strength of the rock.
The stronger and less bendable, less
compressible the rock, the
more force you have to use to compress
it, the higher the moduli of
deformation; then the faster the waves
will travel. Outside the
basins where you have hard volcanics
and Sierran granite, the
the waves are travelling fairly fast.
These wave speeds are on the order of 3
to 6 kilometers per second. But in the
basins the velocity might even
be half of what it is outside the basin.
The basins of course are filled with
volcanic or in this area mostly clastic
sediments. Those sands, gravels and maybe
tuffs and volcanic mudflows
are looser; they're not as compact,
they're not as dense, and they have lower
seismic velocities. It's a property of the
rock, much like density.
Sediments have the lower densities and
lower seismic velocities. As it turns out
they're just looser and more easily
compressible, more easily sheared, and all
that. The moduli are lower. And these are
the delays in the waves that those
produce. Let me play this through
again a couple more times just so you
can see the delayed wave fronts and
then the energy that gets trapped at the
edges of the basins, because the wave
fronts propagate through pretty quickly.
You can see some some energy
rattling around a bit
inside the basins as well.
That's a relatively simple map of
the progress of shaking of
earthquake waves. I''m going to show
you a couple more examples.
Here we have a very complex
example. We're looking again at a
shaded relief map showing the basin
structures. Elko is just off the
map on the lower left side. This boundary
here above which we don't have any basin
information, that's the Nevada-Idaho
border. Nevada on the south and Idaho
where we just haven't put the
basins in to the north. The map
doesn't quite go to the Utah border on
the right-hand side. The map is about 200
kilometers wide. Also almost five
years ago now there was in February
2008 a magnitude 6 earthquake
in the little hamlet of Wells, Nevada
along Interstate 80, about 5 hours drive
east of here. You can see that this
earthquake happened in this very geologically complicated
area where there are all these basins that
are part of the Basin and Range and
provide a very complicated structure
that allows the wave motion to be
channeled and and refracted around.
Again you see a colored area in the
middle where the earthquake is going to
begin to propagate. Let's watch the
the waves as they refract around and get
caught in all these dozens and dozens of
different basins. You can see the
waves are propagating quite slowly
through the low-velocity
sediments of the
basins. They're propagating
more than two times faster in between
the basins. But you'll notice that
within the basins where it's soft there is
also higher wave amplitudes and more
earthquake shaking. That's one of the
reasons that 20 buildings were damaged in Wells, Nevada in 2008 from this
earthquake. You can see
that earthquake shaking is
very strongly channeled and affected by
the velocity property structure- the rock
velocities that are in this area- and are
giving us lots of lots of refraction and
delays in certain waves, and catching
certain waves. Others are just
accelerated right out the side of the model.
Again, it's the interaction here
between the wave propagation and the
velocity property of the rocks that is
really giving us a lot of
the effects that we can look for.
This is of course important in trying to
predict where earthquakes are going
to shake, and where they'll shake harder, and where
they'll shake not as hard. Which critical
facilities to we have to build to a higher
standard?
Where do we have to raise insurance
rates? Where can we lower insurance rates?
It's also possible to look
in detail at the waves,
and decide what they're telling
us about the velocity structure.
When we see these high amplitude waves
that are propagating slowly, then we know
that we're in a basin. When we see lower
amplitude waves that are propagating
faster, then we know we're in between
basis. We can actually explore and get
some idea about the structure by looking
at these
waves and how they arrive at 
different places on the map here.
Here is a another map, which is down in
southern Nevada. Those of you from
Las Vegas, you might recognize the Las Vegas
basin. The Las Vegas Strip is here;
Nellis Air Force base is up here. This
is the outline of the western front of
Frenchman Mountain, which those you from
down south will recognize.
The Strip is is over here, and then Boulder
City is right out down here. We got a
very detailed look at the Las Vegas basin,
and not-very-detailed looks at the
basins that are outside the Las Vegas
basin. This is called Eldorado
Valley down here. There's a fairly
substantial earthquake fault, which is on
the northwest side of Eldorado Valley
and could produce easily a magnitude 6.5
earthquake. There's a good fault
scarp there that shows that it probably
has ruptured relatively recently, just in the last
couple thousand years.
What this model here investigates is-
Where is it going to shake in
Las Vegas when we have that earthquake
on what's called the Black Hills fault?
This fault is actually outside Las Vegas and
and is much closer
to Boulder City than it is to
The Strip, over here. I'm going to
let this propagate. Look down here for
the initial shaking due to the
earthquake. There it comes,
and it's getting funneled into the Las
Vegas basin. You can see the circular
waves going through the Spring
Mountains, where there's
no basins and not a lot of
this velocity-property
heterogeneity to sort of disturb the
waves. So we've seen these
circular waves here on the map. The
waves are getting obviously delayed and
distorted within Las Vegas basin.
They're getting caught within the
Eldorado Valley basin and
especially in the deeper Las Vegas basin.
They're getting caught pretty severely.
Look at the delays there. It just
takes longer to propagate through the
slow sediments with that slow velocity
property. Maybe half the velocity of the
others.
That's that's enough example
of the earthquake hazard
calculations. How then
do we use these waves to investigate
structure? For instance, to find out how deep
basins are, and find out more
about that velocity property?
Is that tied to anything
that might be interesting? Can you
for instance find gold based on the
velocity property? A quick answer
is no, but it still can be
helpful. I have some students
investigating those issues right now.
Here we're looking at an extremely
simple and very low resolution
model of a cross-section. We're going to
look at seismic wave propagation- not a
map as we have- but in a cross-section.
Across here we have distance
across the ground surface, and then
on the vertical axis in this
view we've got depth below the
surface.
If I let the
waves propagate, you see that
this model is supposed
to be only 50 meters wide.
This is the kind of scale of the
experiments that we will do in this
class.  We're looking not at
a map but at a cross-section.
To start out, we hit the ground at the top
center, up here, and then we're
watching the waves propagate
in that cross section. You've
probably noticed by now that there's
something here in the lower right, which
is reflecting a lot of those waves back.
That would be since it's a model of a
cavity like a tunnel or mine addit,
or a utility tunnel- a buried cavity with
buried services. The point of
this wave propagation movie is to see,
what we would be looking at if we wanted
to find those buried utilities?
So let me bring it back here,
at where we've hit the ground
and we've got a wave that is
traveling radially out from where
we hit the ground, and here it is
1/50th of a second later probably.
A little bit later you can see that
it's basically starting to react to
other discontinuities and
heterogeneities here. The
velocity property's not constant here.
But the wavefront, let's say
if I track the between the
black and the white,  the
initial white and the black.
As I track that, it's basically
semi-circular here in cross-section.
The waves are propagating in a fairly
predictable way, from the point where we
hit the hammer on the ground surface, say
right here in the center at the top.
Down here where that
tunnel is, we
start to see that impinging on the waves.
Right here you can see that
the waves are not propagating;
you can see they're highly delayed by the
tunnel. The tunnel's full of air and
air, although it's fast by our standards
at 330 meters per second,
the velocity of air is
one-tenth the velocity of rock. That's
a big difference. This white
part of the wave is delayed all the way
back here by the outline of the
tunnel. The black part of the wave is
delayed back here as well. But there's
another thing happening too.
What you'll see there as we keep going
is that the wave is reflecting
off that top left side of the
tunnel.
That change in velocity
takes some of the energy,
in this case a lot of the
energy, out of the the initial wave
that came straight from the hammer
blow, and puts it into a reflected wave,
which now instead of
propagating down is propagating up!
Up, actually back toward the hammer.
That gets to the
surface and then reflects off the surface.
The surface of the earth is also a pretty
good reflector.
We'll collapse that back- and so that's
the progress of these waves.
If we can if we can detect that reflected
wave, as you can see here would
be hitting back off the surface where we
could measure it? If we detect
that, maybe we could use the time
that the waves arrive and their
curvature and all that, we could use that
to figure out where that tunnel is.
Essentially kinda "back calculate" and
collapse that wave. See, here the
reflection is at the surface, and if I
back-calculate and collapse it back
onto the top of the tunnel then
I can figure out where the
tunnel is. I can see the waves
first, basically, reach the surface right
on top of the tunnel. There's an
indication there- where does
that reflection arrive earliest?
It arrives earliest right over the
point that would be the center of
the reflecting structure, the
center of the tunnel. All those are
are ways that we're going to use,
actually, to use these same seismic
waves, really exactly the same
as earthquake waves. We're going to use
them to explore the earth and look for buried structures and buried
stratigraphy. Now here's another
example. What we have here is a
little bit more labeling. Again, a
very low resolution view. I made these a
long time ago when when it wasn't so
easy to use computers to show these
kinds of animations.
You'll notice that this is more of a
crustal or maybe deep oil and gas
type of exploration problem, perhaps even
deep geothermal. There's some unknown
structure in here within this
cross section again. We're not looking at
a map; we're looking at a cross-section.
Across the top we've got distance
out to ten kilometers.
Here's where we've hit the
ground with something or let off a big
explosion or used "active
source" machines that will vibrate the
ground. Then this vertical axis is
depth.
We're looking at a one-to-one
section here.
The grayscale gives us the amplitude of
the wave and up here on
the upper left you can see the time
after the initiation, after we start
hitting the ground.
Or when we let off the
seismic charge. So I'll go
ahead and let this propagate, and you
can see that there's one main
wave that goes down. But even after that
propagates out of the field of
calculation here, you can see there's
there's other things going on; there's
some reflections coming up; it's a
little hard to see because
the wavelengths are kind of long  compared to the model. But really
you can see some waves moving up.
It's those reflections and other
things that are happening near the
surface here. There are some waves that are
traveling along some interface here, and
we'll be able to use those to figure out
what the velocities are and where the
reflectors are. We can actually
reconstruct the structure, not
in tremendous detail, but in enough
detail to actually make this technique
useful. So I collapse it again. Here you
can see there's there's one reflection
coming back up. I think I can see another
reflection coming back up, clearest right
here- that's another reflection that's coming
back up- a whole series of different reflections. Then there are some
waves that are propagating back down
from the surface of the earth. All of
those are things that we're going to
try to figure out how to use. We'll
principally do that in our in our
labs. We've got a lab first on refraction
and figuring out velocity. Then we'll
have a lab on surface waves and figuring
out shear-wave velocities from those
waves that get so
easily trapped in basins where they're so
large in amplitude. Then we'll have
a third lab that is
specifically on the
reflections; and that's half the labs in
this class. We're going to examine
these different pieces of the wavefield.
You've got one hole [cavity] here with all
these different kinds of waves. We're
going to approach it piece by piece,
break it down, show exactly
what's useful and what you can do with
each little observed piece of wave
here.
All of those examples from
the earthquake hazard work that my
students and I have been doing; these
examples of the waves propagating on the
map and propagating in cross-sections,
I hope has motivated us to
start looking at these waves and
figure out what we can do with them.
First we have to decide how to
describe these waves.
Now we're in the the seismic
overheads, the "Seismic overheads 1".
This illustration here shows a view
of waves propagating through a medium.
You can see it's just one kind of
wave; this might be the the fast
P-wave, and we might be in air or water
where we don't have the slower
S-waves. Or maybe these are just
the S-waves and the fast P-waves have
already propagated out of the picture.
Either way, we can describe those
different kinds of waves
with very similar parameters. So in this
view of compressional waves we have a
source- that's where the waves were let
off- and we could be looking
at either a map or a cross-section.
If this was a
cross-section that would be a buried
source; if this was a map
then what we'd be looking at here is
a source in the middle of the map.
The density of dots kind of represents,
highly exaggerated of course,
what happens when
the compressional wave
passes through the medium.
You can see here behind the
waves, or in front of the waves there's
kind of a medium density of dots.
Then, when the first
compressional wave reaches a
particular place, the dot density is
higher. Then behind that, is what's
called a "rarefaction;" the dot density
goes way down.
How much compression
and rarefaction are
we really talking about here?
The actual strains,
if you studied stress and strain, the stresses
are low and the strengths
are really quite high. The moduli of
rock are really very high. Stresses are
not that great. They can be great
for earthquake waves. But for
exploration waves the stresses are not
that great. So the strains are also very
small and what we're probably looking at
here is a compressional strain of
10^-6. If it's
positive 10^-6 it would be a compression,
and negative it would be a rarefaction.
Now fortunately we have instruments that
can detect these very small compressions
and rarefactions very easily. As
I'm talking to you there are
compressions and rarefactions coming
through the air from your computer
speakers or to your eardrum
from your headphones.
Those compressions and rarefactions
are are very small, but your ear is
sensitive. They're probably on
the order of 10^-5 or 10^-6,
and your ear is perfectly
capable of picking them up,
characterizing them, timing them, and
doing the frequency analysis your cochlea
does to figure out what I'm saying.
[This applies to normal hearing.]
Our instrumentation is
even more sensitive; 10^-8
strain is no problem for
us to detect. We have
robust relatively inexpensive,
field hardened instrumentation that
can measure these compressions
and rarefactions at 10^-6, 10^-8
strain levels with no problem.
That's the kind of equipment we have.
You'll get to use this equipment
and measure these strains.
Later on we'll do that in the
field, we'll practice for that; and you'll
analyze the data. Now, what are we going
to measure? I'm not so
interested yet in measuring
the exact strain.
That's why I'm guessing when I'm
talking about a level of strain.
Really what I want to
look at is this velocity
property. I want to decide
where the reflectors are, that
are generating the reflected waves. I
want to decide: how fast did
that zone of compression of
that wave travel from the source?
So I'm really not going to
be too concerned about the exact level
of strain- which is so
exaggerated here in this plot.
Really what I want to do is time
the wave. If I'm
observing out here, and this wave is
coming toward me, so I'm observing on the
right hand side here,
I'm going to make a recording that looks
like this- the first compression will
will come at me, and then it's going to
rarefy- there's the rarefaction-
that's going to propagate past me next;
and then the secondary
compression is going to come.
These waves tend to organize
themselves like this: there will be a
whole series of up and down motions,
compressions and rarefactions.
All of those will take
these kind of sinusoidal forms.
You'll explore, if
you're a geophysics major and you take
Geophysics and Geodynamics 455 or 655,
you'll explore why the
sine wave seems to be the way that waves
organize themselves.
So there's an upswing on the
seismogram- that's a compression in
this case; the downswing is a rarefaction.
When the wave is past it
all goes back to zero- normal density.
There is the zero line right through there,
the gray average distance.
Now look at the the lower left.
I can't point down there or it gets
covered by the Acrobat tools.
Look down at the lower left where I've
written one
equation there.
V = f lambda. This is a very basic way
of describing wave motion. You might have
seen it in a physics class. I want
you to memorize this because you're
going to use this over and over again.
V = f lambda
Waves travel at velocity V,
so V is for velocity; and waves have a
frequency f, in other
words the number of cycles per second.
The SI unit for
cycles per second is, for one cycle per
second, is one hertz (Hz). The
waves also have a wavelength, lambda.
If I measure from the
most compressed peak over here, to the
most compressed peak on the next
positive wave that comes by,
then that is 1 lambda. Lambda is
measured in meters.
It's a distance; it's a wavelength;
it's a length. I could just as well-
there's always more
positive and negative swings. I
could go from the center of the negative
swing to the center of the next negative
swing. That ought
to be pretty
much the same lambda. Wavelength:
Greek letter lambda for length L.
Another way to do it is to take
this first departure from
normal particle separation-
Zero change on the seismogram and
over the top and then across the
trough, and then here we are going up
again. We know there's
an instant there where we have
normal particle separation.
Looking at the seismogram it is easier
to see this.
We have normal particle separation; it
gets bumped up to the peak; we
swing back and briefly we get
normal particle separation again; and we
go through the negative; and then we come
back to the normal particle separation-
on the way up- but very
briefly were we're at normal particle
separation. So this is between here, and
here.
That's also one lambda. So we can measure
peak to peak; we can measure trough to
trough; or we can measure from zero
crossing to zero crossing.
We'll get slightly different values-
different estimates of lambda-
but like with any dataset there are
uncertainties and distributions of
values. But it's going to be about the
same.
So there's this
cardinal rule here that I want you to
memorize: the velocity is equal to the
frequency times the wavelength.
V = f lambda  That's a very basic wave formula-
the velocity of the wave
propagation, the frequency of the waves,
the wavelength of the waves- those are
basic parameters that we use to measure
waves. You can see that they're
related. If I knew two of them-
if I knew the frequency and the
wavelength, I could calculate the
velocity. If knew the velocity, and I knew the
frequency,
I could take the velocity and
divide it by the frequency and I would get
lambda. That's the useful
thing about having a relationship
between these parameters. If you've
only got two, you can get the third,
by calculating it. Now here's a
relationship from optics that I'm sure
you've all heard of before.
This is the reflection of waves, and
what we're looking at here is a
cross section. Let me just
get it to center- I can't blow it up that
much.
We're looking at a
cross-section and there's this
horizontal line through the middle of it.
Then this dashed line here is
perpendicular to that horizontal line. So
it's like we're down in a trench and
where we're looking at a layer boundary.
Maybe we've got sand above and
gravel below. Or you
might find in Reno diatomite
above and clay below, for instance.
So imagine you're looking at this
cross section and now here's the
the boundary between the two
different units- the horizontal line.
We have a wave that hits from
somewhere up above.
Up at the top of the trench we
hit the ground, and the waves propagate
along- we're tracking one
little piece of wave energy as it gets
towards the boundary. Then it hits the
boundary right there. Then it's
going to reflect. You
probably already know from optics and
physics class that it reflects at the
same angle, alpha here, that it came in at.
The incident wave's path,
called the "ray path," is at
the same angle, alpha, from the normal-
that dashed line is the normal,
perpendicular to the interface- as
the reflected wave. The reflected wave is
going to propagate out this way.
It's got the same alpha from
the normal.
That's a P-wave coming in,
reflecting to a P-wave at the same angle.
When do you get a reflection? Well,
you get a reflection when you have some
sort of interface. That means that the
properties below are not the same as the
properties above. Above we've got density1,
rho1- that's a Greek letter rho, if
you can see it- and P-velocity1.
Below we've got a different density,
rho2, and P-velocity, Vp2. It happens
also that we're going to say there's
also a difference in S-velocity,
and we have Vs1 above and Vs2 below.
So clearly the densities rho1 and rho2
are different,
the P-velocities are different, the
S-velocities are different;
and that's very normal.
When you've got two different kinds of rocks,
it's so easy to have all these
properties be different.
You might ask, "Does all
of the energy of the incident
P-wave completely reflect
from the interface?"
I already told you the surface of the Earth is
also a reflector. You saw that there
was nearly complete reflection
from that tunnel
that had air in it, buried
down inside the rock.
You can calculate the
amount of the amplitude of reflection.
The amplitude of reflection is Ar.
You have the amplitude of the
incident wave Ai, and you multiply it by
this factor here for Ar. This factor is the
difference between the media. It's rho2
times Vp2 minus rho1 times Vp1.
You might have heard the the term "seismic
impedance." The seismic impedance, or
acoustic impedance here, is the
density times the velocity.
So medium 1 here we're taking we're
taking rho1 and multiplying it by Vp1,
and that means that product
is the seismic impedance of
medium 1. And medium 2 also has a
seismic impedance, which
is rho2 times Vp2. That's the
acoustic impedance. So we're taking the
difference of the acoustic impedances.
What's on the denominator here? Well
that's the sum of the acoustic impedances.
So if rho2
was equal to rho1, and Vp1 was
equal to Vp2- you had the same
rock on both sides; same rock above as we
have
below, no difference- then these
two would subtract perfectly and there'd
be zero left on top, which means the
amplitude of the reflected
wave would be zero. That kind of makes sense.
There's no contrast in
density or velocity; there's no contrast
in impedance; there's no reflection.
Here this says that amplitude is zero.
This simple equation here is
strictly true only when the angle is
zero- the incident wave is coming
straight down along the normal
and bounces straight
back up. Then you get this simple
equation here that just involves the
acoustic impedances.
You can see the more difference
there is between the acoustic impedances,
then the stronger that reflected
wave will be. It's going
to be easy for us to record reflections
from strong impedance contrasts,
maybe where the velocity and
the density are both, say, half in the
sediment as they are in the granite
below. That's going to give us
sediment against granite-
a pretty good impedance contrast and
nice strong reflections. If you just go
from fine sand to coarse sand,
there will be some impedance
contrast, but only
3% to 5%.
In that case, we get a reflection coefficient
of maybe 2% to 4%.
That is still detectable in many
situations, and we can go after it.
But it's going to be
more difficult to find that reflection
than to find a very strong reflection
from a strong impedance contrast, like the
bottom of a sedimentary basin.
There's also an equation here that
tells you how the S-wave reflects.
The other thing you should know is that
when you have a
P-wave hitting a reflector like this then
yeah the reflected P-wave is at
exactly the same angle alpha- alpha
equals alpha. But the reflected S-wave-
and the first thing you need to
realize is that an incident P-wave-
will partly reflect, and
some of it reflects as a P-wave- but a
lot more of it in most
situations will reflect as an S-wave.
That's another thing to watch out for.
I said that the reflection
coefficient is only good for the
angle of incidence being perfectly
vertical, zero.
It's a zero angle from the normal
to the reflection path. Here's an
exploration of what happens for
some typical reflector when the
angle is not zero.
So we begin at zero with a low
here that looks like maybe a 7%
reflection coefficient,
and go along
this horizontal scale here that's the
angle of reflection, or the
alpha angle.
You started at some
low amount of reflection,
under ten percent, and it can waver
around a little bit. Then suddenly
you get to a certain angle, which here is
about 37°, and the reflection
amplitude jumps way up.
Sometimes it's very useful to try
to look at larger-angle reflections
because they can be a lot stronger, a lot
easier to record than these normal,
zero-angle reflections.
Then it will drop if you go out to
larger angles, and then gradually rise
to 1.0 [100%]. At a
reflection coefficient of 1.0, that
means that the entire incident
energy, all of it, is reflected.
None of it passes into the
medium below.
That's what these lower
plots are: they tell you the relative
amplitude of the transmission
coefficient, or the refraction
coefficient. It begins, if above is
seven percent reflection, then it might
start at ninety-three percent
refracted transmission.
Then it stays pretty steady for this
typical reflector, whatever it is, and
then when it gets to that critical angle
it drops to zero. Notice that
beyond the critical angle there is no
P-wave energy, there's no amplitude,
zero exactly, that gets
into the lower medium, that is refracted
down. That's why
there's all this energy for the
critical reflection. Now, why doesn't the
the P-wave reflection coefficient jump
up to one?
Well, there's that division of the
energy. Some of it gets reflected as
shear-wave energy, and some of it is
refracted as shear-wave energy.
All of them have the cusp right at
the critical angle. At least that
stays the same in all four plots.
So that's a bit on reflection.
Where we have a sudden change in
the rock properties, that's where we'll
have a non-zero reflection coefficient.
Now, how do those waves propagate and how
do we figure out what the velocity is?
How do the waves propagate,
and can they get disturbed by
other mechanisms than reflection?
That's encapsulated in
this statement called "Fermat's
Principle." Fermat's Principle is: "The
wave path between any two points is the
one along which the time of travel is the
least of all possible paths."
It doesn't say it's the shortest path; it says
it's the least-time path.
The time of travel is the least.
Fermat's Principle is also called:
"The principle of least time."
Let's look at a cross-section
here, much like that cross-section
with the tunnel in it. We'll
set off a source of seismic waves
at the surface,
up here and in the center.
Everywhere in this
cross-section it has the same
seismic velocity property.
We're going to think about it
in a very simple way.
Everywhere is the same velocity, so the
wave isn't delayed by any
basins or reflections or anything.
There are no changes in the
velocity property, so
the wave at 0.1 second is there,
0.2 seconds it's there; 0.3 seconds there.
We're kind of looking here at a
view of the wave fronts. And then it
gets to our receiver that we've put down
a well or something down here at a
distance and some depth.
Now, if we track back the energy that
got to that receiver, we would track it
back perpendicular to the wavefronts,
back to the source.
So we would climb up the hill
as steeply as we could and
track it back to the source. The ray path
is perpendicular to the wave front.
Now, where velocity is constant, the
wavefronts are circular and the
ray paths are straight.
Again, the wavefronts are
circular where velocity is constant-
the velocity property of rocks-
the wavefronts are circular; the ray
paths are radial and perfectly straight.
Now here's a here's a situation
where we have high velocity on the
right-hand side of the cross-section, and
low velocity on the left-hand side of
the cross section. Or if you like, you
could make this a map, as I was
showing you at the beginning, and
maybe we have a basin on the left
and bedrock on the right.
In the high-velocity part,
the ray paths are circular.
Those circles run into
the low-velocity part.
Then what happens? Well, you can see
the low-velocity part has the same circles.
But they're closer together.
It's like you know one wavelength here
in the high velocity is twice as long
at it is in the low-velocity part.
The velociy's like half; it takes twice as
much time to get anywhere on the left
side as it does on the right.
These contours are now kind of
complicated. Fermat's Principle
says the least time path- and
this is actually quite hard to
calculate- and why waves
just follow it, they just do it. It will
propagate along the interface,
just inside the high-velocity area,
and then it will light out here where it
will find that least-time path. You can
see the least time path is still
perpendicular to the
wavefronts. It turns right there,
where it refracts. We're seeing that
this part right here- these are
circular up here at the top, but at the
bottom we're looking at these
straight refractions. This is
not the shortest path from the source to
the receiver.
It's the least time path. It's
like the it's like
going out of your way to spend as
much time on the freeway as possible,
instead of the city streets.
So here we're on the
high-velocity freeway, and then we take
an exit,
that's essentially closest, and
drops right down the perpendicular
to the wavefronts, and drops down along the
least time path, to our receiver.
If I had a receiver over here, I'd
climb the wavefronts to get back to
the source. If I had a receiver over here
somewhere else, I'd climb their
wavefronts to get back to the source,
keeping the path perpendicular to
the wavefront.
That's Fermat's principle.
What we will be able to do is
predict how Fermat's Principle will work,
from this relationship that
you're familiar with from optics called
Snell's Law. The part I want to
discuss first is just where I have an
incident P-wave that's traveling at Vp1.
Here again, we're looking
at the trench wall.
We've got two media; medium number
one above; medium number two below.
Above, we have
rho1, density 1,  Vp1, Vs1. Below we've got
rho2, Vp2, Vs2. We have
an incident wave at some angle "i" or
"alpha." And there's all these other
waves- the reflected waves- the
reflected P-wave comes out at "i" as
we found out. But where does the
refraction come out? Snell's Law
allows us to calculate that.
The P-wave incident angle is alpha,
and Snell's Law says sin(alpha) over
Vp1 is equal to- OK, alpha is in the
medium Vp1- and that ratio is equal to
sin(beta) over Vp2. You may have
seen Snell's Law in the context of
optics before, where instead of
velocity you used the "index of refraction."
Here I think it will be clear that the
velocity is proportional to the inverse
of the index of refraction. That's
why for angle alpha being
in medium one, we divided by the velocity;
and angle beta here, for the P-wave
being in medium 2, we divided by the
velocity in medium 2.
Depending on what wave we're looking at,
at what different angle,
it depends on what the velocity
is in that medium for that kind of wave.
Snell's Law:
another good one to memorize,
just it's form right
in the middle here, where we're only
concerned about P-waves.
Let's look at Snell's Law a little bit
more closely.
We'll just look at it for P-waves only,
and in fact we'll forget about the
reflection for a second, and think
about the refraction only.
We're looking our trench wall; we've got
this horizontal interface- sorry the
slide wasn't straight- and we've got the
incident P-wave coming in at the angle
alpha from the normal
to the refracting
interface; and we've got a refracted
P-wave- a transmitted P-wave-
which has come through the
interface and is headed on down, but at a
different angle beta. There's the
angle beta right there.
We just apply Snell's Law,
 and above we have a Vp1; below we
have Vp2. So for the sine we want to
start with an angle
alpha above. We want to get the angle
beta below. We start alpha, we
take its sine, we multiply it by Vp2, and
divide by Vp1. We work out Snell's Law that
way, and solving for the sine of beta.
You can get that. So, if
you want to solve for beta, you take
the sine of the incident angle, you
multiply it by Vp2, you divide by Vp1.
That gives you the sine of beta.
You just take the inverse sine-
the arcsin- and that will give you the
angle beta.
But there's an effect here.
Let's consider, as we keep increasing
alpha, we get
an incident angle- notice
here we have an incident wave,
it's at alpha, and beta is larger.
So what does that mean?
Sin(alpha) was multiplied by Vp2/Vp1
and we got a larger sine, which led to
a larger angle beta.
What that meant was that Vp2
was greater than Vp1, because this
ratio here had to give more than one,
because sin(beta) is more than
sin(alpha), so Vp2 is greater than Vp1.
Let's come back down here to
this slide.
There's rho1 and V1,
and there's rho2 and
V2. We'll stop talking about Vp,
so it's just whatever kind of wave.
Assume, in this class,
it's a P-wave velocity.
We start increasing
alpha, and beta gets
larger, and eventually beta hits 90
degrees. Then what happens?
Does it make any difference,
whether we keep increasing it after
that? Well, no. So, when does that
happen? That happens when
beta is 90 degrees.
So sin(90°) is sin(alpha),
or sin(90°) is going
to be V1 over V2. So sin(90°) is
what? It's one. The sine of zero
degrees is zero but sin(90°) is one.
After putting in
that one,
we can just cross that out and we
have sin(alpha) is equal to V1 over V2.
That's the alpha at which the beta
first goes to 90 degrees- the refracted
angle first goes to 90 degrees.
We'll call that particular alpha
the "critical angle" or alpha sub c.
So if you have V1 over V2 you
can get the critical angle because the
sine of the critical angle, the sine of
alpha sub c, is equal to V1 over V2.
Now, let's suppose we had the other
case. So far, V1 is less than V2.
V2 is greater.
But what if V1 is greater?
What if V2 was less than
V1? If V2 is less than V1 in
this ratio here, and in calculating the
sine of the critical angle, the ratio
would be greater than one. Can you have a
sine of any angle that's greater than one?
No, you can't. So that means there is
NO critical angle.
There's no refraction, no matter what
you make alpha,
alpha the incident angle, you're
never going to get that refracted
angle beta to 90 degrees.
If V1 is greater, then alpha
will always be greater than beta.
That's the way it has to
work. So here there's only a
critical angle when it's higher velocity
below.
That's the only way there's a
critical angle.
So now, we know a little
bit more about how waves
are going to propagate when there are
changes in the velocity. I want to
start talking about this velocity
property and what makes
some rocks low velocity what makes other
rocks high velocity. I haven't
given you a section on elastic constants-
you may be familiar with them. Especially
the geological engineers may be familiar
with elastic constants such as the
incompressibility, which I call "k"; or the
the rigidity, which I call "mu".
These are seismologist's terms. We've
got the density rho here. The P-wave
velocity is equal to the square root
of the quantity k, which is the the
incompressibility, plus four-thirds times
the rigidity mu, and divide all that
by rho and then take the square root,
you've got the P-wave velocity.
It's clear here that
the higher the moduli, k
and mu- the higher the incompressibility,
the higher the rigidity- the higher the
P-wave velocity is going to be.
What's weird is that density rho is
on the denominator.
So what gives there? For higher
density, the denominator is going
to be larger.
That means the ratio will be less, and
the velocity will be less.
This relationship works
best for a single crystal, or
for a massive, coherent kind of material.
You could make this
relationship work for massive concrete,
that's very well cemented.
The higher the density, the lower the
velocity.
So very light concretes that are
made out of
very light aggregate
like cinders, will have higher velocities,
higher P-wave velocities; than denser
concretes. For another instance,
a block of aluminum will have a higher
velocity than a block of steel,
because the for aluminum and steel,
aluminum is lighter. Let me talk about
titanium and steel. Titanium and
steel have roughly the same k and mu,
but titanium is quite a bit lighter, just
like aluminum is a lot lighter, so
the lighter material- the lighter massive
material- will have a higher velocity.
But that doesn't work,
that doesn't work when you go to
materials like rocks;
materials that are granular, that have
pore space, that have fractures.
This works on single crystals, and we've
got to include some other factors when
we're talking about real rocks.
So what affects rock
velocities? As water saturation
goes up- as air gets replaced by water
in the pore space of a rock or soil,
the velocity will go up.
As a rock becomes more consolidated-
as we weld the grains together
with cements like calcite cement or
quartz cement, opal cement; as
consolidation increases, velocity
increases. You know that welding
those grains together is going to vastly
and hugely increase the k and mu.
You weld the grains together and
the k and mu can go up by a factor of ten.
You weld the grains together,
replace pore space by cement; you do
take the density up too- but how much
is the density going to go up?
Maybe twenty percent, thirty percent at
most. If you've got a whole lot of
pore space to fill with
cement. So the density does go up
by ten percent, whereas k and mu
you are increasing by a factor of 10?
The velocity is going to go up.
Consolidation: velocity goes up.
So a you desaturate a rock-
you lower the
water table, and the
velocity will go down.
What's the opposite of consolidation?
Well, either weathering or
fracturing. Weathering takes
velocity down, so soils typically have
lower velocities than rock.
And fracturing takes velocity down,
because you're breaking those bonds
between the grains, and
drastically lowering the k and mu.
Here's some materials that I'm sure
you're familiar with- some rocks and
other materials. I'm giving
you here the ranges of of Vp: P-wave
velocity or acoustic velocity in units of
kilometers per second [km/s].
To get kilofeet per second [kft/s],
you multiply by a
little more than three [3.28].
In U.S. industry and
commercial work, consulting
work, feet per second is the
rule. In scientific work and research,
in academia, and globally,
we're using meters.
You just have to get used to both systems. This is all in kilometers per second.
ok let's look first of the consolidated
materials. it's a little bit
of a simpler story.
So granite-
I'm talking about good solid
Sierra granite. I'm not talking about
fractured granite; I'm not talking about
faulted granite; I'm not talking about
decomposed granite. Let's talk about
solid granite: 5 to 6 km/s P-wave
velocity.
Not a huge range for
solid granite and pretty fast.
Basalt: faster still, 5.4 to 6.4 km/s,
and that's for solid basalt.
Not fractured basalt;
not a basalt flow that's
that's got columnar jointing in it.
Solid basalt.
Metamorphic rocks: a Sierran roof
pendant- a big range 3.5 to 7 km/s.
A factor of two, easy.
Sandstone and shale: these are
basin basin fill materials-
much lower than granite, much lower than
basalt. Maybe not
much lower than granite or
basalt; lower but maybe not much
at the upper end here. There
are some metamorphic rocks that are old
and buried and solid but they're still
lower velocity that then some of the
some of the younger sandstones and
shales. Big range. Limestone: even
bigger range.
What this range is telling you is
that for that very rare
solid, hard, massive limestone, like
the Redwall Limestone just back
behind the Grand Canyon, and away from
any faults.
It's as fast as
basalt; it's as fast as granite, at
6.0 km/s. But
where it's faulted or
where it's got cavities in it from
dissolution- very low velocity-  2.0 km/s.
It's hard to get that really
massive and undissolved limestone.
One more thing I want to mention: if I
say the velocity is 6.0 km/s,
you've got a lot of choices.
Can you say it's a
limestone? No. Can you say it's
metamorphics? No. You can't say it's basalt,
you can't say it's granite. 6.0 km/s,
that could be any of those four. If
I say the velocity is 2.0 km/s, well,
it's not going to be granite, it's not going to
be basalt, it's not going to be metamorphics.
It could be sandstone or shale, either one.
It could be limestone,
fractured, vuggy limestone too.
So what does that mean? That means
that the velocity is not unique.
None of these materials have a
unique velocity. When you get a
velocity value- which is what we're going
to be measuring a lot with our
seismic surveys, really getting velocity
values- it doesn't tell you which
material you have. It's not enough.
You have to look at a whole
bunch of other properties to to be sure.
It's even worse with the
unconsolidated materials. When we
do seismic surveys we talk about the
"weathered layer,"
that's the soil.
Or it could be deeper than the
soil, but it's whatever is
above the water table. So it's
0.3 to 0.9 km/s, 300 to
900 m/s. That is something that
you might just label as "soil."
0.25 to 0.6 km/s- alluvium.
We've got a lot of that around here.
That has a huge range. 0.5 km/s- I've
seen plenty of alluvium that slow, up
to 2.0 km/s, maybe even higher, 2.5 km/s
in some cases. These ranges are out
of the book, and we've seen even larger
ranges. When the alluvium gets
cemented by caliche, or calcite-cemented;
if you're from Las Vegas
and you've ever tried to dig in your
yard
you've probably encountered this
"calcrete," this "caliche." If you're lucky,
in your yard you've got softer
caliches with a velocity of only 2 km/s.
That's bad enough. But when
it gets really cemented and really thick it
can go up to 6.0 km/s, as hard as
the hardest limestone. So a titanic
factor of 3 in velocity range
there. Whatever you might call "clay"-
1.1 to 2.5 km/s: a big range, a factor of 2.
Unsaturated sand: that can be really
low in velocity and we might measure
that at certain places,
down to 200 m/s, 0.2 km/s,
up to-
unsaturated sand, really
soft, really loose- it doesn't get above
1 km/s. Saturated sand, though,
if it's partially saturated,
it can be down as low as 0.8 km/s
and as high as 2.2 km/s. You add in some
gravel and you can raise the velocities a
little bit, but maybe not
distinctly so. Saturated sand and
gravel: it's another huge range
of velocity depending on the
saturation in that case. Glacial till, where
you take that sand and gravel and you
add a bunch of clay, that can lower
the velocity. Just because it says
1.7 km/s for saturated till doesn't
mean that's all it could be, but
maybe there isn't a huge range there.
But then you compact it and it can
go up to 2.1 km/s.
It's clear that saturation has a big
effect on the velocities of
unconsolidated materials especially.
And why is that?
Here's the
velocities of some fluids. One
thing about fluids: they basically by
definition have a shear velocity of zero.
Shear velocity is
defined to be zero for any fluid.
Some common fluids that we'll encounter
in our surveys are water and air. They're both fluids.
Water has a velocity that
varies from 1.4 km/s to 1.6 km/s.
1.4 km/s if it's fresh
and hot, and 1.6 km/s if it's cold and
quite briny. Most water is
really very close to 1.5 km/s
in velocity. That's one of
those indicator velocities that lets us
figure it out. What does this
mean: if we take sand particles
of quartz - they're going to look
like each sand particle has an internal
velocity of between five and six
km/s. Then we put it
together into an unconsolidated sand,
like the surface of Sand Mountain
just east of here. If
it was totally unsaturated and very
loose, like the top
layer of Sand Mountain on a hot day,
then it's going to be at 0.2 km/s
P-wave velocity. Now, if we take that
same loose sand and we
fill the pore space with water -
so it rains on Sand Mountain and the
water is running off Sand Mountain -
then suddenly we have saturated,
completely saturated sand and
its velocity can easily be 1.5 km/s. Why
is that? Because it's the water
in the pore space that's controlling the
velocity of the sand.
It's very loose sand, and even
though the sand grains themselves are
5 km/s internally, they're
still going to rub against each other
and the overall P-wave velocity is
going to be the same as the
velocity of water.
There's a lot of water in that sand.
Same thing with air-saturated materials.
You saturate a material
with air, and you'd think the velocity
couldn't get lower than the velocity of
air itself, which is 0.32 to 0.34 km/s.
Air has the higher velocity where
the air is less dense,
such as at high elevation up here in Reno
compared to sea level.
In the experiments I've done, the
velocity of the air is not
really noticeably different from
0.33 km/s, 330 m/s.
What's remarkable is that
unsaturated sand, even though it's still
full of air, can have a lower velocity.
A class a few years ago also proved
that unsaturated, dry, very
friable clay can have a similarly
low velocity. I think we got a velocity
of 0.22 km/s in a really dry clay,
in a canal bank or
levee. So that's about the only
case where we can actually get such a low rock
velocity. Unsaturated sand in Sand
Mountain, it's still rock-
by the technical definition. That rock
velocity is less than the velocity of
air. Otherwise that velocity of air is
really a floor to the velocities that we
can have. We really don't see
velocities of hardly anything that's as
low as the velocity of air.
You take those fluids and you
you freeze them- you take water, you
freeze it, and it becomes ice. Ice is a
massive, coherent, but fairly light
crystal, and so it has a pretty high
velocity. It's pretty stiff and it's also
light and massive. So ice itself will
have a velocity like granite: 5 to 6 km/s.
Snow is a sedimentary rock, an
inorganic solid and made of the
mineral ice.
Looking at a
snowbank, like the fresh powder
snow that we're all hoping for -
it's been since December that
we've had some good powder on the slopes
here. That powder snow  is
an extremely unconsolidated,
very very loose soil, and it has a
velocity that's lower than
that of air, 0.2 km/s.
Of course, you compact the snow, as has been
happening on the slopes lately with the
freeze-thaw cycles,
and the velocity can get close
to that of solid ice, as the snow
gets closer to being solid ice.
That's that the huge range there.
Snow is a sedimentary rock or
a soil if you like.
Clastic sediments and soils
have huge velocity ranges, depending on their
physical condition. A note on the shear-
wave velocities- I express them here
in terms of the Vs/Vp ratio.
For a massive crystalline rock
the Vs/Vp ratio is about 1 over the
square root of 3, or 0.6. For sedimentary
rocks it is somewhat less, about 0.5, so the
the shear velocity will be about half
the P-velocity. For unconsolidated materials
the ratio can be 0.4, and I've seen it
as small as 1/15, which is
really remarkably low.
The shear velocity can drop off very
quickly in unconsolidated materials.
Here's a little of a famous chart for P-
velocities of sedimentary rocks
that are of interest
to oil exploration.
The horizontal axis is depth in thousands of feet.
The deepest oil wells
at least in California are 12,000 to
18,000 feet. There are
wells that are even deeper than that in
Oklahoma that produce natural gas and helium.
Most of the oil and geothermal wells
in Nevada are going to be between three
and six thousand feet deep.
This chart addresses that quite well.
On the left hand side the
velocity is given in kilofeet per second,
thousands of feet per second, so 15,000
feet per second is just under five
kilometers per second. That's the
upper range; five or six kilometers per
second is as high as these sandstones
and shales get. As you
bury sandstones and shales the
they get more lithified and
the velocity goes up. That's what
these individual curves are
showing. These summarize
hundreds of thousands of measurements
of velocity in well logs,
using sonic loggers. The other thing
that that you might notice here is that
the youngest rocks are lower in
velocity.
The oldest rocks here are higher in
velocity. If you take
depth of burial "Z", and you make it
in feet, and you take the age of the
formation in years "T",
so that's going to be in the millions,
maybe hundreds of billions.
Then here's this constant K, which
when Z is in feet and
T is in years, then it's 125.3.
You take the depth in feet,
that's going to be thousands of feet, times
millions of years, and then you take the power
of one-sixth. You start with ZT in
millions or billions but then you take
its sixth root so it goes down to
single digits again
or tens anyway, and you multiply it by
125.3 - that's K there - and you get
the P-velocity in feet per second.
This is a little rule of thumb
here that that you can easily use to try
to predict what your what your
P-velocity is going to be. You might ask
yourself: how much
reflection coefficient would I see
between a post-Eocene sandstone
and an Eocene sandstone?
They're the same death, so the Eocene
sandstone is 60 million
years old, and your post-Eocene
sandstone - maybe it's
Quaternary, only two million years old.
So you figure that in, a
two-million-year-old sandstone and maybe
you're observing it at a hundred feet
depth. so you put in Z and
you're going to get value out.
Then you put in a T
of 60 million for the Eocene sandstone.
You go through this, you're going to get
a higher velocity out. That way you can
compare the two Vp values and see whether
you'll get a reasonable reflection
coefficient. One last thing in today's
lecture is the relationship of velocity
to porosity. I've talked about
how in soils and unconsolidated
rocks the saturation makes a
difference, and how loose
and porous the rock is also makes a difference.
There's a formal relationship that
you can use called
the Wyllie time-average relationship.
You have the some kind of fluid in
the pore space, usually water or brine,
VF is the velocity of the fluid in the pore space.
VM is the velocity of the rock matrix.
We're going to try
to compose a sandstone and figure its
velocity. The sand grains themselves
have an internal velocity, to
the extent they're massive,
of five kilometers per second.
The thirty percent porosity is full of water.
Notice here that this is
called a time-average relationship
because the inverse of velocity
is really time. And notice that we're
adding up all these inverses of velocity.
We got a proportional average,
we take one over the velocity of the
fluid VF, and we
multiply that by the fluid fraction,
which is the porosity phi. Maybe that's
thirty percent. Then we take one
over the matrix velocity VM, say
that's 1/(5 km/s),
and we multiply that by
1 minus the porosity, which is
seventy percent. So multiply by 0.7, add
the two together, and that
gives us a time-average slowness.
So then we we just invert that to get
the time-average velocity.
What this is telling you is that
the higher the porosity,  the lower
the velocity. We're looking at
1 over velocity here, and the higher the
porosity the the lower the velocity.
Usually, our fluid is slower
than our matrix. 1.5 km/s for
water versus
5 km/s for sand grains. We can use this
now to see how much
porosity we have. Here's a
reciprocal velocity, microseconds per
foot that we get straight from a sonic
log. We measure it that way.
Here is porosity -
it's really hard to get a porosity
above thirty percent, you have to have
some kind of diatomaceous earth,
which we do have a lot of here in Reno and
it's still pretty close to 30% porosity.
These little triangles right there.
Here's regular
sandstone, which could easily be zero
porosity if all the grains are
perfectly cemented together.
We start at a high velocity,
low reciprocal velocity. Notice
that this scale increases to the left,
which is kinda weird but there it is.
High velocity at zero porosity and then
when we climb up in porosity -
microseconds per foot is starting at
50 here and then by the time we get to
30 percent porosity
microseconds per foot is it a hundred.
That's half the velocity, twice
the time, half the velocity.
So a big effect, especially in the materials that
we'll be surveying and measuring;
a big effect of porosity. You can see it
really counts whether you have
air or water in the pores, because
air has one fifth the P-velocity
of water. 0.33 versus 1.5 km/s.
That's plenty for this introductory seismic lecture.
Next lecture we'll continue to examine basic facts of seismic wave propagation.
