Dr. Abhishek Kumar: Welcome all to lecture
10 of Subsurface Exploration Importance and
Techniques Involved.
So in the last class, we had discussed why
geophysical methods one should use, what are
the advantages when we go for geophysical
methods, particularly related to interpolation
requirements.
Whenever we are interested to find out how
the different layers are varying, horizontally
or laterally along the study area, and then
particularly same way if you're interested
to go for deeper exploration where routine
geotechnical investigation cannot be done.
Third is the findings from geotechnical investigation
you want to extend to deeper layers, you can
go for geotechnical as well as geotechnical
investigation.
So at shallower depth you can develop some
kind of correlation between physical properties
you are obtaining from geotechnical investigation,
and similar properties you are getting from
geophysical investigation.
So then same way you will be able to understand
the geotechnical properties at deeper depth
based on geophysical test.
After that we started discussing like what
are the different geophysical methods is primarily
in use.
Considering the number of topics which we
will be covering under this module, I have
selected few geophysical investigation techniques
which are not commonly discussed.
Two amongst those are seismic reflection survey,
seismic refraction survey, and other methods
as we discussed in the last class.
Followed by in the last class, we discussed
about what is seismic reflection survey, we
also discussed like depending upon what kind
of medium is there, depending upon which method
we are using, each of these geophysical methods
target to measure some variation in the physical
properties of the medium, and we consider
like this variation is happening whenever
there's significant change in the physical
properties of the medium, actual physical
properties of the medium.
So just by correlating the physical properties
of the medium with the measurements of those
physical properties by different geophysical
methods, we can find out what are the different
kind of mediums available at different depth,
what are the physical properties available
at different depth, and so on and so forth.
So sometimes we go for shockwave, sometimes
we go for gravitational properties of the
medium, sometimes we got for magnetic properties
of the medium, sometimes we go for electrical
properties of the medium, and so on.
So based on wherever there's significant change
in the medium characteristics, against each
of those characteristics you will be able
to detect those characteristics as an indication
of possible change in soil type, geology type
and so on and so forth.
So we discussed about seismic reflection survey
in the last class.
In today's class, we will be discussing about
seismic refraction survey, what is seismic
refraction survey, how you can interpret the
data, what is happening in seismic refraction
survey, where the refraction is happening.
In addition, before starting seismic refraction
survey, I insisted last time, like depending
upon the sources, which you are using for
the development of shockwaves, your field
record will be dominated by any particular
kind of wave, whether it can be like different
kinds of waves which we discussed like P waves,
primary waves, S wave or shear waves.
So depending upon the choice of sources, which
you are using to generate shockwaves at the
sources, sometime your ground record will
be dominated by P waves, sometimes it will
be dominated by S waves.
This is more important because particularly
when you are going for artificial sources,
like you have to go for some subsurface investigation
at the site of interest where you are interested
to use some artificial source, so the choice
of artificial sources, suppose if you're interested
to go for shear velocity measurements, but
if you are going for vertical impact load,
definitely vertical impact load will be more
dominating P wave content.
So in that case, your S wave content will
be compromised.
So this understanding is very much important
considering the choice of source which is
going to be used for the generation of shockwaves,
so the selection of source is very much important.
That depends on what kind of medium characteristics
you are interested to find out.
So this understanding is particularly applicable
when you are going for seismic methods.
So in seismic refraction survey which we are
going to start today, let's discuss further
how it works.
So last time we discussed like when we go
for any kind of seismic methods, why it is
called a seismic method, because generally
during earthquakes so seismic activity, different
kinds of waves, as we discussed like P wave
or primary wave, which is causing compression,
rarefaction, then S wave which is causing
shearing in the material, depending upon the
direction in which the waves are propagating,
perpendicular, both perpendicular direction
-- with respect to the direction of wave propagation,
there will be a kind of shearing in the mediums.
So if it passing through the soils, so there
will be some shearing in the material, perpendicular
to the ground level if it is horizontal, and
then another one be perpendicular again in
horizontal plain, but it will be perpendicular
to the direction of wave propagation.
So both waves, it is causing some kind of
shearing, some kind of relative motion between
he particles as a result of which shear stresses
will be developing in the material, and then
considering the resistance offered by the
material, which we call shear modular or shear
strength of the material, that will govern
how quickly that kind of wave will pass through
that particular medium.
If it is able to provide more resistance,
your S wave will be able to pass more quickly.
And then we discussed about like when your
body waves, collectively these are called
as body waves, because these are mostly contained
within the layer of the Earth.
So I was discussing why these are called as
seismic waves, because during an earthquake
whenever we put ground motion recording sensors,
so it will be detecting different kinds of
waves, particularly P waves, S waves, then
P waves sometimes.
Again, there will be when this P wave interacts
at the interface, there will be another component
of P wave, so that will be called PP wave,
SS wave, SPS and so on.
And then second thing, you will be having
your Raleigh waves and Love Wave.
So these are the permanent kinds of waves
which are generally recorded at any ground
motion recording instrument depending upon
the relative position of your source or epicenter,
because it is happening because of seismic
activity, the waves generally classified as
seismic waves or seismic wavs.
So the first two are called as body waves,
the second are called as surface waves.
So depending upon relative distance between
the source and your receivers, at times your
record is dominated by body waves and sometimes
it is dominated by surface waves as well,
both are possible.
So when we discussed about seismic reflection
survey, we discussed like there will be some
kind of shockwaves, which are generated by
means of a source.
The source can be an impact load, it can be
an explosion, like any kind of -- any source
which is able to trigger some kind of vibrations
in the medium, of course depending upon what
is the range of frequency content you are
interested in, those vibrations will be more
interesting, and second thing the vibration
you're generating, it should have significant
amplitude, so that it can be detected at wide
range of -- I mean the receivers which are
kept over varying range of distances.
So it can be impact load, it can be explosion,
it can be traffic load, it can be machine
operation, and so no and so forth.
So explosion can be related to this particular
method.
I am going for some kind of exploration or
sometimes when you are doing similar tests
very near to your stone queries, there also
people are using a lot of blasting, so that
can also be detected and can be used as source
of vibration.
So this is when we discuss about seismic reflection
survey.
In case of seismic refraction survey also,
though the objective is to detect the time
of arrival of refracted waves as the name
suggest, but more or less the setup will remains
same.
So there will be a source as you can see here,
so there will be a source, there will be receiver,
and generally when we are going for seismic
refraction survey, we don't go for single
receiver, we go for an array of receivers,
because the waves which are particular coming
from deeper layers, mostly will be detected
by receivers on some minimal distance.
So you can call as receiver 1, receiver 2,
receiver 3, 4 and so on, n number of receivers.
So again, whenever we generated some kind
of vibrations at the source, what will happen,
there will be wave path, the direction in
which the wave is traveling, and then there
will be wave front.
So the size of the wave front will determine
like what is the area in which, because of
the propagation of a particular wave, the
disturbance or any kind of particle movement
is happening.
Now same movement as it moves deeper and deeper,
you can see it will be covering larger area
and so on.
So if you only consider these wave fronts,
it will continue for ground distances also.
The only thing like as you are going away
from the source, the amplitude of those waves
will be significant less, amplitude will reduce.
Another thing which comes into mind like here
we're only targeting for waves, which are
generated from the sources, but what will
happen when these waves will interact, like
particularly this wave front.
Then it reaches this interface, interface
means too much contrast in physical properties.
To give you an example like VP1, VP2.
The primary wave velocity of the resistance
offered by the material in layer 1 and the
material in layer 2.
That will decide how much will be the VP1
and VP2 value.
So this is like incident wave and depending
upon the angle of incidence, this wave will
be equally reflected.
So this is called as reflected wave.
So up till this we had discussed last time
when we were discussing about reflected wave,
and same wave there will be another, I mean
other frequency -- these wave fronts which
will be reaching later state so you can put
another receiver here which will be detecting.
You can call it as R0, because initially you
had given from R1 onwards.
So again, another wave front will be reaching
some other distance, which will be detected
maybe by this receiver and so on an and so
forth.
So because there will be -- like because of
this wave, there will be wave fronts in all
the direction.
So you will be actually continuously recording
these kinds of reflected wave all along the
receiver lengths.
Not only the receiver where you have put the
waves but only in order to analyze you are
putting the receiver at known distance.
So you will be able to interpret based on
the time of arrival of direct and reflected
wave, what will be thickness and velocities
of different medium.
Now in addition to this, right now we are
targeting for reflected wave, but in addition
to reflection there will be -- because there
is change in 
medium characteristics, so what will happen,
in addition to this reflection, you can call
it as like when the wave reaches, some energy
will start traveling toward the surface and
some energy will be traveling downward.
So what will happen, if you draw some, this
thing, normal, so depending upon whether the
medium characteristic are increasing, like
medium is getting more and more stiffer with
respect to you shockwave characteristics or
shockwave stresses, the medium is getting
more and more stiff, what will happen, once
the wave reaches to the bottom direction,
like the second layer, it will start deflecting
away from the normal.
So if this is your i1, this will be i2.
So if V2 is greater than VP1, that means indication
like medium at deeper layer is stiffer.
That will also indicate the value of i1 -- i2
will be greater than i1, and how much it will
be greater than -- okay, so will be called
as the refracted wave, which will actually
travel in another medium with what velocity,
so that will be corresponding to VP2 velocity,
because this is now -- I mean once it crosses
the interface, once the wave crosses the interface,
it will go to the deeper medium, which is
offering more resistance.
As a result of which the wave propagation
velocity will be significantly higher and
because of this contrast between the medium
characteristics, there will be some reflection
which is from the interface start again traveling
towards the surface and getting detected by
the receiver.
Second will be the refracted wave, so depending
upon if the medium is getting denser, the
refracted wave will be moving away from the
normal.
Okay, so this angle i2 that is angle of refracted
wave I can call it as, that will be function
of three parameters.
First i that is angle of incidence, ic I can
call it as - okay let it be i, because ic
will be very specific - angle of incident
wave, which is undergoing reflection and refraction,
VP1 and VP2 value.
So depending upon the value of VP1, VP2 and
i, the direction of VP if I draw it here again.
So if you consider the value of VP1 and VP2
to be same for different cases which I am
going to discuss now.
So this is i1 that is incident wave.
Another incident wave at the same location
if I am considering, which is significantly
like this where it is i2.
So if i1 is greater than i2, what will happen,
considering same value -- so your wave will
start traveling away from the -- I mean the
value of -- like corresponding to i1 if this
was ir1, as the value of ir2 increases, so
this value will also increase.
So this will become ir1.
It will be like the angle of refraction wave,
because of first incident wave.
That will become ir2, because the angle is
decreasing here, there also the angle of inclination
of refracted wave also decrease.
So as per Snell's law sin ii incident over
V1, rather than VP1, I am calling it as V1,
so VP1, I am calling it as V1, VP2, I am calling
it as V2, so the sin i1 over this will be
equal to sin of ir, so this is angle of inclination
with respect to normal for incident wave and
this is the angle of inclination of refraction
wave with respect to normal.
The same way if you consider multiple cases,
like each incident wave at different, different
angles because finally the angle of inclination,
as you are considering the case, as you move
away from the -- like this is your interface.
What I am trying to say here like some refracted
wave from the source, some incident wave at
this location will reach maybe at angle i1,
but some wave near this location will reach
an angle which is lesser than i1.
So the same thing I am going to show here
-- I mean because the refraction is happening
all along the interface, because the medium
contrast property is existing all along the
interface.
So even the refraction will be happening at
the interface.
So depending upon this, it will be like this,
depending upon this, it might be like this.
This is deciding how much will be your angle
of refracted wave depending upon the angle
of incident wave, keeping VP1 and VP2 as same
value.
So this is the same thing.
At critical angle what will happen, at critical
angle, I am calling it ic of incident wave,
what will happen, your angle of refracted
wave 
will be 90 degree to the vertical.
In order to see it further, let's go to next
slide.
So what I want to say here, it is like this.
So this is your interface.
This is your V1, this is your V2.
Let's consider maybe some more cases here.
So this is like V3.
Now overall, if I am only targeting for refracted
waves.
I am putting a sensor here, R1, R2, this is
like you can call it sensors.
Sensors which are used for seismic refraction
or even for ground motion records at times
you can use.
At times you can go for micro tremor records
also for detecting these.
So when you are going for geotechnical investigation
-- geophysical investigation we generally
for geophones.
Some of you might have heard of geophones.
You put those geophones at regular interval.
So what will happen here.
I am putting geophones at regular interval
for my ease.
Now what will happen.
So there was a wave, which is -- I mean there
will be plenty of waves which are reaching
here like this.
All are incident waves.
Again, this is having some angle.
So all are like -- okay some incident angle
will be there.
This is with respect to vertical, yes.
So if I number here 1, 2, 3, 4, 5, 6 and consider
like the angle of inclination are i1, i2,
i3, i4, i5, i6, depending upon V1, V2 and
there might be an angle which might be called
as critical angle.
So suppose like i5 is critical angle, so as
a result of waves, the refracted wave because
of this critical angle will travel along this
interface.
I am showing you here a little thick link,
so that you don't get confused with the interface.
So this is like refracted wave due to this
fifth incident wave.
So this is like refracted wave, not it is
traveling surface again because it is traveling
at the surface which is having too much contrast.
What will happen?
Again, some component of this will again start
traveling back to the surface depending upon
-- again this will be like critical angle
i5 or maybe other angle.
So I mean it will be traveling at different,
different these things.
So some might be -- no this will not be there.
So this is at critical angle, it may be detected
here.
Some might be detected at the same critical
angle at receiver 1, some might be detected
at this critical angle after certain distance.
So again, this will be called as ic and so
on.
So as you keep more and more number of receivers,
each of these you can put more number of receivers
also here, so that this refracted wave will
be detected more number of receivers, so I
can call it as R2, R3; you can call these
as R4, R5, R6, R7
Now what will happen to other waves which
were not ic or which are not at critical angle?
First of all, we should write.
So this angle ir becomes 90 degree.
Now if you put this as 90 degree, what will
happen.
Your sin ic that is critical divided by V1
will be equal to sin 90/V2 or sin ic = V1/V2.
So that's how you can get to know -- that's
why I told you depending upon the angle of
incident which is you can say here, it is
again a function of -- so critical angle will
be function of the ratio of primary velocities
of both the mediums.
Now there are other waves also like i4 is
there, i3 is there, what will happen, because
the critical angle is less than this, so those
will not be -- I mean not refraction, those
waves will not travel along the interface,
but will travel at slightly lesser inclination,
like this.
So depending upon how much is this inclination,
this angle of inclination will also keep on
-- like depending upon how much is this angle
of inclination, this angle of inclination
also keep on reducing, so that this ratio
is maintained.
So this another wave, which though refracted
but is not traveling at the -- like at V4
-- this is another waves, though refracted
but not at ic, what will happen.
This wave again will reach this interface.
So this interface, if this is your angle i2,
ii should say here.
So I can take i2i which is angle of incidents
at second interface.
So same process which was happening at this
interface will now happen at this interface.
So in order to determine this value of -- in
order to have ii2 to be equal to i critical
at second interface, again, sin ic2 should
be a ratio of V2/V3.
So if this the case, again, there will be
some kind of refracted wave which will travel
at the interface, refracted wave.
Again, those refracted waves will have some
component.
This might be detected at the same receiver,
which you had put there.
So again, this is like ic2.
So another refracted wave, which is not coming
from the first interface, but it coming from
the second interface will also be getting
detected at the receiver, depending upon the
relative position of those receivers with
respect to different layer thicknesses from
which refraction is happening.
It may be possible the refracted wave from
deeper layer may get detected by receivers
which are kept closer to the source, and if
the depth is more, it might be possible that
the refracted wave before it reaches the ground
surface, it may not be detected by the receiver,
which are kept very close to the source.
But overall it will be like -- so you will
be having refracted wave from first interface.
You will be having refracted wave from second
interface and so on and so forth.
Like this one, if you consider one, if you
consider one, it is not happening at 
critical angle for this interface.
So this will again start traveling, so it
will again start traveling.
So what is happening?
Overall, I can say like because shockwaves
will have reflection at interface after which
wave will travel upward or towards ground
surface and detected by receiver.
In addition, there will be a refraction which
is happening.
So there will be like two components.
One after refraction waves traveling downward,
because like angle of incidents was not equal
to the critical angle of interface, angle
of incident of any interface, and was not
equal to the critical angle at that interface.
So they will start traveling downward and
getting refracted at later interfaces.
The next one is, again, there will be refracted
wave at critical angle, which will be refracted.
I mean travel along the interface and then
upward 
and getting detected at geophones.
So overall, all the geophones will detect.
Now let's see if you know like this is your
source.
This is some receiver, which is actually detecting
your -- okay before going to this, I would
like to highlight like seismic refraction
limitation is, I can highlight here you understood.
Like V2 value should be greater than V1 value,
otherwise, though refraction will be there,
but the refracted wave will never reach to
the surface and thus will never be getting
detected by the receiver.
So that's why this is limitation.
This V2 value should be greater than otherwise
refracted wave will not be detected at the
receiver.
So if you're not detected, if you're not able
to detect it, you will not be able to determine
or quantify the physical properties, you will
not be able to determine the thickness, so
no thickness and subsoil properties.
This has to be kept in mind, otherwise seismic
refracted method will not work.
So this is the limitation I would like to
here.
That's why I have written simply here.
Now I am considering one wave, I am considering
a case where the wave is there, which is traveling
at critical angle, traveling along the interface,
and then getting detected at the receiver
1.
So if I number like A, B, C, D, you consider
the thickness of the medium, the layer is
H, this is V2, this is V1 and you have kept
both the source and the receive at the known
distance L. Now the time of arrival, so again
there will be two waves, one is called as
direct wave, which will be td, so that will
be equal to AB/V1 that is L/V1.
Then for time of arrival of refracted wave
that is trfr can be quantified, can be estimated
as trfr = AB in which the wave is traveling
with V1 + BC in which the wave is traveling
with V2 + CD in which the wave is traveling
again with V1.
Now we know the value of AB will be equal
to value of CD considering the interface is
horizontal, so you can call it as 2AB/V1 +
BC/V2.
Now again, we consider sin ic = V1/V2.
In that case, AB will be equal to how much,
AB = H/cos ic and BC = L-2H tan ic, like this
is the thing.
This is ic, this is H, so this will be equal
to AB, which will be equal to H/cos ic, and
this will be equal to L-2H tan ic.
Okay, so this is like this.
Again, I can put it here, 2AB that is H/V1
cos ic + BC = l-2H tan ic/V2.
Okay, so just take L as common here, I can
call it as L/V2 + 2H [1/V1 cos ic - tan ic/V2].
Okay, so that's how if you solve it, you will
be able to understand here, L/V2 + 2H that
will be equal to V2.
So again, I wanted to highlight here, if sin
ic = V1/V2, cos ic = vV22 - V12/V2.
So I can put it here and so on will be about
tan ic.
So that will be equal to V2 - V1 sin ic/V1
V2 cos ic.
So I can put the value of sin ic and cos ic,
I will get here L/V2 + 2H [V2 - V1 V1/V2/V1
V2 vV22 - V12/V2].
So this get cancelled.
You'll get here L/V2 + 2H [V22 - V12/V1 V2
vV22 - V12], which can further be solved as
L/V2 + 2H [(vV22 - V12)2/V1 V2 vV22 - V12],
so this gets cancelled.
You'll get L/V2 = 2H [vV22 - V12/V1 V2].
Okay, now this is again referring to trfr
that is time of arrival of refracted wave.
Now if again at critical distance just like
critical angle, at critical distance we call
at dc, what will happen, the direct wave which
is coming along the surface as well as refracted
wave which is coming from deeper layers, first
layer or first interface will reach the receiver
simultaneously.
That is time of arrival of direct wave will
be equal to time of arrival of refracted wave.
Now the time of arrival of direct wave we
know it will be equal to how much, L/V1.
So the equation which we have calculated here,
we can call it ass number 2.
So equate equation 1 and 2, equations 1 and
2 should be equal 
at L = dc.
So put that, so you will get dc/V1 = dc/V2
+ 2H.
That further equation can be solved at as
v1/V12 - 1/V22.
So you can take this dc [1/V1 - 1/V2] = 2H
v1/V12 - 1/V22.
Okay, so that's how you can get the value
of -- if you solve this equation further,
you will be get the value of dc that is 2H
= dc (vV2 - V1)/vV2 - V1 vV2 + V1, so that
will give you the value as dc/2 vV2 - V1/V2
+ V1, that is the value of H. So 
this is -- you can call this is where H is
thickness of first layer.
Same way you can determine the approach dimension,
but you will be able to determine the value
of second layer, third layer, and so on and
forth.
So the value of dc, you can -- how you get
the value of dc, you will be able to get the
value of dc based on your distance time, because
I mentioned like when you go for field recording,
this derivation I showed for one wave front,
one wave -- if you put more number of receivers,
so each of those receivers will be detecting
different wave coming from different interface,
but because the value of V1 and V2 are constant
for each wave, so overall the wave which is
coming from first interface will give you
the characteristics of first interface whether
it is detected by 1, 2, and more; and second
-- I mean similarly, the waves which are refracted
and coming from second interface will give
you the value of V2 whether it is from R1,
R2 or overall from R1, R2 and so on.
So this is -- now one question which comes
to our mind is once we have the number of
receivers which are detecting the wave, how
you will be distinguish whether the wave detected
by the receiver will be a direct wave, reflected
wave or a refracted wave.
So in order to understand that, we have to
understand like in terms of physical parameters
and the variation of these parameters, you
can call it as direct wave, time of arrival
that is td, that will be called as L/V1.
So it is simply as you keep on increasing
the distance, it will be linearly dependent.
Then you have reflected wave.
So if you remember last time we have retained
also trfr, that is equal to v4H2 + L2/V1,
third one is refracted wave, which we discussed
today, that will be trfr = L/V2 with the same
thing.
Once you know the value of H, you put it back
so you will get the value of rfr for any distance.
I mean if your receiver is at any distance
other than critical distance.
So you will get the value like this, v1/V12
- 1/V22.
So you can see here the time of arrival of
direct wave.
Reflected wave and refracted wave are different.
So if you put more number of receivers over
a range of distance, and this is time, what
you are going to get is, it will be like direct
wave, based on the time of arrival, which
is picked up by the geophone you can get,
like this will be direct wave, then there
will be reflected wave, you can call it as
direct wave.
After certain distance, reflected wave and
direct wave will reach at same time.
At the same time, this is reflected wave,
and then you will be having, completed different
way you will be having refracted wave.
It is observed like after certain distance,
you have refracted wave, because some component
of refracted wave is traveling through stiffer
medium.
So refracted wave will reach like at this
distance, the refracted wave will reach much
earlier than your direct wave.
Again, you see here like this is the location
at which direct wave and refracted wave both
are reaching at same time.
So this distance will be called as dc, you
can get it if you know from distance time
curve obtained from number of geophones or
same geophones kept over different distances
and excited for same source.
So that's how you can get the value of dc.
This will give you the value of 1/V1, this
is going to give you a value of 1/V2, and
so when more number of sources are there,
you will get more and more like this.
This will be 1/V3 and so on.
Why, I told you, because if you remember the
equation, dc/2 vV2 - V1/V2 + V1, so the value
of dc you can get from time distance curve
where refracted and direct wave are meeting,
and one value you can get as the inverse of
the slope of, first phase of field record
which is coming from direct wave, starting
from origin, V2 you can get from the inverse
of the slope of second wave, that is refracted
wave.
So once you know the value of V1, V2 and dc
from you field record, that's how you can
put in this equation and get the value of
your thickness.
Now based on this, let's -- so you can got
for seismic array or you for geophone array
or even you can go for microtremor records
once you are interested to find out for subsoil
exploration 
using shockwaves.
You can got with any of this.
Now let's see one example before going into
detail.
I mentioned here, so that you can see here
how the seismic refraction survey, we can
do the interpretation.
So the problem is like a seismic refraction
survey yields following times of arrival of
P waves, so you have put the sensors at different,
different locations that you can understand
from first column, and corresponding to each
of the sensors, the time of arrival of P waves
is detected.
Based on this record, you are interested to
find out the thickness and P wave velocities
of the medium.
Now based on this time distance first of all,
in order to interpret where is the direct
wave, where is the refracted wave, first of
all we have to develop the distance time curve
here.
So you see that I have just taken those values,
you can simply take those values.
The value of time is giving in milliseconds,
so be careful while giving the final values,
and then distance is given in meters.
So you can simply put those values in Excel
and you can get the value of distance time
curve.
Now the first, as I mentioned here, because
it is starting from origin, this is going
to give you the value of 1/V1, this is going
to give you the value of 1/V2.
You know the values, you can direct get from
the Excel sheet.
Another thing you will be able to understand
here, this is the value of dc, which is if
I remember, I got the value corresponding
to 30-meter in this particular.
You yourself can determine the value.
Like in this case, the time of this critical
distance is matching with the geophone location.
It may be possible like there is no geophone,
but based on the intersection of these two
slopes, you will be able to determine the
value of dc.
So if I put here, if I know the value -- so
based on this, I've got to know the value
of dc, which is coming out as 30 meter.
The value of V1 from this, I have estimated
that is coming out to be 434.78 meter.
You can put it in Excel, you can determine
how much is the value of V1 meter per second.
When you converting, just make sure like this
is given in milliseconds, so you have to convert
it into seconds in order to determine the
value of V1.
Similarly, the value of V2, which is the inverse
of the slope of second part of the curve,
which is given as 3529.41 meter per second.
Now you know the value of dc, you know the
value of V1 and V2, you can determine simply
how much will be the thickness of this layer,
that is layer 1, that is called as dc/2 vV2
- V1/V2 + V1.
So I am just putting the values here 30/2
times v{(3529.41 - 434.78)/(3529.41 + 434.78)}.
If you put 
those 
values here, if you solve it, you will be
able to understand the value is 13.25 meter.
So the stratification is like this and something.
So this is like soil 1, having V1 or VP1 value
equals to 434.78 meter per second, and this
is soil 2 having VP2 or primary wave velocity
as 3529.41 meter per second, and this is your
layer thickness, which you have estimated
as 13.25 meter.
There was a source here and there was a geophone
which is kept at 30 meter, which is at critical
distance I am telling.
This is varying, so you need not put it, I
am just going to give you what is the overall
geometry of the site as obtained from seismic
refraction survey.
So same way, we can go for incline method,
I mean the base bedrock or the interface which
is inclined.
Same way we can got for interpretation with
respect to number of layers, but only thing
which has to be mentioned here, the graph
which I have shown here, it is showing very
simplest case where you are having the refraction
coming from the first interface, but if you
put number of interfaces like from between
soil layer 2, and 3, 3 and 4, and so on, there
will be more sources for refraction, there
will be -- similarly those sources attach
sources for reflection.
Same way if you have some local pockets of
denser material, that will again induce some
more refraction and reflection form within
the layers, which will be also getting detected
at the same receivers.
Another thing, if you have another source
of vibration rather than this source like
some machine operation is happening just in
the region, because of which some shocks are
generating and getting detected by the geophone,
that will add more and more complexity to
your field record.
So generally, if you consider any typical
field record, it may not look very streamlined
like this, the field record I have shown here.
So you have to have more and more expertise
whenever you are going for interpretation
of field record for seismic methods.
But I hope, I tried, though it is giving you
simplest case where you will be distinguish
very clearly between direct wave and reflected
or refracted wave.
That will give you an understanding about
how this method works, how this method is
able to give you the subsurface investigation
or subsurface properties, because this is
objective.
When we go for subsurface investigation, we
have to find out different material.
And depending upon, again, these properties,
you will be able to determine whether this
soil is soft, whether this soil is stiff,
whether the soil is of the order of limestone
or granite like this.
Initially, I had given you some ranges of
VP value of for different materials, so comparing
those values with this value will also get
an idea what kind of soil medium is there
existing below the ground surface, which you
have probably explored based on seismic reflection
survey.
So thank you, thank you so much.
