5. List of Figures
2.1 Different types of seismic waves: Body and surface waves . . . . . . . . . . . 7
2.2 Snell’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1 Different types of multiple reflection . . . . . . . . . . . . . . . . . . . . . . 10
4.1 Different types of multiple reflection . . . . . . . . . . . . . . . . . . . . . . 13
5.1 Travel Time graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5.2 An earth model showing velocity, thickness and raypath . . . . . . . . . . . . 17
5.3 A graph showing the travel-time curve of the 4-layer model in Figure 5.2 . . . 18
5.4 Corrected gather of hyperbolas in Figure 5.3. It can thus be seen that appro-
priate velocities have been applied to correct the NMO effect on the data . . . 19
5.5 (a) CMP gather containing single event with a moveout velocity of 800m/s (b)
NMO corrected gather using the appropriate moveout velocity(500m/s); (c)
overcorrection because a low velocity was used (480m/s); (d) undercorrection
because a high velocity was used (540m/s). . . . . . . . . . . . . . . . . . . 20
6.1 A three-layer model of varying depth Z1,Z2,Z3 . . . . . . . . . . . . . . . . 25
6.2 Root mean square velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.3 Interval velocity curve using Dix’s equation . . . . . . . . . . . . . . . . . . 27
6.4 A three layer model showing variation in thickness . . . . . . . . . . . . . . 28
6.5 Average velocity curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.6 Three different seismic velocities: interval, average and rms velocities . . . . . 30
6.7 NMO magnitude a function of offset and depth for a 10-layer model . . . . . 31
6.8 NMO magnitude at near offset . . . . . . . . . . . . . . . . . . . . . . . . . 32
6.9 NMO magnitude at mid offset . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.10 NMO magnitude at far offset . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6.11 NMO corrected gather overlain with mute curve followingg the chosen NMO
magnitude threshold of 0.0099s . . . . . . . . . . . . . . . . . . . . . . . . . 35
6.12 Muted-NMO-corrected gather . . . . . . . . . . . . . . . . . . . . . . . . . 36
iv
6. List of Tables
5.1 Computed zero offset time, t0 from given velocity, within a range of offset
x and reflector depths Z . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.2 Computed zero offset time, t0 using model parameters of Figure 5.2; t0n
represents zero offset time of nth layer which is the time other time values
at different offset will be corrected to . . . . . . . . . . . . . . . . . . . . 15
v
7. List of Tables
Introduction
This report of my three months industrial training at CGG(Nigeria) from 10th of July
to October 2012. The title of my project is Normal Moveout (NMO) and its aim is to
...
1
8. 1 INTRODUCTION TO
SEISMOLOGY
1.1 Reflection Seismology
Seismology is the study of acoustic waves in the earth. Reflection seismology is a subset
of controlled seismology. This is the primary method oil industry uses to find mineral
resources.
Reflection seismology is a technique for imaging the geological structure beneath the
earth’s surface using sound energy. An acoustic energy source at the surface transmits
an acoustic signal to the earth, which reflects some of the energy back towards the
surface of the geological interface.
1.2 Seismic Data Acquisition
1.2.1 Seismic Sources
The sources are classified as follows
• Explosive sources- dynamite
• Non-explosive sources vibroseis, sources using gas: air gun, water gun(marine
sources).
1.2.2 Geophones
They are connected in arrays. They convert physical movement of the earth caused by
the seismic wave into an electrical signal. Each array records a single, separate trace.
1.2.3 Hydrophones
They convert pressure changes into electrical signals.
2
9. Processing
1.2.4 Seismic Recording Systems
An example is a seismograph.
1.3 Processing
Processing involves reducing lateral offset to zero offset. The greater the two way time
the deeper the reflecting interface. A normal seismic section are displayed as two way
time and not depth.
1.3.1 Objective of seismic data processing
• Improvement of signal to noise ratio; signals are desired energy during seismic
recording while noise are unwanted energy.
• For accuracy and resolution; accuracy of reflected time and highest possible reso-
lution.
1.3.2 Problems multiples can cause
Multiples can present many pitfalls for the interpreter and cause problems in seismic
data interpretation. This is because the feature which multiples create may not reflect
the true approximation of the geology of a structure of an area. For instance, multiples
can enhance geologic features such as small anticlines, so that they appear larger than
what they truly are. This attractive to the oil and gas finder, but can lead to false
conclusions concerning the location and amount of pay.
1.3.3 How can multiples be attenuated
There are several methods for attenuating multiple reflections on seismic section. One
of the most common methods of attenuating multiples is by using:
1.3.4 Basic processing
Processing falls into three basic categories:
• Multiplication processes (scaling/filtering)
• Summation processes (stack)
• Imaging processes (migration/dip moveout).
3
10. 2 REFLECTION, REFRACTION,
BODY WAVES AND SURFACE
WAVES
2.1 Reflection
Seismic waves are mechanical perturbations that travel in the earth at a speed governed
by the acoustic impedance of the medium in which they are traveling.
Z = ρv (2.1)
where Z is the acoustic impedance, and ρ is the density and v is the wave velocity in
the medium.
When a seismic wave encounters an interface between two materials with different acous-
tic impedances, some of the wave energy will reflect off the interface and some will refract
through the interface. The process of the wave reflecting off the interface is known as
Reflection
In essence, the seismic reflection technique consists of generating seismic waves and
measuring the time taken for the waves to travel from the source to various receivers,
and the velocity of the seismic waves in order to build up an image of the subsurface.
2.1.1 Multiple reflection
Multiple reflection: An event on the seismic record that has incurred more than one
reflection is called a multiple. Multiples can be either short path or long-path depending
on whether they interfere with primary reflections or not.
2.1.2 Interpretation of reflection
The time it takes for a reflection from a particular boundary to arrive at the geophone is
called the travel time. If the seismic wave velocity in the rock is known, then the travel
time may be used to estimate the depth of the reflector. For a simple vertical traveling
wave, travel time t
t =
2d
v
(2.2)
4
11. Surface Waves
where d is the depth of the reflector and v is the velocity.
2.1.3 What is an event
A reflection event can be defined as a series of apparently related reflections on several
seismograph. By correlating events, one can create an estimated cross-section of the
geologic structure that generated that reflection.
In addition, there are a number of other seismic responses detected by receivers and they
are either unwanted or unneeded.
2.2 Refraction
When an incident ray impinges upon an interface at a certain critical angle (.c) the
wave is not transmitted downwards as the refraction angle is 90. The wave therefore
propagates itself along the interface with the speed of the lower medium. Head waves are
generated that travel up to the surface with the same critical angle. This phenomenon
is known as Refraction.
2.3 Body Waves
These are the type of waves that can propagate through the internal volume of an elastic
solid and may be of two types:
2.3.1 Compressional or p-waves or longitudinal waves
P-waves propagates by compressional and dilational uniaxial strain in the direction of
the wave travel. Particle motion associated with the passage of a compressional wave
involves oscillation, about a fixed point in the direction of wave propagation.
2.3.2 Shear or transverse or secondary waves
S-waves propagate by a pure shear strain in a direction perpendicular to the direction
of wave travel. If particles oscillation are confined to a plane, the shear wave is said to
be plane-polarized.
2.4 Surface Waves
These are waves that can only propagate along the boundary of the solid.
5
12. Elements of Seismic survey
2.4.1 Rayleigh waves
This wave propagates along a free surface, or along the boundary between two dissimilar
solid media. Rayleigh wave involves a shear strain, therefore it is restricted to solid
media. The waves decreases exponentially with distance below the surface. They have
a propagation velocity lower than that of s-waves and in a homogeneous half space they
will be non-dispersive.
2.4.2 Love waves
Love waves are polarized shear waves with a particle motion parallel to the free surface
and perpendicular to the direction of wave propagation. The velocity of love waves is
intermediate between the shear wave velocity of the surface layer and that of deeper
layers. Love waves are inherently dispersive.
Other type of wave is:
2.4.3 Air waves
This is an example of a coherent noise that travels directly from the source to the
receiver. It is easily recognizable because it travels at a speed of about 340m/s. See
Figure 2.1.
2.5 Elements of Seismic survey
The fundamental physical principles which govern seismic survey are:
• Snell’s law
• Fermat’s principle.
2.5.1 Snell’s law
This law states that the ratio of the sine of angle of incidence to the sine of angle of
reflection is a constant. See Figure 2.2
Snell’s law of reflection applies equally to the optical and seismic cases. Snell defined
the ray parameter, p.
p =
sini
v
(2.3)
where i is the angle of inclination and v= velocity
The generalized form of Snell’s law states that, along any one ray, the ray parameter
remains a constant.
6
13. Elements of Seismic survey
Figure 2.1: Different types of seismic waves: Body and surface waves
2.5.2 Fermat’s law
A ray incident upon a reflective surface will be reflected at an angle to the incident angle.
Both angles are typically measured with respect to the normal to the surface.
The law of reflection θi = θr can be derived from Fermat’s law. Fermat’s law or the
principle of least time is the principle that can be traversed in the least time. In
other words, a wave travels through the path in which it can reach the destination in
the least time.
7
15. 3 TRAVEL TIME CURVES
3.1 Basic Conception
If a number of receivers are positioned at a certain distance away from a source, the wave
front will arrive at the closest to the source and later to subsequent stations. Connecting
the same point on the seismograph leads to a travel-time curve. Travel- time curve for
a layer over a half space for a layer over a half space, there are three types of waves to
consider:
• Direct waves: the travel time t for this kind of wave is easy to compute as
t =
x
c
(3.1)
where x is the distance traveled and c is the speed of sound in air. This means
that the travel time is a straight line.
• Reflected waves: the travel time t for a reflected wave is calculated from two
parts. The first part is the travel time from the surface to layer and the second
is the travel time from the layer back to the surface. This is called the two-way
travel time and it is given as:
t(x) = t2
0 +
x2
v2
(3.2)
• Multiple layers: when there are multiple layer, each layer generates their own
reflected waves and head waves.
3.2 What are Multiples?
Multiple reflections are seismic energy or any event in seismic data that has incurred
more than one reflection on its travel path. Multiples are multiplicative events seen
in seismic sections. They are produced in the data gathering process when the signal
does not take a direct path from the source to the geologic event and finally back to
the receiver on the surface, see Figure 3.1. This causes the signal to arrive back at the
receiver at an erroneous time, which, in turn , causes false result and can result in the
data misinterpretation.
9
16. What are Multiples?
3.2.1 Different types of Multiples
There are different types of multiples depending on their time delay from the primary
events with which they are associated. Multiples are characterized as short-path, imply-
ing that they interfere with the primary reflection, or long path, where they appear as
seperate events. Example of short path multiple include Ghosts, near surface multiples,
(intra-bed) and peg-leg while examples of long path multiples include simple multiple
and inter-formational (inter-bed) multiples, see Figure 3.1.
Figure 3.1: Different types of multiple reflection
10
17. What are Multiples?
3.2.2 Problems multiples can cause
Multiples can present many pitfalls for the interpreter and cause problems in seismic
data interpretation. This is because the feature which multiples create may not reflect
the true approximation of the geology of a structure of an area. For instance, multiples
can enhance geologic features such as small anticlines, so that they appear larger than
what they truly are. This attractive to the oil and gas finder, but can lead to false
conclusions concerning the location and amount of pay.
3.2.3 How can multiples be attenuated
There are several methods for attenuating multiple reflections on seismic section. One
of the most common methods of attenuating multiples is by using:
• Stacking Method: this method is referred to as the commondepth point stacking
during data processing. Multiples spend most of their time in shallower sections,
bouncing off the interface at the same travel time. Thus, multiples have smaller
stacking velocities and they do not align on a continuous velocity log. This makes
them relatively easy to identify.
• Deconvolution mehtod: this is the method by which seismic data may be fil-
tered according to the processor’s preference. Knowledge of the arrival time of
primary reflectors allows the arrival times of multiples from the same surface to be
predicted. By using the arrival time, the deconvolution operators can selectively
pick multiples out of the data.
11
18. 4 INTRODUCTION TO SEISMIC
DATA PROCESSING
4.1 Normal Moveout (NMO)
What is NMO? NMO has two meaning it is both:
• a seismic effect
• a processing step
NMO as an effect: It is the effect that the distance(offset) between a seismic source
and a receiver has on the arrival time of a reflection in the form of an increase of time
with offset. NMO as a processing step: It can be defined as a processing step whereby
reflection events are flattened in a common midpoint gather in preparation for stacking.
4.1.1 Purpose of NMO
• To prepare data for stacking.
• To find the NMO velocity to the reflector.
• It removes the effect of source-receiver separation from reflection records.
• It transforms the record as if recorded at normal incidence.
4.2 Data sorting domains: Shot, Receiver, Offset adn
CMP
Data sorting changes the domain of the data for example common midpoint domain
to common offset domain. Each trace will be assigned a series of identifiers during
acquisition which will be used to sort the data.
4.2.1 Gather
a gather is a subset of the traces from an entire data set. There are different types of
gather which are shot point gather, receiver gather, offset gather and common midpoint
gather, see Figure 4.1.
12
19. Data sorting domains: Shot, Receiver, Offset adn CMP
• Shot Gather: Shot gathers have all stations recording a single shot: this is the
way the data is recorded. A shot gather samples various midpoint and a variety
of angle.
• Receiver Gather: A single receiver with many shot is called a common receiver
gather.
• Offset Gather: It has all the receivers having the same offset distance from the
source.
• Common midpoint Gather: It has all the shot receiver path with the same
midpoint; this is the processing geometry
Figure 4.1: Different types of multiple reflection
13
20. 5 TRAVEL TIME CURVE
A travel time curve is a graph of arrival times, commonly P or S waves, recorded at
different points as a function of distance from the seismic source. Seismic velocities
within the earth can be computed from the slopes of the resulting curves. See Table 5.1
Table 5.1: Computed zero offset time, t0 from given velocity, within a range of offset x
and reflector depths Z
x(m) Velocity(m/s) Z(m) t0(secs)
0-40 500 10 0.04
0-40 500 10 0.04
0-40 500 10 0.04
0-40 500 10 0.04
Where the value of x ranges from 0-40 with an increment of 0.2 (0, 0.2, 0.4, ..., 40), the
velocity of each layer increases with depth. The value of the time at zero offset was
obtain using the formula below:
t2
x =
4h2
+ x2
v2
(5.1)
Where x=0, with each layer having a time at zero layer as 0.04,0.08,0.12, 0.16 respec-
tively.
t0 =
2h
v
(5.2)
Table 5.1 above depicts a dummy graph table that was used to plot the travel time curve.
The diagram show the reflection hyperbolas of time travel at different layers. The travel
time curve of the reflection for different offset between source and receiver is calculated
using:
t2
x = t2
0 +
x2
v2
(5.3)
From Figure 5.1 it can be depicted that low velocity reflection curve (the curve with
t0 = 0.04s) has a stronger curvature than the others with high velocity. That is, the
higher the velocity the closer the curve tends to the horizontal as seen in the last curve
with the green color whose velocity is highest(2000m/s).
Table 5.2 above is obtained so as to the determine the velocity that best corrects the
hyperbolas represented in Figure1 above. With values of x still ranging from 0-40 meters,
the velocity of the data remains unchanged since this is the initial velocity obtained
14
21. CHAPTER 5. TRAVEL TIME CURVE
Figure 5.1: Travel Time graph
Table 5.2: Computed zero offset time, t0 using model parameters of Figure 5.2; t0n rep-
resents zero offset time of nth layer which is the time other time values at
different offset will be corrected to
x v1 v2 v3 v4 t01 t02 t03 t04
0-40 500 1000 1500 2000 0.04 0.06 0.08 0.10
from the field. Therefore, to carry out the Normal move-out(NMO) correction on each
hyperbola, a dummy table is made otherwise known as a model data. The model data
will carry a new velocity( iterated velocity). This velocity can be changed within the
confines of a velocity range. Therefore, to find the travel time at an offset (x) for the
model data we use:
M = t2
0 +
x2
v2
i
(5.4)
where M =model and vi =iterated velocity
dfield = t2
0 +
x2
v2
i
(5.5)
where d= data obtained from field, here V is constant i.e v1 ,v2, v3, v4 equals 500, 1000,
1500, 2000m/s respectively. To calculate the NMO for each hyperbola we use the values
obtained from equation 5.4 above and the travel-time at zero offset. The relationship
appears thus:
NMOcorrection = M − t0 (5.6)
15
22. Overcorrection and Undercorrection
From equation 5.6 above the graph of the corrected data can be plotted. To calculate
for the corrected data that equation 5.6 is subtracted from equation 5.5:
datacorrected = datafield − NMO (5.7)
From the corrected data the velocities that best flatten the hyperbolas are obtained. The
iterated velocity is adjusted until the velocity that corrects the hyperbolas is obtain.
Figure 5.3 below represents the graph of the hyperbolas before NMO correction was
carried out.
5.1 Overcorrection and Undercorrection
For a flat reflector with an overlying homogeneous medium, the reflection hyperbola can
be corrected for offset if the corrected medium velocity is used in the NMO equation.
If a velocity higher than the actual medium velocity is used, the the hyperbola is not
completely flattened. This is called undercorrection. On the other hand, if a lower
velocity is used, then it results into overcorrection. Simply put, when the velocity is
fast (high) it results in the frowning of the hyperbola, and if the velocity is slow(low) it
results in the smiling of the hyperbola.
5.1.1 Conclusion
Generally, it can be observed that as the velocity of the layer increases the more the
hyperbola of the respective layer tends to flatten. Therefore, with increase velocity the
two-way travel time decreases which means that the wave travel faster in a medium with
higher velocity.
16
25. Overcorrection and Undercorrection
Figure 5.4: Corrected gather of hyperbolas in Figure 5.3. It can thus be seen that appropriate
velocities have been applied to correct the NMO effect on the data
19
26. Overcorrection and Undercorrection
Figure 5.5: (a) CMP gather containing single event with a moveout velocity of 800m/s (b)
NMO corrected gather using the appropriate moveout velocity(500m/s); (c) over-
correction because a low velocity was used (480m/s); (d) undercorrection because
a high velocity was used (540m/s).
20
27. 6 SEISMIC VELOCITY
There are various kind of seismic velocity. The objective of this topic is to learn how to
differentiate between the different types of seismic velocity and how they find them from
reflection arrival time, i.e, the Time-Distance curve. The knowledge of seismic velocity
is important so as to know which velocity is suitable for certain subsurface situation.
There are several factors that have great effect on seismic velocity, some of which are:
• Density
• Porosity
• Depth of burial and geological age
• Fluid content and pressure.
6.1 Velocity Analysis
This is the calculation of NMO velocity (stacking velocity)from the measurement of
normal moveout. As the source to geophone distance increases, the time for a signal
to arrive increases, and when plotted on the time-distance graph the data gives an
hyperbola. There is a certain velocity value which is dependent on the properties of
the media that is being observed. This velocity can cause the hyperbola to change to a
straight line. The determination of this velocity value is called the velocity analysis.
6.1.1 Different types of Seismic Velocities
Root mean square velocity (RMS)
In a case in which the subsurface is made of horizontal layer with interval velocities say,
v1,v2,v3..., vn and a two way time t1,t2, t3,...,tn RMS velocity (VRMS) gives a formula:
Vrms =
v2
1t1 + v2
2t2 + v2
3t3 + ... + v2
ntn
t1 + t2 + t3 + ... + tn
(6.1)
RMS velocity gives a first indication of velocity variation in the subsurface. The values
of the Vrms increases with increasing depth. Below is a graph of the root mean square
velocity(Vrms) plotted against Depth (Z) for a layer with 10 interfaces.
21
28. Velocity Analysis
Interval velocity
This is the average velocity within a certain layer. The value of the interval velocity can
be obtain using either of the below formulas:
Vinterval =
Z2 − Z1
t2 − t1
(6.2)
OR
Vinterval =
V 2
2 tn2 − V 2
1 tn1
tn2 − tn1
(6.3)
Average Velocity
Vaverage =
z1 + z2 + z3 + ... + Zn
t1 + t2 + t3 + ... + tn
(6.4)
where zn is the thickness of nth layer and tn is the one way travel time within a layer n.
As seen from Figure 6.7 to 6.10, the minimum NMO correction is -0.01744 while the
maximum is -0.07. Therefore it will take a shorter corrected data for the first curve to
approach a point of zero offset. While the last curve which depicts a shallow offset will
have a greater magnitude of NMO correction, therefore it will take a wider corrected
data value for the curve with the whallowest depth to approach the point of zero offset.
6.1.2 Importance of Seismic velocities
• Interval velocity: interval velocities are used for interpretive purposes lithological
predictions, pore pressure modeling, or time-depth conversion. If the rock interval
is isotropic or less homogeneous, seismic interval velocity calculated from stacking
velocity is considered as real rock parameters. In this case, we can use interval
velocity for rock physic analysis.
• Root mean square velocity: The RMS proves particularly useful when values
run through the positive and negative domain like in sinusoids or seismic traces.
The RMS attribute thus emphasizes the variations in acoustic impedance over a
selected sample interval. Generally the higher the acoustic impedance variation of
stacked lithologies (with bed thicknesses above the seismic resolution) the higher
the RMS values will be. For example, a high RMS in a channel results from either
a high acoustic impedance contrast of channel fill with the surrounding lithology
or acoustic impedance contrasts within the infill.
22
29. NMO Stretching and Muting
6.2 NMO Stretching and Muting
6.2.1 NMO and the stretch factor
In seismic processing, it is a common practice to remove NMO from CMP gathers and
then apply a mute to prevent the inclusion of unwanted noisy data, or data over-stretched
by the NMO process. Some methods apply an automatic mute by limiting the amount of
NMO stretch to a pre-defined limit referred to as the stretch factor. The stretch factor S
is defined by a ratio of incremental times δT and δT0, measured before and after removal
and defined to be:
S =
δT
δT0
(6.5)
As the effect of NMO is being corrected it results into the stretching of the hyperbolas.
Where the magnitude of the NMO corrected value appears to be high, there will be
greater stretch experienced and vice versa. NMO stretching is mainly confined to large
offsets and shallow times because it is directly proportional to the NMO correction
amount, which is , in turn, large at large offsets and shallow times. Stacking NMO-
corrected and stretched traces will severely damage the shallow events at large offsets.
Therefore, to achieve maximum result before stacking takes place the effect of stretching
has to be removed by a process known as MUTING.
6.2.2 Muting
Reflection traces recorded at long offset and short travel time (shallow depth)will be
strongly contaminated by various types of unwanted signal, such as refractions, and will
be distorted by the application of NMO correction which stretches the individual loops.
These stretches are usually removed before stack by setting to zero all trace values for
offsets beyond a specified offset in the TWT curve(as seen in the figure below). The
muted zone is usually set to a threshold in terms of SNMO so that the zones with SNMO
greater than the threshold will be muted. In the figures below, the Figure 6.10, represents
the hyperbolas before muting with a mute curve overlain while the Figure 6.11 represents
the hyperbolas in which muting had taken place. The threshold value, chosen for the
purpose of explanation, is 0.0099 at which any other value beyond it is set at zero. The
muted section is shown in Figure 6.12.
6.2.3 Discussion
At near offset, the magnitude of NMO correction is low. This implies that at short or
near distance the hyperbolas approaches zero faster because the value of NMO is very
low. It also depicts that at shallow depth the value of NMO correction is high(high
magnitude). Therefore at shallow depth there is greater magnitude of NMO correction
applied and at near offset there is a lower magnitude of NMO applied. In each of
23
30. NMO Stretching and Muting
the section represented above(near, mid and far offsets), the hyperbola with the highest
magnitude represents the curve with the shallowest depth (Z = 2m) while the hyperbola
with the least magnitude represent the curve with the deepest depth(Z = 20m).
It can be observed very clearly that the far-offset graph appears to have the curve with
less steep hyperbolas, this depicts that the hyperbolas in this curve will have the highest
NMO magnitude.
24
31. NMO Stretching and Muting
Figure 6.1: A three-layer model of varying depth Z1,Z2,Z3
25
