Download Diffraction of seismic waves

Velocity of seismic waves
From the point of view of seismic methods, the most important
property of a rock is the velocity at which the P-wave (or
compressional wave) propagates through its material.
The velocity of P-wave depends on the density and the elastic
properties (elastic moduli) of a rock.
Actually, the elastic moduli also depend on the density.
Increasing density results in faster than linear increase of elastic
moduli.
Because of that non-linear relationship between the density and
elastic moduli the P-wave propagates faster in a rock with higher
density.
Velocity of seismic waves
Since P-waves can propagate not only in solids but also in
fluids, all the factors affecting the bulk density of a rock
influence the velocity of P-wave.
1. Mineral composition of the rock
Different minerals may have different density.
The density of a mineral depends on its chemical composition
and crystal structure.
If the solid part of a rock is made up of several minerals, both
the volume fractions and the density values of mineral
components are of importance.
Velocity of seismic waves
2. Porosity of the rock
Since the fluids filling the pore space of a rock have significantly less
density than that of solid components, the porosity decreases the
bulk density of rocks.
So, increasing porosity results in decreasing P-wave velocity.
3. Density of the fluid filling in the pore space
When the pore space is occupied by only one fluid phase (e.g. water,
or air), the density of the fluid determines how rate the porosity
decreases the bulk density of rock.
The lower the density of fluid the lower the bulk density of porous
rock.
Note that the density of water depends on its salinity.
Decreasing density of fluid results in decreasing P-wave velocity.
The velocity of P-wave is significantly higher in the case of water filled
porosity than in the case of dry (air filled) porosity.
Velocity of seismic waves
4. Saturation of fluids filling in the pore space
When more than one fluid phase fill in the pore space, not only the
density of fluid phases but also their saturation are of importance.
The higher the saturation of fluid phase with lower density the lower
the bulk density and P-wave velocity of rock.
5. Compaction and consolidation
It is generally true that the compaction and the consolidation increase
the density of sedimentary rocks.
The increase of P-wave velocity with the depth of burial is normally
valid because increasing lithostatic pressure (or overburden
pressure) results in higher rate of compaction which entails less
porosity and higher density.
Velocity of seismic waves
Contrary to the P-wave, S-wave (shear wave) cannot travel through
fluids, therefore the porosity and the fluid in the pore space do not
exert any influence on the velocity of S-wave.
An S-wave avoids the pore space during its propagation, so its
velocity is determined by the properties of the solid rock framework.
Velocity of P-wave in different rocks
Rock or material
air
water
ice
permafrost
weathered layer
alluvium, sand (dry)
sand (water saturated)
clays
glacial moraine
coal
sandstones
slates and shales
marls
limestones and dolomites
anhydrite
rock salt (halite)
granite and gneiss
basalt flow top (highly fractured)
basalt
gabbro
dunite
VP (m/s)
330
1400-1500
3000-4000
3500-4000
250-1000
300-1000
1200-1900
1100-2500
1500-2600
1400-1600
2000-4500
2400-5000
2000-3000
3400-6000
4500-5800
4000-5500
5000-6200
2500-3800
5500-6300
6400-6800
7500-8400
This table shows the Pwave velocity of some
materials and rocks.
Those ones which
frequently occur in
sedimentary basins are
highlighted by red colour.
Prem V. Sharma: Environmental
and engineering geophysics,
Cambridge University Press
Velocity of P-wave in different rocks
The P-wave velocity of rocks varies in a wider range than the density
of rocks.
The highest velocity values are connected to the igneous and high
grade metamorphic rocks (e.g. granite, gneiss )
But fracturing of these rocks decreases the value of velocity (see
basalt flow top).
In the case of sedimentary rocks, there can be great differences
among the velocity values even within the same formation.
The rate of compaction and consolidation, the porosity, the fluid
content, the saturation and the mineral composition are collectively
responsible for the P-wave velocity.
The lowest velocity values, which are less than the velocity in water,
occur in unconsolidated sediments with dry porosity near the surface
(see dry sand and weathered layer).
The zone of these sediments ranging from the surface to the water
table is called weathered layer or low-velocity layer (LVL).
Field techniques in seismic surveys
During a seismic survey, two main operations are implemented
collectively:
• seismic waves must be generated by using a seismic source on
the ground surface,
• and the arrivals of seismic waves must be detected by receivers
called geophones planted in the ground.
The seismic wave packets may reflect off and/or refract at different
subsurface contacts and may penetrate through different types of
rocks.
All the detected wave packets have their own subsurface route
therefore they will arrive at the geophones at different time moments.
The time interval between the wave generation (shot) and the arrival
of a wave packet is the so-called travel-time.
Its value depends on the route of the wave packet as well as the
subsurface structures and rocks through which the wave has
travelled.
Field techniques in seismic surveys
Since the different wave packets actually scan the subsurface
structures, their travel-time values collectively carry information about
the subsurface.
On the basis of the boundary effect (reflection or critical refraction)
used for getting information about the subsurface structures, two
main methods may be distinguished:
• seismic reflection method
• seismic refraction method.
Independently of the method, the following components are required
for a seismic field measurement:
• a seismic source,
• several seismic receivers (called geophones in seismic surveys),
• a seismograph,
• cables (to transmit the signals of detected wave packets).
Field techniques in seismic surveys
The main functions of these components:
• seismic source is used to generate seismic energy which
propagates through rocks in the form of seismic waves,
• geophones detect the arrival of seismic wave packets and
convert the dislocations of ground surface to electric voltage
signal,
• seismograph collects the signals of geophones simultaneously,
filters and amplifies the signals, digitizes them and record the
data set.
• cabels provide the signal transmission between the geophones
and the seismograph.
Seismic source
A man-made seismic source is a device or a material together with
the technique of its application which is used to generate controlled
seismic energy on the ground surface.
The following factors should be considered in choosing the suitable
seismic source for a given survey:
• the depth of investigation (the deeper the range to be investigated
the higher the required energy)
• cost (we always have to manage limited amount of money),
• repeatability (means the ability to repeat the wave generation
several times at the same place),
• convenience (this is a natural demand on any technique),
• efficiency (means the ability to provide high enough energy and
quick operation)
• safety (applying some sources can be very dangerous in some
circumstances)
Seismic source
Repeatability (why may it be important in some cases?)
When a single application of a source device is not able to provide
high enough seismic energy, the recorded signal will be too noisy.
It means that the background noise (unwanted mechanical effects)
significantly distorts the effect of seismic waves (which is the useful
component) in the signal. In such cases we say that the signal-tonoise ratio (SNR) is low.
We can improve the SNR, if we repeat the wave generation and the
detection of wave arrivals at unchanged positions.
If we sum all the recorded signals coming from the repetitions, the
resultant signal will be less noisy.
Namely, the summation is able to attenuate the effect of random
noise and enhance the effect of seismic waves.
This signal processing technique is called vertical stacking and its
result is known as vertical stacked signal.
Seismic source
A seismic source can be considered as point source, because its
dimensions are much smaller then the wavelengths of generated
seismic waves.
So as to select an adequate seismic source, we always have to find
an acceptable compromise between the penetration depth and the
vertical resolution.
The penetration depth or investigation depth gives the vertical
depth of the deepest subsurface contact which can be detected in a
given situation.
It depends on several factors, among other things
• the power of source,
• the frequency band of generated seismic waves,
• the geologic structures,
• and the acoustic properties of rocks.
Seismic source
The vertical resolution of a seismic measurement gives the ability to
provide information about the vertical dimensions of subsurface
objects.
Similarly to the penetration depth, it depends on several factors.
But there is a theoretical limit for the vertical resolution.
It gives the smallest vertical dimension of an inhomogeneity which
can be detected in the given situation.
By this theoretical limit, the vertical resolution of a seismic wave
cannot be better than the quarter of the wavelength belonging to the
dominant frequency of the wave packet:
𝜆
ℎ𝑚𝑖𝑛 ≥
4
where hmin is the minimum layer thickness which can be distinguished
by a seismic wave of wavelength .
Seismic source
Since the wave velocity in a rock is a constant value, the refinement
of the vertical resolution requires the increase of the dominat
frequency (v = f).
But higher frequency seismic waves are not able to travel through the
deeper parts of the subsurface because of their quick attenuation.
This is the reason why we cannot reach arbitrary high vertical
resolution and deep penetration together.
A realistic estimation for the maximum achievable frequency in nearsurface seismic surveys is about 500 Hz.
If we consider the range of typical P-wave velocity in near-surface
sediments (n x 100 m/s) the dominant wavelength is limited to 2 m.
It means a half meter (0.5 m) vertical resolution.
But that would be extremely good!
In practice the resolution like this generally cannot be reached.
Seismic source
There are two main types of sources used in shallow seismic
surveys:
 impulse type sources,
 vibration type sources.
Impulse type sources are characterized by a very short time interval
of the wave generation.
So, the effect of these sources is instantaneous.
The group of impulse type sources can be divided into further three
subgroups:
 impact sources,
 impulsive or shooting sources,
 explosion sources.
Impact sources
In the case of impact sources, the seismic waves are generated by
the impact of a heavy solid body on the surface.
The two most frequently used impact sources are
• striking a steel plate on the ground by a sledge hammer
• and dropping a spherical weight onto the ground.
The advantages of using a sledge hammer or a weight dropper
device are
• the low cost and
• the relatively good repeatability.
But they can provide low seismic energy, so the achievable depth of
penetration is less than a hundred meter.
The dominant frequency of generated seismic waves typically ranges
50-200 Hz.
Sledge hammer
The picture shows a sledge hammer with a steel plate. A cable is led into
the head of the hammer. When we strike at the plate with the hammer, an
electric circuit is closed for a moment. Through this circuit, a trigger impulse
is transmitted to the seismograph in order to start data recording. In such a
way the data recording can be synchronized with the time moment of wave
generation.
http://www.aksgeoscience.com/seismic.html
Weight dropper
This type of seismic source provide accelerated weight dropping. The
acceleration is implemented by a spring. In such a way, the seismic energy
of the source can be increased. The weight can be lifted manually or by an
electric motor. Because of its relatively small weight, it is easy to move
under field circumstances.
http://www.geoexpert.ch/equipment.html
Weight dropper
This is another type of weight dropper which is mounted on a truck. It
can provide a higher seismic energy due to the free fall weight
dropping from a higher level with a heavier weight.
http://www.geoexpert.ch/equipment.html
Impulsive or shooting sources
The working principle of impulsive or shooting sources is the same as
that of a rifle or a shotgun.
The detonation of a small explosive charge in a metal pipe shoots a
bullet or a wadding into the ground.
Because shooting is very dangerous, we have to observe the safety
rules concerning the use of these devices
In most countries, such as Hungary special permission from the
authorities is needed for using them.
Shooting devices are characterized by high repeatability and a depth
of penetration ranging from less than a hundred meter to few hundred
meters.
The depth of penetration depends on the soil conditions, the amount
of charge and the caliber of shooting device.
Firing into a water-filled shallow hole drilled previously is often used
because the repetitions provide nearly the same effect in such a way.
The dominant frequency of the generated seismic waves ranges from
80 to 200 Hz.
Impulsive or shooting sources
The picture shows a shotgun used for
seismic wave generation.
This type of shotguns is also known as
"Betsy Gun".
These special shotguns are designed for
only seismic wave generation so they
cannot be used as regular rifle or
shotgun.
The closed cylindrical end of a Betsy Gun
provides protection against the bullets
rebounding from the ground surface.
http://firearmshistory.blogspot.hu/2011/03/utility-firearms-geology-and-shotguns.html
Impulsive or shooting sources
The charges of a Betsy gun are similar to regular shotgun shells.
http://www.dot.ca.gov/dist1/d1pubinfo/press/2008/08-150-photos.htm
Explosion sources
During an explosion, a significant amount of energy is released
suddenly in a very small volume which generates a pressure wave.
The pressure wave of the explosion exerts an influence on the
ground and generate seismic waves near the source.
The amount of seismic energy depends on the type and the amount
of explosive material.
It can be high enough to support a penetration depth of a kilometer.
But the application of explosive materials is the most dangerous of all
the seismic sources.
In addition, it is rather expensive as well as the storage, the treatment
and the application of explosive materials are strictly regularized.
Therefore special permissions from the authorities are needed to get
similarly to shooting devices.
Explosion sources
The explosive devices can be divided into two classes by their
sensitivity and power:

primary explosives

and secondary explosives.
The primary explosives (e.g. blasting caps) are very sensitive which
means that a relatively small initial energy is enough to induce the
detonation.
Since primary explosives provide a relatively low energy they can be
used for investigating near-surface structures (located less than a
hundred meter).
Another application of primary explosives is detonating secondary
explosives.
Blasting cap
In seismic practice, the electric type blasting caps are used. An
electric blasting cap is fired by a current impulse coming from a
blasting machine. The blasting machine is connected to the blasting
cap by a pair of long wires to ensure remote launching.
A single blasting cap provides dominant seismic energy in the range
of 100-200 Hz.
https://en.wikipedia.org/wiki/Blasting_cap
Explosion sources
The secondary explosives such as TNT, dynamite, and plastic
explosive are more powerful but less sensitive. They require higer
initial energy for the detonation. This is because of avoiding the
spontaneous explosion.
For the detonation of secondary explosives, usually the primary
explosives provide the initial energy.
The explosive charges are usually fired in a shallow hole filled with
water. It is worth drilling shallow holes for the shots because the
explosion becomes more effective and less dangerous in a hole.
Since a small amounts of explosive is generally enough for a shot
(less than 10 gramms), a hole can be used for the repetition.
The secondary explosives produce dominant seismic energy in the
range of 50-200 Hz.
A great drawback of explosive sources that it is not possible to use
them near roads and urban areas.
But in rural areas with high water table an explosive source may be
the better choice
Explosion sources
An explosion of a seismic charge can be seen here. The energy of
the explosion ejects the muddy water high from the hole.
https://www.flickr.com/photos/57768042@N00/2805186128/
Vibration type sources
Vibration type sources generate seismic energy over a period (up to
twenty seconds). So, their effect is not instantaneous.
The frequency of vibration continuously varies as a function of time.
The wave train of the vibration is called “sweep”.
In the case of the most frequently used linear sweep, the frequency
changes linearly from the lowest frequency to the uppermost one
(upsweep).
When a vibration type source was used for a seismic survey, the first
step of data processing is eliminating the effect of vibration source
from the raw data.
It is based on the cross-correlation of the source signal and recorded
signals.
We must perform this operation in order to get signals containing
information only about the subsurface structures and rocks.
This type of seismic wave generation together with the special data
processing workflow is called Vibroseis technique.
Vibration type sources
The main advantages of applying vibration type sources
• they are less dangerous for roads and urban areas
• the recorded data is less sensitive to the background noise (e.g.
footsteps, traffic, single car).
But the application of vibration sources is rather expensive, because
of the special equipment required.
The so-called vibrator unit is often mounted on a vehicle.
By lowering the base of the vibrator unit, physical contact is made
between the ground and the unit.
In such a way the vibration can be transmitted to the ground surface
from where seismic waves start.
The vibration process is controlled from the driver's seat by a
computer.
Vibration type sources
A mini vibrator used for shallow seismic surveys can be seen here.
The vibrator unit is mounted on a small truck and moved by a
hydraulic arm.
It provides a vibration frequency range of 10-500 Hz.
http://www.apigeophysical.com/T2500.pdf
Vibration type sources
For industrial seismic exploration, larger and more expensive
vibrators are used.
https://en.wikipedia.org/wiki/Seismic_vibrator#/media/File:Nomad_90_vibrating.jpg
Vibration type sources
The so-called Mini-Sosie means an
alternative vibration type seismic
source to which a special data
processing workflow belongs.
Actually, a vibratory rammer is used for
generating seismic waves.
It is effective in imaging near-surface
structures.
The source is less expensive, portable
and applicable in both rural and urban
environments.
http://www.velseis.com/velseis/history/
Shot
In seismic practice, the term “shot” means the event of seismic
wave generation independently from the type of source .
A given shot is identified by the time and location of its
occurrence. (Shot points are arranged along seismic lines)
http://gis.stackexchange.com/questions/9672/seismic-shot-points-in-arcgis-desktop
Seismic receiver or geophone
The so-called geophone is a seismic
receiver which is used to transform the
energy of the detected seismic waves
into electric voltage signals.
It usually detects only one component of
the ground displacement, but there are
three-component (3C) geophones as
well.
In most cases, the compressional wave
arrivals are of importance.
Therefore geophones responding to the
vertical component of ground
displacement are used more frequently.
http://www.mitchamindustries.com/products-for-lease/land-seismic/sensors/sensorsm-24/
Seismic receiver or geophone
A geophone contains a motion-sensitive transducer which is able to
convert the ground motions to an electrical signal.
The main components of a moving-coil electrodynamic type
geophone are the following:
 a geophone case,
 a magnet,
 a coil or coils,
 springs.
BurVal Working Group: Groundwater Resources in Buried Valleys, Hannover 2006
Seismic receiver or geophone
A metal spike is also connected to the bottom part of the geophone
case.
By means of this spike, the geophone can be stuck into the soil
easily.
A good mechanical coupling between the case and the ground is very
important in order that the geophone case can follow correctly the
ground motions.
BurVal Working Group: Groundwater Resources in Buried Valleys, Hannover 2006
The working principle of the geophone
The magnet is fixed to the geophone case
and it provide a stationary magnetic field
inside the case.
The coil is suspended by one or more
springs inside the case.
If a seismic wave arrives at a geophone,
the ground motion will move the spike
along with the case and the magnet.
But the coil will not follow this movement
because of its inertia.
The movement of the magnet results in the
change of magnetic field near the coil.
The change of magnetic field in turn
induces electrical voltage across the coil.
This induced voltage is the output of the
geophone.
http://astarmathsandphysics.com/a-level-physics-notes/183-waves-andoscillations/3120-the-geophone.html
Seismic receiver or geophone
Depending on the frequency characteristics, there are two types of
geophone:

velocity geophone

and acceleration geophone.
In the case of a so-called velocity geophone, which is commonly
used, the induced voltage is proportional to the relative velocity of the
coil with respect to the magnet.
This proportionality is fulfilled only if the frequency of the ground
motion is above the natural (or resonance) frequency of the
geophone. (The value of the natural frequency is an important
technical parameter of a geophone type)
A rule of thumb is to choose a geophone whose natural frequency is
at least 10% of the estimated highest frequency of seismic waves.
For shallow reflection seismic surveys, the selection of geophones
whose natural frequency is in the range of 30-50 Hz is recommended.
Seismic receiver or geophone
In the case of an acceleration geophone, the induced voltage is
proportional to the relative acceleration of the coil with respect to the
magnet.
The proportionality is valid only if the frequency of ground motion is
below the natural resonance frequency of the geophone.
During a seismic measurement, several geophones are used
simultaneously.
They are arranged along a seismic line with constant geophone
spacing.
This arrangement of geophones is called geophone spread or
simply spread.
Geophone spread
http://www.brantax.com/brantax-services/
Seismograph
A seismograph is an instrument by which the electric voltage signals
coming from the geophones can be collected and recorded.
This process entails the analog-to-digital (A/D) conversion of
geophone responds.
As a result of this conversion, a continuous (analog) signal is
transformed into a series of digital data. A recorded seismic data set
contains large amount of data series because a particular geophone
signal (or geophone respond) arises at each geophone by the effect
of each shot.
A seismograph has at least 48 but maybe more than 100 channels.
The channels provide parallel communication links to the geophones.
In this communication, the geophones act as transmitters and the
seismograph behaves as the receiver.
The physical connections are established by cables.
There are two ways of signal transmission between the geophones
and the seismograph:
 analog signal transmission,
 digital signal transmission.
Seismograph
When the signal transmission is analog, the voltage signal of a
geophone arrives at a channel of the seismograph in analog form.
The signal of a channel is amplified and filtered by the seismograph.
The application of low-cut filters is necessary to emphasize the high
frequency in the signal and remove the low frequency range.
Next, the signal is digitized by the analog-to-digital converter (A/D
converter) of the channel.
Digitizing a signal means discretizing or sampling it in time and
quantizing its values in voltage.
The outputs of the channels called seismic traces are displayed on
either the built-in monitor of a seismograph (if it has one) or the
screen of a laptop connected to the seismograph.
The traces are also recorded to a hard disk drive.
Seismograph
A seismograph with built-in monitor and printer.
http://www.geometrics.com/geometrics-products/seismographs/
Seismograph
A seismograph connected to a laptop computer.
http://www.expins.com/item/geode-seismograph
Seismograph
When the signal transmission is digital, each active channel of the
seismograph accepts a digital data series.
It means that the A/D conversion of the geophone responds is
performed near the geophones by the so-called acquisition units.
An acquisition unit has at least two but maybe several channels by
which the geophone responds are collected.
The analog geophone responds are amplified, filtered and digitized
by this units.
Next, the digital data series are directly transmitted to a laptop.
In this case, the acquisition units along with the laptop provide the
whole functionality of a seismograph.
Because these components are located different locations during a
measurement, a system like this is called distributed seismograph.
The advantage of a distributed seismograph is that the signal
transmission is less sensitive to electrical noise (e. g. interference
from power lines, crosstalk between wires).
Distributed seismograph
Acquisition units of a distributed seismograph.
http://rtclark.com/product/seistronix-ex-12-distributed-seismograph-cables/
Distributed seismograph
Acquisition units of a distributed seismograph in the field.
http://www.dmt-group.com/en/products/geo-measuring-systems/summit-system.html
Seismograph
By watching the seismic traces on a screen, we can check the status
of the geophones (failed or at work) and the level of background
noise before a shot.
If the noise level is low enough the operator gives the start signal for
the shot.
Each shot triggers a new data record for each geophone respond.
Synchronizing the moment of a shot with the start of data recording is
very important, and it is executed by means of a trigger box.
A trigger box establishes a connection between the source device
and the seismograph or laptop.
It is listening to the electrical circuit connected to the source device.
The circuit sends a trigger pulse when a shot is occurred.
After the trigger box has observed the trigger pulse, it sends a control
signal to the seismograph or laptop in order to start the data
recording.
Distributed seismograph
A seismogram displayed in a data acquisition software.
http://www.seistronix.com/ras_g.htm
Seismograph
An important parameter of a seismograph is the dynamic range.
The dynamic range (I) gives the ratio of the largest (A2) to the
smallest (A1) recoverable signal amplitude in decibel.
Doubling the amplitude means approximately an increase of 6 dB in
signal intensity.
A thousandfold increase in amplitude corresponds to an increase of
60 dB in signal intensity.
Increasing the amplitude by a factor of a million means an increase of
120 dB in signal intensity.
The dynamic ranges of modern seismographs can reach the value of
100 dB or more.
It means that a seismograph is able to transmit very small as well as
very large amplitude values without any distortion during a data
recording period.
Seismic trace and seismogram
Geophone respond (respond of the geophone to the ground motion) or
geophone signal is an analog voltage signal (electrical voltage as a
function of time).
This is the output of a geophone.
The geophone sends its respond to a single channel of the seismograph.
A multi-channel seismograph is able to accept as many geophone responds
as the number of its channels.
In seismology, a seismic trace refers to the recorded signal coming from a
single channel of a seismograph.
The name comes from the early time of seismology when the seismograph
recorded the analog signal of a channel as a curve on a paper.
The plotted curve was called trace.
Today's instruments record the signal digitally and the trace means the
recorded data (data trace).
A seismogram is a plotted or displayed form of the output of a seismograph
which contains the curves of all seismic traces belonging to a single shot.
Seismic trace and seismogram
Raw data of a seismogram on the left and the frequency filtered
seismogram on the right. Each curve is a trace. Each trace belongs to a
geophone respond. The SNR is improved by the filtering.
https://www.researchgate.net/figure/259169858_fig2_The-raw-data-of-the-surfacewaves-seismogram-records-left-panel-after-applying-the