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Transcript
Seismic methods
References and suggested literature
Prem V. Sharma: Environmental and engineering geophysics,
Cambridge University Press
BurVal Working Group: Groundwater Resources in Buried Valleys,
Hannover 2006
Edited by Yoram Rubin and Susan S. Hubbard: Hydrogeophysics,
Springer 2005
Edited by Reinhard Kirsch: Groundwater geophysics, Springer
World Wide Web (but be careful because not everything is vetted)
Seismology
A very simplified and short definition:
seismology is one of the geophysical studies
which examines the propagation of seismic
waves through the Earth.
Seismology can be divided into two major fields
by the energy of the source generating seismic
waves:
• earthquake seismology
• and applied seismology.
Earthquake seismology
In the case of earthquake seismology the seismic
waves mostly originate from earthquakes.
The sources of seismic waves are characterized
by the following properties:
 high energy
 and
random occurrence (scientists cannot
generate them intentionally).
Earthquake seismology
This copper engraving depicts the destruction caused
by the 1755 Lisbon earthquake.
https://en.wikipedia.org/wiki/Earthquake
Earthquake seismology
Due to the high energy of source, the generated seismic
waves can get into the deeper parts of the Earth.
By the surface measurements of reflected and refracted
seismic waves, earthquake seismology is applicable to
the study of the Earth's interior.
http://serc.carleton.edu/quantskills/activities/interior_seismic.html
Earthquake seismology
The receivers of the seismic waves,
the so-called seismometers, are
located at seismological observatories
and stations. These objects form a
global network. The seismometers are
listening to the motions of the Earth
continuously.
The measured time series of soil
displacement, velocity and
acceleration are called seismograms
http://ida.ucsd.edu/?q=sts1-sensor
http://lunar.earth.northwestern.edu/NUEPS/Maps
_and_Images/images.html
Applied seismology
The so-called applied seismology is the other branch of
seismology.
In the case of applied seismology, artificial (man-made)
source devices are used.
The seismic waves can be generated by:
• mechanical impacts
• explosions,
• and vibrations.
An artificial seismic source is characterized by:
• significantly lower energy than that of an earthquake,
• and controlled occurrence of source event both in
time and space.
Applied seismology
Because of the lower energy of sources, the
investigation depth is limited to the upper part of the
Earth's crust (max. n x 1000 m).
The great advantage of applying artificial sources is that
the measurements can be performed in a planned way
both in time and space.
Due to this planned implementation of seismic surveys,
we can map the contacts of different natural and artifical
objects located under the surface.
By means of evaluated seismic images of subsurface,
applied seismology may help the solution of several
geological and geotechnical problems.
Exploration seismology
By the investigated depth intervals, applied seismology
may be divided into two branches:

exploration seismology,

and near-surface seismology.
Exploration seismology focuses on the study of deeper
geologic structures.
Its most important application is profiling and mapping
sedimentary basins to find structures which can be
related to the accumulation or deposition of raw
materials (e.g. hydrocarbons).
The investigation depth typically varies between a few
kilometers and a few hundred meters.
Exploration seismology
An exploration seismic profile with the interpretation of
reflecting horizons and structures.
http://www.sub-surfrocks.co.uk/?page_id=66
Near-surface seismology
As its name indicates, near-surface seismology
concentrates on the subsurface structures which are
relatively close to the surface.
Shallow seismic surveys can help in solving some
hydrogeological, environmental and geotechnical
problems such as:
• location of water table, water bearing fractured
zones, cavities, sinkholes,
• delineation of faults and fractures,
• and determination of depth to bedrock.
Near-surface seismology
Investigation depth of shallow seismic surveys typically
ranges from a few hundred meters to one meter.
Due to the shallow investigation depth, it is enough to
use source devices providing relatively small seismic
energy.
Essentially, this shallow version of applied seismology is
used in hydrogeological investigations.
Therefore we will concentrate on shallow seismic
methods and their applications in hydrogeology.
Near-surface seismology
A shallow seismic reflection profile with a
lithology bar on the left side.
http://qjegh.lyellcollection.org/
Principles of solid mechanics
Seismic investigations are based on the fact that seismic
waves propagate with different velocities in different rocks.
When an initial seismic waves coming from the source point
arrive at a contact of two different rocks, they split into
several waves propagating in different directions with
different velocities.
Some of them will get back to the surface where they can be
detected by receivers.
The arrival time data and the waveforms of signals obtained
by recording waves carry information about the subsurface
structure.
In order to understand how seismic methods work and what
we can expect from them, we must know the principles of
solid mechanics.
The concept of an elastic body
The so-called elastic body is a theoretical model in solid
mechanics.
By means of this model, we can describe the behaviour of
solid materials.
Especially their deformation is studied, when they are under
the action of forces.
The most important property of an elastic body is the
elasticity.
Elasticity is the ability of a body to resist a distorting
influence and to recover its original size and shape when the
influence is removed.
The concept of an elastic body
Fluids do not show elastic behaviour because they have
no definite shapes.
But solid rocks can be considered as elastic bodies in
the range of their very small deformation.
Because the propagation of seismic waves far enough
from the source causes very small deformation inside
the rocks, the seismic behaviour of rocks may be
studied by using the model of elastic body
Stress
When an external force begins to act on the
surface of an elastic body, an internal force will
arise inside the body to resist the external effect.
This internal force called stress is a surface force
which acts across the internal surface elements
of the body.
So, the stress is the consequence of the external
forces acting on a body.
Stress
The figure tries to demonstrate
the stress across a surface
element (yellow ellipse)
separating two volume elements
of the body.
The bottom element exerts a
stress on the top element
The greater purple arrow located
at the center of the surface
element represents the resultant
of the stress distributed over the
surface element (small arrows).
https://en.wikipedia.org/wiki/Stress_(mechanics)
Stress
In other words, stress is a physical quantity which
expresses the internal forces exerted by
the
neighbouring particles of a material on each other.
In a static case, the magnitude and the direction of
stress may change from point to point inside the body
(static case means the external surface force does not
change in time).
So, the stress is described by a vector field
mathematically:
𝜎റ = 𝜎(
റ 𝑟)=
റ 𝜎റ 𝑥, 𝑦, 𝑧
where 𝜎റ is the stress vector at a given point inside a
body, 𝑟റ is the radius vector of the point and x,y,z are the
rectangular Cartesian coordinates of the point.
Stress
In a dynamic case, the stress depends on not only
space but time.
So, a time and space dependent vector field describes
the stress state of a body:
𝜎റ = 𝜎(𝑡,
റ 𝑟)=
റ 𝜎റ 𝑡, 𝑥, 𝑦, 𝑧
where t is the time
The dimension of stress is the same as that of pressure,
so its unit is pascal (Pa, newton per square meter) in the
International System, or psi (pound per square inch) in
the Imperial system.
Since the magnitude of stress expressed in Pa is usually
a very high value, the use of MPa is more common in
engineering practice.
Types of loading
Loading means the application of an external force to
an object.
Depending on the type of loading, different stress and
strain fields arise inside a body.
There are five fundamental types of loading:
 tension,
 compression,
 bending,
 shear,
 and torsion.
From a seismic point of view, tension, compression and
shear loading are of importance.
Types of stress
A stress vector can be decomposed into two components:
• normal stress (is perpendicular to the unit surface)
• and shear stress (is parallel with the unit surface.)
http://homepage.ufp.pt/biblioteca/WebBasPrinTectonics/BasPrincTectonics/Page2.htm
The normal stress component n or  is perpendicular to the unit
surface.
It is also called compressive or tensile stress depending on the type
of loading (compression or tension) induces the normal stress
component.
Normal stress
In the case of compression and tension, the external
surface forces act on the surface of a body at right
angles.
But the directions of forces at the two ends of the body
are opposed.
Compression causes contraction while tension causes
extraction along the axis of loading.
Compression generates compressive stress (with a
negative sign, n< 0) while tension generates tensile
stress (with a positive sign, n> 0) inside the body.
The sign of stress is determined by the sign of change in
length.
Normal stress
Independently from its sign,
a normal stress field always
entails a deformation which
changes both the shape and
the volume of the body.
The figure demonstrates the
effects of tensile (or
tensional) and compressive
(or compressional) stress.
(http://magnet.fsu.edu/~odom/1000/deformation/def.html)
Shear stress
The other component of a stress vector, which is parallel
with the unit surface of two neighbouring volume elements,
is referred to as shear stress or . Shear stress is
caused by external forces acting tangentially to the surface
of a body (tangential force).
A shear stress field entails a deformation which modifies
only the shape of body. The volume does not change.
(http://magnet.fsu.edu/~odom/1000/deformation/def.html)
Volumetric stress
Beside the two fundamental types of stress (normal and shear),
another type of stress, the so-called volumetric stress (V) is also
important in engineering practice.
A volumetric stress field occurs when an elastic body is equally
loaded by compressional forces in all directions.
In nature, hydrostatic and lithostatic pressures cause volumetric
stress in solid materials (e.g. rocks).
Similarly to normal stress, the volumetric stress also entails a
deformation which modifies not only the shape but also the volume of
a body.
(http://magnet.fsu.edu/~odom/1000/deformation/def.html)
Strain
The change in stress field (caused by the effect of
external forces) results in the displacement of particles
inside the body which appears in the form of
deformation (the change of shape and/or volume).
The deformation is described by the so-called strain
which quantifies the relative displacement of particles
inside the body.
Relative displacement means that the actual position of
a particle is related to its initial position.
Relative displacement can be characterized by change
in length and/or angle change between line segments
inside the material.
Strain
The figure shows a simple case of deformation which
occurs when a bar is stretched by tension forces.
Here, the strain is expressed as the ratio of change in
length to the original length.
https://www.nde-ed.org/
EducationResources/CommunityCollege/Materials/Mechanical/StressStrain.htm
Strain
Similarly to stress, the magnitude and direction of strain
may change from point to point inside the body in the
case of static load.
So, also the strain is described by a vector field.
When the body is dynamically loded, the strain
depends not only on space but time.
In the case of elastic deformation, the body completely
recovers its original configuration after the external load
has finished.
It means that elastic deformation is reversible.
On the contrary, plastic deformation is irreversible,
because the body does not recover its original shape
and volume after the load.
Types of strain in engineering practice
The relative change in length is quantified by the so-called
engineering strain or Cauchy strain.
It gives the ratio of change in length to the original length by the
formula below:
∆𝐿
𝜀𝑒𝑛𝑔 = ,
𝐿
where eng denotes the engineering strain, L is the original length of
the line segment and L symbolizes the change in length.
Because this type of strain is obtained by the division of two
quantities with the same unit, it is a dimensionless quantity.
Types of strain in engineering practice
We can often meet the terms longitudinal (or axial) and transverse
strains in relation to compression or tension.
Longitudinal strain is actually the engineering strain measured along
the longer axes of an elongated body, while transverse strain means
the engineering strain measured in the cross-sectional direction of
the body. They can be expressed by the following formulae:
𝜀𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 =
∆𝐿
𝐿
𝜀𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑒 =
∆𝐷
𝐷
where L is the original length in the axial direction, L is the change
in length in the same direction,
D is the original length in the cross-sectional direction and D is the
change in length in the same direction.
Types of strain in engineering practice
This figure demonstrates the meaning of longitudinal and transverse
strains.
A cylinder shaped body is stretched by tensional forces acting on its
two ends. Due to the tensile stress arisen inside the body, the axial
size will increase, while the cross-sectional size will decrease.
The sign of strain is positive if the length of line segments inside the
body increases (in the given direction), and it is negative if they
shorten.
http://physicscatalyst.com/mech/elasticity_2.php
Types of strain in engineering practice
Not only the length of line segments but also the angles between the
line segments may be changed inside the body by the effect of
external loading.
The angle change of line segments is quantified by the angular
distortion.
It gives how the angle has changed between two, originally
perpendicular line segments inside the body.
The so-called shear strain is defined by the tangent of angular
distortion:
𝜀𝑠ℎ𝑒𝑎𝑟 = tan 𝛾
where  is the angular distortion in radian.
The shear strain is also a dimensionless quantity.
Types of strain in engineering practice
This figure tries to illustrate
how the shear strain can be
derived from the angular
distortion , the original
length of a line segment L
and the transverse
displacement x.
https://en.wikipedia.org/wiki/Shear_modulus
The external forces (F) are shearing forces with opposite directions.
This tangential pair of forces produces a shearing stress field 
inside the body which entails the shearing deformation of the body.
This deformation is manifested in the form of angular distortions of
the material line segments.
Types of strain in engineering practice
The so-called volumetric strain is induced by a volumetric stress
field and it is defined as the ratio of change in volume to the original
volume:
∆𝑉
𝜀𝑉 =
𝑉
where V denotes the original volume of a body and V is the volume
change. Similarly to the previous types of strain, it is also a
dimensionless quantity.
(http://magnet.fsu.edu/~odom/1000/deformation/def.html)
Elastic moduli for homogeneous and
isotropic materials
As we have seen, the stress has a connection with the strain.
The mathematical relationship between these two quantity is
established by the so-called elastic modulus.
In the case of homogeneous and isotropic materials, the elastic
modulus is a scalar quantity which measures the resistance of a
material to elastic deformation.
So, it is an important parameter which characterizes the elasticity of a
material.
In the range of elastic deformations the value of elastic modulus is a
constant. Each material has its own constant.
Depending on the type of stress and strain and the measurement
configuration, several types of elastic moduli are defined in practice.
The most frequently used four elastic moduli are the following:
• Young's modulus (or elastic modulus),
• Poisson's ratio,
• shear modulus
• and bulk modulus.
Elastic moduli for homogeneous and
isotropic materials
Young's modulus (commonly denoted by E) measures the tensile
elasticity, or the tendency of a material body to deform along its
longitudinal axis when tensile forces act on it.
It is defined by the ratio of tensile stress to the longitudinal strain:
where E is the Young's modulus,
F is the tensile force,
A is the cross-sectional area on which the force acts
ΔL is the change in length,
and L is the original length of the body.
Its unit is pascal (Pa) in System International.
Elastic moduli for homogeneous and
isotropic materials
(http://hydrogen.physik.uni-wuppertal.de/hyperphysics/hyperphysics/hbase/permot3.html)
This figure demonstrates the measurement configuration by which
the Young's modulus of a material can be determined.
In order to deform a material with a higher value of Young's modulus,
a greater force has to be applied. It has a significant resistance to
deformation.
A soft material has a low value of Young's modulus, while a stiff or
rigid material has a very high value of Young's modulus.
So, we can say that the Young's modulus is the measure of stiffness.
Elastic moduli for homogeneous and
isotropic materials
Poisson's ratio (generally denoted by ) is the measure of the socalled Poisson effect.
This phenomenon means that a body compressed in one direction
modifies its size not only in the direction of loading but also in the
direction perpendicular to the compression.
Poisson's ratio is defined by the negative ratio of transverse strain to
the longitudinal strain.
where L is the original length in the axial direction,
L is the change in axial length,
D is the original length in the transverse direction
and D is the change in transverse length.
It is a dimensionless quantity.
Elastic moduli for homogeneous and
isotropic materials
This figure illustrates the
measurement configuration by
which the Poisson's ratio of a
material can be determined.
http://www.pavementinteractive.org/article/poi
ssons-ratio/
Most of the materials expand in transverse directions when they are
compressed in axial direction. Their Poisson's ratio is positive and
ranges from 0 to 0.5.
A perfectly incompressible (theoretical) material would have a
Poisson's ratio of value 0.5.
Elastic moduli for homogeneous and
isotropic materials
The shear modulus or modulus of rigidity (G or ) measures the
tendency of a material body to the deformation when a pair of sharing
forces acts on its two opposite sides.
(Sharing forces acting in a pair have the same magnitude but
opposite directions. They tangentially act on the surface areas.)
The shear modulus is defined by the ratio of shear stress to the shear
strain.
where Fshear is the magnitude of the shear force,
A is the area on which the force acts
and is the angular distortion.
Its unit is pascal in System International.
Elastic moduli for homogeneous and
isotropic materials
https://en.wikipedia.org/wiki/Shear_modulus
This figure illustrates the measurement configuration by which the
shear modulus of a material can be determined.
A material with a higher value of shear modulus exerts stronger
resistance to shearing deformation.
Fluids have a shear modulus of value 0 which means that they
cannot resist shearing deformations at all.
Elastic moduli for homogeneous and
isotropic materials
The so-called bulk modulus (K) measures the volumetric elasticity,
or the tendency of a body to deform when it is equally compressed in
all directions.
It is defined by the ratio of volumetric stress to the volumetric strain.
where Fcompression is the compressional force acting on the entire
surface of the body,
A is the surface of the body,
V is the original volume of the body
and V is the change in volume.
Its unit is pascal (Pa) in System International.
Elastic moduli for homogeneous and
isotropic materials
This figure demonstrates the
measurement configuration by
which the bulk modulus of a
material can be determined.
http://faculty.uaeu.ac.ae/~maamar/physics1/121.html
The lower the value of the bulk modulus the more compressible the
material.
Gaseous materials are characterized by very low values of bulk
modulus.
The inverse bulk modulus gives the compressibility of a material
().
Actually, the bulk modulus can be considered as an extension of
Young's modulus to three dimensions.