Shear wave splitting
Encyclopedia
Shear wave splitting, also called seismic birefringence
, is the phenomenon that occurs when a polarized shear wave enters an anisotropic media (Fig. 1). The incident shear wave splits into two polarized shear waves (Fig. 2). Shear wave splitting are typically used as a tool for testing the anisotropy of an area of interest. These measurements reflect the degree of anisotropy and leads to a better understanding of the area’s crack density and orientation or crystal alignment.
We can think of the anisotropy of a particular area as a black box
and the shear wave splitting measurements as a way of looking at what is in the box.
]
or character of the medium. When a polarized shear wave enters a new, anisotropic medium, it splits into two shear waves (Fig.2).
One of these shear waves will be faster than the other and oriented parallel to the cracks or crystals in the medium. The second wave will be slower than the first and sometimes orthogonal to both the first shear wave and the cracks or crystals in the media. The time delays observed between the slow and fast shear waves give information about the density of cracks in the medium. The orientation of the fast shear wave records the direction of the cracks in the medium.
When plotted using polarization diagrams, the arrival of split shear waves can be identified by the abrupt changes in direction of the particle motion (Fig.3).
In a homogeneous
material that is weakly anisotropic, the incident shear wave will split into two quasi-shear waves with approximately orthogonal polarizations that reach the receiver at approximately the same time. In the deeper crust
and upper mantle
, the high frequency shear waves split completely into two separate shear waves with different polarizations and a time delay between them that may be up to a few seconds.
azimuthal velocity
variations in oceanic basin
s. This area was chosen for this study because oceanic basins are made of large, relatively uniform homogeneous rocks. Hess observed, from previous seismic velocity experiments with olivine crystals
, that if the crystals had even a slight statistical orientation this would be extremely evident in the seismic velocities recorded using seismic refraction. This concept was tested using seismic refraction profiles from the Mendocino Fracture Zone
. Hess found that the slow shear waves propagated perpendicular to the plane of slip and the higher velocity component was parallel to it. He inferred that the structure of oceanic basins could be recorded quickly and understood better if these techniques were used.
Ando (1980) focused on identifying Shear-wave anisotropy in the upper mantle
. This study focused on shear wave splitting recorded near the Chubu Volcanic Area
in Japan
. Using newly implemented telemetric
seismographic stations, they were able to record both P-wave and S-wave arrivals from earthquakes up to 260 km beneath the volcanic area. The depths of these earthquakes make this area ideal for studying the structure of the upper mantle. They noted the arrivals of two distinct shear waves with different polarizations (N-S, fast and E-W, slow) approximately 0.7 seconds apart. It was concluded that the splitting was not caused by the earthquake source but by the travel path of the waves on the way to the seismometers. Data from other nearby stations were used to constrain the source of the seismic anisotropy. He found the anisotropy to be consistent with the area directly below the volcanic area and was hypothesized to occur due to oriented crystals in a deep rooted magma chamber
. If the magma chamber contained elliptical inclusions oriented approximately N-S, then the maximum velocity direction would also be N-S, accounting for the presence of seismic birefringence
.
Crampin (1980) proposed the theory of earthquake
prediction using shear wave splitting measurements. This theory is based on the fact that microcracks between the grains or crystals in rocks will open wider than normal at high stress levels. After the stress subsides, the microcracks will return to their original positions. This phenomenon of cracks opening and closing in response to changing stress conditions is called dilatancy. Because shear wave splitting signatures are dependent on both the orientation of the microcracks (perpendicular to the dominant stress direction) and the abundance of cracks, the signature will change over time to reflect the stress changes in the area. Once the signatures for an area are recognized, they may then be applied to predict nearby earthquakes with the same signatures.
Crampin (1981) first acknowledged the phenomenon of azimuthally-aligned shear wave splitting in the crust. He reviewed the current theory, updated equations to better understand shear-wave splitting, and presented a few new concepts. Crampin established that the solution to most anisotropic problems can be developed. If a corresponding solution for an isotropic case can be formulated, then the anisotropic case can be arrived at with more calculations. The correct identification of body and surface wave polarizations is the key to determining the degree of anisotropy. The modeling of many two-phase materials can be simplified by the use of anisotropic elastic-constants
. These constants can be found by looking at recorded data. This has been observed in several areas world wide.
crystals present in the medium, then it would act upon these particles like those that make up a liquid
or gas
. The energy would be transferred more slowly through the medium and the velocity would be slower than the first shear wave.
The time delay between the shear wave arrivals depends on several factors including the degree of anisotropy and the distance the waves travel to the recording station. Media with wider, larger cracks will have a longer time delay than a media with small or even closed cracks. Shear wave splitting will continue to occur until the shear-wave velocity anisotropy reaches about 5.5%.
in rectangular Cartesian coordinates can be written as
where t is the time,
is the density
,
is the component of the displacement vector U, and 
represents the elastic parameters.
A wave front can be described by the equation
The solution to can be expressed as a ray series
where the function
satisfies the relation
Substitute into ,
where the vector operators N,M,L are given by the formula:
where
For the first order
, so 
, and only the first component of the equation is left.
Thus,
To obtain the solution of , the eigenvalues and eigenvectors of matrix
are needed,
which can be rewritten as
where the values
and 
are the invariants of the symmetric matrix 
.
The matrix
has three eigenvectors: 
, which correspond to three eigenvalues of
and 
.
where A is the complex vector amplitude,
is the wavelet function (the result of the Fourier transform
ed source time function), and
is a real unit vector pointing in the plane orthogonal to the propagation
.
The process of shear wave splitting can be represented as the application of the splitting operator to the shear wave function.
where
and 
are eigenvectors of the polarization matrix
with eigenvalues corresponding to the two shear wave velocities.
The resulting split waveform is
]
Where
is the time delay between the slow and fast shear waves and 
is the angle between the polarizations of the slow and fast shear waves. These two parameters can be individually estimated from multiple component seismic recordings (Fig. 5).
code and create a demonstration
movie by yourself here on MathWorks website.
Figure 7 is a screen shot of the Matlab Demo output.
According to Crampin shear wave splitting measurements can be used to monitor stress levels in the earth. It is well known that rocks near an earthquake-prone zone will exhibit dilatancy. Shear wave splitting is produced by seismic waves traveling through a medium with oriented cracks or crystals. The changes in shear wave splitting measurements over the time leading up to an impending earthquake can be studied to give insight to the timing and location of the earthquake. These phenomena may be observed many hundreds of kilometers from the epicenter.
The petroleum industry
uses shear-wave splitting measurements to map the fractures throughout a hydrocarbon reservoir
. To date, this is the best method to gain in situ information about the fracture network present in a hydrocarbon reservoir. The best production in a field is associated with an area where there are multiple small fractures that are open, allowing for constant flow of the hydrocarbons. Shear-wave splitting measurements are recorded and analyzed to obtain the degree of anisotropy throughout the reservoir. The area with the largest degree of anisotropy will generally be the best place to drill because it will contain the largest number of open fractures.
, Crampin and his coworkers recognized that time delays between split shear-waves were increasing at two seismic recording stations, BJA and SAU, in southwest Iceland. The following factors lead the group to recognize this as a possible precursor to an earthquake:
These features suggested that the crust was approaching fracture criticality and that an earthquake was likely to occur in the near future.
Based on this information, an alert was sent to the Iceland Meteorological Office (IMO) on October 27 and 29, warning of an approaching earthquake. On November 10, they sent another email specifying that an earthquake was likely to occur within the next 5 months. In the time leading up to an earthquake an area is undergoes continuous stress and is constantly accumulating energy. Therefore the longer it takes for the eruption to occur, the larger and more devastating it has the potential to be.
Three days later, on November 13, IMO reported a magnitude 5 earthquake near the BJA station.
Crampin et al. suggests that this is the first scientifically, as opposed to precursory or statistically, predicted earthquake. They proved that variations of shear-wave splitting can be used to forecast earthquakes.
This technique was not successful again until 2008 due to the lack of appropriate source-geophone
-earthquake geometry needed to evaluate changes in shear wave splitting signatures and time delays.
in Vatnajökull
Icefield. This was the largest eruption in Iceland in several decades.
The pattern of increasing shear wave splitting time-delays is typical of the increase now seen before many earthquakes in Iceland and elsewhere. The time delays just before earthquakes characteristically decrease immediately following the eruption because the majority of the stress is released at that one time. The increase in normalized time-delays in volcanic eruptions does not decrease at the time of the eruption but gradually declines at about
over several. This decrease is approximately linear and there appeared to be no other significant magma
tic disturbances during the period following the eruption.
More observations are needed to confirm whether the increase and decrease time delay pattern is universal for all volcanic eruptions or if each area is different. It is possible that different types of eruptions show different shear wave splitting behaviors.
Continental
Deep Drilling Program (KTB) deep drilling site in southeast Germany
. They observed shear-wave splitting from injection-induced events at a pilot well offset 190 meters form the KTB well. A borehole
recorder
at a depth of 4,000 meters was used to record the splitting measurements.
They found:
No direct interpretation of the decrease is proposed but it is suggested that the decrease is associated with stress release by the induced events.
Shear wave splitting is very sensitive to fine changes in the pore pressure in the Earth's crust. In order to successfully detect the degree of anisotropy in a region there must be more several arrivals that are well distributed in time. Too few events cannot detect the change even if they are from similar waveforms. The
Shear wave splitting varies with both incidence angle and propagation azimuth. Unless this data is viewed in polar projection, the 3-D nature is not reflected and may be misleading.
Shear wave splitting may be caused by more than just one layer that is anisotropic and located anywhere between the source and the receiver station. The shear wave splitting measurements have extensive lateral resolution but very poor vertical resolution. The polarizations of shear waves vary throughout the rock mass. Therefore the observed polarizations may be those of the near surface structure and are not necessarily representative of the structure of interest.
s, they write very complicated signatures. Polarizations and time delays are heavily scattered and vary greatly both in time and space. Because of the variation in signature, it is easy to misinterpret the arrivals and polarization of incoming shear waves. Below is an explanation of a few of the common misunderstandings associated with shear waves, further information can be found in Crampin and Peacock (2008).
Shear waves that propagate along the ray path at a group velocity
have polarizations that are only orthogonal in a few specific directions. Polarizations of body waves are orthogonal in all phase velocity
directions, however this type of propagation is generally very difficult to observe or record.
Even when propagating through parallel cracks or perpendicular
to spreading centers or parallel to cracks, the polarizations of shear waves will always vary in three dimensions with incidence and azimuth within the shear wave window.
This statement only holds true if the fluid in the cracks is somehow removed. This may be accomplished via chemical absorption, drainage, or flow to the surface. However, these occur in relatively rare instances and there is evidence that supports the presence of fluids at depth. This includes data from the Kola deep well and the presence of high conductivity in the lower crust.
Stacking seismic data from a reflection survey is useful because it was collected with a predictable, controlled source. When the source is uncontrolled and unpredictable, stacking the data only degrades the signal. Because recorded shear wave time delays and polarizations vary in their incidence angle and azimuth of radio propagation
, stacking these arrivals will degrade the signal and decrease the signal to noise ratio, resulting in a plot that is noisy and hard to interpret at best.
and for predicting earthquakes
and volcanic eruptions
.
Shear wave splitting measurements have been used successfully to predict several earthquakes. With better equipment and more densely spaced recording stations, we have been able to study the signature variations of shear wave splitting over earthquakes in different regions. These signatures change over time to reflect the amount of stress present in an area. After several earthquakes have been recorded and studied, the signatures of shear wave splitting just before an earthquake occurs become well known and this can be used to predict future events. This same phenomenon can be seen before a volcanic eruption and it is inferred that they may be predicted in the same manner.
The petroleum industry has been using shear wave splitting measurements recorded above hydrocarbon reservoirs to gain invaluable information about the reservoir for years. Equipment is constantly being updated to reveal new images and more information.
Birefringence
Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...
, is the phenomenon that occurs when a polarized shear wave enters an anisotropic media (Fig. 1). The incident shear wave splits into two polarized shear waves (Fig. 2). Shear wave splitting are typically used as a tool for testing the anisotropy of an area of interest. These measurements reflect the degree of anisotropy and leads to a better understanding of the area’s crack density and orientation or crystal alignment.
We can think of the anisotropy of a particular area as a black box
Black box
A black box is a device, object, or system whose inner workings are unknown; only the input, transfer, and output are known characteristics.The term black box can also refer to:-In science and technology:*Black box theory, a philosophical theory...
and the shear wave splitting measurements as a way of looking at what is in the box.
]
Introduction
An incident shear wave may enter an anisotropic medium from an isotropic media by encountering a change in the preferred orientationOrientation (geometry)
In geometry the orientation, angular position, or attitude of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it is in....
or character of the medium. When a polarized shear wave enters a new, anisotropic medium, it splits into two shear waves (Fig.2).
One of these shear waves will be faster than the other and oriented parallel to the cracks or crystals in the medium. The second wave will be slower than the first and sometimes orthogonal to both the first shear wave and the cracks or crystals in the media. The time delays observed between the slow and fast shear waves give information about the density of cracks in the medium. The orientation of the fast shear wave records the direction of the cracks in the medium.
When plotted using polarization diagrams, the arrival of split shear waves can be identified by the abrupt changes in direction of the particle motion (Fig.3).
In a homogeneous
Homogeneous (chemistry)
A substance that is uniform in composition is a definition of homogeneous. This is in contrast to a substance that is heterogeneous.The definition of homogeneous strongly depends on the context used. In Chemistry, a homogeneous suspension of material means that when dividing the volume in half, the...
material that is weakly anisotropic, the incident shear wave will split into two quasi-shear waves with approximately orthogonal polarizations that reach the receiver at approximately the same time. In the deeper crust
Crust (geology)
In geology, the crust is the outermost solid shell of a rocky planet or natural satellite, which is chemically distinct from the underlying mantle...
and upper mantle
Mantle (geology)
The mantle is a part of a terrestrial planet or other rocky body large enough to have differentiation by density. The interior of the Earth, similar to the other terrestrial planets, is chemically divided into layers. The mantle is a highly viscous layer between the crust and the outer core....
, the high frequency shear waves split completely into two separate shear waves with different polarizations and a time delay between them that may be up to a few seconds.
History
Hess (1964) made the first measurements of P-waveP-wave
P-waves are a type of elastic wave, also called seismic waves, that can travel through gases , solids and liquids, including the Earth. P-waves are produced by earthquakes and recorded by seismographs...
azimuthal velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
variations in oceanic basin
Oceanic basin
Hydrologically, an oceanic basin may be anywhere on Earth that is covered by seawater, but geologically ocean basins are large geologic basins that are below sea level...
s. This area was chosen for this study because oceanic basins are made of large, relatively uniform homogeneous rocks. Hess observed, from previous seismic velocity experiments with olivine crystals
Olivine
The mineral olivine is a magnesium iron silicate with the formula 2SiO4. It is a common mineral in the Earth's subsurface but weathers quickly on the surface....
, that if the crystals had even a slight statistical orientation this would be extremely evident in the seismic velocities recorded using seismic refraction. This concept was tested using seismic refraction profiles from the Mendocino Fracture Zone
Mendocino Fracture Zone
The Mendocino Fracture Zone is a fracture zone and transform boundary off the coast of Cape Mendocino in far northern California. It runs westward from a triple junction with the San Andreas Fault and the Cascadia subduction zone to the southern end of the Gorda Ridge...
. Hess found that the slow shear waves propagated perpendicular to the plane of slip and the higher velocity component was parallel to it. He inferred that the structure of oceanic basins could be recorded quickly and understood better if these techniques were used.
Ando (1980) focused on identifying Shear-wave anisotropy in the upper mantle
Mantle (geology)
The mantle is a part of a terrestrial planet or other rocky body large enough to have differentiation by density. The interior of the Earth, similar to the other terrestrial planets, is chemically divided into layers. The mantle is a highly viscous layer between the crust and the outer core....
. This study focused on shear wave splitting recorded near the Chubu Volcanic Area
Volcano
2. Bedrock3. Conduit 4. Base5. Sill6. Dike7. Layers of ash emitted by the volcano8. Flank| 9. Layers of lava emitted by the volcano10. Throat11. Parasitic cone12. Lava flow13. Vent14. Crater15...
in Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
. Using newly implemented telemetric
Telemetry
Telemetry is a technology that allows measurements to be made at a distance, usually via radio wave transmission and reception of the information. The word is derived from Greek roots: tele = remote, and metron = measure...
seismographic stations, they were able to record both P-wave and S-wave arrivals from earthquakes up to 260 km beneath the volcanic area. The depths of these earthquakes make this area ideal for studying the structure of the upper mantle. They noted the arrivals of two distinct shear waves with different polarizations (N-S, fast and E-W, slow) approximately 0.7 seconds apart. It was concluded that the splitting was not caused by the earthquake source but by the travel path of the waves on the way to the seismometers. Data from other nearby stations were used to constrain the source of the seismic anisotropy. He found the anisotropy to be consistent with the area directly below the volcanic area and was hypothesized to occur due to oriented crystals in a deep rooted magma chamber
Magma chamber
A magma chamber is a large underground pool of molten rock found beneath the surface of the Earth. The molten rock in such a chamber is under great pressure, and given enough time, that pressure can gradually fracture the rock around it creating outlets for the magma...
. If the magma chamber contained elliptical inclusions oriented approximately N-S, then the maximum velocity direction would also be N-S, accounting for the presence of seismic birefringence
Birefringence
Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...
.
Crampin (1980) proposed the theory of earthquake
Earthquake
An earthquake is the result of a sudden release of energy in the Earth's crust that creates seismic waves. The seismicity, seismism or seismic activity of an area refers to the frequency, type and size of earthquakes experienced over a period of time...
prediction using shear wave splitting measurements. This theory is based on the fact that microcracks between the grains or crystals in rocks will open wider than normal at high stress levels. After the stress subsides, the microcracks will return to their original positions. This phenomenon of cracks opening and closing in response to changing stress conditions is called dilatancy. Because shear wave splitting signatures are dependent on both the orientation of the microcracks (perpendicular to the dominant stress direction) and the abundance of cracks, the signature will change over time to reflect the stress changes in the area. Once the signatures for an area are recognized, they may then be applied to predict nearby earthquakes with the same signatures.
Crampin (1981) first acknowledged the phenomenon of azimuthally-aligned shear wave splitting in the crust. He reviewed the current theory, updated equations to better understand shear-wave splitting, and presented a few new concepts. Crampin established that the solution to most anisotropic problems can be developed. If a corresponding solution for an isotropic case can be formulated, then the anisotropic case can be arrived at with more calculations. The correct identification of body and surface wave polarizations is the key to determining the degree of anisotropy. The modeling of many two-phase materials can be simplified by the use of anisotropic elastic-constants
Elastic modulus
An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically when a force is applied to it...
. These constants can be found by looking at recorded data. This has been observed in several areas world wide.
Physical Mechanism
The difference in the travel velocities of the two shear waves can be explained by comparing their polarizations with the dominant direction of anisotropy in the area. The interactions between the tiny particles that make up solids and liquids can be used as an analogue for the way a wave travels through a medium. Solids have very tightly bound particles that transmit energy very quickly and efficiently. In a liquid, the particles are much less tightly bound and it generally takes a longer time for the energy to be transmitted. This is because the particles have further to travel to transfer the energy from one to another. If a shear wave is polarized parallel to the cracks in this anisotropic medium, then it may look like the dark blue wave in Figure 4. This wave is acting on the particles like energy being transferred through a solid. It will have a high velocity because of the proximity of the grains to each other. If there is a shear wave that is polarized perpendicular to the liquid-filled cracks or elongated olivineOlivine
The mineral olivine is a magnesium iron silicate with the formula 2SiO4. It is a common mineral in the Earth's subsurface but weathers quickly on the surface....
crystals present in the medium, then it would act upon these particles like those that make up a liquid
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...
or gas
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...
. The energy would be transferred more slowly through the medium and the velocity would be slower than the first shear wave.
The time delay between the shear wave arrivals depends on several factors including the degree of anisotropy and the distance the waves travel to the recording station. Media with wider, larger cracks will have a longer time delay than a media with small or even closed cracks. Shear wave splitting will continue to occur until the shear-wave velocity anisotropy reaches about 5.5%.
Mathematical Explanation(Ray theory)
The equation of motionEquation of motion
Equations of motion are equations that describe the behavior of a system in terms of its motion as a function of time...
in rectangular Cartesian coordinates can be written as
where t is the time,
is the densityDensity
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
,
is the component of the displacement vector U, and represents the elastic parameters.A wave front can be described by the equation
The solution to can be expressed as a ray series
where the function
satisfies the relationSubstitute into ,
where the vector operators N,M,L are given by the formula:
where
For the first order
, so , and only the first component of the equation is left.Thus,
To obtain the solution of , the eigenvalues and eigenvectors of matrix
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
are needed,which can be rewritten as
where the values
and are the invariants of the symmetric matrix .The matrix
has three eigenvectors: , which correspond to three eigenvalues of and .- For isotropic media,
corresponds to the compressional wave and 
corresponds to the two shear waves traveling together. - For anisotropic media,
, indicates that the two shear waves have split.
Modeling
In an isotropic homogeneous medium, the shear wave function can be written aswhere A is the complex vector amplitude,
is the wavelet function (the result of the Fourier transformFourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
ed source time function), and
is a real unit vector pointing in the plane orthogonal to the propagationWave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
.
The process of shear wave splitting can be represented as the application of the splitting operator to the shear wave function.
where
and are eigenvectors of the polarization matrixMatrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
with eigenvalues corresponding to the two shear wave velocities.
The resulting split waveform is
]
Where
is the time delay between the slow and fast shear waves and is the angle between the polarizations of the slow and fast shear waves. These two parameters can be individually estimated from multiple component seismic recordings (Fig. 5).Schematic Model
Figure 6 is a schematic animation showing the process of shear wave splitting and the seismic signature generated by the arrivals of two polarized shear waves at the surface recording station. There is one incident shear wave (blue) traveling vertically along the center grey axis through an isotropic medium (green). This single incident shear wave splits into two shear waves (orange and purple) upon entering the anisotropic media (red). The faster shear wave is oriented parallel to the cracks or crystals in the medium. The arrivals of the shear waves are shown on the right, as they appear at the recording station. The north-south polarized shear wave arrives first (purple) and the east-west polarized shear wave (orange) arrives about a second later.MATLAB Code for demonstration
You can download a MATLABMATLAB
MATLAB is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages,...
code and create a demonstration
Scientific demonstration
A scientific demonstration is a scientific experiment carried out for the purposes of demonstrating scientific principles, rather than for hypothesis testing or knowledge gathering ....
movie by yourself here on MathWorks website.
Figure 7 is a screen shot of the Matlab Demo output.
Applications/Justification/Usefulness
Shear wave splitting measurements have been used to successfully predict earthquakes, and to map fracture networks created by high pressure fracturing of reservoirs.According to Crampin shear wave splitting measurements can be used to monitor stress levels in the earth. It is well known that rocks near an earthquake-prone zone will exhibit dilatancy. Shear wave splitting is produced by seismic waves traveling through a medium with oriented cracks or crystals. The changes in shear wave splitting measurements over the time leading up to an impending earthquake can be studied to give insight to the timing and location of the earthquake. These phenomena may be observed many hundreds of kilometers from the epicenter.
The petroleum industry
Petroleum industry
The petroleum industry includes the global processes of exploration, extraction, refining, transporting , and marketing petroleum products. The largest volume products of the industry are fuel oil and gasoline...
uses shear-wave splitting measurements to map the fractures throughout a hydrocarbon reservoir
Reservoir
A reservoir , artificial lake or dam is used to store water.Reservoirs may be created in river valleys by the construction of a dam or may be built by excavation in the ground or by conventional construction techniques such as brickwork or cast concrete.The term reservoir may also be used to...
. To date, this is the best method to gain in situ information about the fracture network present in a hydrocarbon reservoir. The best production in a field is associated with an area where there are multiple small fractures that are open, allowing for constant flow of the hydrocarbons. Shear-wave splitting measurements are recorded and analyzed to obtain the degree of anisotropy throughout the reservoir. The area with the largest degree of anisotropy will generally be the best place to drill because it will contain the largest number of open fractures.
A successfully stress-forecast earthquake in Iceland
On October 27, 1998, during a four year study of shear wave splitting in IcelandIceland
Iceland , described as the Republic of Iceland, is a Nordic and European island country in the North Atlantic Ocean, on the Mid-Atlantic Ridge. Iceland also refers to the main island of the country, which contains almost all the population and almost all the land area. The country has a population...
, Crampin and his coworkers recognized that time delays between split shear-waves were increasing at two seismic recording stations, BJA and SAU, in southwest Iceland. The following factors lead the group to recognize this as a possible precursor to an earthquake:
- The increase persisted for nearly 4 months.
- It had approximately the same duration and slope as a previously recorded magnitude 5.1 earthquake in Iceland.
- The time delay increase at station BJA started at about
and escalated to approximately 
. -
was the inferred level of fracture for the previous earthquake.
These features suggested that the crust was approaching fracture criticality and that an earthquake was likely to occur in the near future.
Based on this information, an alert was sent to the Iceland Meteorological Office (IMO) on October 27 and 29, warning of an approaching earthquake. On November 10, they sent another email specifying that an earthquake was likely to occur within the next 5 months. In the time leading up to an earthquake an area is undergoes continuous stress and is constantly accumulating energy. Therefore the longer it takes for the eruption to occur, the larger and more devastating it has the potential to be.
Three days later, on November 13, IMO reported a magnitude 5 earthquake near the BJA station.
Crampin et al. suggests that this is the first scientifically, as opposed to precursory or statistically, predicted earthquake. They proved that variations of shear-wave splitting can be used to forecast earthquakes.
This technique was not successful again until 2008 due to the lack of appropriate source-geophone
Geophone
The term geophone derives from the Greek word "geo" meaning "earth" and "phone" meaning "sound".A geophone is a device which converts ground movement into voltage, which may be recorded at a recording station...
-earthquake geometry needed to evaluate changes in shear wave splitting signatures and time delays.
Temporal changes before volcanic eruptions
Volti and Crampin observed temporal increases in Band-1 time-delays for 5 months at approximately 240 kilometer depth in directions N,SW and W,SW before the 1996 Gjalp EruptionBárðarbunga
Bárðarbunga is an Icelandic stratovolcano located under the ice cap of Vatnajökull glacier, rising to 2,009 m above sea level, making it the second highest mountain in Iceland, just about 101 m lower than Hvannadalshnjúkur....
in Vatnajökull
Vatnajökull
Vatnajökull is the largest glacier in Iceland. It is located in the south-east of the island, covering more than 8% of the country.-Size:With an area of 8,100 km², Vatnajökull is the largest ice cap in Europe by volume and the second largest in area Vatnajökull is the largest glacier in...
Icefield. This was the largest eruption in Iceland in several decades.
The pattern of increasing shear wave splitting time-delays is typical of the increase now seen before many earthquakes in Iceland and elsewhere. The time delays just before earthquakes characteristically decrease immediately following the eruption because the majority of the stress is released at that one time. The increase in normalized time-delays in volcanic eruptions does not decrease at the time of the eruption but gradually declines at about
over several. This decrease is approximately linear and there appeared to be no other significant magmaMagma
Magma is a mixture of molten rock, volatiles and solids that is found beneath the surface of the Earth, and is expected to exist on other terrestrial planets. Besides molten rock, magma may also contain suspended crystals and dissolved gas and sometimes also gas bubbles. Magma often collects in...
tic disturbances during the period following the eruption.
More observations are needed to confirm whether the increase and decrease time delay pattern is universal for all volcanic eruptions or if each area is different. It is possible that different types of eruptions show different shear wave splitting behaviors.
Fluid-injection in Petroleum Engineering
Bokelmann and Harjes reported the effects on the shear waves of fluid injection at about 9 kilometer depth in the GermanGermany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
Continental
Deep Drilling Program (KTB) deep drilling site in southeast Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
. They observed shear-wave splitting from injection-induced events at a pilot well offset 190 meters form the KTB well. A borehole
Borehole
A borehole is the generalized term for any narrow shaft bored in the ground, either vertically or horizontally. A borehole may be constructed for many different purposes, including the extraction of water or other liquid or gases , as part of a geotechnical investigation, environmental site...
recorder
Recorder
The recorder is a woodwind musical instrument of the family known as fipple flutes or internal duct flutes—whistle-like instruments which include the tin whistle. The recorder is end-blown and the mouth of the instrument is constricted by a wooden plug, known as a block or fipple...
at a depth of 4,000 meters was used to record the splitting measurements.
They found:
- Temporal variations in shear-wave splitting as a direct result of injection-induced events.
- That the initial ~1% shear wave splitting decreases by 2.5% in the next 12 hours following the injection.
- The largest decrease occurred within two hours after the injection.
- The splitting time to be very stable after the injection ceased.
No direct interpretation of the decrease is proposed but it is suggested that the decrease is associated with stress release by the induced events.
Limitations
Shear-wave splitting measurements can provide the most accurate and in depth information about a particular region. However, there are limits that need to be accounted for when recording or analyzing shear wave splitting measurements. These include the sensitive nature of shear waves, that shear wave splitting varies with incidence and azimuth, and that shear waves may split multiple times throughout an anisotropic medium, possibly every time the orientation changes.Shear wave splitting is very sensitive to fine changes in the pore pressure in the Earth's crust. In order to successfully detect the degree of anisotropy in a region there must be more several arrivals that are well distributed in time. Too few events cannot detect the change even if they are from similar waveforms. The
Shear wave splitting varies with both incidence angle and propagation azimuth. Unless this data is viewed in polar projection, the 3-D nature is not reflected and may be misleading.
Shear wave splitting may be caused by more than just one layer that is anisotropic and located anywhere between the source and the receiver station. The shear wave splitting measurements have extensive lateral resolution but very poor vertical resolution. The polarizations of shear waves vary throughout the rock mass. Therefore the observed polarizations may be those of the near surface structure and are not necessarily representative of the structure of interest.
Common Misunderstandings
Due to the nature of split shear waves, when they are recorded in typical three-component seismogramSeismogram
A seismogram is a graph output by a seismograph. It is a record of the ground motion at a measuring station as a function of time. Seismograms typically record motions in three cartesian axes , with the z axis perpendicular to the Earth's surface and the x- and y- axes parallel to the surface...
s, they write very complicated signatures. Polarizations and time delays are heavily scattered and vary greatly both in time and space. Because of the variation in signature, it is easy to misinterpret the arrivals and polarization of incoming shear waves. Below is an explanation of a few of the common misunderstandings associated with shear waves, further information can be found in Crampin and Peacock (2008).
- Polarizations of split shear waves are orthogonal.
Shear waves that propagate along the ray path at a group velocity
Group velocity
The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....
have polarizations that are only orthogonal in a few specific directions. Polarizations of body waves are orthogonal in all phase velocity
Phase velocity
The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...
directions, however this type of propagation is generally very difficult to observe or record.
- Polarizations of split shear-waves are fixed, parallel to cracks, or normal to spreading centers.
Even when propagating through parallel cracks or perpendicular
Perpendicular
In geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...
to spreading centers or parallel to cracks, the polarizations of shear waves will always vary in three dimensions with incidence and azimuth within the shear wave window.
- Crack anisotropyAnisotropyAnisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties An example of anisotropy is the light...
always decreases with depth as fluid filled cracks are closed by lithostatic pressureOverburden pressureOverburden pressure, also called lithostatic pressure or vertical stress, is the pressure or stress imposed on a layer of soil or rock by the weight of overlying material.The overburden pressure at a depth z is given by...
.
This statement only holds true if the fluid in the cracks is somehow removed. This may be accomplished via chemical absorption, drainage, or flow to the surface. However, these occur in relatively rare instances and there is evidence that supports the presence of fluids at depth. This includes data from the Kola deep well and the presence of high conductivity in the lower crust.
- Signal-to-noise ratioSignal-to-noise ratioSignal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...
s of shear-wave splitting above small earthquakes can be improved by stacking.
Stacking seismic data from a reflection survey is useful because it was collected with a predictable, controlled source. When the source is uncontrolled and unpredictable, stacking the data only degrades the signal. Because recorded shear wave time delays and polarizations vary in their incidence angle and azimuth of radio propagation
Radio propagation
Radio propagation is the behavior of radio waves when they are transmitted, or propagated from one point on the Earth to another, or into various parts of the atmosphere...
, stacking these arrivals will degrade the signal and decrease the signal to noise ratio, resulting in a plot that is noisy and hard to interpret at best.
Future Trends
Our understanding of shear wave splitting and how to best use the measurements is constantly improving. As our knowledge improves in this area, there will invariably be better ways of recording and interpreting these measurements and more opportunities to use the data. Currently, it is being developed for use in the petroleum industryPetroleum industry
The petroleum industry includes the global processes of exploration, extraction, refining, transporting , and marketing petroleum products. The largest volume products of the industry are fuel oil and gasoline...
and for predicting earthquakes
Earthquake prediction
An earthquake prediction is a prediction that an earthquake of a specific magnitude will occur in a particular place at a particular time . Despite considerable research efforts by seismologists, scientifically reproducible predictions cannot yet be made to a specific day or month...
and volcanic eruptions
Volcanic Eruptions
Volcanic Eruptions is a company owned by Crispin Glover. The company produces and issues Glover's work: It has released two films to date, What Is It? and its sequel, It is Fine! EVERYTHING IS FINE . Its current plans include releasing the final film in the trilogy titled It Is Mine...
.
Shear wave splitting measurements have been used successfully to predict several earthquakes. With better equipment and more densely spaced recording stations, we have been able to study the signature variations of shear wave splitting over earthquakes in different regions. These signatures change over time to reflect the amount of stress present in an area. After several earthquakes have been recorded and studied, the signatures of shear wave splitting just before an earthquake occurs become well known and this can be used to predict future events. This same phenomenon can be seen before a volcanic eruption and it is inferred that they may be predicted in the same manner.
The petroleum industry has been using shear wave splitting measurements recorded above hydrocarbon reservoirs to gain invaluable information about the reservoir for years. Equipment is constantly being updated to reveal new images and more information.
Further reading
- Crampin, S., and J.H. Lovell, 1991, A decade of shear-wave splitting in the Earth’s crust: what does it mean? what use can we make of it? and what should we do next? : Geophysics Journal International, v. 107, p. 387-407.
- Crampin, S., and S. Peacock, 2005, A review of shear-wave splitting in the compliant crack-critical anisotropic Earth: Wave MotionWave Motion (journal)Wave Motion is a peer-reviewed scientific journal publishing papers on the physics of waves – with emphasis on the areas of acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics...
, v. 41, p. 59-77. - Long, M. D., Hoop, M. V., and R.D. van der Hilst, 2008, Wave-equation shear wave splitting tomography: Geophysics Journal International, v. 172, p. 311-330.
- Savage, M. K., February 1999, Seismic anisotropy and mantle deformation: What have we learned from shear wave splitting?: Reviews of Geophysics, v. 37, p. 65-106.
- Ucisik, N., l. Gudmundsson, W. Hanka, T. Dahl-Jensen, K. Mosegaard, and K. Priestley, 2008, Variations of shear-wave splitting in Greenland: Mantle anisotropy and possible impact of the Iceland plume: Tectonophysics, v. 462, p. 137-148.