Shear wave splitting
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Shear wave splitting, also called
Introduction
An incident shear wave may enter an anisotropic medium from an
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
History
Hess
Ando
Crampin[5] (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[6] (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 worldwide.[7]
Physical mechanism
The difference in the travel velocities of the two shear waves can be explained by comparing their
Mathematical explanation
Mathematical Explanation(Ray theory)[8]
The
-
(1)
where t is the time, is the density, is the component of the
A wavefront can be described by the equation
-
(2)
The solution to (1) can be expressed as a ray series
-
(3)
where the function satisfies the relation
-
(4)
-
(5)
where the vector operators N,M,L are given by the formula:
-
(6)
where
-
(7)
For the first order , so , and only the first component of the equation (5) is left.
Thus,
-
(8)
To obtain the solution of (
-
(9)
which can be rewritten as
-
(9)
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 waveand corresponds to the twoshear wavestraveling together.
- For anisotropic media,, indicates that the two shear waves have split.
Measurement of shear wave splitting parameters
Modeling
[9] In an isotropic homogeneous medium, the shear wave function can be written as
-
(10)
where A is the
The process of shear wave splitting can be represented as the application of the splitting operator to the shear wave function.
-
(11)
where and are
The resulting split waveform is
-
(12)
Where is the time delay between the slow and fast shear waves and is the angle between the polarization of the incident shear wave and the polarization of the fast shear wave . 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.[5]
Applications, justification, usefulness
Shear wave splitting measurements have been used to explore earthquake prediction, and to map fracture networks created by high pressure fracturing of reservoirs.
According to Crampin[5] 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
Case examples
A successfully stress-forecast earthquake in Iceland
On October 27, 1998, during a four-year study of shear wave splitting in Iceland, 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:[12]
- 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. 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.[7]
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 Eruption 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 magmatic 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.[7][13]
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
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.[15]
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.[7] 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.[7] 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.[16] 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.[17]
Common misunderstandings
Due to the nature of split shear waves, when they are recorded in typical three-component seismograms, 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.[18] 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).[7]
- Polarizations of split shear waves are orthogonal.[7][18]
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.
- Polarizations of split shear-waves are fixed, parallel to cracks, or normal to spreading centers.[7][18]
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.
- Crack anisotropy always decreases with depth as fluid filled cracks are closed by lithostatic pressure.[7][18]
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 ratios of shear-wave splitting above small earthquakes can be improved by stacking.[7][18]
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.[7]
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
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
See also
- Birefringence
- S-wave
- P-wave
- Seismic wave
References
- ^
Aki, K.; Richards, P.G. (2002). "Quantitative Seismology" (Second ed.). University Science Books, Sausalito, CA.
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(help) - ^ Vecsey, L. J.; Babuska, V. (2008). "Shear-wave splitting measurements-Problems and solutions". Tectonophysics. 462 (1–4): 178–196. .
- S2CID 4292928.
- S2CID 4306931.
- ^ S2CID 4237223.
- ^ S. Crampin (1981). "A review of wave motion in anisotropic and cracked elastic-media". .
- ^ a b c d e f g h i j k l m S. Crampin; S. Peacock (2008). "A review of the current understanding of seismic shear-wave splitting in the Earth's crust and common fallacies in interpretation". .
- (PDF) from the original on 2011-07-04. Retrieved 2010-05-11.
- .
- ^ R. Bale; J. Li; B. Mattocks & S. Ronen (2006). "Least-Squares Measurement of Shear-Wave Splitting" (PDF). CSPG / CSEG / CWLS Joint Conference. Archived (PDF) from the original on July 19, 2011. Retrieved May 12, 2010.
- ^ E. LaBarre; T. Davis; R. Benson (March 19, 2008). "Finding the sweet spot". E&P. Archived from the original on September 6, 2014. Retrieved June 5, 2012.
- (PDF) from the original on 2012-03-13. Retrieved 2010-05-11.
- from the original on 2009-05-21. Retrieved 2010-05-11.
- (PDF) from the original on 2011-07-21. Retrieved 2010-05-11.
- ^ R. Hoar; K. Stokoe (1978). "Generation and Measurement of Shear Waves In Situ". Dynamic Geochemical Testing: 3–29. .
- ^ M. K. Savage (February 1999). "Seismic anisotropy and mantle deformation: What have we learned from shear wave splitting?". Reviews of Geophysics. 37 (1): 65–106. .
- ^ S. Crampin; Lovell, John H. (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?". Geophysical Journal International. 107 (3): 387–407. .
- ^ a b c d e S. Crampin; Y. Gao (2006). "A review of techniques for measuring shear-wave splitting above small earthquakes". Physics of the Earth and Planetary Interiors. 159 (1–2): 1–14. .
Further reading
- Aster, R.; Shearer, P. (1991). "Quantitive measurements of shear wave polarizations at the Anza seismic network, southern California - Implications for shear-wave splitting and earthquake prediction". Journal of Geophysical Research. 95 (B8): 12449–12473. .
- Crampin, S.; Lovell, J.H. (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?". Geophysical Journal International. 107 (3): 387–407. .
- Crampin, S.; Peacock, S. (2005). "A review of shear-wave splitting in the compliant crack-critical anisotropic Earth". .
- Long, M. D.; Hoop, M. V. (2008). "Wave-equation shear wave splitting tomography". Geophysical Journal International. 172 (1): 311–330. .
- Pastori, M.; Piccinini, D.; Margheriti, L.; Improta, L.; Valoroso, L.; Chiaraluce, L.; Chiarabba, C. (2009). "Stress aligned cracks in the upper crust of the Val d'Agri region as revealed by shear wave splitting". hdl:2122/5499.
- Piccinini, D; Pastori, M.; Margheriti, L. (2013). "ANISOMAT+: An automatic tool to retrieve seismic anisotropy from local earthquakes". Computers & Geosciences. 56: 62–68. .
- Savage, M. K.; February (1999). "Seismic anisotropy and mantle deformation: What have we learned from shear wave splitting?". Reviews of Geophysics. 37 (1): 65–106. .
- Ucisik, N.; Hanka, W.; Dahl-Jensen, T.; Mosegaard, K.; Priestley, K. (2008). "Variations of shear-wave splitting in Greenland: Mantle anisotropy and possible impact of the Iceland plume". Tectonophysics. 462 (1–4): 137–148. .
External links
- Alfred Wegener Institute for polar and Marine Research(AWI)(Germany)
- Shear-wave splitting in Matlab(France)
- A lot of interesting seismic images(ASU)
- Information on Solids, Liquids, and Gasses
MATLAB Code for demonstration
You can download a MATLAB code and create a demonstration movie by yourself here on MathWorks website.
Figure 7 is a screen shot of the Matlab Demo output.