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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.
1970:
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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
1451:
531:. 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
1965:{\displaystyle {\begin{cases}N_{j}\left(U^{\left(n\right)}\right)=\Gamma _{jk}U_{k}^{\left(n\right)}-U_{j}^{\left(n\right)}\\M_{j}\left(U^{\left(n\right)}\right)=p_{i}~a_{ijkl}{\frac {\partial U_{k}^{\left(n\right)}}{\partial x_{l}}}+\rho ^{-1}{\frac {\partial }{\partial x_{i}}}\left(\rho ~a_{ijkl}~p_{l}U_{k}^{\left(n\right)}\right)\\L_{j}\left(U^{\left(n\right)}\right)=\rho ^{-1}{\frac {\partial }{\partial x_{i}}}\left(\rho ~a_{ijkl}{\frac {\partial U_{k}^{\left(n\right)}}{\partial x_{l}}}\right)\end{cases}}}
571:. 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%.
40:
3901:
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.
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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.
4252:, 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).
524:. 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.
4348:
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.
3924:. 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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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medium (Fig. 1). The incident shear wave splits into two polarized shear waves (Fig. 2). Shear wave splitting is typically used as a tool for testing the anisotropy of an area of interest. These measurements reflect the degree of anisotropy and lead to a better understanding of the area's
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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.
466:. Hess found that the slow compressional 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.
3943:. 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.
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3960:, 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:
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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.
500:. 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
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462:, 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
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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
2628:
1996:
5207:
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".
2283:
5482:
3642:
1294:
3113:
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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".
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458:. 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
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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
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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.
2481:{\displaystyle N_{j}\left(U^{\left(0\right)}\right)=\Gamma _{jk}U_{k}^{\left(0\right)}-U_{j}^{\left(0\right)}==\left(\Gamma _{jk}-\delta _{jk}\right)U_{k}^{\left(0\right)}==0}
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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.
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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".
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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
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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).
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4323:, 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.
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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
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3939:. 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
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No direct interpretation of the decrease is proposed but it is suggested that the decrease is associated with stress release by the induced events.
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1108:{\displaystyle U_{k}\left(x_{i},t\right)=\sum _{n=0}^{\infty }U_{k}^{\left(n\right)}\left(x_{i}\right)f_{n}\left(t-\tau \left(x_{i}\right)\right)}
4563:
S. Crampin; R.Evans; B. Ucer; M.Doyle; et al. (1980). "Observations of dilatancy-induced polarization anomalies and earthquake prediction".
4355:
to gain invaluable information about the reservoir for years. Equipment is constantly being updated to reveal new images and more information.
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348:
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Piccinini, D; Pastori, M.; Margheriti, L. (2013). "ANISOMAT+: An automatic tool to retrieve seismic anisotropy from local earthquakes".
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inclusions oriented approximately N-S, then the maximum velocity direction would also be N-S, accounting for the presence of seismic
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2161:{\displaystyle \Gamma _{jk}=p_{i}~p_{l}~a_{ijkl},\quad a_{ijkl}=c_{ijkl}/\rho ,\quad p_{i}={\frac {\partial \tau }{\partial x_{i}}}}
5238:"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?"
5119:"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?"
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The process of shear wave splitting can be represented as the application of the splitting operator to the shear wave function.
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have polarizations that are only orthogonal in a few specific directions. Polarizations of body waves are orthogonal in all
3768:{\displaystyle u_{s}\left(\omega \right)=A~w\left(\omega \right)\exp \left\Gamma \left(\phi ,\delta t\right)\cdot {\hat {p}}}
96:
1416:{\displaystyle N\left(U^{\left(n\right)}\right)-M\left(U^{\left({n-1}\right)}\right)+L\left(U^{\left({n-2}\right)}\right)=0}
277:
4200:. They observed shear-wave splitting from injection-induced events at a pilot well offset 190 meters form the KTB well. A
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concluded that the splitting was not caused by the earthquake source but by the travel path of the waves on the way to the
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521:
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5271:
Crampin, S.; Peacock, S. (2005). "A review of shear-wave splitting in the compliant crack-critical anisotropic Earth".
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4929:"A four-year study of shear-wave splitting in Iceland: 2. Temporal changes before earthquakes and volcanic eruptions"
4401:
Aki, K.; Richards, P.G. (2002). "Quantitative
Seismology" (Second ed.). University Science Books, Sausalito, CA.
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Bokelmann and Harjes reported the effects on the shear waves of fluid injection at about 9 kilometer depth in the
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535:. These constants can be found by looking at recorded data. This has been observed in several areas worldwide.
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S. Crampin; Y. Gao (2006). "A review of techniques for measuring shear-wave splitting above small earthquakes".
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It had approximately the same duration and slope as a previously recorded magnitude 5.1 earthquake in
Iceland.
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Pastori, M.; Piccinini, D.; Margheriti, L.; Improta, L.; Valoroso, L.; Chiaraluce, L.; Chiarabba, C. (2009).
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M. Ando; Y.Ishikawa; H. Wada (1980). "S-wave anisotropy in the upper mantle under a volcanic area in Japan".
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Figure 4. Schematic diagram of two orthogonal polarized shear waves traveling through an anisotropic medium.
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3892:. These two parameters can be individually estimated from multiple component seismic recordings (Fig. 5).
737:{\displaystyle {\frac {\partial }{\partial x_{i}}}\left=\rho {\frac {\partial ^{2}U_{j}}{\partial t^{2}}}}
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That the initial ~1% shear wave splitting decreases by 2.5% in the next 12 hours following the injection.
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3935:. To date, this is the best method to gain in situ information about the fracture network present in a
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5339:"Stress aligned cracks in the upper crust of the Val d'Agri region as revealed by shear wave splitting"
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density and orientation or crystal alignment. We can think of the anisotropy of a particular area as a
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Crampin (1981) first acknowledged the phenomenon of azimuthally-aligned shear wave splitting in the
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4095:-earthquake geometry needed to evaluate changes in shear wave splitting signatures and time delays.
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The difference in the travel velocities of the two shear waves can be explained by comparing their
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over several. This decrease is approximately linear and there appeared to be no other significant
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Vecsey, L. J.; Babuska, V. (2008). "Shear-wave splitting measurements-Problems and solutions".
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directions, however this type of propagation is generally very difficult to observe or record.
432:, the high frequency shear waves split completely into two separate shear waves with different
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5413:"Seismic anisotropy and mantle deformation: What have we learned from shear wave splitting?"
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5078:"Seismic anisotropy and mantle deformation: What have we learned from shear wave splitting?"
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Shear-Wave-Splitting-in-Anisotropic-Media
Collection (Goethe University Frankfurt, Germany)
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Temporal variations in shear-wave splitting as a direct result of injection-induced events.
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Due to the nature of split shear waves, when they are recorded in typical three-component
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This technique was not successful again until 2008 due to the lack of appropriate source-
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4987:"Evidence for temporal variation of seismic velocity within the upper continental crust"
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1251:{\displaystyle df_{n+1}\left(\vartheta \right)/d\vartheta =f_{n}\left(\vartheta \right)}
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present in the medium, then it would act upon these particles like those that make up a
5262:
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4608:
S. Crampin (1981). "A review of wave motion in anisotropic and cracked elastic-media".
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The petroleum industry has been using shear wave splitting measurements recorded above
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data from the Kola deep well and the presence of high conductivity in the lower crust.
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3280:{\displaystyle u\left(\omega \right)=A~w\left(\omega \right)\exp \left\cdot {\hat {p}}}
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uses shear-wave splitting measurements to map the fractures throughout a hydrocarbon
3539:{\displaystyle \Gamma =\exp \left{\hat {f}}{\hat {f}}+\exp \left{\hat {s}}{\hat {s}}}
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and the shear wave splitting measurements as a way of looking at what is in the box.
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of split shear-waves are fixed, parallel to cracks, or normal to spreading centers.
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is a real unit vector pointing in the displacement direction and contained in the
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R. Hoar; K. Stokoe (1978). "Generation and Measurement of Shear Waves In Situ".
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cracks opening and closing in response to changing stress conditions is called
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H. H. Hess (1964). "Seismic Anisotropy of the Uppermost Mantle under Oceans".
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In an isotropic homogeneous medium, the shear wave function can be written as
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of shear-wave splitting above small earthquakes can be improved by stacking.
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at a depth of 4,000 meters was used to record the splitting measurements.
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On October 27, 1998, during a four-year study of shear wave splitting in
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Icefield. This was the largest eruption in Iceland in several decades.
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stations, they were able to record both P-wave and S-wave arrivals from
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3913:, and to map fracture networks created by high pressure fracturing of
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Ando (1980) focused on identifying shear-wave anisotropy in the upper
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4709:"Seismic rays and ray intensities in inhomogeneous anisotropic media"
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Alfred Wegener Institute for polar and Marine Research(AWI)(Germany)
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The largest decrease occurred within two hours after the injection.
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always decreases with depth as fluid filled cracks are closed by
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is the angle between the polarization of the incident shear wave
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The splitting time to be very stable after the injection ceased.
473:. This study focused on shear wave splitting recorded near the
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was the inferred level of fracture for the previous earthquake.
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and a time delay between them that may be up to a few seconds.
399:
An incident shear wave may enter an anisotropic medium from an
568:
4767:"Shear Wave Splitting and Subcontinental Mantle Deformation"
3909:
Shear wave splitting measurements have been used to explore
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is the time delay between the slow and fast shear waves and
2623:{\displaystyle Det\left(\Gamma _{jk}-G\delta _{jk}\right)=0}
1958:
2278:{\displaystyle U^{\left(-1\right)}=U^{\left(-2\right)}=0}
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The time delay increase at station BJA started at about
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disturbances during the period following the eruption.
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Figure 7 is a screen shot of the Matlab Demo output.
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A successfully stress-forecast earthquake in Iceland
4809:"Least-Squares Measurement of Shear-Wave Splitting"
4807:R. Bale; J. Li; B. Mattocks & S. Ronen (2006).
4263:Shear waves that propagate along the ray path at a
4840:E. LaBarre; T. Davis; R. Benson (March 19, 2008).
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4282:Even when propagating through parallel cracks or
4933:Geological Society, London, Special Publications
3632:corresponding to the two shear wave velocities.
3164:, indicates that the two shear waves have split.
3108:{\displaystyle G_{2}=G_{3}=\beta ^{2}p_{i}p_{i}}
2286:, and only the first component of the equation (
403:media by encountering a change in the preferred
5304:"Wave-equation shear wave splitting tomography"
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3169:Measurement of shear wave splitting parameters
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5169:Physics of the Earth and Planetary Interiors
3863:and the polarization of the fast shear wave
1163:{\displaystyle f_{n}\left(\vartheta \right)}
444:Hess (1964) made the first measurements of
4869:"A successfully stress-forecast earthquake"
4867:S. Crampin; T.Volti; R. Stefánsson (1999).
3964:The increase persisted for nearly 4 months.
3031:{\displaystyle G_{1}=\alpha ^{2}p_{i}p_{i}}
2898:, which correspond to three eigenvalues of
2777:are the invariants of the symmetric matrix
5498:Information on Solids, Liquids, and Gasses
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3753:
3714:
3650:
3644:
3599:
3598:
3596:
3570:
3569:
3567:
3525:
3524:
3513:
3512:
3499:
3459:
3458:
3447:
3446:
3433:
3402:
3358:
3357:
3355:
3316:
3266:
3265:
3251:
3188:
3147:
3134:
3128:
3099:
3089:
3079:
3066:
3053:
3047:
3022:
3012:
3002:
2989:
2983:
2958:
2949:
2925:
2909:
2903:
2882:
2866:
2850:
2844:
2820:
2814:
2788:
2782:
2762:
2736:
2678:
2662:
2656:
2600:
2581:
2561:
2532:
2526:
2458:
2453:
2435:
2419:
2393:
2388:
2367:
2362:
2349:
2324:
2310:
2304:
2250:
2224:
2218:
2190:
2149:
2131:
2122:
2106:
2091:
2069:
2046:
2033:
2020:
2004:
1998:
1941:
1918:
1913:
1903:
1888:
1864:
1851:
1842:
1817:
1803:
1776:
1771:
1761:
1739:
1715:
1702:
1693:
1677:
1654:
1649:
1639:
1624:
1611:
1586:
1572:
1550:
1545:
1524:
1519:
1506:
1481:
1467:
1455:
1453:
1386:
1381:
1346:
1341:
1309:
1296:
1231:
1213:
1190:
1181:
1143:
1137:
1090:
1062:
1048:
1026:
1021:
1011:
1000:
976:
961:
955:
916:{\displaystyle t=\tau \left(x_{i}\right)}
903:
884:
838:
832:
802:
796:
770:
725:
710:
700:
693:
673:
658:
648:
633:
615:
602:
600:
5493:A lot of interesting seismic images(ASU)
4190:German Continental Deep Drilling Program
4184:Fluid-injection in Petroleum Engineering
4814:. CSPG / CSEG / CWLS Joint Conference.
4393:
3905:Applications, justification, usefulness
515:Crampin (1980) proposed the theory of
371:, is the phenomenon that occurs when a
30:
5488:Shear-wave splitting in Matlab(France)
4848:from the original on September 6, 2014
4415:
4404:
3335:{\displaystyle w\left(\omega \right)}
579:Mathematical Explanation(Ray theory)
7:
5117:S. Crampin; Lovell, John H. (1991).
4259:of split shear waves are orthogonal.
3636:
3394:
3180:
2648:
2553:
2296:
1990:
1445:
1288:
1173:
947:
876:
592:
2891:{\displaystyle g_{1},~g_{2},~g_{3}}
2708:{\displaystyle G^{3}-PG^{2}+QG-R=0}
945:) can be expressed as a ray series
5263:10.1111/j.1365-246x.1991.tb01401.x
5236:Crampin, S.; Lovell, J.H. (1991).
5144:10.1111/j.1365-246X.1991.tb01401.x
4821:from the original on July 19, 2011
4737:10.1111/j.1365-246x.1972.tb06147.x
4196:) deep drilling site in southeast
3725:
3404:
2817:
2785:
2578:
2529:
2416:
2346:
2142:
2134:
2001:
1934:
1906:
1857:
1853:
1708:
1704:
1670:
1642:
1503:
1012:
718:
697:
666:
651:
608:
604:
504:. If the magma chamber contained
14:
5344:Geophysical Journal International
5308:Geophysical Journal International
5302:Long, M. D.; Hoop, M. V. (2008).
5242:Geophysical Journal International
5123:Geophysical Journal International
4877:Geophysical Journal International
874:can be described by the equation
5411:Savage, M. K.; February (1999).
5366:10.1111/j.1365-246x.2009.04302.x
5329:10.1111/j.1365-246x.2007.03632.x
4985:G. Bokelmann; H. Harjes (2000).
4899:10.1046/j.1365-246x.1999.00891.x
3634:The resulting split waveform is
38:
5209:Journal of Geophysical Research
5025:from the original on 2011-07-21
4994:Journal of Geophysical Research
4967:from the original on 2009-05-21
4909:from the original on 2012-03-13
4774:Journal of Geophysical Research
4747:from the original on 2011-07-04
4007:and escalated to approximately
3156:{\displaystyle G_{2}\neq G_{3}}
2117:
2064:
5295:10.1016/j.wavemoti.2004.05.006
5076:M. K. Savage (February 1999).
4694:10.1016/j.wavemoti.2008.01.003
3876:
3847:
3759:
3604:
3575:
3530:
3518:
3464:
3452:
3363:
3271:
1:
5509:MATLAB Code for demonstration
4953:10.1144/GSL.SP.2003.212.01.09
4927:T. Volti; S. Crampin (2003).
2937:{\displaystyle G_{1},~G_{2},}
4632:10.1016/0165-2125(81)90026-3
3346:function (the result of the
2832:{\displaystyle \Gamma _{jk}}
2800:{\displaystyle \Gamma _{jk}}
2544:{\displaystyle \Gamma _{jk}}
5468:10.1016/j.tecto.2007.11.074
5404:10.1016/j.cageo.2013.01.012
5384:Computers & Geosciences
5045:Dynamic Geochemical Testing
4765:P. Silver; W. Chan (1991).
4455:10.1016/j.tecto.2008.01.021
4165:{\displaystyle 2ms/km/year}
3350:source time function), and
2506:
2504:To obtain the solution of (
2288:
1439:where the vector operators
1282:
1276:
941:
484:. Using newly implemented
5570:
5189:10.1016/j.pepi.2006.06.002
4716:Geophys. J. R. Astron. Soc
3885:{\displaystyle {\hat {f}}}
3856:{\displaystyle {\hat {p}}}
3613:{\displaystyle {\hat {s}}}
3584:{\displaystyle {\hat {f}}}
3372:{\displaystyle {\hat {p}}}
2646:which can be rewritten as
1443:are given by the formula:
247:Coordinating Committee for
4332:developed for use in the
278:Adams–Williamson equation
4842:"Finding the sweet spot"
4780:(B10): 16, 429–16, 454.
4244:Common misunderstandings
4099:Temporal changes before
3807:{\displaystyle \delta t}
2839:has three eigenvectors:
856:{\displaystyle c_{ijkl}}
819:is the component of the
575:Mathematical explanation
226:Seismic intensity scales
221:Seismic magnitude scales
5229:10.1029/JB095iB08p12449
4076:{\displaystyle 10ms/km}
4037:{\displaystyle 10ms/km}
3115:corresponds to the two
1171:satisfies the relation
464:Mendocino Fracture Zone
4414:Cite journal requires
4353:hydrocarbon reservoirs
4338:predicting earthquakes
4308:Signal-to-noise ratios
4166:
4077:
4038:
4001:
4000:{\displaystyle 4ms/km}
3886:
3857:
3828:
3808:
3769:
3614:
3585:
3540:
3373:
3336:
3281:
3157:
3122:For anisotropic media,
3109:
3032:
2968:
2967:{\displaystyle ~G_{3}}
2938:
2892:
2833:
2801:
2771:
2751:
2709:
2624:
2545:
2482:
2279:
2205:
2162:
1966:
1417:
1252:
1164:
1109:
1016:
917:
857:
812:
779:
738:
548:
288:Earthquake engineering
5417:Reviews of Geophysics
5082:Reviews of Geophysics
4167:
4078:
4039:
4002:
3937:hydrocarbon reservoir
3911:earthquake prediction
3887:
3858:
3829:
3827:{\displaystyle \phi }
3809:
3770:
3615:
3586:
3541:
3374:
3337:
3282:
3158:
3110:
3033:
2978:For isotropic media,
2969:
2939:
2893:
2834:
2802:
2772:
2752:
2710:
2625:
2546:
2483:
2280:
2206:
2163:
1967:
1418:
1253:
1165:
1110:
996:
918:
858:
813:
811:{\displaystyle U_{j}}
780:
778:{\displaystyle \rho }
739:
588:Cartesian coordinates
546:
311:Earth Sciences Portal
283:Flinn–Engdahl regions
249:Earthquake Prediction
5554:Polarization (waves)
5015:10.1029/2000JB900207
5000:(B10): 23879–23894.
4296:lithostatic pressure
4122:
4050:
4011:
3974:
3867:
3838:
3818:
3795:
3643:
3624:of the polarization
3595:
3566:
3401:
3354:
3315:
3187:
3127:
3046:
2982:
2948:
2902:
2843:
2813:
2781:
2761:
2735:
2655:
2560:
2525:
2303:
2217:
2189:
2184:For the first order
1997:
1452:
1295:
1180:
1136:
954:
883:
831:
795:
769:
599:
362:Shear wave splitting
273:Shear wave splitting
5513:You can download a
5460:2008Tectp.462..137U
5429:1999RvGeo..37...65S
5396:2013CG.....56...62P
5357:2009GeoJI.179..601P
5320:2008GeoJI.172..311L
5287:2005WaMot..41...59C
5254:1991GeoJI.107..387C
5221:1990JGR....9512449A
5215:(B8): 12449–12473.
5181:2006PEPI..159....1C
5135:1991GeoJI.107..387C
5094:1999RvGeo..37...65S
5006:2000JGR...10523879B
4945:2003GSLSP.212..135V
4890:1999GeoJI.138....1X
4786:1991JGR....9616429S
4728:1972GeoJ...29....1C
4707:V. Cerveny (1972).
4686:2008WaMot..45..675C
4624:1981WaMot...3..343C
4579:1980Natur.286..874C
4529:1980Natur.286...43A
4484:1964Natur.203..629H
4447:2008Tectp.462..178V
3348:Fourier transformed
3119:traveling together.
3038:corresponds to the
2750:{\displaystyle P,Q}
2471:
2406:
2380:
2204:{\displaystyle n=0}
1931:
1789:
1667:
1563:
1537:
1131:where the function
1039:
821:displacement vector
173:Epicentral distance
16:Physical phenomenon
5521:movie by yourself
5517:code and create a
4342:volcanic eruptions
4334:petroleum industry
4162:
4101:volcanic eruptions
4073:
4034:
3997:
3929:petroleum industry
3882:
3853:
3824:
3804:
3765:
3610:
3581:
3536:
3369:
3332:
3277:
3153:
3105:
3040:compressional wave
3028:
2964:
2934:
2888:
2829:
2797:
2767:
2747:
2705:
2620:
2541:
2478:
2449:
2384:
2358:
2275:
2201:
2158:
1962:
1957:
1909:
1767:
1645:
1541:
1515:
1413:
1248:
1160:
1105:
1017:
913:
853:
808:
775:
734:
590:can be written as
584:equation of motion
549:
539:Physical mechanism
150:Induced seismicity
97:Remotely triggered
5438:10.1029/98rg02075
5103:10.1029/98RG02075
5053:10.1520/STP35669S
4794:10.1029/91JB00899
4573:(5776): 874–877.
4478:(4945): 629–631.
4321:radio propagation
3879:
3850:
3789:
3788:
3762:
3675:
3607:
3578:
3560:
3559:
3533:
3521:
3467:
3455:
3366:
3309:complex amplitude
3301:
3300:
3274:
3212:
2953:
2920:
2877:
2861:
2770:{\displaystyle R}
2731:where the values
2729:
2728:
2644:
2643:
2502:
2501:
2182:
2181:
2156:
2041:
2028:
1986:
1985:
1948:
1883:
1871:
1756:
1734:
1722:
1684:
1619:
1437:
1436:
1272:
1271:
1129:
1128:
939:The solution to (
937:
936:
758:
757:
732:
680:
622:
533:elastic-constants
359:
358:
5561:
5471:
5454:(1–4): 137–148.
5442:
5440:
5407:
5378:
5368:
5333:
5331:
5298:
5267:
5265:
5232:
5193:
5192:
5164:
5149:
5148:
5146:
5114:
5108:
5107:
5105:
5073:
5067:
5066:
5040:
5034:
5033:
5031:
5030:
5024:
5017:
4991:
4982:
4976:
4975:
4973:
4972:
4924:
4918:
4917:
4915:
4914:
4908:
4901:
4873:
4864:
4858:
4857:
4855:
4853:
4837:
4831:
4830:
4828:
4826:
4820:
4813:
4804:
4798:
4797:
4771:
4762:
4756:
4755:
4753:
4752:
4746:
4739:
4713:
4704:
4698:
4697:
4667:
4636:
4635:
4605:
4599:
4598:
4587:10.1038/286874a0
4560:
4549:
4548:
4537:10.1038/286043a0
4510:
4504:
4503:
4492:10.1038/203629a0
4465:
4459:
4458:
4441:(1–4): 178–196.
4430:
4424:
4423:
4417:
4412:
4410:
4402:
4398:
4171:
4169:
4168:
4163:
4149:
4138:
4082:
4080:
4079:
4074:
4066:
4043:
4041:
4040:
4035:
4027:
4006:
4004:
4003:
3998:
3990:
3891:
3889:
3888:
3883:
3881:
3880:
3872:
3862:
3860:
3859:
3854:
3852:
3851:
3843:
3833:
3831:
3830:
3825:
3813:
3811:
3810:
3805:
3783:
3774:
3772:
3771:
3766:
3764:
3763:
3755:
3749:
3745:
3724:
3720:
3719:
3718:
3689:
3673:
3666:
3655:
3654:
3637:
3619:
3617:
3616:
3611:
3609:
3608:
3600:
3590:
3588:
3587:
3582:
3580:
3579:
3571:
3554:
3545:
3543:
3542:
3537:
3535:
3534:
3526:
3523:
3522:
3514:
3511:
3507:
3503:
3469:
3468:
3460:
3457:
3456:
3448:
3445:
3441:
3437:
3395:
3378:
3376:
3375:
3370:
3368:
3367:
3359:
3341:
3339:
3338:
3333:
3331:
3295:
3286:
3284:
3283:
3278:
3276:
3275:
3267:
3261:
3257:
3256:
3255:
3226:
3210:
3203:
3181:
3162:
3160:
3159:
3154:
3152:
3151:
3139:
3138:
3114:
3112:
3111:
3106:
3104:
3103:
3094:
3093:
3084:
3083:
3071:
3070:
3058:
3057:
3037:
3035:
3034:
3029:
3027:
3026:
3017:
3016:
3007:
3006:
2994:
2993:
2973:
2971:
2970:
2965:
2963:
2962:
2951:
2943:
2941:
2940:
2935:
2930:
2929:
2918:
2914:
2913:
2897:
2895:
2894:
2889:
2887:
2886:
2875:
2871:
2870:
2859:
2855:
2854:
2838:
2836:
2835:
2830:
2828:
2827:
2806:
2804:
2803:
2798:
2796:
2795:
2776:
2774:
2773:
2768:
2756:
2754:
2753:
2748:
2723:
2714:
2712:
2711:
2706:
2683:
2682:
2667:
2666:
2649:
2638:
2629:
2627:
2626:
2621:
2613:
2609:
2608:
2607:
2589:
2588:
2554:
2550:
2548:
2547:
2542:
2540:
2539:
2496:
2487:
2485:
2484:
2479:
2470:
2469:
2457:
2448:
2444:
2443:
2442:
2427:
2426:
2405:
2404:
2392:
2379:
2378:
2366:
2357:
2356:
2341:
2337:
2336:
2335:
2315:
2314:
2297:
2284:
2282:
2281:
2276:
2268:
2267:
2266:
2262:
2242:
2241:
2240:
2236:
2210:
2208:
2207:
2202:
2176:
2167:
2165:
2164:
2159:
2157:
2155:
2154:
2153:
2140:
2132:
2127:
2126:
2110:
2105:
2104:
2083:
2082:
2060:
2059:
2039:
2038:
2037:
2026:
2025:
2024:
2012:
2011:
1991:
1980:
1971:
1969:
1968:
1963:
1961:
1960:
1954:
1950:
1949:
1947:
1946:
1945:
1932:
1930:
1929:
1917:
1904:
1902:
1901:
1881:
1872:
1870:
1869:
1868:
1852:
1850:
1849:
1834:
1830:
1829:
1828:
1808:
1807:
1794:
1790:
1788:
1787:
1775:
1766:
1765:
1754:
1753:
1752:
1732:
1723:
1721:
1720:
1719:
1703:
1701:
1700:
1685:
1683:
1682:
1681:
1668:
1666:
1665:
1653:
1640:
1638:
1637:
1617:
1616:
1615:
1603:
1599:
1598:
1597:
1577:
1576:
1562:
1561:
1549:
1536:
1535:
1523:
1514:
1513:
1498:
1494:
1493:
1492:
1472:
1471:
1446:
1431:
1422:
1420:
1419:
1414:
1406:
1402:
1401:
1400:
1396:
1366:
1362:
1361:
1360:
1356:
1326:
1322:
1321:
1320:
1289:
1266:
1257:
1255:
1254:
1249:
1247:
1236:
1235:
1217:
1212:
1201:
1200:
1174:
1169:
1167:
1166:
1161:
1159:
1148:
1147:
1123:
1114:
1112:
1111:
1106:
1104:
1100:
1099:
1095:
1094:
1067:
1066:
1057:
1053:
1052:
1038:
1037:
1025:
1015:
1010:
992:
988:
981:
980:
966:
965:
948:
931:
922:
920:
919:
914:
912:
908:
907:
877:
862:
860:
859:
854:
852:
851:
817:
815:
814:
809:
807:
806:
784:
782:
781:
776:
752:
743:
741:
740:
735:
733:
731:
730:
729:
716:
715:
714:
705:
704:
694:
686:
682:
681:
679:
678:
677:
664:
663:
662:
649:
647:
646:
623:
621:
620:
619:
603:
593:
460:olivine crystals
351:
344:
337:
122:Earthquake swarm
42:
19:
5569:
5568:
5564:
5563:
5562:
5560:
5559:
5558:
5534:
5533:
5530:
5511:
5479:
5474:
5445:
5410:
5381:
5336:
5301:
5270:
5235:
5206:
5202:
5200:Further reading
5197:
5196:
5166:
5165:
5152:
5116:
5115:
5111:
5075:
5074:
5070:
5063:
5042:
5041:
5037:
5028:
5026:
5022:
4989:
4984:
4983:
4979:
4970:
4968:
4926:
4925:
4921:
4912:
4910:
4906:
4871:
4866:
4865:
4861:
4851:
4849:
4839:
4838:
4834:
4824:
4822:
4818:
4811:
4806:
4805:
4801:
4769:
4764:
4763:
4759:
4750:
4748:
4744:
4711:
4706:
4705:
4701:
4669:
4668:
4639:
4607:
4606:
4602:
4562:
4561:
4552:
4523:(5768): 43–46.
4512:
4511:
4507:
4467:
4466:
4462:
4432:
4431:
4427:
4413:
4403:
4400:
4399:
4395:
4390:
4385:
4361:
4329:
4246:
4233:
4186:
4120:
4119:
4104:
4048:
4047:
4009:
4008:
3972:
3971:
3954:
3949:
3907:
3898:
3896:Schematic model
3865:
3864:
3836:
3835:
3816:
3815:
3793:
3792:
3781:
3732:
3728:
3710:
3700:
3696:
3679:
3656:
3646:
3641:
3640:
3633:
3593:
3592:
3564:
3563:
3552:
3483:
3479:
3420:
3416:
3399:
3398:
3391:
3352:
3351:
3321:
3313:
3312:
3293:
3247:
3237:
3233:
3216:
3193:
3185:
3184:
3176:
3171:
3143:
3130:
3125:
3124:
3095:
3085:
3075:
3062:
3049:
3044:
3043:
3018:
3008:
2998:
2985:
2980:
2979:
2954:
2946:
2945:
2921:
2905:
2900:
2899:
2878:
2862:
2846:
2841:
2840:
2816:
2811:
2810:
2808:
2784:
2779:
2778:
2759:
2758:
2733:
2732:
2721:
2674:
2658:
2653:
2652:
2636:
2596:
2577:
2576:
2572:
2558:
2557:
2528:
2523:
2522:
2494:
2459:
2431:
2415:
2414:
2410:
2394:
2368:
2345:
2325:
2320:
2316:
2306:
2301:
2300:
2293:
2255:
2251:
2246:
2229:
2225:
2220:
2215:
2214:
2187:
2186:
2174:
2145:
2141:
2133:
2118:
2087:
2065:
2042:
2029:
2016:
2000:
1995:
1994:
1978:
1956:
1955:
1937:
1933:
1919:
1905:
1884:
1877:
1873:
1860:
1856:
1838:
1818:
1813:
1809:
1799:
1796:
1795:
1777:
1757:
1735:
1728:
1724:
1711:
1707:
1689:
1673:
1669:
1655:
1641:
1620:
1607:
1587:
1582:
1578:
1568:
1565:
1564:
1551:
1525:
1502:
1482:
1477:
1473:
1463:
1456:
1450:
1449:
1429:
1382:
1377:
1373:
1342:
1337:
1333:
1310:
1305:
1301:
1293:
1292:
1264:
1237:
1227:
1202:
1186:
1178:
1177:
1149:
1139:
1134:
1133:
1121:
1086:
1082:
1072:
1068:
1058:
1044:
1040:
1027:
972:
971:
967:
957:
952:
951:
929:
899:
895:
881:
880:
869:
864:represents the
834:
829:
828:
798:
793:
792:
767:
766:
750:
721:
717:
706:
696:
695:
669:
665:
654:
650:
629:
628:
624:
611:
607:
597:
596:
586:in rectangular
577:
541:
442:
397:
355:
303:
302:
268:
260:
259:
251:
248:
241:
231:
230:
211:
203:
202:
163:
162:Characteristics
155:
154:
135:
127:
126:
52:
17:
12:
11:
5:
5567:
5565:
5557:
5556:
5551:
5546:
5544:Wave mechanics
5536:
5535:
5510:
5507:
5506:
5505:
5500:
5495:
5490:
5485:
5478:
5477:External links
5475:
5473:
5472:
5448:Tectonophysics
5443:
5408:
5379:
5351:(1): 601–614.
5334:
5314:(1): 311–330.
5299:
5268:
5248:(3): 387–407.
5233:
5203:
5201:
5198:
5195:
5194:
5150:
5129:(3): 387–407.
5109:
5068:
5061:
5035:
4977:
4939:(1): 135–149.
4919:
4859:
4832:
4799:
4757:
4699:
4680:(6): 675–722.
4637:
4618:(4): 343–391.
4600:
4550:
4505:
4460:
4435:Tectonophysics
4425:
4416:|journal=
4392:
4391:
4389:
4386:
4384:
4383:
4378:
4373:
4368:
4362:
4360:
4357:
4328:
4325:
4312:
4311:
4300:
4299:
4280:
4279:
4269:phase velocity
4265:group velocity
4261:
4260:
4245:
4242:
4232:
4229:
4225:
4224:
4221:
4218:
4215:
4185:
4182:
4161:
4158:
4155:
4152:
4148:
4144:
4141:
4137:
4133:
4130:
4127:
4108:Gjalp Eruption
4103:
4097:
4085:
4084:
4072:
4069:
4065:
4061:
4058:
4055:
4045:
4033:
4030:
4026:
4022:
4019:
4016:
3996:
3993:
3989:
3985:
3982:
3979:
3968:
3965:
3953:
3950:
3948:
3945:
3906:
3903:
3897:
3894:
3878:
3875:
3849:
3846:
3823:
3803:
3800:
3787:
3786:
3777:
3775:
3761:
3758:
3752:
3748:
3744:
3741:
3738:
3735:
3731:
3727:
3723:
3717:
3713:
3709:
3706:
3703:
3699:
3695:
3692:
3688:
3685:
3682:
3678:
3672:
3669:
3665:
3662:
3659:
3653:
3649:
3606:
3603:
3577:
3574:
3558:
3557:
3548:
3546:
3532:
3529:
3520:
3517:
3510:
3506:
3502:
3498:
3495:
3492:
3489:
3486:
3482:
3478:
3475:
3472:
3466:
3463:
3454:
3451:
3444:
3440:
3436:
3432:
3429:
3426:
3423:
3419:
3415:
3412:
3409:
3406:
3365:
3362:
3330:
3327:
3324:
3320:
3299:
3298:
3289:
3287:
3273:
3270:
3264:
3260:
3254:
3250:
3246:
3243:
3240:
3236:
3232:
3229:
3225:
3222:
3219:
3215:
3209:
3206:
3202:
3199:
3196:
3192:
3175:
3172:
3170:
3167:
3166:
3165:
3150:
3146:
3142:
3137:
3133:
3120:
3102:
3098:
3092:
3088:
3082:
3078:
3074:
3069:
3065:
3061:
3056:
3052:
3025:
3021:
3015:
3011:
3005:
3001:
2997:
2992:
2988:
2961:
2957:
2933:
2928:
2924:
2917:
2912:
2908:
2885:
2881:
2874:
2869:
2865:
2858:
2853:
2849:
2826:
2823:
2819:
2794:
2791:
2787:
2766:
2746:
2743:
2740:
2727:
2726:
2717:
2715:
2704:
2701:
2698:
2695:
2692:
2689:
2686:
2681:
2677:
2673:
2670:
2665:
2661:
2642:
2641:
2632:
2630:
2619:
2616:
2612:
2606:
2603:
2599:
2595:
2592:
2587:
2584:
2580:
2575:
2571:
2568:
2565:
2538:
2535:
2531:
2500:
2499:
2490:
2488:
2477:
2474:
2468:
2465:
2462:
2456:
2452:
2447:
2441:
2438:
2434:
2430:
2425:
2422:
2418:
2413:
2409:
2403:
2400:
2397:
2391:
2387:
2383:
2377:
2374:
2371:
2365:
2361:
2355:
2352:
2348:
2344:
2340:
2334:
2331:
2328:
2323:
2319:
2313:
2309:
2274:
2271:
2265:
2261:
2258:
2254:
2249:
2245:
2239:
2235:
2232:
2228:
2223:
2200:
2197:
2194:
2180:
2179:
2170:
2168:
2152:
2148:
2144:
2139:
2136:
2130:
2125:
2121:
2116:
2113:
2109:
2103:
2100:
2097:
2094:
2090:
2086:
2081:
2078:
2075:
2072:
2068:
2063:
2058:
2055:
2052:
2049:
2045:
2036:
2032:
2023:
2019:
2015:
2010:
2007:
2003:
1984:
1983:
1974:
1972:
1959:
1953:
1944:
1940:
1936:
1928:
1925:
1922:
1916:
1912:
1908:
1900:
1897:
1894:
1891:
1887:
1880:
1876:
1867:
1863:
1859:
1855:
1848:
1845:
1841:
1837:
1833:
1827:
1824:
1821:
1816:
1812:
1806:
1802:
1798:
1797:
1793:
1786:
1783:
1780:
1774:
1770:
1764:
1760:
1751:
1748:
1745:
1742:
1738:
1731:
1727:
1718:
1714:
1710:
1706:
1699:
1696:
1692:
1688:
1680:
1676:
1672:
1664:
1661:
1658:
1652:
1648:
1644:
1636:
1633:
1630:
1627:
1623:
1614:
1610:
1606:
1602:
1596:
1593:
1590:
1585:
1581:
1575:
1571:
1567:
1566:
1560:
1557:
1554:
1548:
1544:
1540:
1534:
1531:
1528:
1522:
1518:
1512:
1509:
1505:
1501:
1497:
1491:
1488:
1485:
1480:
1476:
1470:
1466:
1462:
1461:
1459:
1435:
1434:
1425:
1423:
1412:
1409:
1405:
1399:
1395:
1392:
1389:
1385:
1380:
1376:
1372:
1369:
1365:
1359:
1355:
1352:
1349:
1345:
1340:
1336:
1332:
1329:
1325:
1319:
1316:
1313:
1308:
1304:
1300:
1270:
1269:
1260:
1258:
1246:
1243:
1240:
1234:
1230:
1226:
1223:
1220:
1216:
1211:
1208:
1205:
1199:
1196:
1193:
1189:
1185:
1158:
1155:
1152:
1146:
1142:
1127:
1126:
1117:
1115:
1103:
1098:
1093:
1089:
1085:
1081:
1078:
1075:
1071:
1065:
1061:
1056:
1051:
1047:
1043:
1036:
1033:
1030:
1024:
1020:
1014:
1009:
1006:
1003:
999:
995:
991:
987:
984:
979:
975:
970:
964:
960:
935:
934:
925:
923:
911:
906:
902:
898:
894:
891:
888:
866:elastic tensor
850:
847:
844:
841:
837:
805:
801:
774:
756:
755:
746:
744:
728:
724:
720:
713:
709:
703:
699:
692:
689:
685:
676:
672:
668:
661:
657:
653:
645:
642:
639:
636:
632:
627:
618:
614:
610:
606:
576:
573:
540:
537:
456:oceanic basins
454:variations in
441:
438:
396:
393:
364:, also called
357:
356:
354:
353:
346:
339:
331:
328:
327:
326:
325:
323:Related topics
320:
314:
313:
305:
304:
301:
300:
295:
290:
285:
280:
275:
269:
266:
265:
262:
261:
258:
257:
252:
245:
242:
237:
236:
233:
232:
229:
228:
223:
218:
212:
209:
208:
205:
204:
201:
200:
195:
190:
185:
180:
175:
170:
164:
161:
160:
157:
156:
153:
152:
147:
142:
140:Fault movement
136:
133:
132:
129:
128:
125:
124:
119:
114:
109:
104:
99:
94:
89:
84:
79:
74:
69:
64:
59:
53:
48:
47:
44:
43:
35:
34:
28:
27:
15:
13:
10:
9:
6:
4:
3:
2:
5566:
5555:
5552:
5550:
5547:
5545:
5542:
5541:
5539:
5532:
5528:
5524:
5520:
5519:demonstration
5516:
5508:
5504:
5501:
5499:
5496:
5494:
5491:
5489:
5486:
5484:
5481:
5480:
5476:
5469:
5465:
5461:
5457:
5453:
5449:
5444:
5439:
5434:
5430:
5426:
5423:(1): 65–106.
5422:
5418:
5414:
5409:
5405:
5401:
5397:
5393:
5389:
5385:
5380:
5376:
5372:
5367:
5362:
5358:
5354:
5350:
5346:
5345:
5340:
5335:
5330:
5325:
5321:
5317:
5313:
5309:
5305:
5300:
5296:
5292:
5288:
5284:
5280:
5276:
5275:
5269:
5264:
5259:
5255:
5251:
5247:
5243:
5239:
5234:
5230:
5226:
5222:
5218:
5214:
5210:
5205:
5204:
5199:
5190:
5186:
5182:
5178:
5175:(1–2): 1–14.
5174:
5170:
5163:
5161:
5159:
5157:
5155:
5151:
5145:
5140:
5136:
5132:
5128:
5124:
5120:
5113:
5110:
5104:
5099:
5095:
5091:
5088:(1): 65–106.
5087:
5083:
5079:
5072:
5069:
5064:
5062:0-8031-0326-3
5058:
5054:
5050:
5046:
5039:
5036:
5021:
5016:
5011:
5007:
5003:
4999:
4995:
4988:
4981:
4978:
4966:
4962:
4958:
4954:
4950:
4946:
4942:
4938:
4934:
4930:
4923:
4920:
4905:
4900:
4895:
4891:
4887:
4883:
4879:
4878:
4870:
4863:
4860:
4847:
4843:
4836:
4833:
4817:
4810:
4803:
4800:
4795:
4791:
4787:
4783:
4779:
4775:
4768:
4761:
4758:
4743:
4738:
4733:
4729:
4725:
4721:
4717:
4710:
4703:
4700:
4695:
4691:
4687:
4683:
4679:
4675:
4674:
4666:
4664:
4662:
4660:
4658:
4656:
4654:
4652:
4650:
4648:
4646:
4644:
4642:
4638:
4633:
4629:
4625:
4621:
4617:
4613:
4612:
4604:
4601:
4596:
4592:
4588:
4584:
4580:
4576:
4572:
4568:
4567:
4559:
4557:
4555:
4551:
4546:
4542:
4538:
4534:
4530:
4526:
4522:
4518:
4517:
4509:
4506:
4501:
4497:
4493:
4489:
4485:
4481:
4477:
4473:
4472:
4464:
4461:
4456:
4452:
4448:
4444:
4440:
4436:
4429:
4426:
4421:
4408:
4397:
4394:
4387:
4382:
4379:
4377:
4374:
4372:
4369:
4367:
4366:Birefringence
4364:
4363:
4358:
4356:
4354:
4349:
4345:
4343:
4339:
4335:
4327:Future trends
4326:
4324:
4322:
4318:
4309:
4306:
4305:
4304:
4297:
4293:
4289:
4288:
4287:
4285:
4284:perpendicular
4277:
4276:Polarizations
4274:
4273:
4272:
4270:
4266:
4258:
4257:Polarizations
4255:
4254:
4253:
4251:
4243:
4241:
4237:
4230:
4228:
4222:
4219:
4216:
4213:
4212:
4211:
4208:
4206:
4203:
4199:
4195:
4191:
4183:
4181:
4177:
4175:
4159:
4156:
4153:
4150:
4146:
4142:
4139:
4135:
4131:
4128:
4125:
4115:
4113:
4109:
4102:
4098:
4096:
4094:
4089:
4070:
4067:
4063:
4059:
4056:
4053:
4046:
4031:
4028:
4024:
4020:
4017:
4014:
3994:
3991:
3987:
3983:
3980:
3977:
3969:
3966:
3963:
3962:
3961:
3959:
3951:
3947:Case examples
3946:
3944:
3942:
3938:
3934:
3930:
3925:
3923:
3918:
3916:
3912:
3904:
3902:
3895:
3893:
3873:
3844:
3821:
3801:
3798:
3785:
3778:
3776:
3756:
3750:
3746:
3742:
3739:
3736:
3733:
3729:
3721:
3715:
3711:
3707:
3704:
3701:
3697:
3693:
3690:
3686:
3683:
3680:
3676:
3670:
3667:
3663:
3660:
3657:
3651:
3647:
3639:
3638:
3635:
3631:
3627:
3623:
3601:
3572:
3556:
3549:
3547:
3527:
3515:
3508:
3504:
3500:
3496:
3493:
3490:
3487:
3484:
3480:
3476:
3473:
3470:
3461:
3449:
3442:
3438:
3434:
3430:
3427:
3424:
3421:
3417:
3413:
3410:
3407:
3397:
3396:
3393:
3389:
3385:
3382:
3360:
3349:
3345:
3328:
3325:
3322:
3318:
3310:
3306:
3297:
3290:
3288:
3268:
3262:
3258:
3252:
3248:
3244:
3241:
3238:
3234:
3230:
3227:
3223:
3220:
3217:
3213:
3207:
3204:
3200:
3197:
3194:
3190:
3183:
3182:
3179:
3173:
3168:
3163:
3148:
3144:
3140:
3135:
3131:
3121:
3118:
3100:
3096:
3090:
3086:
3080:
3076:
3072:
3067:
3063:
3059:
3054:
3050:
3041:
3023:
3019:
3013:
3009:
3003:
2999:
2995:
2990:
2986:
2977:
2976:
2975:
2959:
2955:
2931:
2926:
2922:
2915:
2910:
2906:
2883:
2879:
2872:
2867:
2863:
2856:
2851:
2847:
2824:
2821:
2792:
2789:
2764:
2744:
2741:
2738:
2725:
2718:
2716:
2702:
2699:
2696:
2693:
2690:
2687:
2684:
2679:
2675:
2671:
2668:
2663:
2659:
2651:
2650:
2647:
2640:
2633:
2631:
2617:
2614:
2610:
2604:
2601:
2597:
2593:
2590:
2585:
2582:
2573:
2569:
2566:
2563:
2556:
2555:
2552:
2536:
2533:
2521:
2517:
2513:
2509:
2508:
2498:
2491:
2489:
2475:
2472:
2466:
2463:
2460:
2454:
2450:
2445:
2439:
2436:
2432:
2428:
2423:
2420:
2411:
2407:
2401:
2398:
2395:
2389:
2385:
2381:
2375:
2372:
2369:
2363:
2359:
2353:
2350:
2342:
2338:
2332:
2329:
2326:
2321:
2317:
2311:
2307:
2299:
2298:
2295:
2291:
2290:
2285:
2272:
2269:
2263:
2259:
2256:
2252:
2247:
2243:
2237:
2233:
2230:
2226:
2221:
2211:
2198:
2195:
2192:
2178:
2171:
2169:
2150:
2146:
2137:
2128:
2123:
2119:
2114:
2111:
2107:
2101:
2098:
2095:
2092:
2088:
2084:
2079:
2076:
2073:
2070:
2066:
2061:
2056:
2053:
2050:
2047:
2043:
2034:
2030:
2021:
2017:
2013:
2008:
2005:
1993:
1992:
1989:
1982:
1975:
1973:
1951:
1942:
1938:
1926:
1923:
1920:
1914:
1910:
1898:
1895:
1892:
1889:
1885:
1878:
1874:
1865:
1861:
1846:
1843:
1839:
1835:
1831:
1825:
1822:
1819:
1814:
1810:
1804:
1800:
1791:
1784:
1781:
1778:
1772:
1768:
1762:
1758:
1749:
1746:
1743:
1740:
1736:
1729:
1725:
1716:
1712:
1697:
1694:
1690:
1686:
1678:
1674:
1662:
1659:
1656:
1650:
1646:
1634:
1631:
1628:
1625:
1621:
1612:
1608:
1604:
1600:
1594:
1591:
1588:
1583:
1579:
1573:
1569:
1558:
1555:
1552:
1546:
1542:
1538:
1532:
1529:
1526:
1520:
1516:
1510:
1507:
1499:
1495:
1489:
1486:
1483:
1478:
1474:
1468:
1464:
1457:
1448:
1447:
1444:
1442:
1433:
1426:
1424:
1410:
1407:
1403:
1397:
1393:
1390:
1387:
1383:
1378:
1374:
1370:
1367:
1363:
1357:
1353:
1350:
1347:
1343:
1338:
1334:
1330:
1327:
1323:
1317:
1314:
1311:
1306:
1302:
1298:
1291:
1290:
1287:
1285:
1284:
1279:
1278:
1268:
1261:
1259:
1244:
1241:
1238:
1232:
1228:
1224:
1221:
1218:
1214:
1209:
1206:
1203:
1197:
1194:
1191:
1187:
1183:
1176:
1175:
1172:
1170:
1156:
1153:
1150:
1144:
1140:
1125:
1118:
1116:
1101:
1096:
1091:
1087:
1083:
1079:
1076:
1073:
1069:
1063:
1059:
1054:
1049:
1045:
1041:
1034:
1031:
1028:
1022:
1018:
1007:
1004:
1001:
997:
993:
989:
985:
982:
977:
973:
968:
962:
958:
950:
949:
946:
944:
943:
933:
926:
924:
909:
904:
900:
896:
892:
889:
886:
879:
878:
875:
873:
867:
863:
848:
845:
842:
839:
835:
825:
822:
818:
803:
799:
789:
785:
772:
764:is the time,
763:
754:
747:
745:
726:
722:
711:
707:
701:
690:
687:
683:
674:
670:
659:
655:
643:
640:
637:
634:
630:
625:
616:
612:
595:
594:
591:
589:
585:
580:
574:
572:
570:
566:
562:
559:
554:
553:polarizations
545:
538:
536:
534:
530:
525:
523:
518:
513:
511:
510:birefringence
507:
503:
502:magma chamber
499:
494:
490:
489:seismographic
487:
483:
479:
478:Volcanic Area
476:
472:
467:
465:
461:
457:
453:
450:
447:
439:
437:
435:
434:polarizations
431:
427:
422:
417:
414:
411:
406:
402:
394:
392:
390:
386:
381:
377:
374:
370:
369:birefringence
367:
363:
352:
347:
345:
340:
338:
333:
332:
330:
329:
324:
321:
319:
316:
315:
312:
309:
308:
307:
306:
299:
296:
294:
291:
289:
286:
284:
281:
279:
276:
274:
271:
270:
264:
263:
256:
253:
250:
244:
243:
240:
235:
234:
227:
224:
222:
219:
217:
214:
213:
207:
206:
199:
196:
194:
191:
189:
188:Seismic waves
186:
184:
181:
179:
176:
174:
171:
169:
166:
165:
159:
158:
151:
148:
146:
143:
141:
138:
137:
131:
130:
123:
120:
118:
115:
113:
110:
108:
105:
103:
100:
98:
95:
93:
90:
88:
85:
83:
80:
78:
75:
73:
70:
68:
65:
63:
60:
58:
55:
54:
51:
46:
45:
41:
37:
36:
33:
29:
25:
21:
20:
5512:
5451:
5447:
5420:
5416:
5387:
5383:
5348:
5342:
5311:
5307:
5281:(1): 59–77.
5278:
5272:
5245:
5241:
5212:
5208:
5172:
5168:
5126:
5122:
5112:
5085:
5081:
5071:
5044:
5038:
5027:. Retrieved
4997:
4993:
4980:
4969:. Retrieved
4936:
4932:
4922:
4911:. Retrieved
4884:(1): F1–F5.
4881:
4875:
4862:
4850:. Retrieved
4835:
4823:. Retrieved
4802:
4777:
4773:
4760:
4749:. Retrieved
4719:
4715:
4702:
4677:
4671:
4615:
4609:
4603:
4570:
4564:
4520:
4514:
4508:
4475:
4469:
4463:
4438:
4434:
4428:
4407:cite journal
4396:
4381:Seismic wave
4350:
4346:
4330:
4313:
4301:
4281:
4262:
4247:
4238:
4234:
4226:
4210:They found:
4209:
4193:
4187:
4178:
4116:
4105:
4090:
4086:
3955:
3941:hydrocarbons
3926:
3919:
3908:
3899:
3790:
3779:
3622:eigenvectors
3561:
3550:
3304:
3302:
3291:
3177:
3123:
2730:
2719:
2645:
2634:
2551:are needed,
2516:eigenvectors
2505:
2503:
2492:
2287:
2213:
2185:
2183:
2172:
1987:
1976:
1440:
1438:
1427:
1281:
1275:
1274:Substitute (
1273:
1262:
1132:
1130:
1119:
940:
938:
927:
827:
823:
791:
765:
761:
759:
748:
581:
578:
550:
526:
514:
498:seismometers
468:
443:
430:upper mantle
418:
415:
398:
395:Introduction
361:
360:
272:
267:Other topics
72:Blind thrust
5274:Wave Motion
4844:. E&P.
4722:(1): 1–13.
4673:Wave Motion
4611:Wave Motion
4250:seismograms
4231:Limitations
4112:Vatnajökull
3630:eigenvalues
3390:direction.
3388:propagation
3117:shear waves
2809:The matrix
2512:eigenvalues
2292:) is left.
493:earthquakes
421:homogeneous
405:orientation
380:anisotropic
255:Forecasting
216:Seismometer
210:Measurement
183:Shadow zone
32:Earthquakes
5549:Seismology
5538:Categories
5029:2010-05-11
4971:2010-05-11
4913:2010-05-11
4751:2010-05-11
4388:References
4315:angle and
4292:anisotropy
3915:reservoirs
3384:orthogonal
517:earthquake
506:elliptical
486:telemetric
410:orthogonal
408:sometimes
378:enters an
376:shear wave
298:Seismology
239:Prediction
178:Hypocenter
112:Supershear
92:Megathrust
87:Intraplate
82:Interplate
67:Aftershock
5529:website.
5527:MathWorks
5390:: 62–68.
5375:2122/5499
4961:129113171
3933:reservoir
3922:dilatancy
3877:^
3848:^
3822:ϕ
3799:δ
3760:^
3751:⋅
3740:δ
3734:ϕ
3726:Γ
3708:ω
3702:−
3694:
3684:ω
3661:ω
3605:^
3576:^
3531:^
3519:^
3494:δ
3491:ω
3485:−
3477:
3465:^
3453:^
3428:δ
3425:ω
3414:
3405:Γ
3364:^
3326:ω
3272:^
3263:⋅
3245:ω
3239:−
3231:
3221:ω
3198:ω
3141:≠
3077:β
3000:α
2818:Γ
2786:Γ
2694:−
2669:−
2598:δ
2591:−
2579:Γ
2530:Γ
2433:δ
2429:−
2417:Γ
2382:−
2347:Γ
2257:−
2231:−
2143:∂
2138:τ
2135:∂
2112:ρ
2002:Γ
1935:∂
1907:∂
1879:ρ
1858:∂
1854:∂
1844:−
1840:ρ
1730:ρ
1709:∂
1705:∂
1695:−
1691:ρ
1671:∂
1643:∂
1539:−
1504:Γ
1391:−
1351:−
1328:−
1242:ϑ
1222:ϑ
1207:ϑ
1154:ϑ
1080:τ
1077:−
1013:∞
998:∑
893:τ
872:wavefront
773:ρ
719:∂
698:∂
691:ρ
667:∂
652:∂
609:∂
605:∂
522:dilatancy
449:azimuthal
401:isotropic
389:black box
373:polarized
168:Epicenter
145:Volcanism
107:Submarine
62:Foreshock
57:Mainshock
5047:: 3–29.
5020:Archived
4965:Archived
4904:Archived
4846:Archived
4816:Archived
4742:Archived
4359:See also
4336:and for
4205:recorder
4202:borehole
4174:magmatic
4093:geophone
3174:Modeling
1280:) into (
561:crystals
452:velocity
318:Category
293:Seismite
24:a series
22:Part of
5456:Bibcode
5425:Bibcode
5392:Bibcode
5353:Bibcode
5316:Bibcode
5283:Bibcode
5250:Bibcode
5217:Bibcode
5177:Bibcode
5131:Bibcode
5090:Bibcode
5002:Bibcode
4941:Bibcode
4886:Bibcode
4852:June 5,
4825:May 12,
4782:Bibcode
4724:Bibcode
4682:Bibcode
4620:Bibcode
4595:4237223
4575:Bibcode
4545:4306931
4525:Bibcode
4500:4292928
4480:Bibcode
4443:Bibcode
4317:azimuth
4198:Germany
3958:Iceland
3791:Where
3386:to the
3344:wavelet
3342:is the
3307:is the
2510:), the
788:density
786:is the
558:olivine
440:History
366:seismic
117:Tsunami
77:Doublet
5515:MATLAB
5059:
4959:
4593:
4566:Nature
4543:
4516:Nature
4498:
4471:Nature
4376:P-wave
4371:S-wave
4290:Crack
3674:
3626:matrix
3562:where
3303:where
3211:
2952:
2919:
2876:
2860:
2520:matrix
2294:Thus,
2040:
2027:
1988:where
1882:
1755:
1733:
1618:
826:, and
760:where
565:liquid
471:mantle
446:P-wave
198:S wave
193:P wave
134:Causes
5023:(PDF)
4990:(PDF)
4957:S2CID
4907:(PDF)
4872:(PDF)
4819:(PDF)
4812:(PDF)
4770:(PDF)
4745:(PDF)
4712:(PDF)
4591:S2CID
4541:S2CID
4496:S2CID
3628:with
3381:plane
3042:and
2212:, so
1441:N,M,L
529:crust
482:Japan
475:Chubu
426:crust
419:In a
385:crack
50:Types
5523:here
5057:ISBN
4854:2012
4827:2010
4420:help
4340:and
3927:The
3620:are
3591:and
2944:and
2757:and
2514:and
582:The
428:and
102:Slow
5525:on
5464:doi
5452:462
5433:doi
5400:doi
5371:hdl
5361:doi
5349:179
5324:doi
5312:172
5291:doi
5258:doi
5246:107
5225:doi
5185:doi
5173:159
5139:doi
5127:107
5098:doi
5049:doi
5010:doi
4998:105
4949:doi
4937:212
4894:doi
4882:138
4790:doi
4732:doi
4690:doi
4628:doi
4583:doi
4571:286
4533:doi
4521:286
4488:doi
4476:203
4451:doi
4439:462
4319:of
4194:KTB
4110:in
3691:exp
3474:exp
3411:exp
3228:exp
2518:of
1286:),
569:gas
567:or
480:in
5540::
5462:.
5450:.
5431:.
5421:37
5419:.
5415:.
5398:.
5388:56
5386:.
5369:.
5359:.
5347:.
5341:.
5322:.
5310:.
5306:.
5289:.
5279:41
5277:.
5256:.
5244:.
5240:.
5223:.
5213:95
5211:.
5183:.
5171:.
5153:^
5137:.
5125:.
5121:.
5096:.
5086:37
5084:.
5080:.
5055:.
5018:.
5008:.
4996:.
4992:.
4963:.
4955:.
4947:.
4935:.
4931:.
4902:.
4892:.
4880:.
4874:.
4788:.
4778:96
4776:.
4772:.
4740:.
4730:.
4720:29
4718:.
4714:.
4688:.
4678:45
4676:.
4640:^
4626:.
4614:.
4589:.
4581:.
4569:.
4553:^
4539:.
4531:.
4519:.
4494:.
4486:.
4474:.
4449:.
4437:.
4411::
4409:}}
4405:{{
4344:.
4054:10
4015:10
3917:.
3782:12
3553:11
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3294:10
2974:.
2807:.
2473:==
2408:==
870:A
868:.
790:,
512:.
26:on
5470:.
5466::
5458::
5441:.
5435::
5427::
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5402::
5394::
5377:.
5373::
5363::
5355::
5332:.
5326::
5318::
5297:.
5293::
5285::
5266:.
5260::
5252::
5231:.
5227::
5219::
5191:.
5187::
5179::
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5065:.
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4951::
4943::
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4754:.
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4616:3
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4502:.
4490::
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4422:)
4418:(
4298:.
4192:(
4160:r
4157:a
4154:e
4151:y
4147:/
4143:m
4140:k
4136:/
4132:s
4129:m
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4071:m
4068:k
4064:/
4060:s
4057:m
4044:.
4032:m
4029:k
4025:/
4021:s
4018:m
3995:m
3992:k
3988:/
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3981:m
3978:4
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3780:(
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3730:(
3722:]
3716:0
3712:T
3705:i
3698:[
3687:)
3681:(
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3668:=
3664:)
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3408:=
3361:p
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3323:(
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3296:)
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3269:p
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3253:0
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3235:[
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3205:=
3201:)
3195:(
3191:u
3149:3
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3136:2
3132:G
3101:i
3097:p
3091:i
3087:p
3081:2
3073:=
3068:3
3064:G
3060:=
3055:2
3051:G
3024:i
3020:p
3014:i
3010:p
3004:2
2996:=
2991:1
2987:G
2960:3
2956:G
2932:,
2927:2
2923:G
2916:,
2911:1
2907:G
2884:3
2880:g
2873:,
2868:2
2864:g
2857:,
2852:1
2848:g
2825:k
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2793:k
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2722:9
2720:(
2703:0
2700:=
2697:R
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2611:)
2605:k
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2583:j
2574:(
2570:t
2567:e
2564:D
2537:k
2534:j
2507:8
2497:)
2495:8
2493:(
2476:0
2467:)
2464:0
2461:(
2455:k
2451:U
2446:)
2440:k
2437:j
2424:k
2421:j
2412:(
2402:)
2399:0
2396:(
2390:j
2386:U
2376:)
2373:0
2370:(
2364:k
2360:U
2354:k
2351:j
2343:=
2339:)
2333:)
2330:0
2327:(
2322:U
2318:(
2312:j
2308:N
2289:5
2273:0
2270:=
2264:)
2260:2
2253:(
2248:U
2244:=
2238:)
2234:1
2227:(
2222:U
2199:0
2196:=
2193:n
2177:)
2175:7
2173:(
2151:i
2147:x
2129:=
2124:i
2120:p
2115:,
2108:/
2102:l
2099:k
2096:j
2093:i
2089:c
2085:=
2080:l
2077:k
2074:j
2071:i
2067:a
2062:,
2057:l
2054:k
2051:j
2048:i
2044:a
2035:l
2031:p
2022:i
2018:p
2014:=
2009:k
2006:j
1981:)
1979:6
1977:(
1952:)
1943:l
1939:x
1927:)
1924:n
1921:(
1915:k
1911:U
1899:l
1896:k
1893:j
1890:i
1886:a
1875:(
1866:i
1862:x
1847:1
1836:=
1832:)
1826:)
1823:n
1820:(
1815:U
1811:(
1805:j
1801:L
1792:)
1785:)
1782:n
1779:(
1773:k
1769:U
1763:l
1759:p
1750:l
1747:k
1744:j
1741:i
1737:a
1726:(
1717:i
1713:x
1698:1
1687:+
1679:l
1675:x
1663:)
1660:n
1657:(
1651:k
1647:U
1635:l
1632:k
1629:j
1626:i
1622:a
1613:i
1609:p
1605:=
1601:)
1595:)
1592:n
1589:(
1584:U
1580:(
1574:j
1570:M
1559:)
1556:n
1553:(
1547:j
1543:U
1533:)
1530:n
1527:(
1521:k
1517:U
1511:k
1508:j
1500:=
1496:)
1490:)
1487:n
1484:(
1479:U
1475:(
1469:j
1465:N
1458:{
1432:)
1430:5
1428:(
1411:0
1408:=
1404:)
1398:)
1394:2
1388:n
1384:(
1379:U
1375:(
1371:L
1368:+
1364:)
1358:)
1354:1
1348:n
1344:(
1339:U
1335:(
1331:M
1324:)
1318:)
1315:n
1312:(
1307:U
1303:(
1299:N
1283:1
1277:3
1267:)
1265:4
1263:(
1245:)
1239:(
1233:n
1229:f
1225:=
1219:d
1215:/
1210:)
1204:(
1198:1
1195:+
1192:n
1188:f
1184:d
1157:)
1151:(
1145:n
1141:f
1124:)
1122:3
1120:(
1102:)
1097:)
1092:i
1088:x
1084:(
1074:t
1070:(
1064:n
1060:f
1055:)
1050:i
1046:x
1042:(
1035:)
1032:n
1029:(
1023:k
1019:U
1008:0
1005:=
1002:n
994:=
990:)
986:t
983:,
978:i
974:x
969:(
963:k
959:U
942:1
932:)
930:2
928:(
910:)
905:i
901:x
897:(
890:=
887:t
849:l
846:k
843:j
840:i
836:c
824:U
804:j
800:U
762:t
753:)
751:1
749:(
727:2
723:t
712:j
708:U
702:2
688:=
684:]
675:l
671:x
660:k
656:U
644:l
641:k
638:j
635:i
631:c
626:[
617:i
613:x
350:e
343:t
336:v
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