On: “Shear‐wave splitting in cross‐hole surveys: Modeling” by Enru Liu, Stuart Crampin, and David C. Booth (GEOPHYSICS, 54, 57–65, January, 1989)

Geophysics ◽  
1989 ◽  
Vol 54 (11) ◽  
pp. 1503-1504
Author(s):  
Don Winterstein
Keyword(s):  
Shear Wave ◽  
A Priori ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
S Wave ◽  
Horizontal Symmetry ◽  
Wave Splitting ◽  
Wave Travel ◽  
Ti Media ◽  
Travel Modeling

Liu et al. extended consideration of shear‐wave (S‐wave) polarization patterns in anisotropic media from the usual vertical to a predominantly horizontal direction of wave travel. Modeling was for transversely isotropic (TI) media with horizontal symmetry axes. The exposition was accurate in major concepts, but the authors could have been more precise in presenting a couple of incidental properties of TI media. These properties have to do with S‐wave polarizations and certain a priori predictions one can make about them from symmetry considerations. I state and prove two predictions here in a tutorial mode, partly to demonstrate the simplicity and power of symmetry concepts as tools for understanding wave behavior in anisotropic media.

scholarly journals Deformation in Rutford Ice Stream, West Antarctica: measuring shear-wave anisotropy from icequakes

2013 ◽  
Vol 54 (64) ◽  
pp. 105-114 ◽  
Author(s):  
S.R. Harland ◽  
J.-M. Kendall ◽  
G.W. Stuart ◽  
G.E. Lloyd ◽  
A.F. Baird ◽  
...  
Keyword(s):  
Shear Wave ◽  
Flow Direction ◽  
Transversely Isotropic ◽  
Shear Wave Splitting ◽  
Ice Crystal ◽  
West Antarctica ◽  
Ice Streams ◽  
Ice Flow ◽  
Ice Stream ◽  
Wave Splitting

Abstract Ice streams provide major drainage pathways for the Antarctic ice sheet. The stress distribution and style of flow in such ice streams produce elastic and rheological anisotropy, which informs ice-flow modelling as to how ice masses respond to external changes such as global warming. Here we analyse elastic anisotropy in Rutford Ice Stream, West Antarctica, using observations of shear-wave splitting from three-component icequake seismograms to characterize ice deformation via crystal-preferred orientation. Over 110 high-quality measurements are made on 41 events recorded at five stations deployed temporarily near the ice-stream grounding line. To the best of our knowledge, this is the first well-documented observation of shear-wave splitting from Antarctic icequakes. The magnitude of the splitting ranges from 2 to 80 ms and suggests a maximum of 6% shear-wave splitting. The fast shear-wave polarization direction is roughly perpendicular to ice-flow direction. We consider three mechanisms for ice anisotropy: a cluster model (vertical transversely isotropic (VTI) model); a girdle model (horizontal transversely isotropic (HTI) model); and crack-induced anisotropy (HTI model). Based on the data, we can rule out a VTI mechanism as the sole cause of anisotropy – an HTI component is needed, which may be due to ice crystal a-axis alignment in the direction of flow or the alignment of cracks or ice films in the plane perpendicular to the flow direction. The results suggest a combination of mechanisms may be at play, which represent vertical variations in the symmetry of ice crystal anisotropy in an ice stream, as predicted by ice fabric models.

Finite-difference modelling of S-wave splitting in anisotropic media

2008 ◽  
Vol 56 (3) ◽  
pp. 293-312 ◽  
Author(s):  
Reeshidev Bansal ◽  
Mrinal K. Sen
Keyword(s):  
Finite Difference ◽  
Anisotropic Media ◽  
S Wave ◽  
Wave Splitting

scholarly journals Diurnal expansion and contraction of englacial fracture networks revealed by seismic shear wave splitting

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Wojciech Gajek ◽  
Dominik Gräff ◽  
Sebastian Hellmann ◽  
Alan W. Rempel ◽  
Fabian Walter
Keyword(s):  
Shear Wave ◽  
Large Scale ◽  
Elastic Anisotropy ◽  
Shear Wave Splitting ◽  
Subsurface Water ◽  
Water Drainage ◽  
Fracture Networks ◽  
S Wave ◽  
Alpine Glacier ◽  
Wave Splitting

AbstractFractures contribute to bulk elastic anisotropy of many materials in the Earth. This includes glaciers and ice sheets, whose fracture state controls the routing of water to the base and thus large-scale ice flow. Here we use anisotropy-induced shear wave splitting to characterize ice structure and probe subsurface water drainage beneath a seismometer network on an Alpine glacier. Shear wave splitting observations reveal diurnal variations in S-wave anisotropy up to 3%. Our modelling shows that when elevated by surface melt, subglacial water pressures induce englacial hydrofractures whose volume amounts to 1-2 percent of the probed ice mass. While subglacial water pressures decrease, these fractures close and no fracture-induced anisotropy variations are observed in the absence of meltwater. Consequently, fracture networks, which are known to dominate englacial water drainage, are highly dynamic and change their volumes by 90-180 % over subdaily time scales.

Shear-wave splitting of SK(K)S-phases beneath the Upper Rhine Graben area: Indications for laterally and vertically varying seismic anisotropy

2021 ◽  
Author(s):  
Yvonne Fröhlich ◽  
Michael Grund ◽  
Joachim R. R. Ritter
Keyword(s):  
Shear Wave ◽  
Seismic Anisotropy ◽  
Symmetry Axis ◽  
Shear Wave Splitting ◽  
Small Scale ◽  
Upper Rhine Graben ◽  
Event Analysis ◽  
Horizontal Symmetry ◽  
Wave Splitting ◽  
Upper Rhine

<p>The observed backazimuthal variations in the shear-wave splitting of core-refracted shear waves (SK(K)S-phases) at the Black Forest Observatory (BFO, SW Germany) indicate small-scale lateral and (partly) vertical variations of the elastic anisotropy in the upper mantle. However, most of the existing seismic anisotropy studies and models in the Upper Rhine Graben (URG) area are based on short-term recordings and thus suffer from a limited backazimuthal coverage and averaging over a wide or the whole backazimuth range. Hence, to find and delimit basic anisotropy regimes, also with respect to the connection to geological and tectonic processes, we carried out further SK(K)S splitting measurements at permanent (BFO, WLS, STU, ECH) and semi-permanent (TMO44, TMO07) broadband seismological recording stations.</p><p>To achieve a sufficient backazimuthal coverage and to be able to resolve and account appropriately for complex anisotropy, we analysed long-term recordings (partly > 20 yrs.). This was done manually using the MATLAB-program SplitLab (single-event analysis) together with the plugin StackSplit (multi-event analysis). The two splitting parameters, the fast polarization direction <em>Φ</em> given relative to north and the delay time <em>δt</em> accumulated between the two quasi shear waves, were determined by applying both the rotation-correlation method and the minimum-energy method for comparison. Structural anisotropy models with one layer with horizontal or tilted symmetry axis and with two layers with horizontal symmetry axes (assuming transvers isotropy with the fast axis being parallel to the symmetry axis) were tested to explain the shear-wave splitting observations, including lateral variations around a recording site.</p><p>The determined anisotropy is placed in the upper mantle due to the duration of the delay times (> 0.3 s) and missing discrepancies between SKS- and SKKS-phases (so not hints for significant lowermost mantle contributions). The spatial distribution and the lateral and backazimuthal variations of the measured (apparent) splitting parameters confirm that the anisotropy in the mantle beneath the URG area varies on small-scale laterally and partly vertically: On the east side of the URG, from the Moldanubian Zone (BFO, STU, ECH) to the Saxothuringian Zone (TMO44, TMO07) a tendency from two layers with horizontal symmetry axes to one layer is suggested. In the Moldanubian Zone, between the east side (STU, BFO) and the west side (ECH) of the URG, a change of the fast polarisation directions of the anisotropy models with two layers with horizontal symmetry axes is observed. Inconsistent measured apparent splitting parameters and the observation of numerous null measurements, especially below the URG may be at least partly related to scattering of the seismic wavefield or a modification of the mantle material.</p>

Application of seismic interferometry to extract P- and S-wave propagation and observation of shear-wave splitting from noise data at Cold Lake, Alberta, Canada

Geophysics ◽  
2008 ◽  
Vol 73 (4) ◽  
pp. D35-D40 ◽  
Author(s):  
Masatoshi Miyazawa ◽  
Roel Snieder ◽  
Anupama Venkataraman
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Structural Parameters ◽  
Shear Wave Splitting ◽  
Seismic Interferometry ◽  
Stress Axis ◽  
S Wave ◽  
S Waves ◽  
Wave Splitting ◽  
Cold Lake

We extract downward-propagating P- and S-waves from industrial noise generated by human and/or machine activity at the surface propagating down a borehole at Cold Lake, Alberta, Canada, and measure shear-wave splitting from these data. The continuous seismic data are recorded at eight sensors along a downhole well during steam injection into a 420–470-m-deep oil reservoir. We crosscorrelate the waveforms observed at the top sensor and other sensors to extract estimates of the direct P- and S-wave components of the Green’s function that account for wave propagation between sensors. Fast high-frequency and slow low-frequency signals propagating vertically from the surface to the bottom are found for the vertical and horizontal components of the wave motion, which are identified with P- and S-waves, respectively. The fastest S-wave polarized in the east-northeast–west-southwest direction is about 1.9% faster than the slowest S-wave polarized in the northwest-southeast direction. The direction of polarization of the fast S-wave is rotated clockwise by [Formula: see text] from the maximum principal stress axis as estimated from the regional stress field. This study demonstrates the useful application of seismic interferometry to field data to determine structural parameters, which are P- and S-wave velocities and a shear-wave-splitting coefficient, with high accuracy.

scholarly journals Deriving micro- to macro-scale seismic velocities from ice-core <i>c</i> axis orientations

2018 ◽  
Vol 12 (5) ◽  
pp. 1715-1734 ◽  
Author(s):  
Johanna Kerch ◽  
Anja Diez ◽  
Ilka Weikusat ◽  
Olaf Eisen
Keyword(s):  
Shear Wave ◽  
Seismic Anisotropy ◽  
Ice Core ◽  
Shear Wave Splitting ◽  
P Wave ◽  
Seismic Velocities ◽  
Polar Ice ◽  
S Wave ◽  
Crystal Anisotropy ◽  
Wave Splitting

Abstract. One of the great challenges in glaciology is the ability to estimate the bulk ice anisotropy in ice sheets and glaciers, which is needed to improve our understanding of ice-sheet dynamics. We investigate the effect of crystal anisotropy on seismic velocities in glacier ice and revisit the framework which is based on fabric eigenvalues to derive approximate seismic velocities by exploiting the assumed symmetry. In contrast to previous studies, we calculate the seismic velocities using the exact c axis angles describing the orientations of the crystal ensemble in an ice-core sample. We apply this approach to fabric data sets from an alpine and a polar ice core. Our results provide a quantitative evaluation of the earlier approximative eigenvalue framework. For near-vertical incidence our results differ by up to 135 m s−1 for P-wave and 200 m s−1 for S-wave velocity compared to the earlier framework (estimated 1 % difference in average P-wave velocity at the bedrock for the short alpine ice core). We quantify the influence of shear-wave splitting at the bedrock as 45 m s−1 for the alpine ice core and 59 m s−1 for the polar ice core. At non-vertical incidence we obtain differences of up to 185 m s−1 for P-wave and 280 m s−1 for S-wave velocities. Additionally, our findings highlight the variation in seismic velocity at non-vertical incidence as a function of the horizontal azimuth of the seismic plane, which can be significant for non-symmetric orientation distributions and results in a strong azimuth-dependent shear-wave splitting of max. 281 m s−1 at some depths. For a given incidence angle and depth we estimated changes in phase velocity of almost 200 m s−1 for P wave and more than 200 m s−1 for S wave and shear-wave splitting under a rotating seismic plane. We assess for the first time the change in seismic anisotropy that can be expected on a short spatial (vertical) scale in a glacier due to strong variability in crystal-orientation fabric (±50 m s−1 per 10 cm). Our investigation of seismic anisotropy based on ice-core data contributes to advancing the interpretation of seismic data, with respect to extracting bulk information about crystal anisotropy, without having to drill an ice core and with special regard to future applications employing ultrasonic sounding.

Synthesis of multicomponent quasi-P and converted quasi-P-S seismograms for intersecting fracture systems

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1261-1271 ◽  
Author(s):  
Andrey A. Ortega ◽  
George A. McMechan
Keyword(s):  
Shear Wave ◽  
Transverse Isotropy ◽  
Normal Incidence ◽  
Shear Wave Splitting ◽  
P Wave ◽  
Orthorhombic Symmetry ◽  
S Wave ◽  
Stiffness Constant ◽  
Wave Splitting ◽  
Vertical Fractures

Dynamic ray shooting with interpolation is an economical way of computing approximate Green’s functions in 3-D heterogeneous anisotropic media. The amplitudes, traveltimes, and polarizations of the reflected rays arriving at the surface are interpolated to synthesize three‐component seismograms at the desired recording points. The algorithm is applied to investigate kinematic quasi-P-wave propagation and converted quasi-P-S-wave splitting variations produced in reflections from the bottom of a layer containing two sets of intersecting dry vertical fractures as a function of the angle between the fracture sets and of the intensity of fracturing. An analytical expression is derived for the stiffness constant C16 that extends Hudson’s second‐order scattering theory to include tetragonal-2 symmetry systems. At any offset, the amount of splitting in nonorthogonal (orthorhombic symmetry) intersecting fracture sets is larger than in orthogonal (tetragonal-1 symmetry) systems, and it increases nonlinearly as a function of the intensity of fracturing as offset increases. Such effects should be visible in field data, provided that the dominant frequency is sufficiently high and the offset is sufficiently large. The amount of shear‐wave splitting at vertical incidence increases nonlinearly as a function of the intensity of fracturing and increases nonlinearly from zero in the transition from tetragonal-1 anisotropy through orthorhombic to horizontal transverse isotropy; the latter corresponds to the two crack systems degenerating to one. The zero shear‐wave splitting corresponds to a singularity, at which the vertical velocities of the two quasi‐shear waves converge to a single value that is both predicted theoretically and illustrated numerically. For the particular case of vertical fractures, there is no P-to-S conversion of vertically propagating (zero‐offset) waves. If the fractures are not vertical, the normal incidence P-to-S reflection coefficient is not zero and thus is a potential diagnostic of fracture orientation.

Refraction across an angular unconformity between nonparallel TI media

Geophysics ◽  
2005 ◽  
Vol 70 (2) ◽  
pp. D19-D28 ◽  
Author(s):  
John Hodgkinson ◽  
R. James Brown
Keyword(s):  
Vertical Plane ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Demonstration Program ◽  
P Waves ◽  
Angular Unconformity ◽  
Isotropic Media ◽  
The Media ◽  
P And Sv Waves ◽  
Ti Media

Assuming elliptical wavefronts, we reformulate refraction theory for transversely isotropic (TI) media based on the use of the auxiliary angle, α, which is intermediate between the phase angle, θ, and the group angle, ϕ. When considering the application of stretching to transform elliptically anisotropic media into isotropic media, the auxiliary angle is a natural one to use because both θ and ϕ → α under such stretching. Our present formulation for TI media makes the assumption of elliptical anisotropy, which is valid generally for SH-waves but only as a special case for P-and SV-waves, where, in the SV case, the only possible ellipses are circles. Nevertheless, the theory has useful applications for P-waves over limited ranges of propagation direction (e.g., in the short-spread approximation). Our formulation provides explicit results for all angles of incidence and for what we term an angular unconformity between two TI media, that is, for all orientations of the axes of symmetry for each of the media, and for all orientations of the interface, assuming these two axes and the interface normal to lie in the same vertical plane. Our conclusions have been verified by showing that the phase angles and phase velocities of the incident and refracted waves obey Snell's law across the interface. We also demonstrate, using auxiliary angles, that the description of refraction between elliptically anisotropic media by stretching the media to make them isotropic, then applying isotropic refraction, is also valid for our general angular-unconformity case. However, both stretching (1D) and either scaling (2D) or shearing must be applied correctly and separately to the two media. The refraction algorithm developed from this theory and another developed by Byun in terms of phase-velocity theory are currently the only published noniterative algorithms known to us for refraction across an angular unconformity where the axes of anisotropy are parallel neither to each other nor to the interface. Based on this theory, we have developed a demonstration program, AUXDEMOC, that computes the refracted-ray angles for any combination of parameters by the two equivalent methods: (1) anisotropic refraction and (2) stretching plus isotropic refraction. This program can be downloaded from http://www.crewes.org/under Free Software.

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