The polarization of P-waves in anisotropic media

Crampin, Stuart; Stephen, Ralph A.; McGonigle, Robert

doi:10.1111/j.1365-246x.1982.tb04910.x

Cited by 59 publications

(23 citation statements)

References 12 publications

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“…The field traces were demultiplexed and sweep crosscorrelated, before reorienting the three-component motion. The orientation of the horizontal geophone elements were determined from maximizing the amplitude of the horizontal P-wave displacements, which can be assumed to be parallel to the direction of wave propagation, even in the presence of significant anisotropy (Crampin, Stephen & McGonigle 1982). The presence of 50 Hz electrical interference on the recorded seismograms (Naville 1986) was found to distort the observed shear-wave motions, and the application of a 0-50 Hz bandpass filter (after rotation) removed the interfering signal without significant change to the shear wavefield.…”

Section: Pre-processingmentioning

confidence: 99%

Paris Basin VSPs: case history establishing combinations of fine-layer (or lithologic) anisotropy and crack anisotropy from modelling shear wavefields near point singularities

Bush

Crampin

1991

Geophysical Journal International

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S U M M A R Y This paper examines shear-wave splitting in multi-offset VSPs at a borehole site in the Paris Basin, and demonstrates that the sedimentary structure must have, at least, orthorhombic anisotropic symmetry. It is suggested that the most likely cause for such an orthorhombic symmetry is the combination of fine-layer (or lithologic) anisotropy and crack anisotropy. Transition zones (close to shear-wave singularities), where there are rapid changes of shear-wave polarizations and delays, can account for the anomalous observed waveforms. Observations of large variations in shear-wave polarizations in propagation directions close to point singularities, are probably the first positive identification of the effects of singularities in sedimentary basins.

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Section: Pre-processingmentioning

confidence: 99%

Paris Basin VSPs: case history establishing combinations of fine-layer (or lithologic) anisotropy and crack anisotropy from modelling shear wavefields near point singularities

Bush

Crampin

1991

Geophysical Journal International

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“…d shows the travel-time difference between the quasi-shear wave arrivals (the shear-wave splitting) in 0.1 s contours. For each of the models shown, qP-wave polarization anomalies are small (as discussed by Crampin, Stephen & McGonigle 1982). qSP and qSR polarizations vary with ray azimuth and incidence angle.…”

Section: Figure 6 a Cross-section Of A Qsr-wave Ray Path (B) Comparementioning

confidence: 94%

Ray tracing in azimuthally anisotropic media-I. Results for models of aligned cracks in the upper crust

Shearer

Chapman

1989

Geophysical Journal International

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Ray tracing through gradients in anisotropic materials is complicated by singularities where the two quasi-shear wave slowness sheets cross or touch. Difficulties associated with such points can be removed by explicitly including polarization in the ray tracing equations. Slowness sheet and wavefront plots show the polarization and velocity behavior of various anisotropy models of aligned cracks in the upper crust. A simple scaling of the elastic tensor with depth can be shown to be approximately correct for models of aligned cracks within an isotropic host matrix with a linear velocity gradient. Ray tracing examples for models of aligned cracks within a strong vertical velocity gradient in the uppermost crust demonstrate various features of azimuthal anisotropy, including amplitude and polarization anomalies and shear-wave splitting. Quasi-shear wave polarizations typically twist along ray paths, with stronger twisting near the symmetry axis in hexagonally symmetric media. Strong anisotropy can cause unusual effects, such as ray paths which have three turning points in laterally homogeneous models.

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“…; Grechka et al . ) because angular deviations of the P‐wave polarization vectors

U_{normalP, e}

from the corresponding ray directions r P , amounting to just a few degrees in such media (Crampin, Stephen and McGonigle ), are smaller than uncertainties in estimating β U even for strong microseismic events (Drew, White and Wolfe ; Eisner, Fischer and Rutledge ). When approximation is satisfactory, the number of unknown coordinates of

ξ_{e}

reduces from three to two:

\begin{matrix} right ξ_{e} & \equiv & left \{ζ_{e, 1} prefixcos β_{e}, ζ_{e, 1} prefixsin β_{e}, ζ_{e, 2}\} \\ \approx & left ({} ζ_{e, 1} cos β_{U}, ζ_{e, 1} sin β_{U}, ζ_{e, 2}), \end{matrix}

(e = 1, ..., N_{e}),

where ζ e , 1 and ζ e , 2 are the radial distance of a microseismic event from a vertical observation well and the event depth, respectively.…”

Section: Notation and Statement Of The Inverse Problemmentioning

confidence: 99%

“…Such small differences, well in line with the findings of Crampin et al . (), ensure the applicability of approximation and allow us to search for vector

boldm

[definition ] that depends on two‐component event coordinates

ζ_{e}

rather than on their three‐component counterparts

ξ_{e}

.…”

Section: Homogeneous Mediummentioning

confidence: 99%

Inversion of microseismic data for triclinic velocity models

Grechka

Yaskevich

2013

Geophysical Prospecting

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Modern downhole microseismic surveys often employ geometries in which ray trajectories generated by a collection of locatable events provide full polar and azimuthal coverage, making it possible to estimate the in situ seismic anisotropy. We show that traveltimes and particle motions of the direct P‐ and shear‐waves acquired in such geometries can constrain stiffness tensors of triclinic media. While obtaining all 21 stiffness coefficients of a homogeneous triclinic space simultaneously with locating pertinent microseismic events from data recorded in a single vertical well is relatively straightforward, the same methodology does not necessarily succeed in layered formations because the combination of their vertical heterogeneity and azimuthal anisotropy might invalidate the commonly adopted approximation of the event azimuths by those of the P‐wave polarization vectors. When the event azimuths cannot be derived from the particle motions, traveltimes observed in two or more wells are required to locate the events and build layered triclinic or higher‐symmetry azimuthally anisotropic velocity models. As our numerical tests indicate, the multi‐well event‐location methods are expected to perform better than their single‐well counterparts because they rely solely on triangulation and eliminate the usually pronounced azimuthal uncertainties in the event locations that stem from noises adversely affecting hodogram analysis.

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The polarization of P-waves in anisotropic media

Cited by 59 publications

References 12 publications

Paris Basin VSPs: case history establishing combinations of fine-layer (or lithologic) anisotropy and crack anisotropy from modelling shear wavefields near point singularities

Paris Basin VSPs: case history establishing combinations of fine-layer (or lithologic) anisotropy and crack anisotropy from modelling shear wavefields near point singularities

Ray tracing in azimuthally anisotropic media-I. Results for models of aligned cracks in the upper crust

Inversion of microseismic data for triclinic velocity models

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