Approximate Conditions for the Off-Axis Triplication in Transversely Isotropic Media

Vavryčuk, Václav

doi:10.1023/b:sgeg.0000015591.55301.84

Cited by 6 publications

(4 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Clearly, SV‐SV wave traveltime approximations break down or essentially lose their accuracy not only when triplication occurs but also when the conditions are close to the cusp situation. The behaviour of traveltime approximations for SV‐waves in case of triplication has been discussed, particularly by Schoenberg and Dayley (), Vavryčuk (), and Stovas (). Insufficient accuracy of the approximations for SV‐waves may arise even in no‐triplication cases.…”

Section: Synthetic Examplementioning

confidence: 99%

Traveltime approximation in vertical transversely isotropic layered media

Ravve

Koren

2017

Geophysical Prospecting

View full text Add to dashboard Cite

The well‐known asymptotic fractional four‐parameter traveltime approximation and the five‐parameter generalised traveltime approximation in stratified multi‐layer transversely isotropic elastic media with a vertical axis of symmetry have been widely used for pure‐mode and converted waves. The first three parameters of these traveltime expansions are zero‐offset traveltime, normal moveout velocity, and quartic coefficient, ensuring high accuracy of traveltimes at short offsets. The additional parameter within the four‐parameter approximation is an effective horizontal velocity accounting for large offsets, which is important to avoid traveltime divergence at large offsets. The two additional parameters in the above‐mentioned five‐parameter approximation ensure higher accuracy up to a given large finite offset with an exact match at this offset. In this paper, we propose two alternative five‐parameter traveltime approximations, which can be considered extensions of the four‐parameter approximation and an alternative to the five‐parameter approximation previously mentioned. The first three short‐offset parameters are the same as before, but the two additional long‐offset parameters are different and have specific physical meaning. One of them describes the propagation in the high‐velocity layer of the overburden (nearly horizontal propagation in the case of very large offsets), and the other characterises the intercept time corresponding to the critical slowness that includes contributions of the lower velocity layers only. Unlike the above‐mentioned approximations, both of the proposed traveltime approximations converge to the theoretical (asymptotic) linear traveltime at the limit case of very large (“infinite”) offsets. Their accuracy for moderate to very large offsets, for quasi‐compressional waves, converted waves, and shear waves polarised in the horizontal plane, is extremely high in cases where the overburden model contains at least one layer with a dominant higher velocity compared with the other layers. We consider the implementation of the proposed traveltime approximations in all classes of problems in which the above‐mentioned approximations are used, such as reflection and diffraction analysis and imaging.

show abstract

Section: Synthetic Examplementioning

confidence: 99%

Traveltime approximation in vertical transversely isotropic layered media

Ravve

Koren

2017

Geophysical Prospecting

View full text Add to dashboard Cite

show abstract

“… Group velocity surfaces for the qSV‐wave in a VTI medium showing (left) vertical triplications, (centre) oblique triplications and (right) horizontal triplications (modified after Vavryčuk 2004). The horizontal and vertical axes correspond to the horizontal and vertical group velocity components respectively.…”

Section: Shear‐wave Triplicationsmentioning

confidence: 99%

A statistical review of mudrock elastic anisotropy

Horne¹

2013

Geophysical Prospecting

View full text Add to dashboard Cite

Mudrocks, defined to be fine‐grained siliclastic sedimentary rocks such as siltstones, claystones, mudstones and shales, are often anisotropic due to lamination and microscopic alignments of clay platelets. The resulting elastic anisotropy is often non‐negligible for many applications in the earth sciences such as wellbore stability, well stimulation and seismic imaging. Anisotropic elastic properties reported in the open literature have been compiled and statistically analysed. Correlations between elastic parameters are observed, which will be useful in the typical case that limited information on a rock's elastic properties is known. For example, it is observed that the highest degree of correlation is between the horizontal elastic stiffnesses C11 and C66. The results of statistical analysis are generally consistent with prior observations. In particular, it is observed that Thomsen's ɛ and γ parameters are almost always positive, Thomsen's ɛ and γ parameters are well correlated, Thomsen's δ is most frequently small and Thomsen's ɛ is generally larger than Thomsen's δ. These observations suggest that the typical range for the elastic properties of mudrocks span a sub‐space less than the five elastic constants required to fully define a Vertical Transversel Isotropic medium. Principal component analysis confirms this and that four principal components can be used to span the space of observed elastic parameters.

show abstract

“…The ray amplitudes in the triplication are expected to be much higher than elsewhere in the synthetic seismograms. However, according to previous studies (Thomsen and Dellinger, 2003;Vavryčuk, 2004), the SH-wave doesn't have the same behavior and its ray spreading diagram shows a more even distribution of rays (Fig. 10d).…”

Section: Multivalued Traveltime Fieldsmentioning

confidence: 74%

“…The magnitude of the Thomsen anisotropy parameter δ controls the occurrence of offaxis qSV-wave triplications in TI media (Thomsen and Dellinger, 2003). Also, (Vavryčuk, 2004) derived other formulas that can identify the conditions under which triplications develop.…”

Section: Introductionmentioning

confidence: 99%