Nonhyperbolic Reflection Moveout for Orthorhombic Media

Considering horizontally layered transversely isotropic media with vertical symmetry axis and all types of pure‐mode and converted waves we present a new wide‐angle series approximation for the kinematical characteristics of reflected waves: horizontal offset, intercept time, and total reflection traveltime as functions of horizontal slowness. The method is based on combining (gluing) both zero‐offset and (large) finite‐offset series coefficients. The horizontal slowness is bounded by the critical value, characterised by nearly horizontal propagation within the layer with the highest horizontal velocity. The suggested approximation uses five parameters to approximate the offset, six parameters to approximate the intercept time or the traveltime, and seven parameters to approximate any two or all three kinematical characteristics. Overall, the method is very accurate for pure‐mode compressional waves and shear waves polarised in the horizontal plane and for converted waves. The application of the method to pure‐mode shear waves polarised in the vertical plane is limited due to cusps and triplications. To demonstrate the high accuracy of the method, we consider a synthetic, multi‐layer model, and we plot the normalised errors with respect to numerical ray tracing.

show abstract

“…Thus, the entire non‐hyperbolic term vanishes, and the induced anellipticity is ignored. One way to resolve this issue is to estimate the effective

V_{H}

from the fourth‐order average (root‐mean‐quad) of the horizontal velocities in the layers (Al‐Dajani and Toksoz ), as follows:

0true V_{H}^{4} t_{o} = \sum Δ t_{o, i} v_{h, i}^{4},

…”

Section: Effective Horizontal Velocitymentioning

confidence: 99%

Slowness domain offset and traveltime approximations in layered vertical transversely isotropic media

Koren

Ravve

2018

Geophysical Prospecting

View full text Add to dashboard Cite

show abstract

“…Thus, the whole non‐hyperbolic term vanishes, and the induced anellipticity would be ignored. One way to resolve this issue is to estimate the effective

V_{h}

from the fourth‐order average (root mean quad) of the horizontal velocities in the layers (Al‐Dajani and Toksoz ), i.e.,

V_{h}^{4} t_{normalo} = \sum normalΔ t_{normalo, i} v_{h, i}^{4},

which increases the estimated effective

V_{h}

with respect to its RMS value.…”

Section: Four‐parameter Long‐offset Traveltime Approximationmentioning

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

“…Nonhyperbolic reflection moveout in a layered transversely isotropic medium with a horizontal symmetry axis (HTI) has been studied in the offset-azimuth domain by Al-Dajani and and in the slowness-azimuth domain by Ravve and Koren (2010) and Koren et al (2010). and Al-Dajani and Toksoz (2001) derive the offset-azimuth domain fourth-order moveout coefficient for a single orthorhombic layer with a horizontal symmetry plane, which overlies a horizontal reflector. Pech et al (2003) derive an exact equation for the quartic moveout coefficient of pure-mode waves in arbitrarily anisotropic, heterogeneous media, and implement their theory for a transversely isotropic layer with a tilted axis of symmetry (TTI).…”

Section: Introductionmentioning

confidence: 99%

Normal moveout coefficients for horizontally layered triclinic media

Koren

Ravve

2017

GEOPHYSICS

View full text Add to dashboard Cite

Sedimentary layers affected by vertical compaction and strong lateral tectonic stresses are often characterized by low anisotropic symmetry (e.g., tilted orthorhombic [TOR]/monoclinic or even triclinic). Considering all types of pure-mode and converted waves, we derive the normal moveout (NMO) series coefficients of near normal-incidence reflected waves in arbitrarily anisotropic horizontally layered media, for a leading error term of order six. The NMO series can be either a function of the invariant horizontal slowness (slowness domain) or the surface offset (offset domain). The NMO series coefficients, referred to also as effective parameters, are associated with the corresponding azimuthally varying NMO velocity functions. We distinguish between local (single-layer) and global (overburden multilayer) effective parameters, which are related by forward and inverse Dix-type transforms. We derive the local effective parameters for an arbitrary anisotropic (triclinic) layer, which is the main contribution of this paper. With some additional geologic constraints, the local effective parameters can then be converted into the interval elastic properties. To demonstrate the applicability of our method, we consider a synthetic layered model in which each layer is characterized with TOR symmetry. The corresponding global effective model loses the symmetries of the individual layers and is characterized by triclinic symmetry.

show abstract

Nonhyperbolic Reflection Moveout for Orthorhombic Media

Cited by 7 publications

References 25 publications

Slowness domain offset and traveltime approximations in layered vertical transversely isotropic media

Slowness domain offset and traveltime approximations in layered vertical transversely isotropic media

Traveltime approximation in vertical transversely isotropic layered media

Normal moveout coefficients for horizontally layered triclinic media

Contact Info

Product

Resources

About