14. Multicomponent True-Amplitude Anisotropic Imaging

2018

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.

“…For near‐vertical rays, the offset and traveltime may be presented as a power series in the horizontal slowness

p_{h}

, where the coefficients depend on the global (i.e., related to a whole multi‐layer model) second‐order and fourth‐order normal moveout (NMO) velocities,

V_{2} and V_{4}

Section: Objectives and Methodsmentioning

confidence: 99%

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

2018

“…Gerea et al . () introduced a similar measure of intrinsic anellipticity for the SV‐wave, i.e.,

κ = - \frac{1 + 2 δ}{{false(1 + 2 σ false)}^{2}} σ .

…”

Section: Four‐parameter Long‐offset Traveltime Approximationmentioning

confidence: 99%

“…For diffraction, h is the horizontal distance between the subsurface and the surface points, and t o is the one‐way zero‐offset traveltime. The fourth‐order coefficient reads (Alkhalifah ; Grechka and Tsvankin ):

A_{4} = - \frac{V_{4}^{4} - V_{2}^{4}}{4 V_{2}^{4}} = - 2 η_{eff},

where V 4 is the global fourth‐order NMO velocity in layered VTI media introduced by Gerea, Nicoletis and Granger (), and η eff is the effective anellipticity (combined induced and intrinsic). Intrinsic anellipticity is defined later in equations and for P‐ and SV‐waves, respectively (there is no intrinsic anellipticity for the SH‐wave).…”

Section: Four‐parameter Long‐offset Traveltime Approximationmentioning

confidence: 99%

Traveltime approximation in vertical transversely isotropic layered media

2017

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.

“…study cannot be extended to multi-layer orthorhombic models. Tsvankin and Grechka (2011) noted that for layered orthorhombic models with depth-varying azimuthal orientation of the vertical symmetry planes, the effective quartic coefficient can be adequately modelled by applying VTI-like averaging for each azimuth (Gerea, Nicoletis and Granger 2000). Stovas (2015) studied the multi-layer orthorhombic media with different azimuths of the vertical symmetry planes and derived approximate expressions for the effective anellipticity in both slowness-azimuth and offset-azimuth domains for compressional waves, applying acoustic approximation.…”

Section: Introductionmentioning

confidence: 99%

Slowness‐domain kinematical characteristics for horizontally layered orthorhombic media. Part I: Critical slowness match

2019

A B S T R A C TKinematical characteristics of reflected waves in anisotropic elastic media play an important role in the seismic imaging workflow. Considering compressional and converted waves, we derive new, azimuthally dependent, slowness-domain approximations for the kinematical characteristics of reflected waves (radial and transverse offsets, intercept time and traveltime) for layered orthorhombic media with varying azimuth of the vertical symmetry planes. The proposed method can be considered an extension of the well-known 'generalized moveout approximation' in the slowness domain, from azimuthally isotropic to azimuthally anisotropic models. For each slowness azimuth, the approximations hold for a wide angle range, combining power series coefficients in the vicinity of both the normal-incidence ray and an additional wide-angle ray. We consider two cases for the wide-angle ray: a 'critical slowness match' and a 'pre-critical slowness match' studied in Parts I and II of this work, respectively. For the critical slowness match, the approximations are valid within the entire slowness range, up to the critical slowness. For the 'pre-critical slowness match', the approximations are valid only within the bounded slowness range; however, the accuracy within the defined range is higher. The critical slowness match is particularly effective when the subsurface model includes a dominant high-velocity layer where, for nearly critical slowness values, the propagation in this layer is almost horizontal. Comparing the approximated kinematical characteristics with those computed by numerical ray tracing, we demonstrate high accuracy.