Extended generalized non-hyperbolic moveout approximation

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A B S T R A C TRadon transform is a powerful tool with many applications in different stages of seismic data processing, because of its capability to focus seismic events in the transform domain. Three-parameter Radon transform can optimally focus and separate different seismic events, if its basis functions accurately match the events. In anisotropic media, the conventional hyperbolic or shifted hyperbolic basis functions lose their accuracy and cannot preserve data fidelity, especially at large offsets. To address this issue, we propose an accurate traveltime approximation for transversely isotropic media with vertical symmetry axis, and derive two versions of Radon basis functions, timevariant and time-invariant. A time-variant basis function can be used in time domain Radon transform algorithms while a time-invariant version can be used in, generally more efficient, frequency domain algorithms. Comparing the time-variant and time-invariant Radon transform by the proposed basis functions, the time-invariant version can better focus different seismic events; it is also more accurate, especially in presence of vertical heterogeneity. However, the proposed time-invariant basis functions are suitable for a specific type of layered anisotropic media, known as factorized media. We test the proposed methods and illustrate successful applications of them for trace interpolation and coherent noise attenuation.

Section: Introductionmentioning

confidence: 99%

Three‐parameter Radon transform in layered transversely isotropic media

Abedi

Riahi

Stovas

2019

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“…In a later study by Stovas and Fomel (2017), the generalized moveout approximation has been modified by defining the fourth-order (nonhyperbolic) parameter from the reference ray, rather than from the zero-offset ray. In a recent study by Abedi and Stovas (2018), the accuracy of the moveout approximation has been essentially improved by the cost of an additional (sixth) parameter: the curvature of the ray at the non-zero reference offset. Sripanich et al (2017) extended the generalized moveout approximation to 3D multi-azimuth case.…”

Section: Introductionmentioning

confidence: 99%

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

Ravve

Koren

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.

“…Shifted hyperbola approximation (Malovichko ; de Bazelaire ), rational approximation (Tsvankin and Thomsen ; Alkhalifah and Tsvankin ) and generalized moveout approximation (GMA; Fomel and Stovas ; Stovas ; Stovas and Fomel ) are more commonly employed, because of their simplicity, applicability or higher accuracy. Other known explicit moveout approximations include methods of Alkhalifah (, ), Zhang and Uren (), Taner, Treitel and Al‐Chalabi (), Ursin and Stovas (), Blias (, , ), Aleixo and Schleicher (), Ravve and Koren () and Abedi and Stovas ().…”

Section: Introductionmentioning

confidence: 99%

“…Traveltime approximations with higher degrees of freedom can be reduced to three‐parameter VTI moveout approximations, by explicit definition of their parameters based on the three VTI parameters. Using an asymptotic match, the five‐parameter equations of Ravve and Koren () are reduced to the rational approximation (Alkhalifah and Tsvankin ); the five‐parameter GMA (Fomel and Stovas ; Stovas and Fomel ) and the six‐parameter Extended GMA (Abedi and Stovas ) are reduced to a single equation, which is called VTI GMA.…”

Section: Introductionmentioning

confidence: 99%

“…These methods use different order of traveltime derivatives obtained from two rays to define five parameters, which results in a model‐dependent higher accuracy. A six‐parameter moveout approximation (Abedi and Stovas ) results in a general improvement, but at each ray it needs the highest order of traveltime derivatives that each of these two methods use.…”

Section: Introductionmentioning

confidence: 99%

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A new parameterization for generalized moveout approximation, based on three rays

Abedi

Stovas

2019

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A B S T R A C TA simple and accurate traveltime approximation is important in many applications in seismic data processing, inversion and modelling stages. Generalized moveout approximation is an explicit equation that approximates reflection traveltimes in general two-dimensional models. Definition of its five parameters can be done from properties of finite offset rays, for general models, or by explicit calculation from model properties, for specific models. Two versions of classical finite-offset parameterization for this approximation use traveltime and traveltime derivatives of two rays to define five parameters, which makes them asymmetrical. Using a third ray, we propose a balance between the number of rays and the order of traveltime derivatives. Our tests using different models also show the higher accuracy of the proposed method. For acoustic transversely isotropic media with a vertical symmetry axis, we calculate a new moveout approximation in the generalized moveout approximation functional form, which is explicitly defined by three independent parameters of zero-offset twoway time, normal moveout velocity and anellipticity parameter. Our test shows that the maximum error of the proposed transversely isotropic moveout approximation is about 1/6 to 1/8 of that of the moveout approximation that had been reported as the most accurate approximation in these media. The higher accuracy is the result of a novel parameterization that do not add any computational complexity. We show a simple example of its application on synthetic seismic data.with a limited number of independent parameters has been the subject of a large amount of research. Shifted hyperbola approximation (Malovichko 1978;de Bazelaire 1988), rational approximation (Tsvankin and Thomsen 1994; Alkhalifah and Tsvankin 1995) and generalized moveout approximation (GMA; Fomel and Stovas 2010; Stovas 2010; Stovas and Fomel 2017) are more commonly employed, because of their simplicity, applicability or higher accuracy. Other known explicit moveout approximations include methods of Alkhalifah