Determination of Fresnel zones from traveltime measurements

Hubral, Peter; Schleicher, Jörg; Tygel, Martin; Hanitzsch, C.

doi:10.1190/1.1443454

Cited by 60 publications

(25 citation statements)

References 10 publications

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“…For more details, we refer the reader to Hubral et al (1992, 1993), Červený (2001, Chap. 4), Hanyga et al (2001), Gjøystdal et al (2002), Chapman (2004), Iversen (2004b), Sun (2004), Moser & Červený (2007), where many other references can be found.…”

Section: Discussionmentioning

confidence: 99%

Ray propagator matrices in three-dimensional anisotropic inhomogeneous layered media

Červený¹,

Moser²

2007

Geophysical Journal International

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SUMMARY Ray propagator matrices contain the complete solutions to the system of dynamic ray‐tracing (DRT) equations connected with a given reference ray. They play an important role in studying the properties of complete four‐parameteric systems of paraxial rays and offer many applications in both numerical modelling and practical interpretational problems of seismic ray fields in the high‐frequency asymptotic approximation. Traditionally, ray propagator matrices have been expressed either in Cartesian or in ray‐centred coordinates, connected with a reference ray. Both coordinate systems have certain advantages. For ray‐centred coordinates, the dimensions of ray propagator matrices can be easily reduced from 6 × 6 to 4 × 4 (in a 3‐D medium), thereby reflecting the strictly four‐parameteric nature of a general paraxial ray field. On the other hand, in Cartesian coordinates, the computations are conceptually simpler and generally valid in isotropic and anisotropic media. In a Cartesian coordinate system, the DRT system and ray propagator matrices are well known both for isotropic and anisotropic layered media. In ray‐centred coordinates, the DRT system and ray propagator matrices are known for isotropic layered structures and for anisotropic smooth media, but not for anisotropic media with structural interfaces. We propose a simple and invertible transformation between ray propagator matrices in both coordinate systems. It allows to perform conventional DRT in Cartesian coordinates, and to transform the resulting ray propagator matrix to ray‐centred coordinates at any point of the ray where we need it. This avoids DRT in ray‐centred coordinates altogether. Vice versa, we can compute, at any point of the reference ray, the ray propagator matrix in Cartesian coordinates by DRT in ray‐centred coordinates. We propose several alternative versions of the transformation, each of them equally valid in isotropic and anisotropic media. For rays hitting a structural interface, the ray propagator matrix has to be transformed across the interface. The relevant transformation matrix is usually referred to as the interface propagator matrix. In Cartesian coordinates, the 6 × 6 interface propagator matrix has been published before, but in ray‐centred coordinates only for the case of isotropic media. Based on the transformation from Cartesian to ray‐centred coordinates, we present the 6 × 6 and 4 × 4 interface propagator matrices in ray‐centred coordinates, valid for general isotropic and anisotropic media. The 4 × 4 interface propagator matrix in ray‐centred coordinates can be factorized and used to derive the 4 × 4 surface‐to‐surface paraxial matrices. These matrices allow to relate the paraxial ray properties at different surfaces crossed by the reference ray and offer many important applications.

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Section: Discussionmentioning

confidence: 99%

Ray propagator matrices in three-dimensional anisotropic inhomogeneous layered media

Červený¹,

Moser²

2007

Geophysical Journal International

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“…But in practice, it is not easy (if at all possible) to estimate this size for arbitrary inhomogeneous media with curved interfaces. In this work we used the concept of the projected Fresnel zone (Hubral et al 1993).…”

Section: O M M O N -O F F S E T S I G N a L E N H A N C E M E N T Bmentioning

confidence: 99%

Imaging improvement by prestack signal enhancement

Buzlukov¹,

Landa²

2013

Geophysical Prospecting

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The quality of recorded seismic data depends on many factors and a low signal‐to‐noise ratio leads to a low quality of processing and imaging. The zero‐offset common‐reflection‐surface stack and multifocusing methods have been successfully applied to improve the prestack signal‐to‐noise ratio by the partial summation of coherent seismic events. However, in the case of non‐hyperbolic traveltime behaviour of seismic events these approaches can result in non‐optimal partial summation. We develop a local common‐offset approximation for the traveltime stacking surface. It allows us to adequately approximate the traveltimes of reflection events in the vicinity of an arbitrary offset. Here, the stacking operator is interpreted as a local second‐order traveltime approximation of the seismic event and it is used for the purpose of partial summation. An algorithm and a numerical implementation scheme are discussed. The proposed signal enhancement procedure was applied to synthetic and real 3D data. Imaging results of the enhanced data show a high potential for reliable imaging in complex subsurface environments.

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“…Hubral and his coworkers define the projected Fresnel zone of a zero-offset reflection onto the subsurface reflector using a standard 3D CMP traveltime analysis, without knowing the overburden (Hubral et al, 1993;Schleicher et al, 1997). Červený (2001) suggests two methods that include FV parameter calculations into the ray tracing procedure in complex 2D and 3D structures.…”

Section: Introductionmentioning

confidence: 99%

Fresnel volume and interface Fresnel zone for reflected and transmitted waves from a curved interface in anisotropic media

2014

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The Fresnel volume and the interface Fresnel zone (IFZ) concepts play an important role in seismic exploration because the IFZ largely contributes to the formation of the reflection and transmission wavefields at an observation point. We derived analytic expressions based on traveltime approximations to evaluate the IFZ size for converted and nonconverted waves reflected (or transmitted) by a curved interface between two homogeneous general anisotropic media, and more specifically for dip-constrained transversely isotropic homogeneous media. The reflectors are of anticline, syncline, or saddle type, and their principal curvature axes may not lie in the incidence plane. As in an anisotropic medium the isochron in most cases assumes a nonelliptical shape, the size and the shape of the IFZ for reflected waves are predominantly dependent on the curvatures of the isochrons together with the curvatures of the interface. The IFZ shapes also exhibit large variation with interface curvature and incidence angle. In addition, the difference between the Thomsen anisotropy parameters ϵ and δ is found to control the size of the IFZ for P-P and P-S reflections. The IFZ for anisotropic media with curved interface can be much larger than that for equivalent isotropic media, and more specifically for positive values of ϵ − δ. The spatial resolution of unmigrated seismic data in anisotropic media would consequently be different from that determined for the same configuration for isotropic models and a planar interface.

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Determination of Fresnel zones from traveltime measurements

Cited by 60 publications

References 10 publications

Ray propagator matrices in three-dimensional anisotropic inhomogeneous layered media

Ray propagator matrices in three-dimensional anisotropic inhomogeneous layered media

Imaging improvement by prestack signal enhancement

Fresnel volume and interface Fresnel zone for reflected and transmitted waves from a curved interface in anisotropic media

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