Wave Front Construction in Smooth Media for Prestack Depth Migration

Ettrich, N.; Gajewski, D.

doi:10.1007/978-3-0348-9049-6_5

Cited by 14 publications

(19 citation statements)

References 16 publications

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“…Our aim is to implement a WFC method which can have a near arbitrary distribution of ray take‐off angles. So, rather than trying to estimate wave front curvature from the spatial derivatives of the ray parameters, we extend the 2‐D approach of Ettrich & Gajewski (1996) to 3‐D media.…”

Section: The Wave Front Construction Methodsmentioning

confidence: 99%

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A practical implementation of wave front construction for 3-D isotropic media

Chambers

Kendall

2008

Geophysical Journal International

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S U M M A R YWave front construction (WFC) methods are a useful tool for tracking wave fronts and are a natural extension to standard ray shooting methods. Here we describe and implement a simple WFC method that is used to interpolate wavefield properties throughout a 3-D heterogeneous medium. Our approach differs from previous 3-D WFC procedures primarily in the use of a ray interpolation scheme, based on approximating the wave front as a 'locally spherical' surface and a 'first arrival mode', which reduces computation times, where only first arrivals are required. Both of these features have previously been included in 2-D WFC algorithms; however, until now they have not been extended to 3-D systems. The wave front interpolation scheme allows for rays to be traced from a nearly arbitrary distribution of take-off angles, and the calculation of derivatives with respect to take-off angles is not required for wave front interpolation. However, in regions of steep velocity gradient, the locally spherical approximation is not valid, and it is necessary to backpropagate rays to a sufficiently homogenous region before interpolation of the new ray. Our WFC technique is illustrated using a realistic velocity model, based on a North Sea oil reservoir. We examine wavefield quantities such as traveltimes, ray angles, source take-off angles and geometrical spreading factors, all of which are interpolated on to a regular grid. We compare geometrical spreading factors calculated using two methods: using the ray Jacobian and by taking the ratio of a triangular area of wave front to the corresponding solid angle at the source. The results show that care must be taken when using ray Jacobians to calculate geometrical spreading factors, as the poles of the source coordinate system produce unreliable values, which can be spread over a large area, as only a few initial rays are traced in WFC. We also show that the use of the first arrival mode can reduce computation time by ∼65 per cent, with the accuracy of the interpolated traveltimes, ray angles and source take-off angles largely unchanged. However, the first arrival mode does lead to inaccuracies in interpolated angles near caustic surfaces, as well as small variations in geometrical spreading factors for ray tubes that have passed through caustic surfaces.

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Section: The Wave Front Construction Methodsmentioning

confidence: 99%

“…In the method of Ettrich & Gajewski (1996), radial paths are projected from the two basis rays that we wish to interpolate between to locate a virtual source (see Fig. 1A).…”

Section: The Wave Front Construction Methodsmentioning

confidence: 99%

A practical implementation of wave front construction for 3-D isotropic media

Chambers

Kendall

2008

Geophysical Journal International

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“…5. A wavefront construction scheme (Vinje et al, 1993) in the inplementation of Ettrich and Gajewski (1996) was applied for the computation of traveltimes and geometrical spreading (with dynamic ray tracing, DRT) on a 12.5-m fine grid. The traveltimes were resampled to the input traveltimes on a 62.5-m coarse grid.…”

Section: Geometrical Spreadingmentioning

confidence: 99%

Determination of geometrical spreading from traveltimes

Vanelle

Gajewski

2003

Journal of Applied Geophysics

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“…To date, WFC has proven to be the most practical scheme developed so far for tracking multi‐arrivals. It is commonly used in the exploration industry, including for migration of reflection data (Ettrich & Gajewski 1996; Xu & Lambaré 2004; Xu et al 2004), and has been used as the forward solver in multi‐arrival traveltime tomography (Hauser et al 2008).…”

Section: Introductionmentioning

confidence: 99%

Multipathing, reciprocal traveltime fields and raylets

Rawlinson

Sambridge

Hauser

2010

Geophysical Journal International

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S U M M A R YA new theory for the calculation of later seismic arrivals in heterogeneous media is presented. We introduce the concept of a 'raylet', which is a segment of a later arriving ray path between source and receiver defined by joint properties of forward and reciprocal traveltime fields. We show that all rays between a single source and receiver in arbitrary heterogeneous media can be divided into a unique set of raylets, any one of which can be used to construct the complete two-point path. A particularly useful property of raylets is that they correspond to stationary curves in the summed (forward and reciprocal) traveltime fields, i.e. adding the first (or second, or even later) arriving traveltime field from some point A to the first (or second, or even later) arriving traveltime field from some point B. We show that many raylets, each corresponding to a later arriving phase, require only earlier arrival traveltime fields for their construction. The theory describing the properties of raylets is the primary result of the paper. One practical consequence is that many later arrivals between source and receiver in heterogeneous media can be found from just two first-arrival traveltime fields, one from the source and the other (the reciprocal field) from the receiver.The theory and a method for constructing later arrivals is demonstrated though numerical experiments in 2-D but holds without change in 3-D. We use a simple grid-based eikonal solver to compute forward and reciprocal first-arrival traveltime fields, and validate our results with a ray-based wave front construction (WFC) technique. In one test involving a simple wave front triplication (or swallowtail), all three arrivals are retrieved. In another example featuring severe velocity heterogeneities, 16 out of a total of 37 arrivals are found. The theory shows that combining second and higher order traveltime fields from source and receiver yields all raylets and hence all later arrivals. In practice only first-arrival traveltime fields are usually available and for this case we describe a simple procedure to find any remaining arrivals using intermediate artificial sources together with their first-arrival traveltime fields. The properties of raylets and their manifestation in the joint traveltime field appears to be a previously unrecognized feature and provides a novel new approach to the calculation of later arrivals.

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Wave Front Construction in Smooth Media for Prestack Depth Migration

Cited by 14 publications

References 16 publications

A practical implementation of wave front construction for 3-D isotropic media

A practical implementation of wave front construction for 3-D isotropic media

Determination of geometrical spreading from traveltimes

Multipathing, reciprocal traveltime fields and raylets

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