A method for inverse scattering based on the generalized Bremmer coupling series

Malcolm, Alison; Hoop, Maarten V. de

doi:10.1088/0266-5611/21/3/021

Cited by 22 publications

(31 citation statements)

References 37 publications

(88 reference statements)

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“…The method builds on previous work in Malcolm and de Hoop (2005) that combines two series approaches: the generalized Bremmer series (de Hoop, 1996) and the Born series discussed by Weglein et al, (2003).…”

Section: Summary Of Methodsmentioning

confidence: 99%

Recursive imaging with multiply scattered waves using partial image regularization: A North Sea case study

2011

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As more resources are directed toward reverse time migration, an accurate velocity model, including strong reflectors, is necessary to form a clear image of the subsurface. This is of particular importance in the vicinity of salt, where singly scattered waves are often not ideal for imaging the salt flanks. This has led to interest in processing doubly scattered waves (also called duplex or prismatic waves) for imaging salt flanks and thus improving the location of salt boundaries in a velocity model. We used doubly scattered waves in a two-pass, one-way method to image salt flanks in a North Sea data set. By working in the one-way framework we were able to separately construct images with singly, doubly, and triply scattered waves. We used a multistep imaging process that includes multiply scattered waves by using an imaged reflector to fix one (or more) of the scattering points, allowing for multiply scattered energy from several reflectors, potentially with poor continuity, to be included without picking each reflector individually. With this method we were able to image the flank of a North Sea salt body.

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Section: Summary Of Methodsmentioning

confidence: 99%

Recursive imaging with multiply scattered waves using partial image regularization: A North Sea case study

2011

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“…This procedure has its roots in a hybrid series based on the LippmannSchwinger series, discussed in the seismic context by Weglein et al ͑1997͒, and the generalized Bremmer series introduced by de Hoop ͑1996͒. The appendices highlight primarily how the LippmannSchwinger series enters our method; further details can be found in Malcolm and de Hoop ͑2005͒. Constructing the hybrid series begins by decomposing the acoustic wavefield, u, into its up-and downgoing constituents u ± , as is done in the Bremmer series and in the development of the DSR equation ͑Claerbout, 1985͒. We first write the wave equation…”

Section: Appendix a The Scattering Seriesmentioning

confidence: 99%

Identification of image artifacts from internal multiples

2007

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First-order internal multiples are a source of coherent noise in seismic images because they do not satisfy the single-scattering assumption fundamental to most seismic processing. There are a number of techniques to estimate internal multiples in data; in many cases, these algorithms leave some residual multiple energy in the data. This energy produces artifacts in the image, and the location of these artifacts is unknown because the multiples were estimated in the data before the image was formed. To avoid this problem, we propose a method by which the artifacts caused by internal multiples are estimated directly in the image. We use ideas from the generalized Bremmer series and the LippmannSchwinger scattering series to create a forward-scattering series to model multiples and an inverse-scattering series to describe the impact these multiples have on the common-image gather and the image. We present an algorithm that implements the third term of this series, responsible for the formation of first-order internal multiples. The algorithm works as part of a wave-equation migration; the multiple estimation is made at each depth using a technique related to one used to estimate surface-related multiples. This method requires knowledge of the velocity model to the depth of the shallowest reflector involved in the generation of the multiple of interest. This information allows us to estimate internal multiples without assumptions inherent to other methods. In particular, we account for the formation of caustics. Results of the techniques on synthetic data illustrate the kinematic accuracy of predicted multiples, and results on field data illustrate the potential of estimating artifacts caused by internal multiples in the image rather than in the data.

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“…Internal multiple reflections can also be estimated from the third (and higher order) term(s) in the inverse scattering series (ISS), derived from the Lippmann-Schwinger equation (Weglein et al, 1997) or from the Bremmer coupling series (Malcolm and de Hoop, 2004). Unlike in IME, all internal multiples are estimated at once, rather than through layer stripping.…”

Section: Introductionmentioning

confidence: 99%

Adaptive overburden elimination with the multidimensional Marchenko equation

2016

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Iterative substitution of the multidimensional Marchenko equation has been introduced recently to integrate internal multiple reflections in the seismic imaging process. In so-called Marchenko imaging, a macro velocity model of the subsurface is required to meet this objective. The model is used to back-propagate the data during the first iteration and to truncate integrals in time during all successive iterations. In case of an erroneous model, the image will be blurred (akin to conventional imaging) and artifacts may arise from inaccurate integral truncations. However, the scheme is still successful in removing artifacts from internal multiple reflections. Inspired by these observations, we rewrote the Marchenko equation, such that it can be applied early in a processing flow, without the need of a macro velocity model. Instead, we have required an estimate of the two-way traveltime surface of a selected horizon in the subsurface. We have introduced an approximation, such that adaptive subtraction can be applied. As a solution, we obtained a new data set, in which all interactions (primaries and multiples) with the part of the medium above the picked horizon had been eliminated. Unlike various other internal multiple elimination algorithms, the method can be applied at any specified target horizon, without having to resolve for internal multiples from shallower horizons. We successfully applied the method on synthetic data, where limitations were reported due to thin layers, diffraction-like discontinuities, and a finite acquisition aperture. A field data test was also performed, in which the kinematics of the predicted updates were demonstrated to match with internal multiples in the recorded data, but it appeared difficult to subtract them.

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A method for inverse scattering based on the generalized Bremmer coupling series

Cited by 22 publications

References 37 publications

Recursive imaging with multiply scattered waves using partial image regularization: A North Sea case study

Recursive imaging with multiply scattered waves using partial image regularization: A North Sea case study

Identification of image artifacts from internal multiples

Adaptive overburden elimination with the multidimensional Marchenko equation

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