Pseudo-depth/intercept-time monotonicity requirements in the inverse scattering algorithm for predicting internal multiple reflections

Bogdan Nita, Arthur B. Weglein

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

Abstract

In this paper we discuss the inverse scattering algorithm for predicting internal multiple reflections (reverberation artefacts), focusing our attention on the construction mechanisms. Roughly speaking, the algorithm combines amplitude and phase information of three different arrivals (sub-events) in the data set to predict one multiple reflection. The three events are conditioned by a certain relation which requires that their pseudo-depths, defined as the depths of their turning points relative to the constant background velocity, satisfy a lower-higher-lower relationship. This implicitly assumes a pseudo-depth monotonicity condition, i.e., the relation between the actual depths and the pseudo-depths of any two sub-events is the same. We study this relation in pseudo-depth and show that it is directly connected with a similar relation between the vertical or intercept times of the sub-events. The paper also provides the first multidimensional analysis of the algorithm (for a vertically varying acoustic model) with analytical data. We show that the construction of internal multiples is performed in the plane waves domain and, as a consequence, the internal multiples with headwaves sub-events are also predicted by the algorithm. Furthermore we analyze the differences between the time monotonicity condition in vertical or intercept time and total travel time and show a 2D example which satisfies the former but not the latter. Finally we discuss one case in which the monotonicity condition is not satisfied by the sub-events of an internal multiple and discuss ways of lowering these restrictions and of expanding the algorithm to address these types of multiples.

Original languageEnglish
Pages (from-to)163-182
Number of pages20
JournalCommunications in Computational Physics
Volume5
Issue number1
StatePublished - 1 Jan 2009

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inverse scattering
requirements
reverberation
travel
arrivals
artifacts
constrictions
plane waves
acoustics

Keywords

  • Inverse scattering
  • Multiple reflections
  • Seismic imaging

Cite this

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abstract = "In this paper we discuss the inverse scattering algorithm for predicting internal multiple reflections (reverberation artefacts), focusing our attention on the construction mechanisms. Roughly speaking, the algorithm combines amplitude and phase information of three different arrivals (sub-events) in the data set to predict one multiple reflection. The three events are conditioned by a certain relation which requires that their pseudo-depths, defined as the depths of their turning points relative to the constant background velocity, satisfy a lower-higher-lower relationship. This implicitly assumes a pseudo-depth monotonicity condition, i.e., the relation between the actual depths and the pseudo-depths of any two sub-events is the same. We study this relation in pseudo-depth and show that it is directly connected with a similar relation between the vertical or intercept times of the sub-events. The paper also provides the first multidimensional analysis of the algorithm (for a vertically varying acoustic model) with analytical data. We show that the construction of internal multiples is performed in the plane waves domain and, as a consequence, the internal multiples with headwaves sub-events are also predicted by the algorithm. Furthermore we analyze the differences between the time monotonicity condition in vertical or intercept time and total travel time and show a 2D example which satisfies the former but not the latter. Finally we discuss one case in which the monotonicity condition is not satisfied by the sub-events of an internal multiple and discuss ways of lowering these restrictions and of expanding the algorithm to address these types of multiples.",
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Pseudo-depth/intercept-time monotonicity requirements in the inverse scattering algorithm for predicting internal multiple reflections. / Nita, Bogdan; Weglein, Arthur B.

In: Communications in Computational Physics, Vol. 5, No. 1, 01.01.2009, p. 163-182.

Research output: Contribution to journalArticleResearchpeer-review

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AB - In this paper we discuss the inverse scattering algorithm for predicting internal multiple reflections (reverberation artefacts), focusing our attention on the construction mechanisms. Roughly speaking, the algorithm combines amplitude and phase information of three different arrivals (sub-events) in the data set to predict one multiple reflection. The three events are conditioned by a certain relation which requires that their pseudo-depths, defined as the depths of their turning points relative to the constant background velocity, satisfy a lower-higher-lower relationship. This implicitly assumes a pseudo-depth monotonicity condition, i.e., the relation between the actual depths and the pseudo-depths of any two sub-events is the same. We study this relation in pseudo-depth and show that it is directly connected with a similar relation between the vertical or intercept times of the sub-events. The paper also provides the first multidimensional analysis of the algorithm (for a vertically varying acoustic model) with analytical data. We show that the construction of internal multiples is performed in the plane waves domain and, as a consequence, the internal multiples with headwaves sub-events are also predicted by the algorithm. Furthermore we analyze the differences between the time monotonicity condition in vertical or intercept time and total travel time and show a 2D example which satisfies the former but not the latter. Finally we discuss one case in which the monotonicity condition is not satisfied by the sub-events of an internal multiple and discuss ways of lowering these restrictions and of expanding the algorithm to address these types of multiples.

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