Commun. Comput. Phys., 5 (2009), pp. 163-182.


Pseudo-Depth Intercept-Time Monotonicity Requirements in the Inverse Scattering Algorithm for Predicting Internal Multiple Reflections

Bogdan G. Nita 1*, Arthur B. Weglein 2

1 Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ 07043, USA.
2 Department of Physics, University of Houston, 617 Science and Research Bldg. 1, Houston, TX 77004, USA.

Received 28 January 2008; Accepted (in revised version) 22 May 2008
Available online 15 July 2008

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.

AMS subject classifications: 86A22, 35P25, 86-08

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Key words: Multiple reflections, seismic imaging, inverse scattering.

*Corresponding author.
Email: nitab@mail.montclair.edu (B. G. Nita), aweglein@uh.edu (A. B. Weglein)
 

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