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ISRN Applied Mathematics
Volume 2012 (2012), Article ID 539359, 10 pages
http://dx.doi.org/10.5402/2012/539359
Research Article

Green's Theorem for Sign Data

The University of Louisiana at Lafayette, Lafayette, LA 70504-4210, USA

Received 14 March 2012; Accepted 19 April 2012

Academic Editors: A. Bellouquid and M.-H. Hsu

Copyright © 2012 Louis M. Houston. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Sign data are the signs of signal added to noise. It is well known that a constant signal can be recovered from sign data. In this paper, we show that an integral over variant signal can be recovered from an integral over sign data based on the variant signal. We refer to this as a generalized sign data average. We use this result to derive a Green's theorem for sign data. Green's theorem is important to various seismic processing methods, including seismic migration. Results in this paper generalize reported results for 2.5D data volumes in which Green's theorem applies to sign data based only on traditional sign data recovery.