Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

Statics, structure, and residual normal moveout: Exact mathematical solutions in simple form


Author: I. Lerche
Journal: Quart. Appl. Math. 44 (1986), 511-517
DOI: https://doi.org/10.1090/qam/99615
MathSciNet review: QAM99615
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Abstract | References | Additional Information

Abstract: The separation of seismic reflection times into the component parts due to source static, receiver static, structure time, and residual normal moveout is exhibited in terms of simple differential and integral operations on the reflection time. The solution is valid for all component parts which possess an $ {L_2}$ norm on the open one-dimensional domain of common midpoint. The equations yield simple, explicit solutions for each separate component. Possible methods of implementing these direct solutions for real travel-time data are presented with suggestions for avoiding, or bypassing, the differential operations. These solutions are presented both to provide a novel viewpoint for examining the so-called statics equation and as an aid to those who are actively pursuing the problem of finding methods for successfully optimizing statics problems in divers and diverse situations.


References [Enhancements On Off] (What's this?)

  • [1] F. Kirchheimer, Long period static analysis by trigonometric approximation, Paper S6.1, presented at the S.E.G. Meeting, Las Vegas, Nevada (September 14, 1983)
  • [2] M. O. Marcoux, On the resolution of statics, structure and residual normal movement, Geophysics 46, 984-993 (1981)
  • [3] R. A. Wiggins, K. L. Larner. R. C. Wisecup, Residual static analysis as a general linear inverse problem, Geophysics 41, 922--938 (1976)


Additional Information

DOI: https://doi.org/10.1090/qam/99615
Article copyright: © Copyright 1986 American Mathematical Society


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