Intersections, ideals, and inversion

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Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in ... continued below

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32 pages

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Vasco, D.W. October 1, 1998.

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Description

Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly onedimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons.

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32 pages

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  • Other: DE00006448
  • Report No.: LBNL--42397
  • Grant Number: AC03-76SF00098
  • DOI: 10.2172/6448 | External Link
  • Office of Scientific & Technical Information Report Number: 6448
  • Archival Resource Key: ark:/67531/metadc690439

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  • October 1, 1998

Added to The UNT Digital Library

  • Aug. 14, 2015, 8:43 a.m.

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  • April 4, 2016, 1:23 p.m.

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Vasco, D.W. Intersections, ideals, and inversion, report, October 1, 1998; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc690439/: accessed August 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.