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dc.contributor.authorBlazek, Kirk D.
Stolk, Christiaan
Symes, William W.
dc.date.accessioned 2016-02-02T19:17:44Z
dc.date.available 2016-02-02T19:17:44Z
dc.date.issued 2013
dc.identifier.citation Blazek, Kirk D., Stolk, Christiaan and Symes, William W.. "A mathematical framework for inverse wave problems in heterogeneous media." Inverse Problems, 29, (2013) IOP Publishing: 065001. http://dx.doi.org/10.1088/0266-5611/29/6/065001.
dc.identifier.urihttps://hdl.handle.net/1911/88303
dc.description.abstract This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The coefficients of these time-dependent partial differential equations represent parametrically the spatially varying mechanical properties of materials. Rocks, manufactured materials, and other wave propagation environments often exhibit spatial heterogeneity in mechanical properties at a wide variety of scales, and coefficient functions representing these properties must mimic this heterogeneity. We show how to choose domains (classes of nonsmooth coefficient functions) and data definitions (traces of weak solutions) so that optimization formulations of inverse wave problems satisfy some of the prerequisites for application of Newton's method and its relatives. These results follow from the properties of a class of abstract first-order evolution systems, of which various physical wave systems appear as concrete instances. Finite speed of propagation for linear waves with bounded, measurable mechanical parameter fields is one of the by-products of this theory.
dc.language.iso eng
dc.publisher IOP Publishing
dc.rights Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/
dc.title A mathematical framework for inverse wave problems in heterogeneous media
dc.type Journal article
dc.citation.journalTitle Inverse Problems
dc.contributor.org The Rice Inversion Project
dc.citation.volumeNumber 29
dc.type.dcmi Text
dc.identifier.doihttp://dx.doi.org/10.1088/0266-5611/29/6/065001
dc.type.publication publisher version
dc.citation.firstpage 065001


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