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SUMMARY:Inverse problems for wave propagation in heterogeneous media - W.W
 . Symes (Rice University\, Houston)
DTSTART:20111124T150000Z
DTEND:20111124T160000Z
UID:TALK34333@talks.cam.ac.uk
CONTACT:6743
DESCRIPTION:Inverse problems in wave propagation rely upon hyperbolic part
 ial (integro-)differential systems to model physical wave motion. However\
 , rocks\, manufactured materials\, and other natural and human-made wave p
 ropagation environments may exhibit spatial heterogeneity at a wide variet
 y of scales. Therefore accuracy in modeling (hence in inversion) requires 
 tha coefficient functions representing material parameter fields be permit
 ted some degree of nonsmoothness. I will show how to formulate well-posed 
 initial/boundary-value problems for hyperbolic systems with bounded and me
 asureable coefficients\, as instances of a class of abstract first-order e
 volution problems. This framework yields well-defined realizations of the 
 mappings occurring in widely-used optimization formulations of inverse pro
 blems\, and justifies the use of Newton's method and its relatives for the
 ir solution. The finite speed of propagation for waves in material models 
 with bounded and measurable heterogeneity also follows from this framework
 . Another useful by-product is a mathematical foundation for (unphysical) 
 hyperbolic systems with operator coefficients\, which are crucial componen
 ts of a class of seismic inversion algorithms.\n\nThe content of this talk
  is the result of collaboration with Christiaan Stolk and Kirk Blazek.
LOCATION:MR14\, CMS
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