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CATEGORIES:Applied and Computational Analysis
SUMMARY:Inverse problems for wave propagation in heterogen
eous media - W.W. Symes (Rice University\, Houston
)
DTSTART;TZID=Europe/London:20111124T150000
DTEND;TZID=Europe/London:20111124T160000
UID:TALK34333AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/34333
DESCRIPTION:Inverse problems in wave propagation rely upon hyp
erbolic partial (integro-)differential systems to
model physical wave motion. However\, rocks\, manu
factured materials\, and other natural and human-m
ade wave propagation environments may exhibit spat
ial heterogeneity at a wide variety of scales. The
refore accuracy in modeling (hence in inversion) r
equires tha coefficient functions representing mat
erial parameter fields be permitted some degree of
nonsmoothness. I will show how to formulate well-
posed initial/boundary-value problems for hyperbol
ic systems with bounded and measureable coefficien
ts\, as instances of a class of abstract first-ord
er evolution problems. This framework yields well-
defined realizations of the mappings occurring in
widely-used optimization formulations of inverse p
roblems\, and justifies the use of Newton's method
and its relatives for their solution. The finite
speed of propagation for waves in material models
with bounded and measurable heterogeneity also fol
lows from this framework. Another useful by-produc
t is a mathematical foundation for (unphysical) hy
perbolic systems with operator coefficients\, whic
h are crucial components of a class of seismic inv
ersion algorithms.\n\nThe content of this talk is
the result of collaboration with Christiaan Stolk
and Kirk Blazek.
LOCATION:MR14\, CMS
CONTACT:
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