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DTSTART:20070311T020000
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DTSTAMP:20190906T181548
DTSTART;TZID=America/Detroit:20190906T150000
DTEND;TZID=America/Detroit:20190906T160000
SUMMARY:Workshop / Seminar:Applied Interdisciplinary Mathematics (AIM) Seminar
DESCRIPTION:The inverse wave problem in strongly scattering media is highly non-linear. In this seminar talk we show how ideas from reduced-order modeling can be used to mitigate this nonlinearity. \nFirst we will study the one-dimensional dissipative wave equation and show that the wave impedance and losses can be directly recovered from measurements in the frequency-domain. This is an extension of results from Mark Krein's studies of strings with point masses and their connection to Stieltjes continued fractions.\nUsing the intuition and insights from this one-dimensional problem we will tackle the time-domain inverse problem in higher dimensions.  From the measured data\, we construct a small dynamical system\, a so-called reduced-order model\, which explains the observed data and has the structure of a discretized wave operator. Rather than minimizing a data misfit (as is done in classical full waveform inversion)\, we propose to minimize the misfit in these reduced-order models. To be more specific\, we try to find a medium that generates the same reduced-order model as the measured data\, rather than a medium that generates that same data. We show that this mitigates the nonlinearity of this problem. Speaker(s): Jörn Zimmerling (University of Michigan)
UID:62210-15313280@events.umich.edu
URL:https://events.umich.edu/event/62210
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1084
CONTACT:
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