Date: Friday, September 06, 2019
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: Reducedorder modeling of wave equations for forward modeling and imaging
Abstract: The inverse wave problem in strongly scattering media is highly nonlinear. In this seminar talk we show how ideas from reducedorder modeling can be used to mitigate this nonlinearity.
First we will study the onedimensional dissipative wave equation and show that the wave impedance and losses can be directly recovered from measurements in the frequencydomain. This is an extension of results from Mark Krein's studies of strings with point masses and their connection to Stieltjes continued fractions.
Using the intuition and insights from this onedimensional problem we will tackle the timedomain inverse problem in higher dimensions. From the measured data, we construct a small dynamical system, a socalled reducedorder 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 reducedorder models. To be more specific, we try to find a medium that generates the same reducedorder model as the measured data, rather than a medium that generates that same data. We show that this mitigates the nonlinearity of this problem.
Files:
Speaker: Jörn Zimmerling
Institution: University of Michigan
Event Organizer: AIM Seminar Organizers millerpd@umich.edu
