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Research Overview
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Each of my current research projects is described briefly below. If you're interested in my past work, have a look at my CV (pdf), for my guess at what I might be up to in the future, you can check out my
research statement.
Modeling Ultrasound vibro-acoustography
Collaborators: Fernando Reitich , Jiaqi Yang, Fanbin Bu in the School of Mathematics at the University of Minnesota and James Greenleaf, Mostafa Fatemi , Farid Mitra at the Mayo Clinic. Ultrasound vibro-acoustography is a new imaging modality developed
at the Mayo Clinic that combines the high resolution possible with
high-frequency imaging methods with the clean (scatter-free) images
possible using low-frequency waves. It was first introduced by Fatemi
and Greenleaf in 1999; that paper can be found here . We
are working to model these experiments with the goal of improving the
understanding of the underlying physics which we hope will result in
improved images of abnormal tissue. The image below shows the current
state of our model, on the left is an experimental image of an
aluminum rod submerged in water and on the right is the result of our
model for the same configuration. More details can be found in a conference proceedings paper
we wrote about a year ago, or email me and I will send a copy of
our book chapter.
Improving Illumination with Multiply-Scattered Waves
Collaborators: Bjørn Ursin at the Technical University in Trondheim and Maarten de Hoop in the Center for Computational and Applied Math at Purdue University In typical seismic experiments for oil prospecting sources and
receivers are restricted to lie on the Earth's surface. Waves are
also typically assumed to reflect only once in the subsurface and to
travel primarily downwards into the Earth before reflecting and
upwards afterwards. The combination of these restrictions limits the
region of the Earth imaged. We are working to extend this region by
relaxing the restriction that waves scatter only once in the
subsurface. From doubly scattered waves this improves images of
steeply dipping structures and from triply scattered waves we are able
to image some structures from below. A summary of this work can be
found on this poster or
in this SEG abstract . The
image below shows an example of imaging a fault, with a standard image
on the left and our improved image on the right; this example is
similar to that presented by Jin, Xu and Walraven at SEG in 2006,
available through the Society of
Exploration Geophysicists.
Understanding Wavefront Healing
Collaborators: Jeannot Trampert at Utrecht University and Jesper Spetzler at Delft Technical University. Wavefront healing is the name given to the phenomena by which traveltime delays decay, from the interference of diffractions with direct arrivals, as waves travel over long distances. We are studying the physics and underlying mathematics of this problem to better understand the seismological implications of this effect. Time-domain Topological Derivative
Collaborators: Bojan Guzina University of Minnesota. The topological derivative is a method of locating variations in
material parameters relatively quickly. The basic idea is to define a
cost function and then compute the derivative of this cost function
with respect to the introduction of an infinitesimal inclusion
(variation from the background parameters). This concept was first
introduced in the PhD thesis of Schumacher in 1995 and has been
extensively studied since then, primarily in the frequency domain. We
have extended it to the time-domain, focusing on acoustic obstacles
to more closely correspond to seismic applications. Below you can see
the utility of the method in that we are able to locate two inclusions
(outlined in black) with this method; the negative regions (blue)
indicate points expected to be within the inclusion.
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Publications
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Journal Articles:
Book Chapter: Theses: |
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Teaching Overview
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Personal
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