Research Interests
1. Inverse scattering of elastic waves
An effective, real-time 3D imaging of
subsurface volumes by seismic (i.e. elasic) waves is one of the Holy Grails
of engineering owng to its relevance
to applications such as underground object identification, oil prospecting, delineation of hazardous
waste, and seismic design. On a smaller scale suited for
laboratory applications, the use of elastic waves is also critical to
non-destructive
material testing and diagnosis of medical ailments such as skin cancer
and edema.
The goal of the ongoing research
program is to advance the theoretical and physical framework of seismic
wave methods for imaging and
characterization of sites and materials that may have natural or
man-made geometric and material variations. In this setting, of
particular interest is the wave-based identification of dicrete
subsurface objects (tunnels, material defects, cancerous tissues) that
falls under a wide umbrella of inverse scattering problems.
With reference to Fig.1 which plots the
surface ground motion due to seismic waves scattered by (i.e. bounced
of) an underground cavity, the inverse scattering problem can be posed
as a task of reconstructing the scatterer (ellipsoidal cavity in red)
from the knowledge/measurements of the surface ground motion.
Fig.1: Simulation of the forward scattering problem.
As
an example, Fig. 2 illustates a
solution to the inverse scattering problem in the context of boundary
integral methods, non-lineaer minimization, and adjoint sensitivity
estimates. The initial guess and final iteration (the latter coinciding
with the true cavity) are indicated in dark blue and red, respectively.
Fig.2: Evolution of trial
cavity in the boundary-only imaging process (testing surface
indicated in gray).
Recently, two new techniques, termed the Linear Sampling Method
and
the Topological Sensitivity
Approach have been developed to deal with near- and
far-field
inverse scattering of elastic waves in a robust, yet
computationally-effficient way that eliminates the need for an "initial
guess" (see also Selected Projects).
2. Biomedical imaging
Keen application areas of the foregoing research are Elastography and Sonoelasticity; new medical
imaging techniques that sense e.g. cancerous tissue via its elastic
modulus. Experiments have shown that the elastic modulus of a cancer is
typically higher (as much as 10 times) than that of the surrounding
(healthy) tissue. To illustarte the potential utility of ongoing
research for
the advancement of these techniques, consider an active imaging
configuration involving a square testing (source/observation) grid
located on the surface of a semi-infinite solid as shown in Fig. 3. The
elastic half-space containts two defects, a spherical cavity and an
ellipsoidal (stiff) inclusion.
Fig.3: Synthetic testing
configuraton.
With reference to such testing
setup, Fig.4 plots the distribution of "optimal"
shear moduls (in the horizonttal plane z/a=3) stemming from the
Topological Sensitivity Approach. As can be seen from the display where
the intersection with true obstacles is indicated in red, the latter
imaging technique is capable of idenfifying not onlly the geometry, but
also the elastic modulus of both obstacles,
Fig.4: Subsurface image of
an elastic tissue, plotted in terms of the shear modulus distribution
(µo is the modulus of the matrix).
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3. Dynamic site
characterization
To
cater for civil engineering applications, research efforts have
involved the development of rigorous, yet compact waveform analyses for
the vertical subsurface delineation of elastic and damping parameters
characterizing common geotechnical and pavement profiles.
Fig.5:
Field setup for the
spectral analysis of Love Waves.
Examples
of such research
include the development of the Spectral
Analysis of Love Waves
(Fig.5) and a dynamic interpertation of the Falling Weight
Deflectometer measurements (Fig.6), used worldwilde for
non-desrttructive pavement diagnosis.
Fig.6: Falling
Weight Deflectometer.
4. Prediction of thermal crack spacing
When
natural and engineered systems are subjected to shrinkage—driven by
cooling or drying—the resulting stresses may lead to the formation
of cracks. In many cases these cracks form patterns, which exhibit
distinct length scales. A keen area of research in engineered systems
looks at
the cracking patterns in thin films, caused by e.g. thermal shrinkage
or mechanical loading (Fig.7). The focus of this research is the
development
Fig.7: Cracking
pattern in a thin ceramic (TiN) film
placed on a steel substrate (After Chen et al, 2000).
of mathematical models to
predict the length scale for the spacing of transverse cracks that
form in a coating subjected to an axial strain. In a departure from
previous work in this area, our engineering motivation for the study is
not
an improved understanding of thin film coatings but an understanding
of how so called thermal cracks, a feature of cold climates, form in
asphalt pavements placed on a granular base. Typically, these cracks
form after an extreme cooling
event. Although thermal cracking of pavements occurs at a larger scale
than
the cracking of thin films (meters as opposed to micrometers), the
fundamental problem components are the same, i.e., a relatively thin
coating (the asphalt lift) placed on a thicker substrate (the
granular base) subjected to an axial strain. As such, it is expected
that the pavement thermal cracking model should also be applicable to
situations involving thin film coatings. This point is demonstrated by
using the model to successfully
predict the average crack spacing observed in titanium nitride (TiN)
ceramic coatings subjected to an applied axial strain (Fig.8); a
problem where the crack spaces are six orders of
magnitude smaller than those found in pavements.
Fig.8: Observed
versus predicted crack density in a 1.3micrometer-thin TiN
coating.
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