Applied Inverse Problems in NDE, Geophysics & Medicine
We aim to apply our expertise in solid mechanics, wave propagation, and inverse problems to a variety of engineering and technological problems where non-invasive diagnosis of subterranean regions, materials, structures, or living tissues is required.
3D seismic sensing of heterogeneous fractures
The goal of this research is to establish a comprehensive platform for the 3D reconstruction and interfacial characterization of arbitrarily-shaped, partially closed fractures by way of seismic or ultrasonic waves. In the ongoing work  that is relevant to both mine safety and hydraulic fracturing , this goal is made possible via an extension to the so-called Generalized Linear Sampling Method (GLSM) to enable accurate geometric reconstruction of subsurface fractures regardless of their interfacial condition. Aided by this result, our inverse solution deploys a 3-step hybrid approach where: 1) the fracture surface is reconstructed without the knowledge of its contact condition; 2) given the geometry, the fracture opening displacement (FOD) profile is recovered from an integral transform relating FOD to the scattered seismic waveforms; and 3) given FOD, the spatial distribution of specific stiffnesses is resolved from the boundary integral equation for a fracture, incorporating its (inhomogeneous) elastic contact condition. The proposed developments are being verified in a laboratory setting, making use of the recently acquired Scanning Laser Doppler Vibrometer (SLDV) as a motion sensing tool. In parallel, the concept of topological sensitivity (TS) is extended  to enable simultaneous 3D reconstruction of partially closed fractures and qualitative characterization of their interfacial condition by way of elastic waves. Interactions between the two surfaces of a fracture, due to e.g. presence of asperities, fluid, or proppant, are described via the Schoenberg’s linear slip model. The proposed TS sensing platform is formulated in the frequency domain, and entails point-wise interrogation of the subsurface by infinitesimal fissures endowed with interfacial stiffness. For completeness, the featured elastic polarization tensor – central to the TS formula – is mathematically described in terms of the shear and normal specific stiffnesses (κs,κn) of a vanishing fracture. Simulations demonstrate that, irrespective of the contact condition between the faces of a hidden fracture, the TS is capable of reconstructing its geometry and identifying the normal vector to the fracture surface without iterations. On the basis of such geometrical information, it is further shown via asymptotic analysis – assuming “low frequency” illumination, that by certain choices of (κs,κn) characterizing the trial (infinitesimal) fracture, the ratio between the shear and normal specific stiffness along the surface of nearly-planar (finite) fractures can be qualitatively identified.
Elastodynamic reconstruction of a partially-closed cylindrical fracture by the Linear Sampling Method 
Viscoelastic characterization of soft tissues
In this suite of works, we develop customized solutions for the vibration- i.e. wave-based identification of viscoelastic properties of soft tissues  with an emphasis on skin [38, 44]. One example is a theoretical and computational platform behind the operation of a piezoelectric sensor array for the surface monitoring of tissue motion that can be used as a basis for the reconstruction of layered viscoelastic skin properties . This is accomplished by the scale reduction of the Multi-channel Analysis of Surface Waves (MASW), a methodology that is successfully used in engineering geophysics for the seismic-wave reconstruction of vertical geological profiles. The utility of the new sensor, containing an array of hair-thin PVDF sensors that are sensitive to surficial tissue motion, is enhanced through a comprehensive skin-fiber interaction analysis that furnishes integral information, cumulative over the length of a fiber, about the attenuation and dispersion of surface waves. Having such predictive model as a lynchpin of the back-analysis of electric charges furnished by the fibers, the methodology allows for an effective reconstruction and viscoelastic characterization of cutaneous and subcutaneous tissue sublayers on a millimeter scale. Another example of research in this direction revolves around the use of modulated ARF as a vibration source , which enables (via the analysis of Scholte waves) viscoelastic characterization of skin layers less than a millimeter in thickness.
Testing configuration  for the viscoelastic characterization of mm-thin tissue mimicking phantoms.
Probing nonlinear tissue elasticity by ARF
Prompted by a recent finding that the magnitude of the acoustic radiation force (ARF) in isotropic tissue-like solids depends linearly on a particular third-order elastic modulus — hereon denoted by C,this study  investigates the possibility of estimating C from the amplitude of ARF-generated shear waves. The featured coefficient of nonlinear elasticity, which captures the incipient nonlinear interaction between the volumetric and deviatoric modes of deformation, has so far received only a limited attention in the context of soft tissues due to the fact that the latter are often approximated as (i) fluid-like when considering ultrasound waves, and (ii) incompressible under static deformations. On establishing the analytical and computational platform for the proposed sensing methodology, the study proceeds with applying the prototype technique toward estimating via ARF the third-order modulus C in a series of tissue-mimicking phantoms. To help validate the concept and its implementation, the germane third-order modulus is independently estimated in each phantom via an established technique known as acoustoelasticity. The C-estimates obtained respectively via acoustoelasticity and the new theory of ARF show a significant degree of consistency. The key features of the new sensing methodology are that: (a) it requires no external deformation of an organ other than that produced by the ARF, and (b) it estimates the nonlinear C-modulus locally, over the (mm-sized) focal region of an ultrasound beam—where the shear waves are being generated.
Schematics (left) and picture (right) of the experimental setup  for measuring the third-order moduli C and D in tissue-mimicking phantoms by way of acoustoelasticity.
MR elastography and Vibro-acoustography
This research deploys the concept of Topological Sensitivity (TS) toward boosting the performance of existing techniques for tissue elasticity imaging such as Magnetic Resonance Elastography (MRE) and Vibro-acoustography [48, 51, 57]. The work in , for instance, investigates the application of TS toward reconstructing and identifying tissue anomalies from MRE measurements. The basic idea behind MRE imaging is to apply time–harmonic vibration to a tissue inside the magnetic resonance (MR) scanner, and to capture thus induced 3D wave motion via suitable sequencing of the phase-coordinated, freeze-frame MR scans. To account for the facts that (i) the displacement of a material point captured by the MRE signifies the volume average over a reference voxel size, and (ii) any given measurement voxel may contain, at least partially, the lesion of interest, the concept of TS is extended to allow for (1) averaged volumetric measurements and (2) overlapping interrogation and measurement domains. To circumvent the difficulties involved in numerical modeling of an entire organ, the latter is subdivided into an array of cubic subdomains, each consisting of N3 voxels and playing the role of a reference body for TS imaging. To accomplish the sought partitioning, triaxial displacements along the boundary of each subdomain (captured by the MR scanner) are deployed as Dirichlet data — thus specifying a separate boundary value problem, whereas the internal measurements within the subdomain are taken as the observations for lesion reconstruction. The performance of our methodology for lesion reconstruction and tissue characterization is examined via both numerical examples and a preliminary application to in vivo MRE data. The results highlight the potential of the TS method toward elevating the resolution of tissue (visco-) elasticity reconstruction by MRE.
MRE experimental setup  (adapted from Sinkus, 2005). The breast tissue is vibrated by a shaker acting on its side; both the patient and the shaker are placed inside the MR scanner
Nondestructive evaluation of roads
In this work, we apply elastodynamic and electromagnetic model-based inversion toward an enhanced diagnosis of pavement systems via Falling Weight Deflectometer (FWD), Light Weight Deflectometer (LWD), and Ground Penetrating Radar (GPR) [13, 20, 30, 45, 46]. The FWD test is one of the most commonly used tools for nondestructive evaluation of flexible pavements. Although the test is intrinsically dynamic, the state-of-practice backcalculation techniques used to interpret the FWD data are primarily based on elastostatic solutions due to high computational cost of dynamic multilayered analyses. It has long been known that the foregoing discrepancy may lead to systematic errors in the estimation of pavement moduli, especially in the situations of pronounced inertial phenomena due to shallow bedrock or seasonal stiff layer. In this investigation a simple, yet effective algorithm is proposed that allows the static backcalculation analyses to perform well even when dynamic effects are significant. The technique is based on the use of discrete Fourier transform as a preprocessing tool to filter the dynamic effects and extract the static pavement response from transient FWD records. Using the filtered (i.e. zero-frequency) force and deflection values in lieu of their peak counterparts, the static backcalculation can be further performed in a conventional manner, but free of inconsistencies associated with the neglect of inertial effects. Our results based on synthetic deflection records demonstrate a marked improvement in the elastostatic prediction of pavement moduli when the proposed modification is used. This approach has been implemented, together with a state-of-the-art waveform analysis of GPR data , into a computer platform GopherCalc for high-fidelity diagnosis of pavement systems.
GopherCalc graphical user interface  for the interpretation of FWD and GPR data.
Dynamic site characterization
The goal of this research [1, 10, 23, 39] is to develop advanced inverse solutions for dynamic site characterization via e.g. Spectral Analysis of Surface Waves that are free of the customary modeling simplifications. For example in  we investigate shallow seismic profiling via the dispersion and attenuation analysis of Love surface waves. Although the Rayleigh waves are now commonly used as an engineering tool for nonintrusive identification of shallow subsurface stratigraphy, little attention has so far been paid to utilizing their horizontally polarized, Love-wave counterpart. The proposed methodology revolves around a causal viscoelastic model for the wave motion in a layered half-space caused by action of a surficial, torsionally vibrating disc. It is shown that the use of Love waves as a sounding tool reduces the number of material parameters relevant to viscoelastic site characterization by precluding the effect of the Poisson’s ratio and the P-wave quality factor in each geologic layer. For practical purposes, solution to the inverse problem is reduced to the minimization of a spectral misfit between experimental observations and theoretical predictions of the horizontally polarized surface ground motion. To maintain the rigor and robustness of the inverse solution, sensitivities of the forward model with respect to layer parameters are computed analytically, while the germane cost functional is established within the framework of the maximum-likelihood inverse theory. The Love-wave testing methodology for which this article establishes a necessary theoretical framework may be used either in a stand-alone fashion, or as a complement to the spectral analysis of Rayleigh waves. The proposed technique may be especially useful for (i) shallow surveys where material dissipation is of interest, and (ii) accurate characterization of saturated layers in which vertically polarized waves find limited use owing to their sensitivity to the pore fluid.
Experimental setup for the Spectral Analysis of Love Waves